Entrants' Sample Solutions

Beagle 0.9.22

Sample solution for DAT013=1

% SZS status Theorem for DAT013=1.p

% SZS output start CNFRefutation for DAT013=1.p
tff(f_77, negated_conjecture, ~(![U:array, Va:$int, Wa:$int]: ((![Xa:$int]: (($lesseq(Va, Xa) & $lesseq(Xa, Wa)) => $greater(read(U, Xa), 0))) => (![Ya:$int]: (($lesseq($sum(Va, 3), Ya) & $lesseq(Ya, Wa)) => $greater(read(U, Ya), 0))))), file('DAT013=1.p', co1)).
tff(c_9, plain, ($lesseq(skF_4, skF_3)), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_7, plain, (~$greater(read(skF_1, skF_4), 0)), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_13, plain, (![X_1a: $int]: ($greater(read(skF_1, X_1a), 0) | ~$lesseq(skF_2, X_1a) | ~$lesseq(X_1a, skF_3))), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_11, plain, ($lesseq($sum(skF_2, 3), skF_4)), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_10, plain, (~$less(skF_3, skF_4)), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_9])).
tff(c_21, plain, (~$less(0, read(skF_1, skF_4))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_7])).
tff(c_24, plain, (read(skF_1, skF_4)=skE_1), inference(define, [status(thm), theory('equality')], [c_21])).
tff(c_23, plain, (~$less(0, read(skF_1, skF_4))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_7])).
tff(c_26, plain, (~$less(0, skE_1)), inference(demodulation, [status(thm), theory('equality')], [c_24, c_23])).
tff(c_30, plain, (read(skF_1, skF_4)=skE_1), inference(define, [status(thm), theory('equality')], [c_21])).
tff(c_68, plain, (![X_15a: $int]: ($less(0, read(skF_1, X_15a)) | $less(X_15a, skF_2) | $less(skF_3, X_15a))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_13])).
tff(c_70, plain, ($less(0, skE_1) | $less(skF_4, skF_2) | $less(skF_3, skF_4)), inference(superposition, [status(thm), theory('equality')], [c_30, c_68])).
tff(c_73, plain, ($less(skF_4, skF_2) | $less(skF_3, skF_4)), inference(negUnitSimplification, [status(thm)], [c_26, c_70])).
tff(c_75, plain, ($less(skF_4, skF_2)), inference(negUnitSimplification, [status(thm)], [c_10, c_73])).
tff(c_12, plain, (~$less(skF_4, $sum(3, skF_2))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_11])).
tff(c_77, plain, $false, inference(close, [status(thm), theory('LIA')], [c_75, c_12])).
% SZS output end CNFRefutation for DAT013=1.p

CVC4 1.5

CVC4 uses the SMT2 format for models. In this format, the model for function and predicate symbols are provided using the define-fun command. All models produced by CVC4 are finite. In other words, for unsorted inputs, the input is interpreted as a problem having a single uninterpreted sort, $$unsorted, which all models interpret as a finite set. In the output of these models, the domain elements of $$unsorted are named @uc___unsorted_0, ..., @uc___unsorted_n, where n is finite. The cardinality of $$unsorted is specified in a line of the form "; cardinality of $$unsorted is n". For instance, the cardinality of $$unsorted is 4 in the model for NLP042+1, and 2 in the model for SWV017+1.

For proofs, CVC4 provides the (fresh) skolem constants it used when witnessing the negation of universally quantified formulas, and a set of tuples of ground terms it used for instantiating universal quantified formulas. The corresponding ground instances of these formulas, along with the ground formulas from the input (if any), are unsatisfiable at the ground level.

Sample solution for DAT013=1

% SZS status Theorem for DAT013=1
% SZS output start Proof for DAT013=1
Skolem constants of (let ((_let_0 (* (- 1) X))) (let ((_let_1 (* (- 1) BOUND_VAR
IABLE_345))) (forall ((U array) (V Int) (W Int) (BOUND_VARIABLE_345 Int)) (or (n
ot (forall ((X Int)) (or (>= (+ V _let_0) 1) (not (>= (+ W _let_0) 0)) (>= (read
 U X) 1)) )) (>= (+ V _let_1) (- 2)) (not (>= (+ W _let_1) 0)) (>= (read U BOUND
_VARIABLE_345) 1)) ))) :
  ( skv_1, skv_2, skv_3, skv_4 )

Instantiations of (forall ((X Int)) (or (not (>= (+ X (* (- 1) skv_2)) 0)) (>= (
+ X (* (- 1) skv_3)) 1) (>= (read skv_1 X) 1)) ) :
  ( skv_4 )

% SZS output end Proof for DAT013=1

Sample solution for SEU140+2

% SZS status Theorem for SEU140+2
% SZS output start Proof for SEU140+2
Skolem constants of (forall ((A $$unsorted)) (not (empty A)) ) :
  ( skv_1 )

Skolem constants of (forall ((A $$unsorted)) (empty A) ) :
  ( skv_2 )

Skolem constants of (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (subset A B)) (not (disjoint B C)) (disjoint A C)) ) :
  ( skv_3, skv_4, skv_5 )

Skolem constants of (forall ((C $$unsorted)) (or (not (in C skv_3)) (not (in C skv_5))) ) :
  ( skv_6 )

Skolem constants of (forall ((C $$unsorted)) (not (in C (set_intersection2 skv_3 skv_5))) ) :
  ( skv_7 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (subset A B) (subset B A))) ) :
  ( skv_3, skv_4 )
  ( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (proper_subset A B) (and (subset A B) (not (= A B)))) ) :
  ( skv_3, skv_4 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (subset (set_intersection2 A B) A) ) :
  ( skv_3, skv_4 )
  ( skv_3, skv_5 )
  ( skv_4, skv_5 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (subset (set_difference A B) A) ) :
  ( skv_3, skv_4 )
  ( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (in A B)) (not (in B A))) ) :
  ( skv_3, skv_6 )
  ( skv_5, skv_6 )
  ( (set_intersection2 skv_3 skv_5), skv_7 )
  ( skv_6, skv_3 )
  ( skv_6, skv_5 )
  ( skv_7, (set_intersection2 skv_3 skv_5) )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (set_union2 B A) (set_union2 A B)) ) :
  ( skv_3, skv_4 )
  ( skv_3, (set_difference skv_4 skv_3) )
  ( skv_4, skv_3 )
  ( (set_difference skv_4 skv_3), skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (set_intersection2 B A) (set_intersection2 A B)) ) :
  ( skv_3, skv_4 )
  ( skv_3, skv_5 )
  ( skv_4, skv_3 )
  ( skv_4, skv_5 )
  ( skv_5, skv_3 )
  ( skv_5, skv_4 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (subset A B) (forall ((C $$unsorted)) (or (not (in C A)) (in C B)) )) ) :
  ( skv_3, skv_4 )
  ( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (disjoint A B) (= empty_set (set_intersection2 A B))) ) :
  ( skv_3, skv_4 )
  ( skv_3, skv_5 )
  ( skv_4, skv_5 )
  ( skv_5, skv_3 )
  ( skv_5, skv_4 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (empty A) (not (empty (set_union2 A B)))) ) :
  ( skv_3, skv_4 )
  ( skv_3, (set_difference skv_4 skv_3) )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (empty A) (not (empty (set_union2 B A)))) ) :
  ( skv_4, skv_3 )
  ( (set_difference skv_4 skv_3), skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (= empty_set (set_difference A B)) (subset A B)) ) :
  ( skv_3, skv_4 )
  ( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (disjoint A B)) (disjoint B A)) ) :
  ( skv_4, skv_5 )
  ( skv_5, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (subset A B)) (= B (set_union2 A B))) ) :
  ( skv_3, skv_4 )
  ( skv_3, (set_difference skv_4 skv_3) )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (subset A B)) (= A (set_intersection2 A B))) ) :
  ( skv_3, skv_4 )
  ( skv_3, skv_5 )
  ( skv_4, skv_5 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (= empty_set (set_difference A B)) (subset A B)) ) :
  ( skv_3, skv_4 )
  ( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (set_union2 A B) (set_union2 A (set_difference B A))) ) :
  ( skv_3, (set_difference skv_4 skv_3) )
  ( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (disjoint A B) (not (forall ((C $$unsorted)) (or (not (in C A)) (not (in C B))) ))) ) :
  ( skv_3, skv_5 )
  ( skv_5, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_789 $$unsorted)) (or (not (disjoint A B)) (not (in BOUND_VARIABLE_789 A)) (not (in BOUND_VARIABLE_789 B))) ) :
  ( skv_5, skv_4, skv_6 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (set_difference A B) (set_difference (set_union2 A B) B)) ) :
  ( skv_3, skv_4 )
  ( skv_3, (set_difference skv_4 skv_3) )
  ( skv_4, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (subset A B)) (= B (set_union2 A (set_difference B A)))) ) :
  ( skv_3, skv_4 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (= (set_intersection2 A B) (set_difference A (set_difference A B))) ) :
  ( skv_3, skv_4 )
  ( skv_3, skv_5 )
  ( skv_4, skv_3 )
  ( skv_4, skv_5 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (disjoint A B) (not (forall ((C $$unsorted)) (not (in C (set_intersection2 A B))) ))) ) :
  ( skv_3, skv_5 )
  ( skv_5, skv_3 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_829 $$unsorted)) (or (not (in BOUND_VARIABLE_829 (set_intersection2 A B))) (not (disjoint A B))) ) :
  ( skv_3, skv_4, skv_6 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (subset A B)) (not (proper_subset B A))) ) :
  ( skv_3, skv_4 )

Instantiations of (forall ((A $$unsorted)) (or (not (empty A)) (= empty_set A)) ) :
  ( skv_1 )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (in A B)) (not (empty B))) ) :
  ( skv_6, skv_3 )
  ( skv_6, skv_5 )
  ( skv_7, (set_intersection2 skv_3 skv_5) )

Instantiations of (forall ((A $$unsorted) (B $$unsorted)) (or (not (empty A)) (= A B) (not (empty B))) ) :
  ( empty_set, skv_1 )
  ( skv_1, empty_set )

Instantiations of (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (subset A B)) (not (subset C B)) (subset (set_union2 A C) B)) ) :
  ( skv_3, skv_3, (set_difference skv_4 skv_3) )

Instantiations of (forall ((C $$unsorted)) (or (not (in C skv_3)) (in C skv_4)) ) :
  ( skv_6 )

% SZS output end Proof for SEU140+2

Sample solution for NLP042+1

% SZS status CounterSatisfiable for NLP042+1
% SZS output start FiniteModel for NLP042+1
(define-fun woman (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsorte
d_0 $x1) (= @uc___unsorted_1 $x2)))
(define-fun female (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsort
ed_0 $x1) (= @uc___unsorted_1 $x2)))
(define-fun human_person (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___
unsorted_0 $x1) (= @uc___unsorted_1 $x2)))
(define-fun animate (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsor
ted_0 $x1) (= @uc___unsorted_1 $x2)))
(define-fun human (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsorte
d_0 $x1) (= @uc___unsorted_1 $x2)))
(define-fun organism (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unso
rted_0 $x1) (= @uc___unsorted_1 $x2)))
(define-fun living (($x1 $$unsorted) ($x2 $$unsorted)) Bool (not (and (= @uc___u
nsorted_0 $x1) (= @uc___unsorted_2 $x2))))
(define-fun impartial (($x1 $$unsorted) ($x2 $$unsorted)) Bool true)
(define-fun entity (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc___u
nsorted_0 $x1) (= @uc___unsorted_2 $x2)) true (and (= @uc___unsorted_0 $x1) (= @
uc___unsorted_1 $x2))))
(define-fun mia_forename (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @
uc___unsorted_0 $x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted
_0 $x1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0 $x1) (= @u
c___unsorted_1 $x2))))))
(define-fun forename (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc__
_unsorted_0 $x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted_0 $
x1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___
unsorted_1 $x2))))))
(define-fun abstraction (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @u
c___unsorted_0 $x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted_
0 $x1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc
___unsorted_1 $x2))))))
(define-fun unisex (($x1 $$unsorted) ($x2 $$unsorted)) Bool (not (and (= @uc___u
nsorted_0 $x1) (= @uc___unsorted_1 $x2))))
(define-fun general (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc___
unsorted_0 $x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted_0 $x
1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___u
nsorted_1 $x2))))))
(define-fun nonhuman (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc__
_unsorted_0 $x1) (= @uc___unsorted_1 $x2)) false (ite (and (= @uc___unsorted_0 $
x1) (= @uc___unsorted_3 $x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___
unsorted_2 $x2))))))
(define-fun thing (($x1 $$unsorted) ($x2 $$unsorted)) Bool true)
(define-fun relation (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc__
_unsorted_0 $x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted_0 $
x1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___
unsorted_1 $x2))))))
(define-fun relname (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc___
unsorted_0 $x1) (= @uc___unsorted_3 $x2)) false (ite (and (= @uc___unsorted_0 $x
1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___u
nsorted_1 $x2))))))
(define-fun object (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsort
ed_0 $x1) (= @uc___unsorted_2 $x2)))
(define-fun nonliving (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___uns
orted_0 $x1) (= @uc___unsorted_2 $x2)))
(define-fun existent (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc__
_unsorted_0 $x1) (= @uc___unsorted_2 $x2)) true (and (= @uc___unsorted_0 $x1) (=
 @uc___unsorted_1 $x2))))
(define-fun specific (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @uc__
_unsorted_0 $x1) (= @uc___unsorted_3 $x2)) true (ite (and (= @uc___unsorted_0 $x
1) (= @uc___unsorted_2 $x2)) true (and (= @uc___unsorted_0 $x1) (= @uc___unsorte
d_1 $x2)))))
(define-fun substance_matter (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @u
c___unsorted_0 $x1) (= @uc___unsorted_2 $x2)))
(define-fun food (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsorted
_0 $x1) (= @uc___unsorted_2 $x2)))
(define-fun beverage (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unso
rted_0 $x1) (= @uc___unsorted_2 $x2)))
(define-fun shake_beverage (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc_
__unsorted_0 $x1) (= @uc___unsorted_2 $x2)))
(define-fun order (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsorte
d_0 $x1) (= @uc___unsorted_3 $x2)))
(define-fun event (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsorte
d_0 $x1) (= @uc___unsorted_3 $x2)))
(define-fun eventuality (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___u
nsorted_0 $x1) (= @uc___unsorted_3 $x2)))
(define-fun nonexistent (($x1 $$unsorted) ($x2 $$unsorted)) Bool (ite (and (= @u
c___unsorted_0 $x1) (= @uc___unsorted_2 $x2)) false (not (and (= @uc___unsorted_
0 $x1) (= @uc___unsorted_1 $x2)))))
(define-fun singleton (($x1 $$unsorted) ($x2 $$unsorted)) Bool true)
(define-fun act (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___unsorted_
0 $x1) (= @uc___unsorted_3 $x2)))
(define-fun of (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) Bool true)
(define-fun nonreflexive (($x1 $$unsorted) ($x2 $$unsorted)) Bool (and (= @uc___
unsorted_0 $x1) (= @uc___unsorted_3 $x2)))
(define-fun agent (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) Bool (ite
 (and (= @uc___unsorted_0 $x1) (= @uc___unsorted_3 $x2) (= @uc___unsorted_2 $x3)
) false (ite (and (= @uc___unsorted_0 $x1) (= @uc___unsorted_3 $x2) (= @uc___uns
orted_3 $x3)) false (not (and (= @uc___unsorted_0 $x1) (= @uc___unsorted_3 $x2)
(= @uc___unsorted_0 $x3))))))
(define-fun patient (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) Bool (n
ot (and (= @uc___unsorted_0 $x1) (= @uc___unsorted_3 $x2) (= @uc___unsorted_1 $x
3))))
(define-fun actual_world ((_ufmt_1 $$unsorted)) Bool true)
(define-fun past ((_ufmt_1 $$unsorted) (_ufmt_2 $$unsorted)) Bool true)
; cardinality of $$unsorted is 4
(declare-sort $$unsorted 0)
; rep: @uc___unsorted_0
; rep: @uc___unsorted_1
; rep: @uc___unsorted_2
; rep: @uc___unsorted_3
% SZS output end FiniteModel for NLP042+1

Sample solution for SWV017+1

% SZS status Satisfiable for SWV017+1
% SZS output start FiniteModel for SWV017+1
(define-fun at () $$unsorted @uc___unsorted_0)
(define-fun t () $$unsorted @uc___unsorted_0)
(define-fun key (($x1 $$unsorted) ($x2 $$unsorted)) $$unsorted @uc___unsorted_0)
(define-fun a_holds (($x1 $$unsorted)) Bool true)
(define-fun a () $$unsorted @uc___unsorted_0)
(define-fun party_of_protocol (($x1 $$unsorted)) Bool true)
(define-fun b () $$unsorted @uc___unsorted_0)
(define-fun an_a_nonce () $$unsorted @uc___unsorted_0)
(define-fun pair (($x1 $$unsorted) ($x2 $$unsorted)) $$unsorted @uc___unsorted_0
)
(define-fun sent (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) $$unsorted
 @uc___unsorted_0)
(define-fun message (($x1 $$unsorted)) Bool true)
(define-fun a_stored (($x1 $$unsorted)) Bool true)
(define-fun quadruple (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted) ($x4 $
$unsorted)) $$unsorted @uc___unsorted_0)
(define-fun encrypt (($x1 $$unsorted) ($x2 $$unsorted)) $$unsorted @uc___unsorte
d_0)
(define-fun triple (($x1 $$unsorted) ($x2 $$unsorted) ($x3 $$unsorted)) $$unsort
ed @uc___unsorted_0)
(define-fun bt () $$unsorted @uc___unsorted_0)
(define-fun b_holds (($x1 $$unsorted)) Bool true)
(define-fun fresh_to_b (($x1 $$unsorted)) Bool true)
(define-fun generate_b_nonce (($x1 $$unsorted)) $$unsorted @uc___unsorted_0)
(define-fun generate_expiration_time (($x1 $$unsorted)) $$unsorted @uc___unsorte
d_0)
(define-fun b_stored (($x1 $$unsorted)) Bool true)
(define-fun a_key (($x1 $$unsorted)) Bool (= @uc___unsorted_1 $x1))
(define-fun t_holds (($x1 $$unsorted)) Bool true)
(define-fun a_nonce (($x1 $$unsorted)) Bool (not (= @uc___unsorted_1 $x1)))
(define-fun generate_key (($x1 $$unsorted)) $$unsorted @uc___unsorted_1)
(define-fun intruder_message (($x1 $$unsorted)) Bool true)
(define-fun intruder_holds (($x1 $$unsorted)) Bool true)
(define-fun an_intruder_nonce () $$unsorted @uc___unsorted_0)
(define-fun fresh_intruder_nonce (($x1 $$unsorted)) Bool true)
(define-fun generate_intruder_nonce (($x1 $$unsorted)) $$unsorted @uc___unsorted
_0)
; cardinality of $$unsorted is 2
(declare-sort $$unsorted 0)
; rep: @uc___unsorted_0
; rep: @uc___unsorted_1
% SZS output end FiniteModel for SWV017+1

E 1.9.1

Sample solution for SEU140+2

# No SInE strategy applied
# Trying AutoSched0 for 151 seconds
# AutoSched0-Mode selected heuristic G_E___107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
# and selection function SelectMaxLComplexAvoidPosPred.
#
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation.
fof(c_0_0, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(c_0_1, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(c_0_2, axiom, (![X1]:![X2]:![X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2)))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', d4_xboole_0)).
fof(c_0_3, axiom, (![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', d1_xboole_0)).
fof(c_0_4, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', l32_xboole_1)).
fof(c_0_5, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_0])).
fof(c_0_6, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_1])).
fof(c_0_7, plain, (![X1]:![X2]:![X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~in(X4,X2))))), inference(fof_simplification,[status(thm)],[c_0_2])).
fof(c_0_8, plain, (![X1]:(X1=empty_set<=>![X2]:~in(X2,X1))), inference(fof_simplification,[status(thm)],[c_0_3])).
fof(c_0_9, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])).
fof(c_0_10, negated_conjecture, (((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])).
fof(c_0_11, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:(((((in(X8,X5)|~in(X8,X7))|X7!=set_difference(X5,X6))&((~in(X8,X6)|~in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(X9,X5)|in(X9,X6))|in(X9,X7))|X7!=set_difference(X5,X6)))&(((~in(esk5_3(X10,X11,X12),X12)|(~in(esk5_3(X10,X11,X12),X10)|in(esk5_3(X10,X11,X12),X11)))|X12=set_difference(X10,X11))&(((in(esk5_3(X10,X11,X12),X10)|in(esk5_3(X10,X11,X12),X12))|X12=set_difference(X10,X11))&((~in(esk5_3(X10,X11,X12),X11)|in(esk5_3(X10,X11,X12),X12))|X12=set_difference(X10,X11)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])])).
fof(c_0_12, lemma, (![X3]:![X4]:![X5]:![X6]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X5,X6)|set_difference(X5,X6)=empty_set))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])).
fof(c_0_13, plain, (![X3]:![X4]:![X5]:((X3!=empty_set|~in(X4,X3))&(in(esk1_1(X5),X5)|X5=empty_set))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])).
cnf(c_0_14,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_15,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_16,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_17,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_18,plain,(in(X4,X1)|in(X4,X3)|X1!=set_difference(X2,X3)|~in(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_19,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_20,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_21,plain,(~in(X1,X2)|X2!=empty_set), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_22,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_14, c_0_15])).
cnf(c_0_23,negated_conjecture,(in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_16, c_0_17])).
cnf(c_0_24,plain,(in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2)), inference(er,[status(thm)],[c_0_18])).
cnf(c_0_25,negated_conjecture,(set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_19, c_0_20])).
cnf(c_0_26,plain,(~in(X1,empty_set)), inference(er,[status(thm)],[c_0_21])).
cnf(c_0_27,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_28,negated_conjecture,(~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_22, c_0_23])).
cnf(c_0_29,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_26])).
cnf(c_0_30,negated_conjecture,(in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_16, c_0_27])).
cnf(c_0_31,negated_conjecture,($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30])]), ['proof']).
# SZS output end CNFRefutation.

Sample solution for NLP042+1

# No SInE strategy applied
# Trying AutoSched0 for 151 seconds
# AutoSched0-Mode selected heuristic H_____047_C18_F1_AE_R8_CS_SP_S2S
# and selection function SelectNewComplexAHP.
#

# No proof found!
# SZS status CounterSatisfiable
# SZS output start Saturation.
fof(c_0_0, conjecture, (~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', co1)).
fof(c_0_1, axiom, (![X1]:![X2]:(shake_beverage(X1,X2)=>beverage(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax27)).
fof(c_0_2, axiom, (![X1]:![X2]:(beverage(X1,X2)=>food(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax26)).
fof(c_0_3, axiom, (![X1]:![X2]:(food(X1,X2)=>substance_matter(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax25)).
fof(c_0_4, axiom, (![X1]:![X2]:(forename(X1,X2)=>relname(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax16)).
fof(c_0_5, axiom, (![X1]:![X2]:(woman(X1,X2)=>human_person(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax8)).
fof(c_0_6, axiom, (![X1]:![X2]:(substance_matter(X1,X2)=>object(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax24)).
fof(c_0_7, axiom, (![X1]:![X2]:(relname(X1,X2)=>relation(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax15)).
fof(c_0_8, axiom, (![X1]:![X2]:(human_person(X1,X2)=>organism(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax7)).
fof(c_0_9, axiom, (![X1]:![X2]:(object(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax23)).
fof(c_0_10, axiom, (![X1]:![X2]:(relation(X1,X2)=>abstraction(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax14)).
fof(c_0_11, axiom, (![X1]:![X2]:(event(X1,X2)=>eventuality(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax34)).
fof(c_0_12, axiom, (![X1]:![X2]:(organism(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax6)).
fof(c_0_13, axiom, (![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax38)).
fof(c_0_14, axiom, (![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax41)).
fof(c_0_15, axiom, (![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax40)).
fof(c_0_16, axiom, (![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax39)).
fof(c_0_17, axiom, (![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax37)).
fof(c_0_18, axiom, (![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax42)).
fof(c_0_19, axiom, (![X1]:![X2]:(entity(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax21)).
fof(c_0_20, axiom, (![X1]:![X2]:(object(X1,X2)=>nonliving(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax19)).
fof(c_0_21, axiom, (![X1]:![X2]:(object(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax17)).
fof(c_0_22, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>nonhuman(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax12)).
fof(c_0_23, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax10)).
fof(c_0_24, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>nonexistent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax30)).
fof(c_0_25, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax31)).
fof(c_0_26, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax29)).
fof(c_0_27, axiom, (![X1]:![X2]:![X3]:![X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>X3!=X4)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax44)).
fof(c_0_28, axiom, (![X1]:![X2]:(entity(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax22)).
fof(c_0_29, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax13)).
fof(c_0_30, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax33)).
fof(c_0_31, axiom, (![X1]:![X2]:![X3]:(((entity(X1,X2)&forename(X1,X3))&of(X1,X3,X2))=>~(?[X4]:((forename(X1,X4)&X4!=X3)&of(X1,X4,X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax43)).
fof(c_0_32, axiom, (![X1]:![X2]:(order(X1,X2)=>act(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax36)).
fof(c_0_33, axiom, (![X1]:![X2]:(thing(X1,X2)=>singleton(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax32)).
fof(c_0_34, axiom, (![X1]:![X2]:(entity(X1,X2)=>existent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax20)).
fof(c_0_35, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>general(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax11)).
fof(c_0_36, axiom, (![X1]:![X2]:(object(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax18)).
fof(c_0_37, axiom, (![X1]:![X2]:(organism(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax5)).
fof(c_0_38, axiom, (![X1]:![X2]:(organism(X1,X2)=>living(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax4)).
fof(c_0_39, axiom, (![X1]:![X2]:(human_person(X1,X2)=>human(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax3)).
fof(c_0_40, axiom, (![X1]:![X2]:(human_person(X1,X2)=>animate(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax2)).
fof(c_0_41, axiom, (![X1]:![X2]:(act(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax35)).
fof(c_0_42, axiom, (![X1]:![X2]:(woman(X1,X2)=>female(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax1)).
fof(c_0_43, axiom, (![X1]:![X2]:(order(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax28)).
fof(c_0_44, axiom, (![X1]:![X2]:(mia_forename(X1,X2)=>forename(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/NLP042+1.p', ax9)).
fof(c_0_45, negated_conjecture, (~(~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5)))))), inference(assume_negation,[status(cth)],[c_0_0])).
fof(c_0_46, plain, (![X3]:![X4]:(~shake_beverage(X3,X4)|beverage(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])).
fof(c_0_47, negated_conjecture, ((actual_world(esk1_0)&((((((((((of(esk1_0,esk3_0,esk2_0)&woman(esk1_0,esk2_0))&mia_forename(esk1_0,esk3_0))&forename(esk1_0,esk3_0))&shake_beverage(esk1_0,esk4_0))&event(esk1_0,esk5_0))&agent(esk1_0,esk5_0,esk2_0))&patient(esk1_0,esk5_0,esk4_0))&past(esk1_0,esk5_0))&nonreflexive(esk1_0,esk5_0))&order(esk1_0,esk5_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])).
fof(c_0_48, plain, (![X3]:![X4]:(~beverage(X3,X4)|food(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])).
cnf(c_0_49,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_50,negated_conjecture,(shake_beverage(esk1_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
fof(c_0_51, plain, (![X3]:![X4]:(~food(X3,X4)|substance_matter(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])).
cnf(c_0_52,plain,(food(X1,X2)|~beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_53,negated_conjecture,(beverage(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_49, c_0_50]), ['final']).
fof(c_0_54, plain, (![X3]:![X4]:(~forename(X3,X4)|relname(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])).
fof(c_0_55, plain, (![X3]:![X4]:(~woman(X3,X4)|human_person(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])).
fof(c_0_56, plain, (![X3]:![X4]:(~substance_matter(X3,X4)|object(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])).
cnf(c_0_57,plain,(substance_matter(X1,X2)|~food(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_58,negated_conjecture,(food(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_52, c_0_53]), ['final']).
fof(c_0_59, plain, (![X3]:![X4]:(~relname(X3,X4)|relation(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])).
cnf(c_0_60,plain,(relname(X1,X2)|~forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54])).
cnf(c_0_61,negated_conjecture,(forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
fof(c_0_62, plain, (![X3]:![X4]:(~human_person(X3,X4)|organism(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])).
cnf(c_0_63,plain,(human_person(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_55])).
cnf(c_0_64,negated_conjecture,(woman(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
fof(c_0_65, plain, (![X3]:![X4]:(~object(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])).
cnf(c_0_66,plain,(object(X1,X2)|~substance_matter(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_56])).
cnf(c_0_67,negated_conjecture,(substance_matter(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_57, c_0_58]), ['final']).
fof(c_0_68, plain, (![X3]:![X4]:(~relation(X3,X4)|abstraction(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])).
cnf(c_0_69,plain,(relation(X1,X2)|~relname(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59])).
cnf(c_0_70,negated_conjecture,(relname(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_60, c_0_61]), ['final']).
fof(c_0_71, plain, (![X3]:![X4]:(~event(X3,X4)|eventuality(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])).
fof(c_0_72, plain, (![X3]:![X4]:(~organism(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])).
cnf(c_0_73,plain,(organism(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62])).
cnf(c_0_74,negated_conjecture,(human_person(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_63, c_0_64]), ['final']).
fof(c_0_75, plain, (![X1]:![X2]:(existent(X1,X2)=>~nonexistent(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_13])).
fof(c_0_76, plain, (![X1]:![X2]:(specific(X1,X2)=>~general(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_14])).
fof(c_0_77, plain, (![X1]:![X2]:(nonliving(X1,X2)=>~living(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_15])).
fof(c_0_78, plain, (![X1]:![X2]:(nonhuman(X1,X2)=>~human(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_16])).
fof(c_0_79, plain, (![X1]:![X2]:(animate(X1,X2)=>~nonliving(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_17])).
fof(c_0_80, plain, (![X1]:![X2]:(unisex(X1,X2)=>~female(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_18])).
fof(c_0_81, plain, (![X3]:![X4]:(~entity(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])).
cnf(c_0_82,plain,(entity(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_65])).
cnf(c_0_83,negated_conjecture,(object(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_66, c_0_67]), ['final']).
fof(c_0_84, plain, (![X3]:![X4]:(~object(X3,X4)|nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])).
fof(c_0_85, plain, (![X3]:![X4]:(~object(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])).
fof(c_0_86, plain, (![X3]:![X4]:(~abstraction(X3,X4)|nonhuman(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])).
cnf(c_0_87,plain,(abstraction(X1,X2)|~relation(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_68])).
cnf(c_0_88,negated_conjecture,(relation(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_69, c_0_70]), ['final']).
fof(c_0_89, plain, (![X3]:![X4]:(~abstraction(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])).
fof(c_0_90, plain, (![X3]:![X4]:(~eventuality(X3,X4)|nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])).
cnf(c_0_91,plain,(eventuality(X1,X2)|~event(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_71])).
cnf(c_0_92,negated_conjecture,(event(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
fof(c_0_93, plain, (![X3]:![X4]:(~eventuality(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])).
cnf(c_0_94,plain,(entity(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_72])).
cnf(c_0_95,negated_conjecture,(organism(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_73, c_0_74]), ['final']).
fof(c_0_96, plain, (![X3]:![X4]:(~eventuality(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])).
fof(c_0_97, plain, (![X5]:![X6]:![X7]:![X8]:(((~nonreflexive(X5,X6)|~agent(X5,X6,X7))|~patient(X5,X6,X8))|X7!=X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])).
fof(c_0_98, plain, (![X3]:![X4]:(~entity(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])).
fof(c_0_99, plain, (![X3]:![X4]:(~abstraction(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])).
fof(c_0_100, plain, (![X3]:![X4]:(~eventuality(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])).
fof(c_0_101, plain, (![X5]:![X6]:![X7]:![X8]:(((~entity(X5,X6)|~forename(X5,X7))|~of(X5,X7,X6))|((~forename(X5,X8)|X8=X7)|~of(X5,X8,X6)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])).
fof(c_0_102, plain, (![X3]:![X4]:(~order(X3,X4)|act(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])).
fof(c_0_103, plain, (![X3]:![X4]:(~thing(X3,X4)|singleton(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])).
fof(c_0_104, plain, (![X3]:![X4]:(~entity(X3,X4)|existent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])).
fof(c_0_105, plain, (![X3]:![X4]:(~abstraction(X3,X4)|general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])).
fof(c_0_106, plain, (![X3]:![X4]:(~object(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])).
fof(c_0_107, plain, (![X3]:![X4]:(~organism(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])).
fof(c_0_108, plain, (![X3]:![X4]:(~organism(X3,X4)|living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])).
fof(c_0_109, plain, (![X3]:![X4]:(~human_person(X3,X4)|human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])).
fof(c_0_110, plain, (![X3]:![X4]:(~human_person(X3,X4)|animate(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])).
fof(c_0_111, plain, (![X3]:![X4]:(~act(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])).
fof(c_0_112, plain, (![X3]:![X4]:(~woman(X3,X4)|female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])).
fof(c_0_113, plain, (![X3]:![X4]:(~order(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])).
fof(c_0_114, plain, (![X3]:![X4]:(~mia_forename(X3,X4)|forename(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])).
fof(c_0_115, plain, (![X3]:![X4]:(~existent(X3,X4)|~nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])).
fof(c_0_116, plain, (![X3]:![X4]:(~specific(X3,X4)|~general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])).
fof(c_0_117, plain, (![X3]:![X4]:(~nonliving(X3,X4)|~living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])).
fof(c_0_118, plain, (![X3]:![X4]:(~nonhuman(X3,X4)|~human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])).
fof(c_0_119, plain, (![X3]:![X4]:(~animate(X3,X4)|~nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])).
fof(c_0_120, plain, (![X3]:![X4]:(~unisex(X3,X4)|~female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])).
cnf(c_0_121,plain,(specific(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_122,negated_conjecture,(entity(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_82, c_0_83]), ['final']).
cnf(c_0_123,plain,(nonliving(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_84])).
cnf(c_0_124,plain,(unisex(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85])).
cnf(c_0_125,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_86])).
cnf(c_0_126,negated_conjecture,(abstraction(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_87, c_0_88]), ['final']).
cnf(c_0_127,plain,(unisex(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_89])).
cnf(c_0_128,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_90])).
cnf(c_0_129,negated_conjecture,(eventuality(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_91, c_0_92]), ['final']).
cnf(c_0_130,plain,(specific(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_93])).
cnf(c_0_131,negated_conjecture,(entity(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_94, c_0_95]), ['final']).
cnf(c_0_132,plain,(unisex(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_96])).
cnf(c_0_133,plain,(X1!=X2|~patient(X3,X4,X2)|~agent(X3,X4,X1)|~nonreflexive(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_97])).
cnf(c_0_134,plain,(thing(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_98])).
cnf(c_0_135,plain,(thing(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_99])).
cnf(c_0_136,plain,(thing(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_100])).
cnf(c_0_137,plain,(X2=X4|~of(X1,X2,X3)|~forename(X1,X2)|~of(X1,X4,X3)|~forename(X1,X4)|~entity(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_101])).
cnf(c_0_138,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_139,plain,(act(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_102])).
cnf(c_0_140,plain,(singleton(X1,X2)|~thing(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_103])).
cnf(c_0_141,plain,(existent(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_104])).
cnf(c_0_142,plain,(general(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_105])).
cnf(c_0_143,plain,(impartial(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_106])).
cnf(c_0_144,plain,(impartial(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_107])).
cnf(c_0_145,plain,(living(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_108])).
cnf(c_0_146,plain,(human(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_109])).
cnf(c_0_147,plain,(animate(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_110])).
cnf(c_0_148,plain,(event(X1,X2)|~act(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_111])).
cnf(c_0_149,plain,(female(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_112])).
cnf(c_0_150,plain,(event(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_113])).
cnf(c_0_151,plain,(forename(X1,X2)|~mia_forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_114])).
cnf(c_0_152,plain,(~nonexistent(X1,X2)|~existent(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_115])).
cnf(c_0_153,plain,(~general(X1,X2)|~specific(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_116])).
cnf(c_0_154,plain,(~living(X1,X2)|~nonliving(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_117])).
cnf(c_0_155,plain,(~human(X1,X2)|~nonhuman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_118])).
cnf(c_0_156,plain,(~nonliving(X1,X2)|~animate(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_119])).
cnf(c_0_157,plain,(~female(X1,X2)|~unisex(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_120])).
cnf(c_0_158,negated_conjecture,(specific(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_121, c_0_122]), ['final']).
cnf(c_0_159,negated_conjecture,(nonliving(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_123, c_0_83]), ['final']).
cnf(c_0_160,negated_conjecture,(unisex(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_124, c_0_83]), ['final']).
cnf(c_0_161,negated_conjecture,(nonhuman(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_125, c_0_126]), ['final']).
cnf(c_0_162,negated_conjecture,(unisex(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_127, c_0_126]), ['final']).
cnf(c_0_163,negated_conjecture,(nonexistent(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_128, c_0_129]), ['final']).
cnf(c_0_164,negated_conjecture,(specific(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_130, c_0_129]), ['final']).
cnf(c_0_165,negated_conjecture,(specific(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_131]), ['final']).
cnf(c_0_166,negated_conjecture,(unisex(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_132, c_0_129]), ['final']).
cnf(c_0_167,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)), inference(er,[status(thm)],[c_0_133]), ['final']).
cnf(c_0_168,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_169,negated_conjecture,(nonreflexive(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_170,negated_conjecture,(thing(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_134, c_0_122]), ['final']).
cnf(c_0_171,negated_conjecture,(thing(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_135, c_0_126]), ['final']).
cnf(c_0_172,negated_conjecture,(thing(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_136, c_0_129]), ['final']).
cnf(c_0_173,negated_conjecture,(order(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_174,negated_conjecture,(thing(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_134, c_0_131]), ['final']).
cnf(c_0_175,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_176,negated_conjecture,(past(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_177,negated_conjecture,(mia_forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_178,negated_conjecture,(actual_world(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_179,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138]), c_0_61]), c_0_131])]), ['final']).
cnf(c_0_180,plain,(X1=X2|~of(X3,X2,X4)|~of(X3,X1,X4)|~forename(X3,X2)|~forename(X3,X1)|~entity(X3,X4)), c_0_137, ['final']).
cnf(c_0_181,plain,(act(X1,X2)|~order(X1,X2)), c_0_139, ['final']).
cnf(c_0_182,plain,(singleton(X1,X2)|~thing(X1,X2)), c_0_140, ['final']).
cnf(c_0_183,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)), c_0_128, ['final']).
cnf(c_0_184,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)), c_0_49, ['final']).
cnf(c_0_185,plain,(specific(X1,X2)|~eventuality(X1,X2)), c_0_130, ['final']).
cnf(c_0_186,plain,(specific(X1,X2)|~entity(X1,X2)), c_0_121, ['final']).
cnf(c_0_187,plain,(existent(X1,X2)|~entity(X1,X2)), c_0_141, ['final']).
cnf(c_0_188,plain,(nonliving(X1,X2)|~object(X1,X2)), c_0_123, ['final']).
cnf(c_0_189,plain,(relname(X1,X2)|~forename(X1,X2)), c_0_60, ['final']).
cnf(c_0_190,plain,(thing(X1,X2)|~eventuality(X1,X2)), c_0_136, ['final']).
cnf(c_0_191,plain,(thing(X1,X2)|~abstraction(X1,X2)), c_0_135, ['final']).
cnf(c_0_192,plain,(thing(X1,X2)|~entity(X1,X2)), c_0_134, ['final']).
cnf(c_0_193,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)), c_0_125, ['final']).
cnf(c_0_194,plain,(general(X1,X2)|~abstraction(X1,X2)), c_0_142, ['final']).
cnf(c_0_195,plain,(unisex(X1,X2)|~eventuality(X1,X2)), c_0_132, ['final']).
cnf(c_0_196,plain,(unisex(X1,X2)|~object(X1,X2)), c_0_124, ['final']).
cnf(c_0_197,plain,(unisex(X1,X2)|~abstraction(X1,X2)), c_0_127, ['final']).
cnf(c_0_198,plain,(impartial(X1,X2)|~object(X1,X2)), c_0_143, ['final']).
cnf(c_0_199,plain,(impartial(X1,X2)|~organism(X1,X2)), c_0_144, ['final']).
cnf(c_0_200,plain,(living(X1,X2)|~organism(X1,X2)), c_0_145, ['final']).
cnf(c_0_201,plain,(organism(X1,X2)|~human_person(X1,X2)), c_0_73, ['final']).
cnf(c_0_202,plain,(human(X1,X2)|~human_person(X1,X2)), c_0_146, ['final']).
cnf(c_0_203,plain,(animate(X1,X2)|~human_person(X1,X2)), c_0_147, ['final']).
cnf(c_0_204,plain,(eventuality(X1,X2)|~event(X1,X2)), c_0_91, ['final']).
cnf(c_0_205,plain,(event(X1,X2)|~act(X1,X2)), c_0_148, ['final']).
cnf(c_0_206,plain,(female(X1,X2)|~woman(X1,X2)), c_0_149, ['final']).
cnf(c_0_207,plain,(event(X1,X2)|~order(X1,X2)), c_0_150, ['final']).
cnf(c_0_208,plain,(food(X1,X2)|~beverage(X1,X2)), c_0_52, ['final']).
cnf(c_0_209,plain,(substance_matter(X1,X2)|~food(X1,X2)), c_0_57, ['final']).
cnf(c_0_210,plain,(object(X1,X2)|~substance_matter(X1,X2)), c_0_66, ['final']).
cnf(c_0_211,plain,(relation(X1,X2)|~relname(X1,X2)), c_0_69, ['final']).
cnf(c_0_212,plain,(abstraction(X1,X2)|~relation(X1,X2)), c_0_87, ['final']).
cnf(c_0_213,plain,(forename(X1,X2)|~mia_forename(X1,X2)), c_0_151, ['final']).
cnf(c_0_214,plain,(entity(X1,X2)|~object(X1,X2)), c_0_82, ['final']).
cnf(c_0_215,plain,(entity(X1,X2)|~organism(X1,X2)), c_0_94, ['final']).
cnf(c_0_216,plain,(human_person(X1,X2)|~woman(X1,X2)), c_0_63, ['final']).
cnf(c_0_217,plain,(~nonexistent(X1,X2)|~existent(X1,X2)), c_0_152, ['final']).
cnf(c_0_218,plain,(~specific(X1,X2)|~general(X1,X2)), c_0_153, ['final']).
cnf(c_0_219,plain,(~nonliving(X1,X2)|~living(X1,X2)), c_0_154, ['final']).
cnf(c_0_220,plain,(~nonhuman(X1,X2)|~human(X1,X2)), c_0_155, ['final']).
cnf(c_0_221,plain,(~nonliving(X1,X2)|~animate(X1,X2)), c_0_156, ['final']).
cnf(c_0_222,plain,(~unisex(X1,X2)|~female(X1,X2)), c_0_157, ['final']).
cnf(c_0_223,negated_conjecture,(~general(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_153, c_0_158]), ['final']).
cnf(c_0_224,negated_conjecture,(~living(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_154, c_0_159]), ['final']).
cnf(c_0_225,negated_conjecture,(~animate(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_156, c_0_159]), ['final']).
cnf(c_0_226,negated_conjecture,(~female(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_157, c_0_160]), ['final']).
cnf(c_0_227,negated_conjecture,(~human(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_155, c_0_161]), ['final']).
cnf(c_0_228,negated_conjecture,(~female(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_157, c_0_162]), ['final']).
cnf(c_0_229,negated_conjecture,(~existent(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_152, c_0_163]), ['final']).
cnf(c_0_230,negated_conjecture,(~general(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_153, c_0_164]), ['final']).
cnf(c_0_231,negated_conjecture,(~general(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_153, c_0_165]), ['final']).
cnf(c_0_232,negated_conjecture,(~female(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_157, c_0_166]), ['final']).
cnf(c_0_233,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167, c_0_168]), c_0_169])]), ['final']).
cnf(c_0_234,negated_conjecture,(singleton(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_140, c_0_170]), ['final']).
cnf(c_0_235,negated_conjecture,(existent(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_141, c_0_122]), ['final']).
cnf(c_0_236,negated_conjecture,(impartial(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_143, c_0_83]), ['final']).
cnf(c_0_237,negated_conjecture,(singleton(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_140, c_0_171]), ['final']).
cnf(c_0_238,negated_conjecture,(general(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_142, c_0_126]), ['final']).
cnf(c_0_239,negated_conjecture,(singleton(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_140, c_0_172]), ['final']).
cnf(c_0_240,negated_conjecture,(act(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_139, c_0_173]), ['final']).
cnf(c_0_241,negated_conjecture,(singleton(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_140, c_0_174]), ['final']).
cnf(c_0_242,negated_conjecture,(existent(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_141, c_0_131]), ['final']).
cnf(c_0_243,negated_conjecture,(impartial(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_144, c_0_95]), ['final']).
cnf(c_0_244,negated_conjecture,(living(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_145, c_0_95]), ['final']).
cnf(c_0_245,negated_conjecture,(human(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_146, c_0_74]), ['final']).
cnf(c_0_246,negated_conjecture,(animate(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_147, c_0_74]), ['final']).
cnf(c_0_247,negated_conjecture,(female(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_149, c_0_64]), ['final']).
cnf(c_0_248,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)), c_0_168, ['final']).
cnf(c_0_249,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)), c_0_175, ['final']).
cnf(c_0_250,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)), c_0_138, ['final']).
cnf(c_0_251,negated_conjecture,(past(esk1_0,esk5_0)), c_0_176, ['final']).
cnf(c_0_252,negated_conjecture,(nonreflexive(esk1_0,esk5_0)), c_0_169, ['final']).
cnf(c_0_253,negated_conjecture,(event(esk1_0,esk5_0)), c_0_92, ['final']).
cnf(c_0_254,negated_conjecture,(order(esk1_0,esk5_0)), c_0_173, ['final']).
cnf(c_0_255,negated_conjecture,(shake_beverage(esk1_0,esk4_0)), c_0_50, ['final']).
cnf(c_0_256,negated_conjecture,(forename(esk1_0,esk3_0)), c_0_61, ['final']).
cnf(c_0_257,negated_conjecture,(mia_forename(esk1_0,esk3_0)), c_0_177, ['final']).
cnf(c_0_258,negated_conjecture,(woman(esk1_0,esk2_0)), c_0_64, ['final']).
cnf(c_0_259,negated_conjecture,(actual_world(esk1_0)), c_0_178, ['final']).
# SZS output end Saturation.

Sample solution for SWV017+1

# No SInE strategy applied
# Trying AutoSched0 for 151 seconds
# AutoSched0-Mode selected heuristic H_____047_C18_F1_PI_AE_R8_CS_SP_S2S
# and selection function SelectNewComplexAHP.
#

# No proof found!
# SZS status Satisfiable
# SZS output start Saturation.
fof(c_0_0, axiom, (![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:((((message(sent(X1,t,triple(X1,X2,encrypt(triple(X3,X4,X5),X6))))&t_holds(key(X6,X1)))&t_holds(key(X7,X3)))&a_nonce(X4))=>message(sent(t,X3,triple(encrypt(quadruple(X1,X4,generate_key(X4),X5),X7),encrypt(triple(X3,generate_key(X4),X5),X6),X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', server_t_generates_key)).
fof(c_0_1, axiom, (![X1]:![X2]:((message(sent(X1,b,pair(X1,X2)))&fresh_to_b(X2))=>(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)).
fof(c_0_2, axiom, (t_holds(key(bt,b))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)).
fof(c_0_3, axiom, (![X1]:![X2]:![X3]:(message(sent(X1,X2,X3))=>intruder_message(X3))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_can_record)).
fof(c_0_4, axiom, (message(sent(a,b,pair(a,an_a_nonce)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)).
fof(c_0_5, axiom, (fresh_to_b(an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)).
fof(c_0_6, axiom, (![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((message(sent(t,a,triple(encrypt(quadruple(X5,X6,X3,X2),at),X4,X1)))&a_stored(pair(X5,X6)))=>(message(sent(a,X5,pair(X4,encrypt(X1,X3))))&a_holds(key(X3,X5))))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_forwards_secure)).
fof(c_0_7, axiom, (t_holds(key(at,a))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)).
fof(c_0_8, axiom, (![X1]:![X2]:![X3]:(((intruder_message(X1)&party_of_protocol(X2))&party_of_protocol(X3))=>message(sent(X2,X3,X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_message_sent)).
fof(c_0_9, axiom, (![X1]:![X2]:![X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_decomposes_triples)).
fof(c_0_10, axiom, (a_stored(pair(b,an_a_nonce))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_stored_message_i)).
fof(c_0_11, axiom, (a_nonce(an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)).
fof(c_0_12, axiom, (party_of_protocol(b)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_is_party_of_protocol)).
fof(c_0_13, axiom, (![X1]:![X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_composes_pairs)).
fof(c_0_14, axiom, (party_of_protocol(t)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', t_is_party_of_protocol)).
fof(c_0_15, axiom, (![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_composes_triples)).
fof(c_0_16, axiom, (party_of_protocol(a)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_is_party_of_protocol)).
fof(c_0_17, axiom, (![X2]:![X4]:![X5]:(((message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2))))&a_key(X2))&b_stored(pair(X4,X5)))=>b_holds(key(X2,X4)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)).
fof(c_0_18, axiom, (![X1]:![X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)).
fof(c_0_19, axiom, (![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(encrypt(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_key_encrypts)).
fof(c_0_20, axiom, (![X2]:![X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_holds_key)).
fof(c_0_21, axiom, (![X1]:a_key(generate_key(X1))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', generated_keys_are_keys)).
fof(c_0_22, axiom, (![X1]:~(a_nonce(generate_key(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)).
fof(c_0_23, axiom, (![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)).
fof(c_0_24, axiom, (![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)).
fof(c_0_25, axiom, (![X1]:![X2]:![X3]:(((intruder_message(encrypt(X1,X2))&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_interception)).
fof(c_0_26, axiom, (![X1]:![X2]:![X3]:![X4]:(intruder_message(quadruple(X1,X2,X3,X4))=>(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_decomposes_quadruples)).
fof(c_0_27, axiom, (![X1]:![X2]:![X3]:![X4]:((((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4))=>intruder_message(quadruple(X1,X2,X3,X4)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', intruder_composes_quadruples)).
fof(c_0_28, axiom, (![X1]:~((a_key(X1)&a_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)).
fof(c_0_29, axiom, (![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1)))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)).
fof(c_0_30, axiom, (fresh_intruder_nonce(an_intruder_nonce)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)).
fof(c_0_31, axiom, (b_holds(key(bt,t))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)).
fof(c_0_32, axiom, (a_holds(key(at,t))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)).
fof(c_0_33, plain, (![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:![X14]:((((~message(sent(X8,t,triple(X8,X9,encrypt(triple(X10,X11,X12),X13))))|~t_holds(key(X13,X8)))|~t_holds(key(X14,X10)))|~a_nonce(X11))|message(sent(t,X10,triple(encrypt(quadruple(X8,X11,generate_key(X11),X12),X14),encrypt(triple(X10,generate_key(X11),X12),X13),X9))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_0])])).
fof(c_0_34, plain, (![X3]:![X4]:((message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))|(~message(sent(X3,b,pair(X3,X4)))|~fresh_to_b(X4)))&(b_stored(pair(X3,X4))|(~message(sent(X3,b,pair(X3,X4)))|~fresh_to_b(X4))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])).
cnf(c_0_35,plain,(message(sent(t,X1,triple(encrypt(quadruple(X2,X3,generate_key(X3),X4),X5),encrypt(triple(X1,generate_key(X3),X4),X6),X7)))|~a_nonce(X3)|~t_holds(key(X5,X1))|~t_holds(key(X6,X2))|~message(sent(X2,t,triple(X2,X7,encrypt(triple(X1,X3,X4),X6))))), inference(split_conjunct,[status(thm)],[c_0_33])).
cnf(c_0_36,plain,(t_holds(key(bt,b))), inference(split_conjunct,[status(thm)],[c_0_2])).
fof(c_0_37, plain, (![X4]:![X5]:![X6]:(~message(sent(X4,X5,X6))|intruder_message(X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])).
cnf(c_0_38,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_34])).
cnf(c_0_39,plain,(message(sent(a,b,pair(a,an_a_nonce)))), inference(split_conjunct,[status(thm)],[c_0_4])).
cnf(c_0_40,plain,(fresh_to_b(an_a_nonce)), inference(split_conjunct,[status(thm)],[c_0_5])).
fof(c_0_41, plain, (![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:((message(sent(a,X11,pair(X10,encrypt(X7,X9))))|(~message(sent(t,a,triple(encrypt(quadruple(X11,X12,X9,X8),at),X10,X7)))|~a_stored(pair(X11,X12))))&(a_holds(key(X9,X11))|(~message(sent(t,a,triple(encrypt(quadruple(X11,X12,X9,X8),at),X10,X7)))|~a_stored(pair(X11,X12)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])).
cnf(c_0_42,plain,(message(sent(t,X1,triple(encrypt(quadruple(b,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),bt),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(b,t,triple(b,X5,encrypt(triple(X1,X2,X3),bt))))), inference(spm,[status(thm)],[c_0_35, c_0_36]), ['final']).
cnf(c_0_43,plain,(t_holds(key(at,a))), inference(split_conjunct,[status(thm)],[c_0_7])).
fof(c_0_44, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~party_of_protocol(X5))|~party_of_protocol(X6))|message(sent(X5,X6,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])).
fof(c_0_45, plain, (![X4]:![X5]:![X6]:(((intruder_message(X4)|~intruder_message(triple(X4,X5,X6)))&(intruder_message(X5)|~intruder_message(triple(X4,X5,X6))))&(intruder_message(X6)|~intruder_message(triple(X4,X5,X6))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])).
cnf(c_0_46,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_47,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40])]), ['final']).
cnf(c_0_48,plain,(message(sent(a,X1,pair(X5,encrypt(X6,X3))))|~a_stored(pair(X1,X2))|~message(sent(t,a,triple(encrypt(quadruple(X1,X2,X3,X4),at),X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_49,plain,(a_stored(pair(b,an_a_nonce))), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_50,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(a,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_42, c_0_43]), ['final']).
cnf(c_0_51,plain,(a_nonce(an_a_nonce)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_52,plain,(b_stored(pair(X2,X1))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_34])).
cnf(c_0_53,plain,(message(sent(X1,X2,X3))|~party_of_protocol(X2)|~party_of_protocol(X1)|~intruder_message(X3)), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_54,plain,(party_of_protocol(b)), inference(split_conjunct,[status(thm)],[c_0_12])).
fof(c_0_55, plain, (![X3]:![X4]:((~intruder_message(X3)|~intruder_message(X4))|intruder_message(pair(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])).
cnf(c_0_56,plain,(party_of_protocol(t)), inference(split_conjunct,[status(thm)],[c_0_14])).
fof(c_0_57, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~intruder_message(X5))|~intruder_message(X6))|intruder_message(triple(X4,X5,X6)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])).
cnf(c_0_58,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_59,plain,(intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))), inference(spm,[status(thm)],[c_0_46, c_0_47]), ['final']).
cnf(c_0_60,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2)))), inference(spm,[status(thm)],[c_0_48, c_0_49]), ['final']).
cnf(c_0_61,plain,(party_of_protocol(a)), inference(split_conjunct,[status(thm)],[c_0_16])).
cnf(c_0_62,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_47]), c_0_51])]), ['final']).
fof(c_0_63, plain, (![X6]:![X7]:![X8]:(((~message(sent(X7,b,pair(encrypt(triple(X7,X6,generate_expiration_time(X8)),bt),encrypt(generate_b_nonce(X8),X6))))|~a_key(X6))|~b_stored(pair(X7,X8)))|b_holds(key(X6,X7)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])).
cnf(c_0_64,plain,(b_stored(pair(X1,X2))|~intruder_message(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54])]), ['final']).
cnf(c_0_65,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_55])).
fof(c_0_66, plain, (![X3]:![X4]:((intruder_message(X3)|~intruder_message(pair(X3,X4)))&(intruder_message(X4)|~intruder_message(pair(X3,X4))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])).
cnf(c_0_67,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_53]), c_0_56]), c_0_54])]), ['final']).
cnf(c_0_68,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_57])).
cnf(c_0_69,plain,(intruder_message(b)), inference(spm,[status(thm)],[c_0_58, c_0_59]), ['final']).
cnf(c_0_70,plain,(intruder_message(X3)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_71,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(pair(X2,X1))|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_53]), c_0_54])]), ['final']).
cnf(c_0_72,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_53]), c_0_61]), c_0_56])]), ['final']).
cnf(c_0_73,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))), inference(spm,[status(thm)],[c_0_46, c_0_62]), ['final']).
cnf(c_0_74,plain,(b_holds(key(X1,X2))|~b_stored(pair(X2,X3))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))), inference(split_conjunct,[status(thm)],[c_0_63])).
cnf(c_0_75,plain,(b_stored(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_64, c_0_65]), ['final']).
fof(c_0_76, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~intruder_holds(key(X5,X6)))|~party_of_protocol(X6))|intruder_message(encrypt(X4,X5)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])).
fof(c_0_77, plain, (![X4]:![X5]:((~intruder_message(X4)|~party_of_protocol(X5))|intruder_holds(key(X4,X5)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])).
cnf(c_0_78,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_66])).
cnf(c_0_79,plain,(intruder_message(pair(a,an_a_nonce))), inference(spm,[status(thm)],[c_0_46, c_0_39]), ['final']).
cnf(c_0_80,plain,(b_stored(pair(a,an_a_nonce))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_39]), c_0_40])]), ['final']).
cnf(c_0_81,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_69])]), ['final']).
cnf(c_0_82,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_70, c_0_59]), ['final']).
cnf(c_0_83,plain,(message(sent(t,X1,triple(encrypt(quadruple(a,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),at),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(a,t,triple(a,X5,encrypt(triple(X1,X2,X3),at))))), inference(spm,[status(thm)],[c_0_35, c_0_43]), ['final']).
cnf(c_0_84,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_71, c_0_65]), ['final']).
cnf(c_0_85,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X3,X4),at))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_72, c_0_68]), ['final']).
cnf(c_0_86,plain,(intruder_message(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at))), inference(spm,[status(thm)],[c_0_58, c_0_73]), ['final']).
cnf(c_0_87,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_74, c_0_75]), ['final']).
cnf(c_0_88,plain,(intruder_message(encrypt(X1,X2))|~party_of_protocol(X3)|~intruder_holds(key(X2,X3))|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_89,plain,(intruder_holds(key(X1,X2))|~party_of_protocol(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_77])).
cnf(c_0_90,plain,(intruder_message(a)), inference(spm,[status(thm)],[c_0_78, c_0_79]), ['final']).
cnf(c_0_91,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))), inference(spm,[status(thm)],[c_0_60, c_0_62]), ['final']).
cnf(c_0_92,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(b,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_42, c_0_36]), ['final']).
cnf(c_0_93,plain,(b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))), inference(spm,[status(thm)],[c_0_74, c_0_80]), ['final']).
cnf(c_0_94,plain,(a_holds(key(X3,X1))|~a_stored(pair(X1,X2))|~message(sent(t,a,triple(encrypt(quadruple(X1,X2,X3,X4),at),X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_95,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_51])]), ['final']).
cnf(c_0_96,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(a,X1,X2),at))))), inference(spm,[status(thm)],[c_0_83, c_0_43]), ['final']).
cnf(c_0_97,plain,(intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_46, c_0_84]), ['final']).
cnf(c_0_98,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_85, c_0_86]), ['final']).
cnf(c_0_99,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(b,X1,X2),at))))), inference(spm,[status(thm)],[c_0_83, c_0_36]), ['final']).
cnf(c_0_100,plain,(b_holds(key(X1,X2))|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_53]), c_0_54])]), ['final']).
cnf(c_0_101,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_88, c_0_89])).
cnf(c_0_102,plain,(intruder_message(X2)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_103,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_84]), c_0_90]), c_0_61])]), ['final']).
fof(c_0_104, plain, (![X2]:a_key(generate_key(X2))), inference(variable_rename,[status(thm)],[c_0_21])).
cnf(c_0_105,plain,(intruder_message(X2)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_66])).
cnf(c_0_106,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))), inference(spm,[status(thm)],[c_0_46, c_0_91]), ['final']).
cnf(c_0_107,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_53]), c_0_56]), c_0_54])]), ['final']).
cnf(c_0_108,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_84]), c_0_69]), c_0_54])]), ['final']).
cnf(c_0_109,plain,(b_holds(key(X1,a))|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_53]), c_0_54]), c_0_61])]), ['final']).
cnf(c_0_110,plain,(a_holds(key(X1,b))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4)))), inference(spm,[status(thm)],[c_0_94, c_0_49]), ['final']).
fof(c_0_111, plain, (![X1]:~a_nonce(generate_key(X1))), inference(fof_simplification,[status(thm)],[c_0_22])).
fof(c_0_112, plain, (![X2]:((fresh_to_b(X2)|~fresh_intruder_nonce(X2))&(intruder_message(X2)|~fresh_intruder_nonce(X2)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])).
cnf(c_0_113,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_60, c_0_95]), ['final']).
cnf(c_0_114,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_53]), c_0_56]), c_0_61])]), ['final']).
cnf(c_0_115,plain,(intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_70, c_0_97]), ['final']).
cnf(c_0_116,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_98]), ['final']).
cnf(c_0_117,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_53]), c_0_56]), c_0_61])]), ['final']).
cnf(c_0_118,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_100, c_0_65]), ['final']).
cnf(c_0_119,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_101, c_0_54]), ['final']).
cnf(c_0_120,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_102, c_0_97]), ['final']).
cnf(c_0_121,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_103]), ['final']).
cnf(c_0_122,plain,(a_key(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_104])).
cnf(c_0_123,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))), inference(spm,[status(thm)],[c_0_105, c_0_106]), ['final']).
cnf(c_0_124,plain,(intruder_message(an_a_nonce)), inference(spm,[status(thm)],[c_0_105, c_0_79]), ['final']).
cnf(c_0_125,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_68]), c_0_69])]), ['final']).
cnf(c_0_126,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_108]), ['final']).
cnf(c_0_127,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~a_key(X1)), inference(spm,[status(thm)],[c_0_109, c_0_65]), ['final']).
cnf(c_0_128,plain,(intruder_message(generate_b_nonce(an_a_nonce))), inference(spm,[status(thm)],[c_0_102, c_0_59]), ['final']).
cnf(c_0_129,plain,(a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_53]), c_0_61]), c_0_56])]), ['final']).
fof(c_0_130, plain, (![X2]:(~fresh_intruder_nonce(X2)|fresh_intruder_nonce(generate_intruder_nonce(X2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])).
fof(c_0_131, plain, (![X4]:![X5]:![X6]:(((~intruder_message(encrypt(X4,X5))|~intruder_holds(key(X5,X6)))|~party_of_protocol(X6))|intruder_message(X5))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])).
fof(c_0_132, plain, (![X5]:![X6]:![X7]:![X8]:((((intruder_message(X5)|~intruder_message(quadruple(X5,X6,X7,X8)))&(intruder_message(X6)|~intruder_message(quadruple(X5,X6,X7,X8))))&(intruder_message(X7)|~intruder_message(quadruple(X5,X6,X7,X8))))&(intruder_message(X8)|~intruder_message(quadruple(X5,X6,X7,X8))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])).
fof(c_0_133, plain, (![X5]:![X6]:![X7]:![X8]:((((~intruder_message(X5)|~intruder_message(X6))|~intruder_message(X7))|~intruder_message(X8))|intruder_message(quadruple(X5,X6,X7,X8)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])).
fof(c_0_134, plain, (![X2]:(~a_key(X2)|~a_nonce(X2))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])).
fof(c_0_135, plain, (![X2]:~a_nonce(generate_key(X2))), inference(variable_rename,[status(thm)],[c_0_111])).
fof(c_0_136, plain, (![X2]:![X3]:(a_nonce(generate_expiration_time(X2))&a_nonce(generate_b_nonce(X3)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_29])])])).
cnf(c_0_137,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_71, c_0_106]), ['final']).
cnf(c_0_138,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_112])).
cnf(c_0_139,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_113]), ['final']).
cnf(c_0_140,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_68]), c_0_90])]), ['final']).
cnf(c_0_141,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_115]), c_0_90]), c_0_61])]), ['final']).
cnf(c_0_142,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_71, c_0_116]), ['final']).
cnf(c_0_143,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_68]), c_0_90])]), ['final']).
cnf(c_0_144,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119]), c_0_120]), ['final']).
cnf(c_0_145,plain,(intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_102, c_0_121]), ['final']).
cnf(c_0_146,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_64, c_0_106]), ['final']).
cnf(c_0_147,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_98]), c_0_90])]), ['final']).
cnf(c_0_148,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_116]), c_0_122])]), c_0_120]), ['final']).
cnf(c_0_149,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_105, c_0_116])).
cnf(c_0_150,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_64, c_0_116]), ['final']).
cnf(c_0_151,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_98]), c_0_90])]), ['final']).
cnf(c_0_152,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_123]), c_0_124]), c_0_122]), c_0_40])]), ['final']).
cnf(c_0_153,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_115]), c_0_69]), c_0_54])]), ['final']).
cnf(c_0_154,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_102, c_0_126]), ['final']).
cnf(c_0_155,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_119]), c_0_128])]), ['final']).
cnf(c_0_156,plain,(a_holds(key(X1,b))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X1,X2),at))|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_129, c_0_68]), ['final']).
cnf(c_0_157,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_112])).
cnf(c_0_158,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_130])).
cnf(c_0_159,plain,(intruder_message(X1)|~party_of_protocol(X2)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_131])).
cnf(c_0_160,plain,(intruder_message(X1)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])).
cnf(c_0_161,plain,(intruder_message(X2)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])).
cnf(c_0_162,plain,(intruder_message(quadruple(X1,X2,X3,X4))|~intruder_message(X4)|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_133])).
cnf(c_0_163,plain,(intruder_message(X3)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])).
cnf(c_0_164,plain,(intruder_message(X4)|~intruder_message(quadruple(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_132])).
cnf(c_0_165,plain,(~a_nonce(X1)|~a_key(X1)), inference(split_conjunct,[status(thm)],[c_0_134])).
cnf(c_0_166,plain,(~a_nonce(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_135])).
cnf(c_0_167,plain,(fresh_intruder_nonce(an_intruder_nonce)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_168,plain,(b_holds(key(bt,t))), inference(split_conjunct,[status(thm)],[c_0_31])).
cnf(c_0_169,plain,(a_holds(key(at,t))), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_170,plain,(a_nonce(generate_expiration_time(X1))), inference(split_conjunct,[status(thm)],[c_0_136])).
cnf(c_0_171,plain,(a_nonce(generate_b_nonce(X1))), inference(split_conjunct,[status(thm)],[c_0_136])).
cnf(c_0_172,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_137, c_0_138]), ['final']).
cnf(c_0_173,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_71, c_0_139]), ['final']).
cnf(c_0_174,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_140, c_0_119]), ['final']).
cnf(c_0_175,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_141]), ['final']).
cnf(c_0_176,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_64, c_0_139]), ['final']).
cnf(c_0_177,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_142, c_0_138]), ['final']).
cnf(c_0_178,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_95]), ['final']).
cnf(c_0_179,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_143, c_0_119]), ['final']).
cnf(c_0_180,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_81, c_0_119]), ['final']).
cnf(c_0_181,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_145]), c_0_90]), c_0_122]), c_0_61])]), ['final']).
cnf(c_0_182,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_58, c_0_121]), ['final']).
cnf(c_0_183,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_146, c_0_138]), ['final']).
cnf(c_0_184,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_125, c_0_119]), ['final']).
cnf(c_0_185,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_147, c_0_138]), ['final']).
cnf(c_0_186,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_119]), c_0_58]), ['final']).
cnf(c_0_187,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_148, c_0_115]), ['final']).
cnf(c_0_188,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_149, c_0_73]), ['final']).
cnf(c_0_189,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_150, c_0_138]), ['final']).
cnf(c_0_190,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_151, c_0_138]), ['final']).
cnf(c_0_191,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_119]), c_0_58]), ['final']).
cnf(c_0_192,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_153]), ['final']).
cnf(c_0_193,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_144, c_0_115]), ['final']).
cnf(c_0_194,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_119]), c_0_102]), c_0_58]), ['final']).
cnf(c_0_195,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_154]), c_0_69]), c_0_122]), c_0_54])]), ['final']).
cnf(c_0_196,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_58, c_0_126]), ['final']).
cnf(c_0_197,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_70, c_0_126]), ['final']).
cnf(c_0_198,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(quadruple(b,an_a_nonce,X3,X4))|~intruder_message(at)|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_85, c_0_119]), ['final']).
cnf(c_0_199,plain,(b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_119]), c_0_102]), ['final']).
cnf(c_0_200,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_82]), c_0_124])]), ['final']).
cnf(c_0_201,plain,(a_holds(key(X1,b))|~intruder_message(quadruple(b,an_a_nonce,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_156, c_0_119]), ['final']).
cnf(c_0_202,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(spm,[status(thm)],[c_0_157, c_0_158]), ['final']).
cnf(c_0_203,plain,(message(sent(t,X1,triple(encrypt(quadruple(X2,X3,generate_key(X3),X4),X5),encrypt(triple(X1,generate_key(X3),X4),X6),X7)))|~a_nonce(X3)|~t_holds(key(X6,X2))|~t_holds(key(X5,X1))|~message(sent(X2,t,triple(X2,X7,encrypt(triple(X1,X3,X4),X6))))), c_0_35, ['final']).
cnf(c_0_204,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), c_0_38, ['final']).
cnf(c_0_205,plain,(message(sent(a,X1,pair(X2,encrypt(X3,X4))))|~a_stored(pair(X1,X5))|~message(sent(t,a,triple(encrypt(quadruple(X1,X5,X4,X6),at),X2,X3)))), c_0_48, ['final']).
cnf(c_0_206,plain,(b_holds(key(X1,X2))|~a_key(X1)|~b_stored(pair(X2,X3))|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))), c_0_74, ['final']).
cnf(c_0_207,plain,(a_holds(key(X1,X2))|~a_stored(pair(X2,X3))|~message(sent(t,a,triple(encrypt(quadruple(X2,X3,X1,X4),at),X5,X6)))), c_0_94, ['final']).
cnf(c_0_208,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~message(sent(X1,b,pair(X1,X2)))), c_0_52, ['final']).
cnf(c_0_209,plain,(intruder_message(X1)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))|~party_of_protocol(X2)), c_0_159, ['final']).
cnf(c_0_210,plain,(intruder_message(encrypt(X1,X2))|~intruder_holds(key(X2,X3))|~intruder_message(X1)|~party_of_protocol(X3)), c_0_88, ['final']).
cnf(c_0_211,plain,(intruder_message(X1)|~intruder_message(quadruple(X1,X2,X3,X4))), c_0_160, ['final']).
cnf(c_0_212,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X1,X3,X4))), c_0_161, ['final']).
cnf(c_0_213,plain,(intruder_message(quadruple(X1,X2,X3,X4))|~intruder_message(X4)|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), c_0_162, ['final']).
cnf(c_0_214,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), c_0_68, ['final']).
cnf(c_0_215,plain,(message(sent(X1,X2,X3))|~intruder_message(X3)|~party_of_protocol(X2)|~party_of_protocol(X1)), c_0_53, ['final']).
cnf(c_0_216,plain,(intruder_holds(key(X1,X2))|~intruder_message(X1)|~party_of_protocol(X2)), c_0_89, ['final']).
cnf(c_0_217,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)), c_0_65, ['final']).
cnf(c_0_218,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), c_0_158, ['final']).
cnf(c_0_219,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X3,X1,X4))), c_0_163, ['final']).
cnf(c_0_220,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X3,X4,X1))), c_0_164, ['final']).
cnf(c_0_221,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), c_0_58, ['final']).
cnf(c_0_222,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))), c_0_46, ['final']).
cnf(c_0_223,plain,(intruder_message(X1)|~intruder_message(triple(X2,X1,X3))), c_0_102, ['final']).
cnf(c_0_224,plain,(intruder_message(X1)|~intruder_message(triple(X2,X3,X1))), c_0_70, ['final']).
cnf(c_0_225,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))), c_0_78, ['final']).
cnf(c_0_226,plain,(intruder_message(X1)|~intruder_message(pair(X2,X1))), c_0_105, ['final']).
cnf(c_0_227,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)), c_0_138, ['final']).
cnf(c_0_228,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)), c_0_157, ['final']).
cnf(c_0_229,plain,(~a_nonce(X1)|~a_key(X1)), c_0_165, ['final']).
cnf(c_0_230,plain,(~a_nonce(generate_key(X1))), c_0_166, ['final']).
cnf(c_0_231,plain,(b_holds(key(generate_key(an_a_nonce),b))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_154]), c_0_69]), c_0_54]), c_0_124]), c_0_51]), c_0_40])]), ['final']).
cnf(c_0_232,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_78, c_0_106]), ['final']).
cnf(c_0_233,plain,(b_holds(key(generate_key(an_a_nonce),a))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_91]), c_0_124]), c_0_90]), c_0_122]), c_0_40]), c_0_61])]), ['final']).
cnf(c_0_234,plain,(a_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_110, c_0_62]), ['final']).
cnf(c_0_235,plain,(intruder_message(an_intruder_nonce)), inference(spm,[status(thm)],[c_0_157, c_0_167]), ['final']).
cnf(c_0_236,plain,(message(sent(a,b,pair(a,an_a_nonce)))), c_0_39, ['final']).
cnf(c_0_237,plain,(t_holds(key(bt,b))), c_0_36, ['final']).
cnf(c_0_238,plain,(t_holds(key(at,a))), c_0_43, ['final']).
cnf(c_0_239,plain,(b_holds(key(bt,t))), c_0_168, ['final']).
cnf(c_0_240,plain,(a_stored(pair(b,an_a_nonce))), c_0_49, ['final']).
cnf(c_0_241,plain,(a_holds(key(at,t))), c_0_169, ['final']).
cnf(c_0_242,plain,(a_nonce(generate_expiration_time(X1))), c_0_170, ['final']).
cnf(c_0_243,plain,(a_nonce(generate_b_nonce(X1))), c_0_171, ['final']).
cnf(c_0_244,plain,(a_key(generate_key(X1))), c_0_122, ['final']).
cnf(c_0_245,plain,(fresh_intruder_nonce(an_intruder_nonce)), c_0_167, ['final']).
cnf(c_0_246,plain,(a_nonce(an_a_nonce)), c_0_51, ['final']).
cnf(c_0_247,plain,(fresh_to_b(an_a_nonce)), c_0_40, ['final']).
cnf(c_0_248,plain,(party_of_protocol(b)), c_0_54, ['final']).
cnf(c_0_249,plain,(party_of_protocol(a)), c_0_61, ['final']).
cnf(c_0_250,plain,(party_of_protocol(t)), c_0_56, ['final']).
# SZS output end Saturation.

ePrincess 1.0

The proof trees are built top-down, with the first line(s) stating what formulas are assumed (this is after preprocessing and simplification has been applied). Afterwards each step is presented one-by-one stating from what formula(s) and by what kind of reasoning it is derived. Alpha-rule is simply breaking a conjunction in its pieces, and beta-rule is breaking a disjunction into two branches. Every formula is written in TPTP-like negation normal form and is contained between "% SZS output start Proof for xxxx" and "% SZS output end Proof for xxxx".

Sample solution for SEU140+2

% SZS output start Proof for SEU140+2
Assumed formulas after preprocessing and simplification:
| (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v5 = 0) &  ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & disjoint(v1, v2) = 0 & disjoint(v0, v2) = v3 & subset(v0, v1) = 0 &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (set_difference(v8, v9) = v11) |  ~ (set_difference(v7, v9) = v10) |  ~ (subset(v10, v11) = v12) |  ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(v10, v11) = v12) |  ~ (set_intersection2(v8, v9) = v11) |  ~ (set_intersection2(v7, v9) = v10) |  ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (subset(v10, v8) = v11) |  ~ (set_union2(v7, v9) = v10) |  ? [v12] :  ? [v13] : (subset(v9, v8) = v13 & subset(v7, v8) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (subset(v7, v10) = v11) |  ~ (set_intersection2(v8, v9) = v10) |  ? [v12] :  ? [v13] : (subset(v7, v9) = v13 & subset(v7, v8) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (set_union2(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v11 = 0 &  ~ (v13 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_union2(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v13 & in(v10, v8) = v12 & (v13 = 0 | ( ~ (v12 = 0) &  ~ (v11 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (set_difference(v8, v7) = v9) |  ~ (set_union2(v7, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (set_difference(v7, v8) = v9) |  ~ (subset(v9, v7) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v9, v7) = v10) |  ~ (set_intersection2(v7, v8) = v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v7, v9) = v10) |  ~ (subset(v7, v8) = 0) |  ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v7, v9) = v10) |  ~ (set_union2(v7, v8) = v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (disjoint(v10, v9) = v8) |  ~ (disjoint(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_difference(v10, v9) = v8) |  ~ (set_difference(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (subset(v10, v9) = v8) |  ~ (subset(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_intersection2(v10, v9) = v8) |  ~ (set_intersection2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_union2(v10, v9) = v8) |  ~ (set_union2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (proper_subset(v10, v9) = v8) |  ~ (proper_subset(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (in(v10, v9) = v8) |  ~ (in(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v9, v8) = v10) |  ~ (set_union2(v7, v8) = v9) | set_difference(v7, v8) = v10) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v8, v7) = v9) |  ~ (set_union2(v7, v9) = v10) | set_union2(v7, v8) = v10) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v7, v9) = v10) |  ~ (set_difference(v7, v8) = v9) | set_intersection2(v7, v8) = v10) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v7, v8) = v9) |  ~ (in(v10, v7) = 0) |  ? [v11] :  ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & (v12 = 0 | v11 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ (in(v10, v7) = 0) |  ? [v11] :  ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & ( ~ (v11 = 0) | v12 = 0))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_difference(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0) | v14 = 0) & (v12 = 0 | (v13 = 0 &  ~ (v14 = 0))))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_intersection2(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v14 = 0) |  ~ (v13 = 0) |  ~ (v12 = 0)) & (v12 = 0 | (v14 = 0 & v13 = 0)))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_union2(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v12 = 0) | ( ~ (v14 = 0) &  ~ (v13 = 0))) & (v14 = 0 | v13 = 0 | v12 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_union2(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (set_intersection2(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = empty_set |  ~ (set_difference(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = v7 |  ~ (proper_subset(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (disjoint(v7, v8) = v9) |  ? [v10] :  ? [v11] : (set_intersection2(v7, v8) = v10 & in(v11, v10) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (disjoint(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = empty_set) & set_intersection2(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (disjoint(v7, v8) = v9) |  ? [v10] : (in(v10, v8) = 0 & in(v10, v7) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v7, v8) = v9) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (empty(v9) = v8) |  ~ (empty(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (disjoint(v7, v8) = 0) |  ~ (in(v9, v7) = 0) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (subset(v7, v8) = 0) |  ~ (in(v9, v7) = 0) | in(v9, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v8, v7) = v9) |  ? [v10] :  ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) |  ? [v10] :  ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (empty(v8) = 0) |  ~ (empty(v7) = 0)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_difference(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (subset(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & subset(v8, v7) = v9)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_intersection2(v7, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_union2(v7, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_union2(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : (v8 = empty_set |  ~ (set_difference(empty_set, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = empty_set |  ~ (set_intersection2(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (subset(v7, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (subset(empty_set, v7) = v8)) &  ! [v7] :  ! [v8] : ( ~ (disjoint(v7, v8) = 0) | disjoint(v8, v7) = 0) &  ! [v7] :  ! [v8] : ( ~ (disjoint(v7, v8) = 0) | set_intersection2(v7, v8) = empty_set) &  ! [v7] :  ! [v8] : ( ~ (disjoint(v7, v8) = 0) |  ? [v9] : (set_intersection2(v7, v8) = v9 &  ! [v10] :  ~ (in(v10, v9) = 0))) &  ! [v7] :  ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8) = 0) &  ! [v7] :  ! [v8] : ( ~ (proper_subset(v8, v7) = 0) |  ? [v9] : ( ~ (v9 = 0) & subset(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (proper_subset(v7, v8) = 0) | subset(v7, v8) = 0) &  ! [v7] :  ! [v8] : ( ~ (proper_subset(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & proper_subset(v8, v7) = v9)) &  ! [v7] :  ! [v8] : ( ~ (in(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (in(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) &  ! [v7] : (v7 = empty_set |  ~ (empty(v7) = 0)) &  ! [v7] : (v7 = empty_set |  ~ (subset(v7, empty_set) = 0)) &  ! [v7] :  ~ (proper_subset(v7, v7) = 0) &  ! [v7] :  ~ (in(v7, empty_set) = 0) &  ? [v7] :  ? [v8] : (v8 = v7 |  ? [v9] :  ? [v10] :  ? [v11] : (in(v9, v8) = v11 & in(v9, v7) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0)) & (v11 = 0 | v10 = 0))) &  ? [v7] : (v7 = empty_set |  ? [v8] : in(v8, v7) = 0))
| Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
| (1)  ~ (all_0_1_1 = 0) &  ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & disjoint(all_0_5_5, all_0_4_4) = 0 & disjoint(all_0_6_6, all_0_4_4) = all_0_3_3 & subset(all_0_6_6, all_0_5_5) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ (subset(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (subset(v3, v4) = v5) |  ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v1) = v4) |  ~ (set_union2(v0, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v0, v3) = v4) |  ~ (set_intersection2(v1, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 &  ~ (v6 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) &  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (set_difference(v0, v1) = v2) |  ~ (subset(v2, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v2, v0) = v3) |  ~ (set_intersection2(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (set_union2(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (proper_subset(v3, v2) = v1) |  ~ (proper_subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 &  ~ (v7 = 0))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (proper_subset(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] :  ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_difference(empty_set, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) &  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) &  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) |  ? [v2] : (set_intersection2(v0, v1) = v2 &  ! [v3] :  ~ (in(v3, v2) = 0))) &  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (proper_subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) &  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0)) &  ! [v0] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0)) &  ! [v0] :  ~ (proper_subset(v0, v0) = 0) &  ! [v0] :  ~ (in(v0, empty_set) = 0) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) &  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
|
| Applying alpha-rule on (1) yields:
| (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ (subset(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
| (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
| (4)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
| (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
| (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 &  ~ (v6 = 0)))))
| (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
| (8)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
| (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
| (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
| (11)  ! [v0] :  ~ (proper_subset(v0, v0) = 0)
| (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
| (13)  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
| (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
| (15)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
| (16)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
| (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
| (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
| (19)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
| (20) disjoint(all_0_6_6, all_0_4_4) = all_0_3_3
| (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
| (22) empty(empty_set) = 0
| (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
| (24)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1))
| (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
| (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (subset(v3, v4) = v5) |  ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
| (27)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
| (28)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
| (29)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
| (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (set_union2(v0, v1) = v2))
| (31)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
| (32)  ! [v0] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0))
| (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (proper_subset(v3, v2) = v1) |  ~ (proper_subset(v3, v2) = v0))
| (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
| (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
| (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v1) = v4) |  ~ (set_union2(v0, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0))))
| (37)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
| (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
| (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) &  ~ (v4 = 0)))))
| (40) empty(all_0_0_0) = 0
| (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
| (42)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] :  ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
| (43)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
| (44)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
| (45)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
| (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v2, v0) = v3) |  ~ (set_intersection2(v0, v1) = v2))
| (47)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
| (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
| (49)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
| (50)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (proper_subset(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
| (51)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
| (52)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
| (53)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
| (54)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
| (55)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 &  ~ (v7 = 0)))))
| (56)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
| (57)  ! [v0] :  ~ (in(v0, empty_set) = 0)
| (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
| (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v0, v3) = v4) |  ~ (set_intersection2(v1, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0))))
| (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (set_difference(v0, v1) = v2) |  ~ (subset(v2, v0) = v3))
| (61) empty(all_0_2_2) = all_0_1_1
| (62)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
| (63)  ~ (all_0_1_1 = 0)
| (64)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
| (65)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
| (66)  ~ (all_0_3_3 = 0)
| (67)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
| (68) disjoint(all_0_5_5, all_0_4_4) = 0
| (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
| (70)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) |  ? [v2] : (set_intersection2(v0, v1) = v2 &  ! [v3] :  ~ (in(v3, v2) = 0)))
| (71)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
| (72) subset(all_0_6_6, all_0_5_5) = 0
| (73)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
| (74)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_difference(empty_set, v0) = v1))
| (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0))
| (76)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1))
| (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
|
| Instantiating formula (52) with all_0_4_4, all_0_5_5 and discharging atoms disjoint(all_0_5_5, all_0_4_4) = 0, yields:
| (78) disjoint(all_0_4_4, all_0_5_5) = 0
|
| Instantiating formula (65) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
| (79) all_0_3_3 = 0 |  ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_6_6, all_0_4_4) = v0)
|
| Instantiating formula (15) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
| (80) all_0_3_3 = 0 |  ? [v0] : (in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = 0)
|
+-Applying beta-rule and splitting (79), into two cases.
|-Branch one:
| (81) all_0_3_3 = 0
|
all_0_3_3| Equations (81) can reduce 66 to:
to| (82) $false
false|
false|-The branch is then unsatisfiable
|-Branch two:
| (66)  ~ (all_0_3_3 = 0)
| (84)  ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_6_6, all_0_4_4) = v0)
|
v0+-Applying beta-rule and splitting (80), into two cases.
cases|-Branch one:
one| (81) all_0_3_3 = 0
all_0_3_3|
81| Equations (81) can reduce 66 to:
66| (82) $false
82|
false|-The branch is then unsatisfiable
unsatisfiable|-Branch two:
two| (66)  ~ (all_0_3_3 = 0)
all_0_3_3| (88)  ? [v0] : (in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = 0)
all_0_6_6|
v0| Instantiating (88) with all_33_0_15 yields:
all_33_0_15| (89) in(all_33_0_15, all_0_4_4) = 0 & in(all_33_0_15, all_0_6_6) = 0
all_33_0_15|
all_0_6_6| Applying alpha-rule on (89) yields:
89| (90) in(all_33_0_15, all_0_4_4) = 0
all_33_0_15| (91) in(all_33_0_15, all_0_6_6) = 0
all_33_0_15|
all_0_6_6| Instantiating formula (14) with all_33_0_15, all_0_5_5, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_5_5) = 0, in(all_33_0_15, all_0_4_4) = 0, yields:
all_0_4_4| (92)  ? [v0] : ( ~ (v0 = 0) & in(all_33_0_15, all_0_5_5) = v0)
all_0_5_5|
v0| Instantiating formula (41) with all_33_0_15, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, in(all_33_0_15, all_0_6_6) = 0, yields:
all_0_6_6| (93) in(all_33_0_15, all_0_5_5) = 0
all_33_0_15|
all_0_5_5| Instantiating (92) with all_80_0_21 yields:
all_80_0_21| (94)  ~ (all_80_0_21 = 0) & in(all_33_0_15, all_0_5_5) = all_80_0_21
all_0_5_5|
all_80_0_21| Applying alpha-rule on (94) yields:
94| (95)  ~ (all_80_0_21 = 0)
95| (96) in(all_33_0_15, all_0_5_5) = all_80_0_21
all_0_5_5|
all_80_0_21| Instantiating formula (38) with all_33_0_15, all_0_5_5, 0, all_80_0_21 and discharging atoms in(all_33_0_15, all_0_5_5) = all_80_0_21, in(all_33_0_15, all_0_5_5) = 0, yields:
all_0_5_5| (97) all_80_0_21 = 0
97|
all_80_0_21| Equations (97) can reduce 95 to:
95| (82) $false
82|
false|-The branch is then unsatisfiable
% SZS output end Proof for SEU140+2

ET 0.2

Sample solution for SEU140+2

# No SInE strategy applied
# Trying AutoSched4 for 1 seconds
# AutoSched4-Mode selected heuristic G_E___042_C18_F1_PI_AE_Q4_CS_SP_PS_S4S
# and selection function SelectNewComplexAHPNS.
#
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation.
fof(c_0_0, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', t3_xboole_0)).
fof(c_0_1, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', t63_xboole_1)).
fof(c_0_2, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', d3_tarski)).
fof(c_0_3, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), file('/tmp/SystemOnTPTP11427/SEU140+2.tptp', symmetry_r1_xboole_0)).
fof(c_0_4, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_0])).
fof(c_0_5, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_1])).
fof(c_0_6, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), c_0_2).
fof(c_0_7, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])])).
fof(c_0_8, negated_conjecture, (((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])).
fof(c_0_9, plain, (![X4]:![X5]:![X6]:![X7]:![X8]:((~subset(X4,X5)|(~in(X6,X4)|in(X6,X5)))&((in(esk3_2(X7,X8),X7)|subset(X7,X8))&(~in(esk3_2(X7,X8),X8)|subset(X7,X8))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])])).
cnf(c_0_10,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])).
cnf(c_0_11,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_8])).
cnf(c_0_12,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_13,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_8])).
fof(c_0_14, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), c_0_3).
cnf(c_0_15,lemma,(~in(X3,X2)|~in(X3,X1)|~disjoint(X1,X2)), c_0_10).
cnf(c_0_16,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_11).
cnf(c_0_17,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_7])).
cnf(c_0_18,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)), c_0_12).
cnf(c_0_19,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_13).
cnf(c_0_20,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_7])).
fof(c_0_21, plain, (![X3]:![X4]:(~disjoint(X3,X4)|disjoint(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])).
cnf(c_0_22,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_15).
cnf(c_0_23,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_16).
cnf(c_0_24,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_17).
cnf(c_0_25,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_18).
cnf(c_0_26,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_19).
cnf(c_0_27,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_20).
cnf(c_0_28,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_29,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_22).
cnf(c_0_30,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_23).
cnf(c_0_31,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_24).
cnf(c_0_32,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_25).
cnf(c_0_33,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_26).
cnf(c_0_34,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_27).
cnf(c_0_35,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_8])).
cnf(c_0_36,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_28).
cnf(c_0_37,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_29, c_0_30, theory(equality)])).
cnf(c_0_38,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_31).
cnf(c_0_39,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)), inference(spm,[status(thm)],[c_0_32, c_0_33, theory(equality)])).
cnf(c_0_40,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_34).
cnf(c_0_41,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_35).
cnf(c_0_42,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_36).
cnf(c_0_43,lemma,(disjoint(esk13_0,X1)|~in(esk9_2(esk13_0,X1),esk12_0)), inference(spm,[status(thm)],[c_0_37, c_0_38, theory(equality)])).
cnf(c_0_44,lemma,(disjoint(X1,esk11_0)|in(esk9_2(X1,esk11_0),esk12_0)), inference(spm,[status(thm)],[c_0_39, c_0_40, theory(equality)])).
cnf(c_0_45,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_41).
cnf(c_0_46,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_42).
cnf(c_0_47,lemma,(disjoint(esk13_0,esk11_0)), inference(spm,[status(thm)],[c_0_43, c_0_44, theory(equality)])).
cnf(c_0_48,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_45).
cnf(c_0_49,lemma,($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47, theory(equality)]), c_0_48, theory(equality)]), ['proof']).
# SZS output end CNFRefutation.

Geo-III 2015E

In proofs, exists(X,Y) denotes existential resolution, resolve(X,Y) is standard hyperresolution. + denotes Horn clause resolution. mergings( ) means that variables are merged by instantiation.

A model is just a list of flat atoms. Elements in the model have form E0, E1, E2, ... etc. Atoms of form #_{T} Ei mean that element Ei is introduced. The other atoms have form p_{T}( E1, E2, E3, E4 ), where T is the truth value, and p the predicate name. At CASC, only T is possible, because CASC is two-valued.

Sample solution for SEU140+2

% SZS status Theorem for /home/nivelle/TPTP-v6.1.0/Problems/SEU/SEU140+2.p
% SZS output start Refutation for /home/nivelle/TPTP-v6.1.0/Problems/SEU/SEU140+2.p

RuleSystem INPUT:

Initial Rules:
#0: input, references = 6, size of lhs = 2:
   in_{F}(V0,V1), in_{F}(V1,V0) | FALSE
      (used 0 times, uses = {})

#1: input, references = 3, size of lhs = 2:
   proper_subset_{F}(V0,V1), proper_subset_{F}(V1,V0) | FALSE
      (used 0 times, uses = {})

#2: input, references = 4, size of lhs = 3:
   P_set_union2_{F}(V0,V1,V2), P_set_union2_{F}(V1,V0,V3), V2 == V3 | FALSE
      (used 0 times, uses = {})

#3: input, references = 5, size of lhs = 3:
   P_set_intersection2_{F}(V0,V1,V2), P_set_intersection2_{F}(V1,V0,V3), V2 == V3 | FALSE
      (used 0 times, uses = {})

#4: input, references = 3, size of lhs = 1:
   #_{F} V1 | pppp0_{T}(V1,V1)
      (used 0 times, uses = {})

#5: input, references = 3, size of lhs = 2:
   pppp0_{F}(V0,V1), V0 == V1 | FALSE
      (used 0 times, uses = {})

#6: input, references = 3, size of lhs = 1:
   pppp0_{F}(V0,V1) | subset_{T}(V0,V1)
      (used 0 times, uses = {})

#7: input, references = 3, size of lhs = 1:
   pppp0_{F}(V0,V1) | subset_{T}(V1,V0)
      (used 0 times, uses = {})

#8: input, references = 3, size of lhs = 2:
   subset_{F}(V0,V1), subset_{F}(V1,V0) | pppp0_{T}(V0,V1)
      (used 0 times, uses = {})

#9: input, references = 3, size of lhs = 1:
   P_empty_set_{F}(V0) | pppp1_{T}(V0)
      (used 0 times, uses = {})

#10: input, references = 3, size of lhs = 3:
   pppp1_{F}(V1), P_empty_set_{F}(V0), V1 == V0 | FALSE
      (used 0 times, uses = {})

#11: input, references = 5, size of lhs = 3:
   P_empty_set_{F}(V0), pppp1_{F}(V1), in_{F}(V2,V1) | FALSE
      (used 0 times, uses = {})

#12: input, references = 4, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | pppp1_{T}(V1), pppp23_{T}(V1)
      (used 0 times, uses = {})

#13: input, references = 3, size of lhs = 1:
   pppp23_{F}(V0) | EXISTS V1: pppp10_{T}(V0,V1)
      (used 0 times, uses = {})

#14: input, references = 3, size of lhs = 1:
   pppp10_{F}(V0,V1) | in_{T}(V1,V0)
      (used 0 times, uses = {})

#15: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V4) | pppp3_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#16: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), pppp3_{F}(V1,V2,V3), P_set_union2_{F}(V1,V2,V4), V3 == V4 | FALSE
      (used 0 times, uses = {})

#17: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V4,V3), pppp3_{F}(V1,V2,V3) | pppp2_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#18: input, references = 7, size of lhs = 3:
   P_empty_set_{F}(V0), pppp2_{F}(V1,V2,V4), pppp3_{F}(V1,V2,V3) | in_{T}(V4,V3)
      (used 0 times, uses = {})

#19: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, #_{F} V3 | pppp3_{T}(V1,V2,V3), pppp24_{T}(V1,V2,V3)
      (used 0 times, uses = {})

#20: input, references = 3, size of lhs = 1:
   pppp24_{F}(V0,V1,V2) | EXISTS V3: pppp11_{T}(V0,V1,V2,V3)
      (used 0 times, uses = {})

#21: input, references = 4, size of lhs = 3:
   in_{F}(V3,V2), pppp11_{F}(V0,V1,V2,V3), pppp2_{F}(V0,V1,V3) | FALSE
      (used 0 times, uses = {})

#22: input, references = 6, size of lhs = 1:
   pppp11_{F}(V0,V1,V2,V3) | in_{T}(V3,V2), pppp2_{T}(V0,V1,V3)
      (used 0 times, uses = {})

#23: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), pppp2_{F}(V1,V2,V3) | in_{T}(V3,V1), in_{T}(V3,V2)
      (used 0 times, uses = {})

#24: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V3,V1), #_{F} V2 | pppp2_{T}(V1,V2,V3)
      (used 0 times, uses = {})

#25: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V3,V2), #_{F} V1 | pppp2_{T}(V1,V2,V3)
      (used 0 times, uses = {})

#26: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), subset_{F}(V1,V2) | pppp4_{T}(V1,V2)
      (used 0 times, uses = {})

#27: input, references = 4, size of lhs = 2:
   P_empty_set_{F}(V0), pppp4_{F}(V1,V2) | subset_{T}(V1,V2)
      (used 0 times, uses = {})

#28: input, references = 7, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V3,V1), pppp4_{F}(V1,V2) | in_{T}(V3,V2)
      (used 0 times, uses = {})

#29: input, references = 5, size of lhs = 3:
   P_empty_set_{F}(V0), #_{F} V1, #_{F} V2 | pppp4_{T}(V1,V2), pppp25_{T}(V1,V2)
      (used 0 times, uses = {})

#30: input, references = 3, size of lhs = 1:
   pppp25_{F}(V0,V1) | EXISTS V2: pppp12_{T}(V0,V1,V2)
      (used 0 times, uses = {})

#31: input, references = 3, size of lhs = 2:
   in_{F}(V2,V1), pppp12_{F}(V0,V1,V2) | FALSE
      (used 0 times, uses = {})

#32: input, references = 3, size of lhs = 1:
   pppp12_{F}(V0,V1,V2) | in_{T}(V2,V0)
      (used 0 times, uses = {})

#33: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V4) | pppp6_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#34: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), pppp6_{F}(V1,V2,V3), P_set_intersection2_{F}(V1,V2,V4), V3 == V4 | FALSE
      (used 0 times, uses = {})

#35: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V4,V3), pppp6_{F}(V1,V2,V3) | pppp5_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#36: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), pppp5_{F}(V1,V2,V4), pppp6_{F}(V1,V2,V3) | in_{T}(V4,V3)
      (used 0 times, uses = {})

#37: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, #_{F} V3 | pppp6_{T}(V1,V2,V3), pppp26_{T}(V1,V2,V3)
      (used 0 times, uses = {})

#38: input, references = 3, size of lhs = 1:
   pppp26_{F}(V0,V1,V2) | EXISTS V3: pppp13_{T}(V0,V1,V2,V3)
      (used 0 times, uses = {})

#39: input, references = 3, size of lhs = 3:
   in_{F}(V3,V2), pppp13_{F}(V0,V1,V2,V3), pppp5_{F}(V0,V1,V3) | FALSE
      (used 0 times, uses = {})

#40: input, references = 4, size of lhs = 1:
   pppp13_{F}(V0,V1,V2,V3) | in_{T}(V3,V2), pppp5_{T}(V0,V1,V3)
      (used 0 times, uses = {})

#41: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), pppp5_{F}(V1,V2,V3) | in_{T}(V3,V1)
      (used 0 times, uses = {})

#42: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), pppp5_{F}(V1,V2,V3) | in_{T}(V3,V2)
      (used 0 times, uses = {})

#43: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V3,V2), in_{F}(V3,V1) | pppp5_{T}(V1,V2,V3)
      (used 0 times, uses = {})

#44: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V4) | pppp8_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#45: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), pppp8_{F}(V1,V2,V3), P_set_difference_{F}(V1,V2,V4), V3 == V4 | FALSE
      (used 0 times, uses = {})

#46: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V4,V3), pppp8_{F}(V1,V2,V3) | pppp7_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#47: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), pppp7_{F}(V1,V2,V4), pppp8_{F}(V1,V2,V3) | in_{T}(V4,V3)
      (used 0 times, uses = {})

#48: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, #_{F} V3 | pppp8_{T}(V1,V2,V3), pppp27_{T}(V1,V2,V3)
      (used 0 times, uses = {})

#49: input, references = 3, size of lhs = 1:
   pppp27_{F}(V0,V1,V2) | EXISTS V3: pppp14_{T}(V0,V1,V2,V3)
      (used 0 times, uses = {})

#50: input, references = 3, size of lhs = 3:
   in_{F}(V3,V2), pppp14_{F}(V0,V1,V2,V3), pppp7_{F}(V0,V1,V3) | FALSE
      (used 0 times, uses = {})

#51: input, references = 5, size of lhs = 1:
   pppp14_{F}(V0,V1,V2,V3) | in_{T}(V3,V2), pppp7_{T}(V0,V1,V3)
      (used 0 times, uses = {})

#52: input, references = 6, size of lhs = 2:
   P_empty_set_{F}(V0), pppp7_{F}(V1,V2,V3) | in_{T}(V3,V1)
      (used 0 times, uses = {})

#53: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V3,V2), pppp7_{F}(V1,V2,V3) | FALSE
      (used 0 times, uses = {})

#54: input, references = 5, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V3,V1), #_{F} V2 | pppp7_{T}(V1,V2,V3), in_{T}(V3,V2)
      (used 0 times, uses = {})

#55: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), disjoint_{F}(V1,V2), P_set_intersection2_{F}(V1,V2,V3), V3 == V0 | FALSE
      (used 0 times, uses = {})

#56: input, references = 4, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V0) | disjoint_{T}(V1,V2)
      (used 0 times, uses = {})

#57: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), proper_subset_{F}(V1,V2) | pppp9_{T}(V1,V2)
      (used 0 times, uses = {})

#58: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), pppp9_{F}(V1,V2) | proper_subset_{T}(V1,V2)
      (used 0 times, uses = {})

#59: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), pppp9_{F}(V1,V2) | subset_{T}(V1,V2)
      (used 0 times, uses = {})

#60: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), pppp9_{F}(V2,V2) | FALSE
      (used 0 times, uses = {})

#61: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), V1 == V2 | pppp9_{T}(V1,V2)
      (used 0 times, uses = {})

#62: input, references = 3, size of lhs = 1:
   P_empty_set_{F}(V0) | empty_{T}(V0)
      (used 0 times, uses = {})

#63: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), empty_{F}(V3), P_set_union2_{F}(V1,V2,V3) | empty_{T}(V1)
      (used 0 times, uses = {})

#64: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), empty_{F}(V3), P_set_union2_{F}(V2,V1,V3) | empty_{T}(V1)
      (used 0 times, uses = {})

#65: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_union2_{F}(V1,V1,V2), V2 == V1 | FALSE
      (used 0 times, uses = {})

#66: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V1,V2), V2 == V1 | FALSE
      (used 0 times, uses = {})

#67: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), proper_subset_{F}(V1,V1) | FALSE
      (used 0 times, uses = {})

#68: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V0) | subset_{T}(V1,V2)
      (used 0 times, uses = {})

#69: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V1,V2,V3), V3 == V0 | FALSE
      (used 0 times, uses = {})

#70: input, references = 4, size of lhs = 1:
   P_empty_set_{F}(V0) | EXISTS V1: pppp15_{T}(V1)
      (used 0 times, uses = {})

#71: input, references = 5, size of lhs = 1:
   pppp15_{F}(V0) | empty_{T}(V0)
      (used 0 times, uses = {})

#72: input, references = 3, size of lhs = 1:
   P_empty_set_{F}(V0) | EXISTS V1: pppp16_{T}(V1)
      (used 0 times, uses = {})

#73: input, references = 3, size of lhs = 2:
   pppp16_{F}(V0), empty_{F}(V0) | FALSE
      (used 0 times, uses = {})

#74: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | subset_{T}(V1,V1)
      (used 0 times, uses = {})

#75: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), disjoint_{F}(V1,V2) | disjoint_{T}(V2,V1)
      (used 0 times, uses = {})

#76: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_union2_{F}(V1,V2,V3), V3 == V2 | FALSE
      (used 0 times, uses = {})

#77: input, references = 5, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3) | subset_{T}(V3,V1)
      (used 0 times, uses = {})

#78: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V1,V3), subset_{F}(V1,V2), P_set_intersection2_{F}(V3,V2,V4) | subset_{T}(V1,V4)
      (used 0 times, uses = {})

#79: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_union2_{F}(V1,V0,V2), V2 == V1 | FALSE
      (used 0 times, uses = {})

#80: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), subset_{F}(V3,V1), subset_{F}(V1,V2) | subset_{T}(V3,V2)
      (used 0 times, uses = {})

#81: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_intersection2_{F}(V1,V3,V4), P_set_intersection2_{F}(V2,V3,V5) | subset_{T}(V4,V5)
      (used 0 times, uses = {})

#82: input, references = 5, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_intersection2_{F}(V1,V2,V3), V3 == V1 | FALSE
      (used 0 times, uses = {})

#83: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V0,V2), V2 == V0 | FALSE
      (used 0 times, uses = {})

#84: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), #_{F} V1, #_{F} V2, V1 == V2 | EXISTS V3: pppp17_{T}(V1,V2,V3)
      (used 0 times, uses = {})

#85: input, references = 3, size of lhs = 3:
   in_{F}(V2,V1), in_{F}(V2,V0), pppp17_{F}(V0,V1,V2) | FALSE
      (used 0 times, uses = {})

#86: input, references = 4, size of lhs = 1:
   pppp17_{F}(V0,V1,V2) | in_{T}(V2,V0), in_{T}(V2,V1)
      (used 0 times, uses = {})

#87: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | subset_{T}(V0,V1)
      (used 0 times, uses = {})

#88: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V1,V3,V4), P_set_difference_{F}(V2,V3,V5) | subset_{T}(V4,V5)
      (used 0 times, uses = {})

#89: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3) | subset_{T}(V3,V1)
      (used 0 times, uses = {})

#90: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V0) | subset_{T}(V1,V2)
      (used 0 times, uses = {})

#91: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V1,V2,V3), V3 == V0 | FALSE
      (used 0 times, uses = {})

#92: input, references = 3, size of lhs = 5:
   P_empty_set_{F}(V0), P_set_difference_{F}(V2,V1,V3), P_set_union2_{F}(V1,V3,V4), P_set_union2_{F}(V1,V2,V5), V4 == V5 | FALSE
      (used 0 times, uses = {})

#93: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V0,V2), V2 == V1 | FALSE
      (used 0 times, uses = {})

#94: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), #_{F} V1, #_{F} V2 | disjoint_{T}(V1,V2), pppp28_{T}(V1,V2)
      (used 0 times, uses = {})

#95: input, references = 3, size of lhs = 1:
   pppp28_{F}(V0,V1) | EXISTS V2: pppp18_{T}(V0,V1,V2)
      (used 0 times, uses = {})

#96: input, references = 7, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V3,V1), in_{F}(V3,V2), disjoint_{F}(V1,V2) | FALSE
      (used 0 times, uses = {})

#97: input, references = 3, size of lhs = 1:
   pppp18_{F}(V0,V1,V2) | in_{T}(V2,V1)
      (used 0 times, uses = {})

#98: input, references = 3, size of lhs = 1:
   pppp18_{F}(V0,V1,V2) | in_{T}(V2,V0)
      (used 0 times, uses = {})

#99: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), subset_{F}(V1,V0), V1 == V0 | FALSE
      (used 0 times, uses = {})

#100: input, references = 3, size of lhs = 5:
   P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V3), P_set_difference_{F}(V3,V2,V4), P_set_difference_{F}(V1,V2,V5), V4 == V5 | FALSE
      (used 0 times, uses = {})

#101: input, references = 3, size of lhs = 5:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_difference_{F}(V2,V1,V3), P_set_union2_{F}(V1,V3,V4), V2 == V4 | FALSE
      (used 0 times, uses = {})

#102: input, references = 4, size of lhs = 5:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3), P_set_difference_{F}(V1,V3,V4), P_set_intersection2_{F}(V1,V2,V5), V4 == V5 | FALSE
      (used 0 times, uses = {})

#103: input, references = 4, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_difference_{F}(V0,V1,V2), V2 == V0 | FALSE
      (used 0 times, uses = {})

#104: input, references = 4, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3) | disjoint_{T}(V1,V2), pppp29_{T}(V3)
      (used 0 times, uses = {})

#105: input, references = 3, size of lhs = 1:
   pppp29_{F}(V0) | EXISTS V1: pppp19_{T}(V0,V1)
      (used 0 times, uses = {})

#106: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V4,V3), disjoint_{F}(V1,V2), P_set_intersection2_{F}(V1,V2,V3) | FALSE
      (used 0 times, uses = {})

#107: input, references = 3, size of lhs = 1:
   pppp19_{F}(V0,V1) | in_{T}(V1,V0)
      (used 0 times, uses = {})

#108: input, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), proper_subset_{F}(V2,V1) | FALSE
      (used 0 times, uses = {})

#109: input, references = 4, size of lhs = 1:
   P_empty_set_{F}(V0) | EXISTS V1: pppp22_{T}(V1)
      (used 0 times, uses = {})

#110: input, references = 4, size of lhs = 1:
   pppp22_{F}(V0) | EXISTS V1: pppp21_{T}(V0,V1)
      (used 0 times, uses = {})

#111: input, references = 4, size of lhs = 1:
   pppp21_{F}(V0,V1) | EXISTS V2: pppp20_{T}(V2,V0,V1)
      (used 0 times, uses = {})

#112: input, references = 4, size of lhs = 1:
   pppp21_{F}(V0,V1) | disjoint_{T}(V0,V1)
      (used 0 times, uses = {})

#113: input, references = 4, size of lhs = 2:
   disjoint_{F}(V0,V2), pppp20_{F}(V0,V1,V2) | FALSE
      (used 0 times, uses = {})

#114: input, references = 4, size of lhs = 1:
   pppp20_{F}(V0,V1,V2) | subset_{T}(V0,V1)
      (used 0 times, uses = {})

#115: input, references = 4, size of lhs = 3:
   empty_{F}(V1), P_empty_set_{F}(V0), V1 == V0 | FALSE
      (used 0 times, uses = {})

#116: input, references = 5, size of lhs = 3:
   P_empty_set_{F}(V0), empty_{F}(V1), in_{F}(V2,V1) | FALSE
      (used 0 times, uses = {})

#117: input, references = 3, size of lhs = 2:
   P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V3) | subset_{T}(V1,V3)
      (used 0 times, uses = {})

#118: input, references = 4, size of lhs = 4:
   P_empty_set_{F}(V0), empty_{F}(V2), empty_{F}(V1), V2 == V1 | FALSE
      (used 0 times, uses = {})

#119: input, references = 3, size of lhs = 4:
   P_empty_set_{F}(V0), subset_{F}(V3,V1), subset_{F}(V2,V1), P_set_union2_{F}(V3,V2,V4) | subset_{T}(V4,V1)
      (used 0 times, uses = {})

#120: input, references = 5, size of lhs = 2:
   #_{F} V0, #_{F} V1 | EXISTS V2: P_set_union2_{T}(V0,V1,V2)
      (used 0 times, uses = {})

#121: input, references = 8, size of lhs = 2:
   #_{F} V0, #_{F} V1 | EXISTS V2: P_set_intersection2_{T}(V0,V1,V2)
      (used 0 times, uses = {})

#122: input, references = 4, size of lhs = 0:
   TRUE | EXISTS V0: P_empty_set_{T}(V0)
      (used 0 times, uses = {})

#123: input, references = 5, size of lhs = 2:
   #_{F} V0, #_{F} V1 | EXISTS V2: P_set_difference_{T}(V0,V1,V2)
      (used 0 times, uses = {})

number of initial rules = 124

Simplifiers:
#124: unsound, references = 3, size of lhs = 3:
   P_set_union2_{F}(V0,V1,V2), P_set_union2_{F}(V0,V1,V5), V2 == V5 | FALSE
      (used 0 times, uses = {})

#125: unsound, references = 3, size of lhs = 3:
   P_set_intersection2_{F}(V0,V1,V2), P_set_intersection2_{F}(V0,V1,V5), V2 == V5 | FALSE
      (used 0 times, uses = {})

#126: unsound, references = 3, size of lhs = 3:
   P_empty_set_{F}(V0), P_empty_set_{F}(V1), V0 == V1 | FALSE
      (used 0 times, uses = {})

#127: unsound, references = 3, size of lhs = 3:
   P_set_difference_{F}(V0,V1,V2), P_set_difference_{F}(V0,V1,V5), V2 == V5 | FALSE
      (used 0 times, uses = {})

#128: unsound, references = 3, size of lhs = 3:
   pppp10_{F}(V0,V1), pppp10_{F}(V0,V3), V1 == V3 | FALSE
      (used 0 times, uses = {})

#129: unsound, references = 3, size of lhs = 3:
   pppp11_{F}(V0,V1,V2,V3), pppp11_{F}(V0,V1,V2,V7), V3 == V7 | FALSE
      (used 0 times, uses = {})

#130: unsound, references = 3, size of lhs = 3:
   pppp12_{F}(V0,V1,V2), pppp12_{F}(V0,V1,V5), V2 == V5 | FALSE
      (used 0 times, uses = {})

#131: unsound, references = 3, size of lhs = 3:
   pppp13_{F}(V0,V1,V2,V3), pppp13_{F}(V0,V1,V2,V7), V3 == V7 | FALSE
      (used 0 times, uses = {})

#132: unsound, references = 3, size of lhs = 3:
   pppp14_{F}(V0,V1,V2,V3), pppp14_{F}(V0,V1,V2,V7), V3 == V7 | FALSE
      (used 0 times, uses = {})

#133: unsound, references = 3, size of lhs = 3:
   pppp15_{F}(V0), pppp15_{F}(V1), V0 == V1 | FALSE
      (used 0 times, uses = {})

#134: unsound, references = 3, size of lhs = 3:
   pppp16_{F}(V0), pppp16_{F}(V1), V0 == V1 | FALSE
      (used 0 times, uses = {})

#135: unsound, references = 3, size of lhs = 3:
   pppp17_{F}(V0,V1,V2), pppp17_{F}(V0,V1,V5), V2 == V5 | FALSE
      (used 0 times, uses = {})

#136: unsound, references = 3, size of lhs = 3:
   pppp18_{F}(V0,V1,V2), pppp18_{F}(V0,V1,V5), V2 == V5 | FALSE
      (used 0 times, uses = {})

#137: unsound, references = 3, size of lhs = 3:
   pppp19_{F}(V0,V1), pppp19_{F}(V0,V3), V1 == V3 | FALSE
      (used 0 times, uses = {})

#138: unsound, references = 3, size of lhs = 3:
   pppp20_{F}(V0,V1,V2), pppp20_{F}(V3,V1,V2), V0 == V3 | FALSE
      (used 0 times, uses = {})

#139: unsound, references = 3, size of lhs = 3:
   pppp20_{F}(V0,V1,V2), pppp20_{F}(V3,V1,V5), V2 == V5 | FALSE
      (used 0 times, uses = {})

#140: unsound, references = 3, size of lhs = 3:
   pppp20_{F}(V0,V1,V2), pppp20_{F}(V3,V4,V5), V1 == V4 | FALSE
      (used 0 times, uses = {})

#141: unsound, references = 3, size of lhs = 3:
   pppp21_{F}(V0,V1), pppp21_{F}(V0,V3), V1 == V3 | FALSE
      (used 0 times, uses = {})

#142: unsound, references = 3, size of lhs = 3:
   pppp21_{F}(V0,V1), pppp21_{F}(V2,V3), V0 == V2 | FALSE
      (used 0 times, uses = {})

#143: unsound, references = 3, size of lhs = 3:
   pppp22_{F}(V0), pppp22_{F}(V1), V0 == V1 | FALSE
      (used 0 times, uses = {})

number of simplifiers = 20

Learnt:
#151: mergings( V0 == V2; #147 ), references = 1, size of lhs = 1:
   P_empty_set_{F}(V0) | pppp15_{T}(V0)
      (used 0 times, uses = {})

#153: mergings( V0 == V2; #148 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), empty_{F}(V1) | pppp15_{T}(V1)
      (used 0 times, uses = {})

#157: exists( #120, #65 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | P_set_union2_{T}(V1,V1,V1)
      (used 0 times, uses = {})

#158: exists( #120, #79 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | P_set_union2_{T}(V1,V0,V1)
      (used 0 times, uses = {})

#159: exists( #120, #76 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), subset_{F}(V1,V2) | P_set_union2_{T}(V1,V2,V2)
      (used 0 times, uses = {})

#163: exists( #121, #66 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | P_set_intersection2_{T}(V1,V1,V1)
      (used 0 times, uses = {})

#164: exists( #121, #83 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | P_set_intersection2_{T}(V1,V0,V0)
      (used 0 times, uses = {})

#165: exists( #121, #82 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), subset_{F}(V1,V2) | P_set_intersection2_{T}(V1,V2,V1)
      (used 0 times, uses = {})

#169: exists( #123, #93 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | P_set_difference_{T}(V1,V0,V1)
      (used 0 times, uses = {})

#170: exists( #123, #103 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), #_{F} V1 | P_set_difference_{T}(V0,V1,V0)
      (used 0 times, uses = {})

#171: exists( #123, #69 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), subset_{F}(V1,V2) | P_set_difference_{T}(V1,V2,V0)
      (used 0 times, uses = {})

#174: mergings( V0 == V3; #172 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), V3 == V0 | pppp28_{T}(V1,V2)
      (used 0 times, uses = {})

#179: mergings( V0 == V2; #176 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), #_{F} V1, V1 == V0 | pppp23_{T}(V1)
      (used 0 times, uses = {})

#182: mergings( V0 == V2, V1 == V2; #177 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), in_{F}(V1,V0) | pppp23_{T}(V0)
      (used 0 times, uses = {})

#185: mergings( V0 == V4; #183 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), P_set_union2_{F}(V1,V2,V3), #_{F} V4, V4 == V3 | pppp24_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#191: mergings( V3 == V5, V0 == V4; #186 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), V3 == V0 | pppp29_{T}(V3)
      (used 0 times, uses = {})

#194: mergings( V0 == V4, V3 == V4; #187 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V1,V3), P_set_intersection2_{F}(V2,V3,V0) | pppp29_{T}(V0)
      (used 0 times, uses = {})

#198: mergings( V6 == V3, V0 == V4, V3 == V4; #188 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), in_{F}(V1,V0), P_set_intersection2_{F}(V2,V3,V0) | pppp29_{T}(V0)
      (used 0 times, uses = {})

#204: mergings( V0 == V4; #202 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), #_{F} V4, V4 == V3 | pppp26_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#208: mergings( V0 == V4; #206 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3), #_{F} V4, V4 == V3 | pppp27_{T}(V1,V2,V4)
      (used 0 times, uses = {})

#212: disj( #22, #18+#0 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), pppp3_{F}(V1,V2,V3), pppp11_{F}(V1,V2,V4,V3) | in_{T}(V3,V4)
      (used 0 times, uses = {})

#229: exists( #120, #2 ), references = 1, size of lhs = 1:
   P_set_union2_{F}(V0,V1,V2) | P_set_union2_{T}(V1,V0,V2)
      (used 0 times, uses = {})

#243: exists( #121, #3 ), references = 3, size of lhs = 1:
   P_set_intersection2_{F}(V0,V1,V2) | P_set_intersection2_{T}(V1,V0,V2)
      (used 0 times, uses = {})

#259: mergings( V0 == V3; #255 ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), in_{F}(V1,V2) | pppp25_{T}(V2,V1)
      (used 0 times, uses = {})

#261: mergings( V0 == V3; #256 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V1,V2), pppp2_{F}(V3,V4,V1), pppp11_{F}(V3,V4,V5,V1) | pppp25_{T}(V2,V5)
      (used 0 times, uses = {})

#300: mergings( V4 == V5; #296 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), pppp1_{F}(V1), pppp3_{F}(V2,V3,V1), pppp11_{F}(V2,V3,V4,V5) | in_{T}(V5,V4)
      (used 0 times, uses = {})

#302: mergings( V4 == V5; #297 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), empty_{F}(V1), pppp3_{F}(V2,V3,V1), pppp11_{F}(V2,V3,V4,V5) | in_{T}(V5,V4)
      (used 0 times, uses = {})

#304: mergings( V4 == V5; #298 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), disjoint_{F}(V1,V1), pppp3_{F}(V2,V3,V1), pppp11_{F}(V2,V3,V4,V5) | in_{T}(V5,V4)
      (used 0 times, uses = {})

#316: disj( #22, input ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), pppp1_{F}(V1), pppp11_{F}(V2,V3,V1,V4) | pppp2_{T}(V2,V3,V4)
      (used 0 times, uses = {})

#317: disj( #22, input ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), empty_{F}(V1), pppp11_{F}(V2,V3,V1,V4) | pppp2_{T}(V2,V3,V4)
      (used 0 times, uses = {})

#318: disj( #22, input ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), disjoint_{F}(V1,V1), pppp11_{F}(V2,V3,V1,V4) | pppp2_{T}(V2,V3,V4)
      (used 0 times, uses = {})

#370: mergings( V0 == V4; #367 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V3,V1), pppp8_{F}(V2,V4,V3) | in_{T}(V1,V4)
      (used 0 times, uses = {})

#377: disj( #54, input ), references = 1, size of lhs = 2:
   P_empty_set_{F}(V0), in_{F}(V1,V2) | pppp7_{T}(V2,V1,V1)
      (used 0 times, uses = {})

#378: disj( #54, input ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V1,V2), pppp7_{F}(V3,V4,V1), pppp14_{F}(V3,V4,V5,V1) | pppp7_{T}(V2,V5,V1)
      (used 0 times, uses = {})

#432: disj( #40, input ), references = 1, size of lhs = 1:
   pppp13_{F}(V0,V1,V2,V2) | pppp5_{T}(V0,V1,V2)
      (used 0 times, uses = {})

#520: exists( #121, #55 ), references = 2, size of lhs = 2:
   P_empty_set_{F}(V0), disjoint_{F}(V1,V2) | P_set_intersection2_{T}(V1,V2,V0)
      (used 0 times, uses = {})

#587: mergings( V0 == V3, V3 == V4; #582 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_intersection2_{F}(V1,V2,V3), V3 == V1 | pppp25_{T}(V1,V2)
      (used 0 times, uses = {})

#590: mergings( V0 == V3, V3 == V4; #583 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V1,V3), disjoint_{F}(V3,V4) | pppp25_{T}(V2,V4)
      (used 0 times, uses = {})

#593: mergings( V0 == V3, V3 == V4; #584 ), references = 1, size of lhs = 4:
   P_empty_set_{F}(V0), in_{F}(V1,V2), in_{F}(V1,V3), disjoint_{F}(V4,V3) | pppp25_{T}(V2,V4)
      (used 0 times, uses = {})

#663: mergings( V4 == V5; #659 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), pppp1_{F}(V1), pppp14_{F}(V1,V2,V3,V4) | in_{T}(V4,V3)
      (used 0 times, uses = {})

#665: mergings( V4 == V5; #660 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), empty_{F}(V1), pppp14_{F}(V1,V2,V3,V4) | in_{T}(V4,V3)
      (used 0 times, uses = {})

#667: mergings( V4 == V5; #661 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), disjoint_{F}(V1,V1), pppp14_{F}(V1,V2,V3,V4) | in_{T}(V4,V3)
      (used 0 times, uses = {})

#720: disj( #86, input ), references = 1, size of lhs = 2:
   in_{F}(V0,V1), pppp17_{F}(V0,V2,V1) | in_{T}(V1,V2)
      (used 0 times, uses = {})

#786: disj( #51, input ), references = 1, size of lhs = 1:
   pppp14_{F}(V0,V1,V2,V2) | pppp7_{T}(V0,V1,V2)
      (used 0 times, uses = {})

#957: exists( #123, #102 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), P_set_difference_{F}(V1,V2,V3), P_set_intersection2_{F}(V1,V2,V4) | P_set_difference_{T}(V1,V3,V4)
      (used 0 times, uses = {})

#1117: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #1112 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), subset_{F}(V1,V2), P_set_intersection2_{F}(V3,V2,V0) | P_set_intersection2_{T}(V3,V1,V0)
      (used 0 times, uses = {})

#1127: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #1122 ), references = 1, size of lhs = 3:
   P_empty_set_{F}(V0), pppp21_{F}(V1,V2), P_set_intersection2_{F}(V2,V1,V0) | FALSE
      (used 0 times, uses = {})

#1136: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #1131 ), references = 1, size of lhs = 2:
   pppp22_{F}(V0), P_empty_set_{F}(V1) | FALSE
      (used 0 times, uses = {})

#1143: mergings( V0 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #1137 ), references = 1, size of lhs = 1:
   P_empty_set_{F}(V0) | FALSE
      (used 0 times, uses = {})

#1145: #122+#1137, references = 1, size of lhs = 0:
   TRUE | FALSE
      (used 0 times, uses = {})

number of learnt formulas = 50


% SZS output end Refutation for /home/nivelle/TPTP-v6.1.0/Problems/SEU/SEU140+2.p

Sample solution for NLP042+1

% SZS status CounterSatisfiable for /home/nivelle/TPTP-v6.1.0/Problems/NLP/NLP042+1.p
% SZS output start Model for /home/nivelle/TPTP-v6.1.0/Problems/NLP/NLP042+1.p

Interpretation 4:
Guesses:
0 : guesser 1, 0, ( | 1, 0 ), 0, 0s old, 0 lemmas
1 : guesser 4, 2, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
2 : guesser 17, 15, ( 0 | 2, 1 ), 0, 0s old, 1 lemmas
3 : guesser 29, 26, ( 2 | 1, 3, 0 ), 1, 0s old, 1 lemmas
4 : guesser 44, 41, ( 1, 0 | 3, 2 ), 2, 0s old, 2 lemmas

Elements:
   { E0, E1, E2, E3 }

Atoms:
0 : #_{T} E0                     { }
1 : #_{T} E1                     { 0 }
2 : pppp5_{T}(E1)                     { 0 }
3 : actual_world_{T}(E1)                     { 0 }
4 : pppp4_{T}(E1,E0)                     { 0, 1 }
5 : pppp3_{T}(E1,E0)                     { 0, 1 }
6 : order_{T}(E1,E0)                     { 0, 1 }
7 : nonreflexive_{T}(E1,E0)                     { 0, 1 }
8 : past_{T}(E1,E0)                     { 0, 1 }
9 : event_{T}(E1,E0)                     { 0, 1 }
10 : act_{T}(E1,E0)                     { 0, 1 }
11 : eventuality_{T}(E1,E0)                     { 0, 1 }
12 : unisex_{T}(E1,E0)                     { 0, 1 }
13 : nonexistent_{T}(E1,E0)                     { 0, 1 }
14 : specific_{T}(E1,E0)                     { 0, 1 }
15 : thing_{T}(E1,E0)                     { 0, 1 }
16 : singleton_{T}(E1,E0)                     { 0, 1 }
17 : #_{T} E2                     { 0, 1, 2 }
18 : pppp2_{T}(E1,E2,E0)                     { 0, 1, 2 }
19 : forename_{T}(E1,E2)                     { 0, 1, 2 }
20 : mia_forename_{T}(E1,E2)                     { 0, 1, 2 }
21 : relname_{T}(E1,E2)                     { 0, 1, 2 }
22 : relation_{T}(E1,E2)                     { 0, 1, 2 }
23 : abstraction_{T}(E1,E2)                     { 0, 1, 2 }
24 : unisex_{T}(E1,E2)                     { 0, 1, 2 }
25 : general_{T}(E1,E2)                     { 0, 1, 2 }
26 : nonhuman_{T}(E1,E2)                     { 0, 1, 2 }
27 : thing_{T}(E1,E2)                     { 0, 1, 2 }
28 : singleton_{T}(E1,E2)                     { 0, 1, 2 }
29 : pppp0_{T}(E1,E1,E0)                     { 0, 1, 3 }
30 : patient_{T}(E1,E0,E1)                     { 0, 1, 3 }
31 : shake_beverage_{T}(E1,E1)                     { 0, 1, 3 }
32 : beverage_{T}(E1,E1)                     { 0, 1, 3 }
33 : food_{T}(E1,E1)                     { 0, 1, 3 }
34 : substance_matter_{T}(E1,E1)                     { 0, 1, 3 }
35 : object_{T}(E1,E1)                     { 0, 1, 3 }
36 : unisex_{T}(E1,E1)                     { 0, 1, 3 }
37 : impartial_{T}(E1,E1)                     { 0, 1, 3 }
38 : nonliving_{T}(E1,E1)                     { 0, 1, 3 }
39 : entity_{T}(E1,E1)                     { 0, 1, 3 }
40 : existent_{T}(E1,E1)                     { 0, 1, 3 }
41 : specific_{T}(E1,E1)                     { 0, 1, 3 }
42 : thing_{T}(E1,E1)                     { 0, 1, 3 }
43 : singleton_{T}(E1,E1)                     { 0, 1, 3 }
44 : #_{T} E3                     { 0, 1, 2, 4 }
45 : pppp1_{T}(E1,E3,E2,E0)                     { 0, 1, 2, 4 }
46 : agent_{T}(E1,E0,E3)                     { 0, 1, 2, 4 }
47 : woman_{T}(E1,E3)                     { 0, 1, 2, 4 }
48 : of_{T}(E1,E2,E3)                     { 0, 1, 2, 4 }
49 : female_{T}(E1,E3)                     { 0, 1, 2, 4 }
50 : human_person_{T}(E1,E3)                     { 0, 1, 2, 4 }
51 : animate_{T}(E1,E3)                     { 0, 1, 2, 4 }
52 : human_{T}(E1,E3)                     { 0, 1, 2, 4 }
53 : organism_{T}(E1,E3)                     { 0, 1, 2, 4 }
54 : living_{T}(E1,E3)                     { 0, 1, 2, 4 }
55 : impartial_{T}(E1,E3)                     { 0, 1, 2, 4 }
56 : entity_{T}(E1,E3)                     { 0, 1, 2, 4 }
57 : existent_{T}(E1,E3)                     { 0, 1, 2, 4 }
58 : specific_{T}(E1,E3)                     { 0, 1, 2, 4 }
59 : thing_{T}(E1,E3)                     { 0, 1, 2, 4 }
60 : singleton_{T}(E1,E3)                     { 0, 1, 2, 4 }


% SZS output end Model for /home/nivelle/TPTP-v6.1.0/Problems/NLP/NLP042+1.p

Sample solution for SWV017+1

% SZS status Satisfiable for /home/nivelle/TPTP-v6.1.0/Problems/SWV/SWV017+1.p
% SZS output start Model for /home/nivelle/TPTP-v6.1.0/Problems/SWV/SWV017+1.p

Interpretation 0:
Guesses:
0 : guesser 1, 0, ( | 1, 0 ), 0, 0s old, 0 lemmas
1 : guesser 3, 1, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
2 : guesser 4, 2, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
3 : guesser 5, 3, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
4 : guesser 6, 4, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
5 : guesser 7, 5, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
6 : guesser 8, 6, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
7 : guesser 9, 7, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
8 : guesser 10, 8, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
9 : guesser 11, 9, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
10 : guesser 12, 10, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
11 : guesser 13, 11, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
12 : guesser 14, 12, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
13 : guesser 15, 13, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
14 : guesser 16, 14, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
15 : guesser 17, 15, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
16 : guesser 18, 16, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
17 : guesser 19, 17, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
18 : guesser 20, 18, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
19 : guesser 21, 19, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
20 : guesser 22, 20, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
21 : guesser 23, 21, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
22 : guesser 24, 22, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
23 : guesser 25, 23, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
24 : guesser 28, 26, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
25 : guesser 44, 42, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
26 : guesser 45, 43, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
27 : guesser 46, 44, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
28 : guesser 47, 45, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
29 : guesser 48, 46, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
30 : guesser 49, 47, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
31 : guesser 50, 48, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
32 : guesser 52, 50, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
33 : guesser 53, 51, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
34 : guesser 54, 52, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
35 : guesser 55, 53, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
36 : guesser 56, 54, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
37 : guesser 57, 55, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
38 : guesser 58, 56, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
39 : guesser 59, 57, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
40 : guesser 63, 61, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
41 : guesser 64, 62, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
42 : guesser 65, 63, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
43 : guesser 66, 64, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
44 : guesser 67, 65, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
45 : guesser 68, 66, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
46 : guesser 69, 67, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
47 : guesser 70, 68, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
48 : guesser 72, 70, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
49 : guesser 73, 71, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
50 : guesser 74, 72, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
51 : guesser 75, 73, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
52 : guesser 76, 74, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
53 : guesser 77, 75, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
54 : guesser 78, 76, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
55 : guesser 79, 77, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
56 : guesser 80, 78, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas
57 : guesser 81, 79, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
58 : guesser 82, 80, ( | 0, 2, 1 ), 0, 0s old, 0 lemmas

Elements:
   { E0, E1 }

Atoms:
0 : #_{T} E0                     { }
1 : #_{T} E1                     { 0 }
2 : P_at_{T}(E1)                     { 0 }
3 : P_t_{T}(E1)                     { 1 }
4 : P_a_{T}(E0)                     { 2 }
5 : P_b_{T}(E0)                     { 3 }
6 : P_an_a_nonce_{T}(E1)                     { 4 }
7 : P_bt_{T}(E1)                     { 5 }
8 : P_an_intruder_nonce_{T}(E1)                     { 6 }
9 : P_generate_b_nonce_{T}(E0,E1)                     { 7 }
10 : P_generate_expiration_time_{T}(E0,E1)                     { 8 }
11 : P_generate_key_{T}(E0,E0)                     { 9 }
12 : P_generate_intruder_nonce_{T}(E0,E1)                     { 10 }
13 : P_key_{T}(E0,E0,E1)                     { 11 }
14 : P_pair_{T}(E0,E0,E1)                     { 12 }
15 : P_encrypt_{T}(E0,E0,E0)                     { 13 }
16 : P_sent_{T}(E0,E0,E0,E0)                     { 14 }
17 : P_triple_{T}(E0,E0,E0,E1)                     { 15 }
18 : P_quadruple_{T}(E0,E0,E0,E0,E0)                     { 16 }
19 : P_generate_b_nonce_{T}(E1,E1)                     { 0, 17 }
20 : P_generate_expiration_time_{T}(E1,E1)                     { 0, 18 }
21 : P_generate_key_{T}(E1,E0)                     { 0, 19 }
22 : P_generate_intruder_nonce_{T}(E1,E0)                     { 0, 20 }
23 : P_key_{T}(E0,E1,E1)                     { 0, 21 }
24 : P_key_{T}(E1,E0,E0)                     { 0, 22 }
25 : P_key_{T}(E1,E1,E0)                     { 0, 23 }
26 : a_holds_{T}(E0)                     { 0, 1, 23 }
27 : party_of_protocol_{T}(E0)                     { 0, 1, 2, 23 }
28 : P_pair_{T}(E0,E1,E0)                     { 0, 24 }
29 : message_{T}(E0)                     { 0, 1, 2, 3, 4, 14, 23, 24 }
30 : a_stored_{T}(E0)                     { 0, 1, 2, 3, 4, 14, 23, 24 }
31 : b_holds_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 14, 23, 24 }
32 : fresh_to_b_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 14, 23, 24 }
33 : t_holds_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 }
34 : party_of_protocol_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 }
35 : a_nonce_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 }
36 : intruder_message_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 }
37 : intruder_message_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 }
38 : fresh_intruder_nonce_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 6, 14, 22, 23, 24 }
39 : a_key_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 9, 14, 22, 23, 24 }
40 : intruder_holds_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24 }
41 : intruder_holds_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 11, 14, 22, 23, 24 }
42 : fresh_intruder_nonce_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 6, 14, 20, 22, 23, 24 }
43 : fresh_to_b_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 6, 14, 20, 22, 23, 24 }
44 : P_pair_{T}(E1,E0,E1)                     { 0, 25 }
45 : P_pair_{T}(E1,E1,E1)                     { 0, 26 }
46 : P_encrypt_{T}(E0,E1,E0)                     { 0, 27 }
47 : P_encrypt_{T}(E1,E0,E0)                     { 0, 28 }
48 : P_encrypt_{T}(E1,E1,E1)                     { 0, 29 }
49 : P_sent_{T}(E0,E0,E1,E0)                     { 0, 30 }
50 : P_sent_{T}(E0,E1,E0,E1)                     { 0, 31 }
51 : message_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 14, 22, 23, 24, 31 }
52 : P_sent_{T}(E0,E1,E1,E0)                     { 0, 32 }
53 : P_sent_{T}(E1,E0,E0,E0)                     { 0, 33 }
54 : P_sent_{T}(E1,E0,E1,E1)                     { 0, 34 }
55 : P_sent_{T}(E1,E1,E0,E0)                     { 0, 35 }
56 : P_sent_{T}(E1,E1,E1,E1)                     { 0, 36 }
57 : P_triple_{T}(E0,E0,E1,E1)                     { 0, 37 }
58 : P_triple_{T}(E0,E1,E0,E0)                     { 0, 38 }
59 : P_triple_{T}(E0,E1,E1,E1)                     { 0, 39 }
60 : b_stored_{T}(E0)                     { 0, 1, 2, 3, 4, 5, 14, 17, 18, 23, 24, 29, 32, 39 }
61 : b_stored_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 6, 7, 8, 12, 14, 20, 22, 23, 24, 29, 30, 32, 37, 39 }
62 : b_holds_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 9, 11, 14, 17, 18, 22, 23, 24, 25, 28, 29, 30, 32, 37, 39 }
63 : P_triple_{T}(E1,E0,E0,E0)                     { 0, 40 }
64 : P_triple_{T}(E1,E0,E1,E0)                     { 0, 41 }
65 : P_triple_{T}(E1,E1,E0,E0)                     { 0, 42 }
66 : P_triple_{T}(E1,E1,E1,E0)                     { 0, 43 }
67 : P_quadruple_{T}(E0,E0,E0,E1,E0)                     { 0, 44 }
68 : P_quadruple_{T}(E0,E0,E1,E0,E0)                     { 0, 45 }
69 : P_quadruple_{T}(E0,E0,E1,E1,E1)                     { 0, 46 }
70 : P_quadruple_{T}(E0,E1,E0,E0,E0)                     { 0, 47 }
71 : a_holds_{T}(E1)                     { 0, 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 22, 23, 24, 27, 30, 31, 34, 47 }
72 : P_quadruple_{T}(E0,E1,E0,E1,E0)                     { 0, 48 }
73 : P_quadruple_{T}(E0,E1,E1,E0,E1)                     { 0, 49 }
74 : P_quadruple_{T}(E0,E1,E1,E1,E1)                     { 0, 50 }
75 : P_quadruple_{T}(E1,E0,E0,E0,E1)                     { 0, 51 }
76 : P_quadruple_{T}(E1,E0,E0,E1,E1)                     { 0, 52 }
77 : P_quadruple_{T}(E1,E0,E1,E0,E0)                     { 0, 53 }
78 : P_quadruple_{T}(E1,E0,E1,E1,E0)                     { 0, 54 }
79 : P_quadruple_{T}(E1,E1,E0,E0,E0)                     { 0, 55 }
80 : P_quadruple_{T}(E1,E1,E0,E1,E0)                     { 0, 56 }
81 : P_quadruple_{T}(E1,E1,E1,E0,E1)                     { 0, 57 }
82 : P_quadruple_{T}(E1,E1,E1,E1,E0)                     { 0, 58 }


% SZS output end Model for /home/nivelle/TPTP-v6.1.0/Problems/SWV/SWV017+1.p

iProver 1.0

Sample solution for NLP042+1

% SZS output start Saturation

fof(f236,plain,(
  ( ! [Xxs0,X1] : (~general(X0,X1) | ~specific(X0,X1)) )),
  inference(cnf_transformation,[],[f194])).

fof(f194,plain,(
  ! [X0,X1] : (~specific(X0,X1) | ~general(X0,X1))),
  inference(ennf_transformation,[],[f51])).

fof(f51,plain,(
  ! [X0,X1] : (specific(X0,X1) => ~general(X0,X1))),
  inference(flattening,[],[f41])).

fof(f41,axiom,(
  ! [X0,X1] : (specific(X0,X1) => ~general(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f219,plain,(
  ( ! [X0,X1] : (specific(X0,X1) | ~entity(X0,X1)) )),
  inference(cnf_transformation,[],[f177])).

fof(f177,plain,(
  ! [X0,X1] : (~entity(X0,X1) | specific(X0,X1))),
  inference(ennf_transformation,[],[f21])).

fof(f21,axiom,(
  ! [X0,X1] : (entity(X0,X1) => specific(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f211,plain,(
  ( ! [X0,X1] : (general(X0,X1) | ~abstraction(X0,X1)) )),
  inference(cnf_transformation,[],[f169])).

fof(f169,plain,(
  ! [X0,X1] : (~abstraction(X0,X1) | general(X0,X1))),
  inference(ennf_transformation,[],[f11])).

fof(f11,axiom,(
  ! [X0,X1] : (abstraction(X0,X1) => general(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f213,plain,(
  ( ! [X0,X1] : (abstraction(X0,X1) | ~relation(X0,X1)) )),
  inference(cnf_transformation,[],[f171])).

fof(f171,plain,(
  ! [X0,X1] : (~relation(X0,X1) | abstraction(X0,X1))),
  inference(ennf_transformation,[],[f14])).

fof(f14,axiom,(
  ! [X0,X1] : (relation(X0,X1) => abstraction(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f214,plain,(
  ( ! [X0,X1] : (relation(X0,X1) | ~relname(X0,X1)) )),
  inference(cnf_transformation,[],[f172])).

fof(f172,plain,(
  ! [X0,X1] : (~relname(X0,X1) | relation(X0,X1))),
  inference(ennf_transformation,[],[f15])).

fof(f15,axiom,(
  ! [X0,X1] : (relname(X0,X1) => relation(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f215,plain,(
  ( ! [X0,X1] : (relname(X0,X1) | ~forename(X0,X1)) )),
  inference(cnf_transformation,[],[f173])).

fof(f173,plain,(
  ! [X0,X1] : (~forename(X0,X1) | relname(X0,X1))),
  inference(ennf_transformation,[],[f16])).

fof(f16,axiom,(
  ! [X0,X1] : (forename(X0,X1) => relname(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f243,plain,(
  forename(sK5,sK7)),
  inference(cnf_transformation,[],[f201])).

fof(f201,plain,(
  of(sK5,sK7,sK6) & woman(sK5,sK6) & mia_forename(sK5,sK7) & forename(sK5,sK7) & shake_beverage(sK5,sK8) & event(sK5,sK9) & agent(sK5,sK9,sK6) & patient(sK5,sK9,sK8) & nonreflexive(sK5,sK9) & order(sK5,sK9)),
  inference(skolemisation,[status(esa)],[f153])).
fof(f153,plain,(
  ? [X0,X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & nonreflexive(X0,X4) & order(X0,X4))),
  inference(pure_predicate_removal,[],[f152])).

fof(f152,plain,(
  ? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & nonreflexive(X0,X4) & order(X0,X4)))),
  inference(pure_predicate_removal,[],[f53])).

fof(f53,plain,(
  ? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & past(X0,X4) & nonreflexive(X0,X4) & order(X0,X4)))),
  inference(flattening,[],[f46])).

fof(f46,negated_conjecture,(
  ~~? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & past(X0,X4) & nonreflexive(X0,X4) & order(X0,X4)))),
  inference(negated_conjecture,[],[f45])).

fof(f45,conjecture,(
  ~? [X0] : (actual_world(X0) & ? [X1,X2,X3,X4] : (of(X0,X2,X1) & woman(X0,X1) & mia_forename(X0,X2) & forename(X0,X2) & shake_beverage(X0,X3) & event(X0,X4) & agent(X0,X4,X1) & patient(X0,X4,X3) & past(X0,X4) & nonreflexive(X0,X4) & order(X0,X4)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f206,plain,(
  ( ! [X0,X1] : (entity(X0,X1) | ~organism(X0,X1)) )),
  inference(cnf_transformation,[],[f164])).

fof(f164,plain,(
  ! [X0,X1] : (~organism(X0,X1) | entity(X0,X1))),
  inference(ennf_transformation,[],[f6])).

fof(f6,axiom,(
  ! [X0,X1] : (organism(X0,X1) => entity(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f235,plain,(
  ( ! [X0,X1] : (~living(X0,X1) | ~nonliving(X0,X1)) )),
  inference(cnf_transformation,[],[f193])).

fof(f193,plain,(
  ! [X0,X1] : (~nonliving(X0,X1) | ~living(X0,X1))),
  inference(ennf_transformation,[],[f50])).

fof(f50,plain,(
  ! [X0,X1] : (nonliving(X0,X1) => ~living(X0,X1))),
  inference(flattening,[],[f40])).

fof(f40,axiom,(
  ! [X0,X1] : (nonliving(X0,X1) => ~living(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f217,plain,(
  ( ! [X0,X1] : (nonliving(X0,X1) | ~object(X0,X1)) )),
  inference(cnf_transformation,[],[f175])).

fof(f175,plain,(
  ! [X0,X1] : (~object(X0,X1) | nonliving(X0,X1))),
  inference(ennf_transformation,[],[f19])).

fof(f19,axiom,(
  ! [X0,X1] : (object(X0,X1) => nonliving(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f221,plain,(
  ( ! [X0,X1] : (object(X0,X1) | ~substance_matter(X0,X1)) )),
  inference(cnf_transformation,[],[f179])).

fof(f179,plain,(
  ! [X0,X1] : (~substance_matter(X0,X1) | object(X0,X1))),
  inference(ennf_transformation,[],[f24])).

fof(f24,axiom,(
  ! [X0,X1] : (substance_matter(X0,X1) => object(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f222,plain,(
  ( ! [X0,X1] : (substance_matter(X0,X1) | ~food(X0,X1)) )),
  inference(cnf_transformation,[],[f180])).

fof(f180,plain,(
  ! [X0,X1] : (~food(X0,X1) | substance_matter(X0,X1))),
  inference(ennf_transformation,[],[f25])).

fof(f25,axiom,(
  ! [X0,X1] : (food(X0,X1) => substance_matter(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f223,plain,(
  ( ! [X0,X1] : (food(X0,X1) | ~beverage(X0,X1)) )),
  inference(cnf_transformation,[],[f181])).

fof(f181,plain,(
  ! [X0,X1] : (~beverage(X0,X1) | food(X0,X1))),
  inference(ennf_transformation,[],[f26])).

fof(f26,axiom,(
  ! [X0,X1] : (beverage(X0,X1) => food(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f224,plain,(
  ( ! [X0,X1] : (beverage(X0,X1) | ~shake_beverage(X0,X1)) )),
  inference(cnf_transformation,[],[f182])).

fof(f182,plain,(
  ! [X0,X1] : (~shake_beverage(X0,X1) | beverage(X0,X1))),
  inference(ennf_transformation,[],[f27])).

fof(f27,axiom,(
  ! [X0,X1] : (shake_beverage(X0,X1) => beverage(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f244,plain,(
  shake_beverage(sK5,sK8)),
  inference(cnf_transformation,[],[f201])).

fof(f205,plain,(
  ( ! [X0,X1] : (living(X0,X1) | ~organism(X0,X1)) )),
  inference(cnf_transformation,[],[f163])).

fof(f163,plain,(
  ! [X0,X1] : (~organism(X0,X1) | living(X0,X1))),
  inference(ennf_transformation,[],[f4])).

fof(f4,axiom,(
  ! [X0,X1] : (organism(X0,X1) => living(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f207,plain,(
  ( ! [X0,X1] : (organism(X0,X1) | ~human_person(X0,X1)) )),
  inference(cnf_transformation,[],[f165])).

fof(f165,plain,(
  ! [X0,X1] : (~human_person(X0,X1) | organism(X0,X1))),
  inference(ennf_transformation,[],[f7])).

fof(f7,axiom,(
  ! [X0,X1] : (human_person(X0,X1) => organism(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f234,plain,(
  ( ! [X0,X1] : (~human(X0,X1) | ~nonhuman(X0,X1)) )),
  inference(cnf_transformation,[],[f192])).

fof(f192,plain,(
  ! [X0,X1] : (~nonhuman(X0,X1) | ~human(X0,X1))),
  inference(ennf_transformation,[],[f49])).

fof(f49,plain,(
  ! [X0,X1] : (nonhuman(X0,X1) => ~human(X0,X1))),
  inference(flattening,[],[f39])).

fof(f39,axiom,(
  ! [X0,X1] : (nonhuman(X0,X1) => ~human(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f212,plain,(
  ( ! [X0,X1] : (nonhuman(X0,X1) | ~abstraction(X0,X1)) )),
  inference(cnf_transformation,[],[f170])).

fof(f170,plain,(
  ! [X0,X1] : (~abstraction(X0,X1) | nonhuman(X0,X1))),
  inference(ennf_transformation,[],[f12])).

fof(f12,axiom,(
  ! [X0,X1] : (abstraction(X0,X1) => nonhuman(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f204,plain,(
  ( ! [X0,X1] : (human(X0,X1) | ~human_person(X0,X1)) )),
  inference(cnf_transformation,[],[f162])).

fof(f162,plain,(
  ! [X0,X1] : (~human_person(X0,X1) | human(X0,X1))),
  inference(ennf_transformation,[],[f3])).

fof(f3,axiom,(
  ! [X0,X1] : (human_person(X0,X1) => human(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f208,plain,(
  ( ! [X0,X1] : (human_person(X0,X1) | ~woman(X0,X1)) )),
  inference(cnf_transformation,[],[f166])).

fof(f166,plain,(
  ! [X0,X1] : (~woman(X0,X1) | human_person(X0,X1))),
  inference(ennf_transformation,[],[f8])).

fof(f8,axiom,(
  ! [X0,X1] : (woman(X0,X1) => human_person(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f233,plain,(
  ( ! [X0,X1] : (~nonexistent(X0,X1) | ~existent(X0,X1)) )),
  inference(cnf_transformation,[],[f191])).

fof(f191,plain,(
  ! [X0,X1] : (~existent(X0,X1) | ~nonexistent(X0,X1))),
  inference(ennf_transformation,[],[f48])).

fof(f48,plain,(
  ! [X0,X1] : (existent(X0,X1) => ~nonexistent(X0,X1))),
  inference(flattening,[],[f38])).

fof(f38,axiom,(
  ! [X0,X1] : (existent(X0,X1) => ~nonexistent(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f227,plain,(
  ( ! [X0,X1] : (nonexistent(X0,X1) | ~eventuality(X0,X1)) )),
  inference(cnf_transformation,[],[f185])).

fof(f185,plain,(
  ! [X0,X1] : (~eventuality(X0,X1) | nonexistent(X0,X1))),
  inference(ennf_transformation,[],[f30])).

fof(f30,axiom,(
  ! [X0,X1] : (eventuality(X0,X1) => nonexistent(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f229,plain,(
  ( ! [X0,X1] : (eventuality(X0,X1) | ~event(X0,X1)) )),
  inference(cnf_transformation,[],[f187])).

fof(f187,plain,(
  ! [X0,X1] : (~event(X0,X1) | eventuality(X0,X1))),
  inference(ennf_transformation,[],[f34])).

fof(f34,axiom,(
  ! [X0,X1] : (event(X0,X1) => eventuality(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f245,plain,(
  event(sK5,sK9)),
  inference(cnf_transformation,[],[f201])).

fof(f218,plain,(
  ( ! [X0,X1] : (existent(X0,X1) | ~entity(X0,X1)) )),
  inference(cnf_transformation,[],[f176])).

fof(f176,plain,(
  ! [X0,X1] : (~entity(X0,X1) | existent(X0,X1))),
  inference(ennf_transformation,[],[f20])).

fof(f20,axiom,(
  ! [X0,X1] : (entity(X0,X1) => existent(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f232,plain,(
  ( ! [X0,X1] : (~nonliving(X0,X1) | ~animate(X0,X1)) )),
  inference(cnf_transformation,[],[f190])).

fof(f190,plain,(
  ! [X0,X1] : (~animate(X0,X1) | ~nonliving(X0,X1))),
  inference(ennf_transformation,[],[f47])).

fof(f47,plain,(
  ! [X0,X1] : (animate(X0,X1) => ~nonliving(X0,X1))),
  inference(flattening,[],[f37])).

fof(f37,axiom,(
  ! [X0,X1] : (animate(X0,X1) => ~nonliving(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f203,plain,(
  ( ! [X0,X1] : (animate(X0,X1) | ~human_person(X0,X1)) )),
  inference(cnf_transformation,[],[f161])).

fof(f161,plain,(
  ! [X0,X1] : (~human_person(X0,X1) | animate(X0,X1))),
  inference(ennf_transformation,[],[f2])).

fof(f2,axiom,(
  ! [X0,X1] : (human_person(X0,X1) => animate(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f228,plain,(
  ( ! [X0,X1] : (specific(X0,X1) | ~eventuality(X0,X1)) )),
  inference(cnf_transformation,[],[f186])).

fof(f186,plain,(
  ! [X0,X1] : (~eventuality(X0,X1) | specific(X0,X1))),
  inference(ennf_transformation,[],[f31])).

fof(f31,axiom,(
  ! [X0,X1] : (eventuality(X0,X1) => specific(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f237,plain,(
  ( ! [X0,X1] : (~female(X0,X1) | ~unisex(X0,X1)) )),
  inference(cnf_transformation,[],[f195])).

fof(f195,plain,(
  ! [X0,X1] : (~unisex(X0,X1) | ~female(X0,X1))),
  inference(ennf_transformation,[],[f52])).

fof(f52,plain,(
  ! [X0,X1] : (unisex(X0,X1) => ~female(X0,X1))),
  inference(flattening,[],[f42])).

fof(f42,axiom,(
  ! [X0,X1] : (unisex(X0,X1) => ~female(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f210,plain,(
  ( ! [X0,X1] : (unisex(X0,X1) | ~abstraction(X0,X1)) )),
  inference(cnf_transformation,[],[f168])).

fof(f168,plain,(
  ! [X0,X1] : (~abstraction(X0,X1) | unisex(X0,X1))),
  inference(ennf_transformation,[],[f10])).

fof(f10,axiom,(
  ! [X0,X1] : (abstraction(X0,X1) => unisex(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f226,plain,(
  ( ! [X0,X1] : (unisex(X0,X1) | ~eventuality(X0,X1)) )),
  inference(cnf_transformation,[],[f184])).

fof(f184,plain,(
  ! [X0,X1] : (~eventuality(X0,X1) | unisex(X0,X1))),
  inference(ennf_transformation,[],[f29])).

fof(f29,axiom,(
  ! [X0,X1] : (eventuality(X0,X1) => unisex(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f216,plain,(
  ( ! [X0,X1] : (unisex(X0,X1) | ~object(X0,X1)) )),
  inference(cnf_transformation,[],[f174])).

fof(f174,plain,(
  ! [X0,X1] : (~object(X0,X1) | unisex(X0,X1))),
  inference(ennf_transformation,[],[f17])).

fof(f17,axiom,(
  ! [X0,X1] : (object(X0,X1) => unisex(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f238,plain,(
  ( ! [X2,X0,X3,X1] : (~of(X0,X3,X1) | X2 = X3 | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1)) )),
  inference(cnf_transformation,[],[f197])).

fof(f197,plain,(
  ! [X0,X1,X2] : (~entity(X0,X1) | ~forename(X0,X2) | ~of(X0,X2,X1) | ! [X3] : (~forename(X0,X3) | X2 = X3 | ~of(X0,X3,X1)))),
  inference(flattening,[],[f196])).

fof(f196,plain,(
  ! [X0,X1,X2] : ((~entity(X0,X1) | ~forename(X0,X2) | ~of(X0,X2,X1)) | ! [X3] : (~forename(X0,X3) | X2 = X3 | ~of(X0,X3,X1)))),
  inference(ennf_transformation,[],[f43])).

fof(f43,axiom,(
  ! [X0,X1,X2] : ((entity(X0,X1) & forename(X0,X2) & of(X0,X2,X1)) => ~? [X3] : (forename(X0,X3) & X2 != X3 & of(X0,X3,X1)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f240,plain,(
  of(sK5,sK7,sK6)),
  inference(cnf_transformation,[],[f201])).

fof(f220,plain,(
  ( ! [X0,X1] : (entity(X0,X1) | ~object(X0,X1)) )),
  inference(cnf_transformation,[],[f178])).

fof(f178,plain,(
  ! [X0,X1] : (~object(X0,X1) | entity(X0,X1))),
  inference(ennf_transformation,[],[f23])).

fof(f23,axiom,(
  ! [X0,X1] : (object(X0,X1) => entity(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f239,plain,(
  ( ! [X2,X0,X1] : (~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X2)) )),
  inference(cnf_transformation,[],[f200])).

fof(f200,plain,(
  ! [X0,X1,X2] : (~patient(X0,X1,X2) | ~agent(X0,X1,X2) | ~nonreflexive(X0,X1))),
  inference(equality_propagation,[],[f199])).

fof(f199,plain,(
  ! [X0,X1,X2,X3] : (~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X3) | X2 != X3)),
  inference(flattening,[],[f198])).

fof(f198,plain,(
  ! [X0,X1,X2,X3] : ((~nonreflexive(X0,X1) | ~agent(X0,X1,X2) | ~patient(X0,X1,X3)) | X2 != X3)),
  inference(ennf_transformation,[],[f44])).

fof(f44,axiom,(
  ! [X0,X1,X2,X3] : ((nonreflexive(X0,X1) & agent(X0,X1,X2) & patient(X0,X1,X3)) => X2 != X3)),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f247,plain,(
  patient(sK5,sK9,sK8)),
  inference(cnf_transformation,[],[f201])).

fof(f248,plain,(
  nonreflexive(sK5,sK9)),
  inference(cnf_transformation,[],[f201])).

fof(f202,plain,(
  ( ! [X0,X1] : (female(X0,X1) | ~woman(X0,X1)) )),
  inference(cnf_transformation,[],[f160])).

fof(f160,plain,(
  ! [X0,X1] : (~woman(X0,X1) | female(X0,X1))),
  inference(ennf_transformation,[],[f1])).

fof(f1,axiom,(
  ! [X0,X1] : (woman(X0,X1) => female(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f241,plain,(
  woman(sK5,sK6)),
  inference(cnf_transformation,[],[f201])).

fof(f242,plain,(
  mia_forename(sK5,sK7)),
  inference(cnf_transformation,[],[f201])).

fof(f246,plain,(
  agent(sK5,sK9,sK6)),
  inference(cnf_transformation,[],[f201])).

fof(f249,plain,(
  order(sK5,sK9)),
  inference(cnf_transformation,[],[f201])).

fof(f231,plain,(
  ( ! [X0,X1] : (act(X0,X1) | ~order(X0,X1)) )),
  inference(cnf_transformation,[],[f189])).

fof(f189,plain,(
  ! [X0,X1] : (~order(X0,X1) | act(X0,X1))),
  inference(ennf_transformation,[],[f36])).

fof(f36,axiom,(
  ! [X0,X1] : (order(X0,X1) => act(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f230,plain,(
  ( ! [X0,X1] : (event(X0,X1) | ~act(X0,X1)) )),
  inference(cnf_transformation,[],[f188])).

fof(f188,plain,(
  ! [X0,X1] : (~act(X0,X1) | event(X0,X1))),
  inference(ennf_transformation,[],[f35])).

fof(f35,axiom,(
  ! [X0,X1] : (act(X0,X1) => event(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f225,plain,(
  ( ! [X0,X1] : (event(X0,X1) | ~order(X0,X1)) )),
  inference(cnf_transformation,[],[f183])).

fof(f183,plain,(
  ! [X0,X1] : (~order(X0,X1) | event(X0,X1))),
  inference(ennf_transformation,[],[f28])).

fof(f28,axiom,(
  ! [X0,X1] : (order(X0,X1) => event(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

fof(f209,plain,(
  ( ! [X0,X1] : (forename(X0,X1) | ~mia_forename(X0,X1)) )),
  inference(cnf_transformation,[],[f167])).

fof(f167,plain,(
  ! [X0,X1] : (~mia_forename(X0,X1) | forename(X0,X1))),
  inference(ennf_transformation,[],[f9])).

fof(f9,axiom,(
  ! [X0,X1] : (mia_forename(X0,X1) => forename(X0,X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/NLP/NLP042+1.p',unknown)).

cnf(c_573,plain,
    ( specific(X0_$i,X1_$i)
    | ~ specific(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_500,plain,( X0_$i = X0_$i ),theory(equality) ).

cnf(c_1761,plain,
    ( specific(X0_$i,X1_$i) | ~ specific(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_573,c_500]) ).

cnf(c_564,plain,
    ( organism(X0_$i,X1_$i)
    | ~ organism(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1748,plain,
    ( organism(X0_$i,X1_$i) | ~ organism(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_564,c_500]) ).

cnf(c_562,plain,
    ( human_person(X0_$i,X1_$i)
    | ~ human_person(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1736,plain,
    ( human_person(X0_$i,X1_$i)
    | ~ human_person(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_562,c_500]) ).

cnf(c_557,plain,
    ( general(X0_$i,X1_$i)
    | ~ general(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1724,plain,
    ( general(X0_$i,X1_$i) | ~ general(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_557,c_500]) ).

cnf(c_555,plain,
    ( abstraction(X0_$i,X1_$i)
    | ~ abstraction(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1703,plain,
    ( abstraction(X0_$i,X1_$i)
    | ~ abstraction(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_555,c_500]) ).

cnf(c_553,plain,
    ( relation(X0_$i,X1_$i)
    | ~ relation(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1682,plain,
    ( relation(X0_$i,X1_$i) | ~ relation(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_553,c_500]) ).

cnf(c_551,plain,
    ( relname(X0_$i,X1_$i)
    | ~ relname(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1661,plain,
    ( relname(X0_$i,X1_$i) | ~ relname(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_551,c_500]) ).

cnf(c_548,plain,
    ( unisex(X0_$i,X1_$i)
    | ~ unisex(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1638,plain,
    ( unisex(X0_$i,X1_$i) | ~ unisex(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_548,c_500]) ).

cnf(c_546,plain,
    ( female(X0_$i,X1_$i)
    | ~ female(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1569,plain,
    ( female(X0_$i,X1_$i) | ~ female(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_546,c_500]) ).

cnf(c_543,plain,
    ( nonhuman(X0_$i,X1_$i)
    | ~ nonhuman(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1557,plain,
    ( nonhuman(X0_$i,X1_$i) | ~ nonhuman(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_543,c_500]) ).

cnf(c_541,plain,
    ( human(X0_$i,X1_$i)
    | ~ human(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1545,plain,
    ( human(X0_$i,X1_$i) | ~ human(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_541,c_500]) ).

cnf(c_538,plain,
    ( entity(X0_$i,X1_$i)
    | ~ entity(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1533,plain,
    ( entity(X0_$i,X1_$i) | ~ entity(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_538,c_500]) ).

cnf(c_536,plain,
    ( eventuality(X0_$i,X1_$i)
    | ~ eventuality(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1520,plain,
    ( eventuality(X0_$i,X1_$i)
    | ~ eventuality(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_536,c_500]) ).

cnf(c_528,plain,
    ( act(X0_$i,X1_$i)
    | ~ act(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1508,plain,
    ( act(X0_$i,X1_$i) | ~ act(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_528,c_500]) ).

cnf(c_34,plain,
    ( ~ general(X0_$i,X1_$i) | ~ specific(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f236]) ).

cnf(c_574,plain,
    ( ~ general(X0_$i,X1_$i) | ~ specific(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_34]) ).

cnf(c_17,plain,
    ( ~ entity(X0_$i,X1_$i) | specific(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f219]) ).

cnf(c_558,plain,
    ( ~ entity(X0_$i,X1_$i) | specific(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_17]) ).

cnf(c_1166,plain,
    ( ~ entity(X0_$i,X1_$i) | ~ general(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_574,c_558]) ).

cnf(c_9,plain,
    ( ~ abstraction(X0_$i,X1_$i) | general(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_556,plain,
    ( ~ abstraction(X0_$i,X1_$i) | general(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_9]) ).

cnf(c_1325,plain,
    ( ~ entity(X0_$i,X1_$i) | ~ abstraction(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_1166,c_556]) ).

cnf(c_11,plain,
    ( abstraction(X0_$i,X1_$i) | ~ relation(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f213]) ).

cnf(c_554,plain,
    ( abstraction(X0_$i,X1_$i) | ~ relation(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_11]) ).

cnf(c_12,plain,
    ( relation(X0_$i,X1_$i) | ~ relname(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_552,plain,
    ( relation(X0_$i,X1_$i) | ~ relname(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_12]) ).

cnf(c_13,plain,
    ( ~ forename(X0_$i,X1_$i) | relname(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_550,plain,
    ( ~ forename(X0_$i,X1_$i) | relname(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_13]) ).

cnf(c_1054,plain,
    ( ~ forename(X0_$i,X1_$i) | relation(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_552,c_550]) ).

cnf(c_1065,plain,
    ( ~ forename(X0_$i,X1_$i) | abstraction(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_554,c_1054]) ).

cnf(c_1393,plain,
    ( ~ entity(X0_$i,X1_$i) | ~ forename(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_1325,c_1065]) ).

cnf(c_44,plain,
    ( forename(sK5,sK7) ),
    inference(cnf_transformation,[],[f243]) ).

cnf(c_539,plain,
    ( forename(sK5,sK7) ),
    inference(subtyping,[status(esa)],[c_44]) ).

cnf(c_1401,plain,
    ( ~ entity(sK5,sK7) ),
    inference(resolution,[status(thm)],[c_1393,c_539]) ).

cnf(c_4,plain,
    ( ~ organism(X0_$i,X1_$i) | entity(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_565,plain,
    ( ~ organism(X0_$i,X1_$i) | entity(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_4]) ).

cnf(c_1405,plain,
    ( ~ organism(sK5,sK7) ),
    inference(resolution,[status(thm)],[c_1401,c_565]) ).

cnf(c_524,plain,
    ( nonexistent(X0_$i,X1_$i)
    | ~ nonexistent(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1385,plain,
    ( nonexistent(X0_$i,X1_$i)
    | ~ nonexistent(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_524,c_500]) ).

cnf(c_522,plain,
    ( existent(X0_$i,X1_$i)
    | ~ existent(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1373,plain,
    ( existent(X0_$i,X1_$i) | ~ existent(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_522,c_500]) ).

cnf(c_519,plain,
    ( substance_matter(X0_$i,X1_$i)
    | ~ substance_matter(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1361,plain,
    ( substance_matter(X0_$i,X1_$i)
    | ~ substance_matter(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_519,c_500]) ).

cnf(c_517,plain,
    ( food(X0_$i,X1_$i)
    | ~ food(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1349,plain,
    ( food(X0_$i,X1_$i) | ~ food(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_517,c_500]) ).

cnf(c_515,plain,
    ( beverage(X0_$i,X1_$i)
    | ~ beverage(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1337,plain,
    ( beverage(X0_$i,X1_$i) | ~ beverage(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_515,c_500]) ).

cnf(c_33,plain,
    ( ~ living(X0_$i,X1_$i) | ~ nonliving(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f235]) ).

cnf(c_509,plain,
    ( ~ living(X0_$i,X1_$i) | ~ nonliving(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_33]) ).

cnf(c_15,plain,
    ( ~ object(X0_$i,X1_$i) | nonliving(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f217]) ).

cnf(c_510,plain,
    ( ~ object(X0_$i,X1_$i) | nonliving(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_15]) ).

cnf(c_1157,plain,
    ( ~ living(X0_$i,X1_$i) | ~ object(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_509,c_510]) ).

cnf(c_19,plain,
    ( object(X0_$i,X1_$i) | ~ substance_matter(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f221]) ).

cnf(c_520,plain,
    ( object(X0_$i,X1_$i) | ~ substance_matter(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_19]) ).

cnf(c_20,plain,
    ( substance_matter(X0_$i,X1_$i) | ~ food(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f222]) ).

cnf(c_518,plain,
    ( substance_matter(X0_$i,X1_$i) | ~ food(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_20]) ).

cnf(c_21,plain,
    ( food(X0_$i,X1_$i) | ~ beverage(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f223]) ).

cnf(c_516,plain,
    ( food(X0_$i,X1_$i) | ~ beverage(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_21]) ).

cnf(c_22,plain,
    ( beverage(X0_$i,X1_$i) | ~ shake_beverage(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f224]) ).

cnf(c_514,plain,
    ( beverage(X0_$i,X1_$i) | ~ shake_beverage(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_22]) ).

cnf(c_43,plain,
    ( shake_beverage(sK5,sK8) ),
    inference(cnf_transformation,[],[f244]) ).

cnf(c_512,plain,
    ( shake_beverage(sK5,sK8) ),
    inference(subtyping,[status(esa)],[c_43]) ).

cnf(c_600,plain,
    ( beverage(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_514,c_512]) ).

cnf(c_765,plain,
    ( food(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_516,c_600]) ).

cnf(c_925,plain,
    ( substance_matter(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_518,c_765]) ).

cnf(c_1013,plain,
    ( object(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_520,c_925]) ).

cnf(c_1309,plain,
    ( ~ living(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_1157,c_1013]) ).

cnf(c_3,plain,
    ( living(X0_$i,X1_$i) | ~ organism(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_507,plain,
    ( living(X0_$i,X1_$i) | ~ organism(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_3]) ).

cnf(c_5,plain,
    ( ~ human_person(X0_$i,X1_$i) | organism(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_563,plain,
    ( ~ human_person(X0_$i,X1_$i) | organism(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_5]) ).

cnf(c_1092,plain,
    ( ~ human_person(X0_$i,X1_$i) | living(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_507,c_563]) ).

cnf(c_1313,plain,
    ( ~ human_person(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_1309,c_1092]) ).

cnf(c_32,plain,
    ( ~ human(X0_$i,X1_$i) | ~ nonhuman(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f234]) ).

cnf(c_542,plain,
    ( ~ human(X0_$i,X1_$i) | ~ nonhuman(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_32]) ).

cnf(c_10,plain,
    ( ~ abstraction(X0_$i,X1_$i) | nonhuman(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_544,plain,
    ( ~ abstraction(X0_$i,X1_$i) | nonhuman(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_10]) ).

cnf(c_1125,plain,
    ( ~ human(X0_$i,X1_$i) | ~ abstraction(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_542,c_544]) ).

cnf(c_1285,plain,
    ( ~ human(X0_$i,X1_$i) | ~ forename(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_1125,c_1065]) ).

cnf(c_1292,plain,
    ( ~ human(sK5,sK7) ),
    inference(resolution,[status(thm)],[c_1285,c_539]) ).

cnf(c_2,plain,
    ( ~ human_person(X0_$i,X1_$i) | human(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f204]) ).

cnf(c_540,plain,
    ( ~ human_person(X0_$i,X1_$i) | human(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_2]) ).

cnf(c_1296,plain,
    ( ~ human_person(sK5,sK7) ),
    inference(resolution,[status(thm)],[c_1292,c_540]) ).

cnf(c_6,plain,
    ( ~ woman(X0_$i,X1_$i) | human_person(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_561,plain,
    ( ~ woman(X0_$i,X1_$i) | human_person(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_6]) ).

cnf(c_1300,plain,
    ( ~ woman(sK5,sK7) ),
    inference(resolution,[status(thm)],[c_1296,c_561]) ).

cnf(c_31,plain,
    ( ~ existent(X0_$i,X1_$i) | ~ nonexistent(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f233]) ).

cnf(c_525,plain,
    ( ~ existent(X0_$i,X1_$i) | ~ nonexistent(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_31]) ).

cnf(c_25,plain,
    ( ~ eventuality(X0_$i,X1_$i) | nonexistent(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f227]) ).

cnf(c_523,plain,
    ( ~ eventuality(X0_$i,X1_$i) | nonexistent(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_25]) ).

cnf(c_1118,plain,
    ( ~ existent(X0_$i,X1_$i) | ~ eventuality(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_525,c_523]) ).

cnf(c_27,plain,
    ( ~ event(X0_$i,X1_$i) | eventuality(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f229]) ).

cnf(c_535,plain,
    ( ~ event(X0_$i,X1_$i) | eventuality(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_27]) ).

cnf(c_1196,plain,
    ( ~ existent(X0_$i,X1_$i) | ~ event(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_1118,c_535]) ).

cnf(c_42,plain,( event(sK5,sK9) ),inference(cnf_transformation,[],[f245]) ).

cnf(c_534,plain,
    ( event(sK5,sK9) ),
    inference(subtyping,[status(esa)],[c_42]) ).

cnf(c_1260,plain,
    ( ~ existent(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_1196,c_534]) ).

cnf(c_16,plain,
    ( ~ entity(X0_$i,X1_$i) | existent(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f218]) ).

cnf(c_521,plain,
    ( ~ entity(X0_$i,X1_$i) | existent(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_16]) ).

cnf(c_1264,plain,
    ( ~ entity(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_1260,c_521]) ).

cnf(c_1268,plain,
    ( ~ organism(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_1264,c_565]) ).

cnf(c_1272,plain,
    ( ~ human_person(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_1268,c_563]) ).

cnf(c_1276,plain,
    ( ~ woman(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_1272,c_561]) ).

cnf(c_511,plain,
    ( object(X0_$i,X1_$i)
    | ~ object(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1253,plain,
    ( object(X0_$i,X1_$i) | ~ object(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_511,c_500]) ).

cnf(c_508,plain,
    ( living(X0_$i,X1_$i)
    | ~ living(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1241,plain,
    ( living(X0_$i,X1_$i) | ~ living(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_508,c_500]) ).

cnf(c_506,plain,
    ( nonliving(X0_$i,X1_$i)
    | ~ nonliving(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1229,plain,
    ( nonliving(X0_$i,X1_$i) | ~ nonliving(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_506,c_500]) ).

cnf(c_504,plain,
    ( animate(X0_$i,X1_$i)
    | ~ animate(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_1217,plain,
    ( animate(X0_$i,X1_$i) | ~ animate(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_504,c_500]) ).

cnf(c_499,plain,
    ( X0_$i != X1_$i | X2_$i != X1_$i | X2_$i = X0_$i ),
    theory(equality) ).

cnf(c_1205,plain,
    ( X0_$i != X1_$i | X1_$i = X0_$i ),
    inference(resolution,[status(thm)],[c_499,c_500]) ).

cnf(c_30,plain,
    ( ~ animate(X0_$i,X1_$i) | ~ nonliving(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f232]) ).

cnf(c_505,plain,
    ( ~ animate(X0_$i,X1_$i) | ~ nonliving(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_30]) ).

cnf(c_1107,plain,
    ( ~ animate(X0_$i,X1_$i) | ~ object(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_505,c_510]) ).

cnf(c_1183,plain,
    ( ~ animate(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_1107,c_1013]) ).

cnf(c_1,plain,
    ( animate(X0_$i,X1_$i) | ~ human_person(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_503,plain,
    ( animate(X0_$i,X1_$i) | ~ human_person(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_1]) ).

cnf(c_755,plain,
    ( ~ woman(X0_$i,X1_$i) | animate(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_503,c_561]) ).

cnf(c_1187,plain,
    ( ~ woman(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_1183,c_755]) ).

cnf(c_26,plain,
    ( specific(X0_$i,X1_$i) | ~ eventuality(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f228]) ).

cnf(c_537,plain,
    ( specific(X0_$i,X1_$i) | ~ eventuality(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_26]) ).

cnf(c_946,plain,
    ( specific(X0_$i,X1_$i) | ~ event(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_537,c_535]) ).

cnf(c_962,plain,
    ( specific(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_946,c_534]) ).

cnf(c_1165,plain,
    ( ~ general(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_574,c_962]) ).

cnf(c_1170,plain,
    ( ~ abstraction(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_1165,c_556]) ).

cnf(c_1174,plain,
    ( ~ forename(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_1170,c_1065]) ).

cnf(c_35,plain,
    ( ~ female(X0_$i,X1_$i) | ~ unisex(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f237]) ).

cnf(c_547,plain,
    ( ~ female(X0_$i,X1_$i) | ~ unisex(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_35]) ).

cnf(c_8,plain,
    ( unisex(X0_$i,X1_$i) | ~ abstraction(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_549,plain,
    ( unisex(X0_$i,X1_$i) | ~ abstraction(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_8]) ).

cnf(c_1071,plain,
    ( ~ forename(X0_$i,X1_$i) | unisex(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_549,c_1065]) ).

cnf(c_1136,plain,
    ( ~ female(X0_$i,X1_$i) | ~ forename(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_547,c_1071]) ).

cnf(c_1148,plain,
    ( ~ female(sK5,sK7) ),
    inference(resolution,[status(thm)],[c_1136,c_539]) ).

cnf(c_24,plain,
    ( unisex(X0_$i,X1_$i) | ~ eventuality(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f226]) ).

cnf(c_526,plain,
    ( unisex(X0_$i,X1_$i) | ~ eventuality(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_24]) ).

cnf(c_940,plain,
    ( unisex(X0_$i,X1_$i) | ~ event(X0_$i,X1_$i) ),
    inference(resolution,[status(thm)],[c_526,c_535]) ).

cnf(c_954,plain,
    ( unisex(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_940,c_534]) ).

cnf(c_1135,plain,
    ( ~ female(sK5,sK9) ),
    inference(resolution,[status(thm)],[c_547,c_954]) ).

cnf(c_14,plain,
    ( unisex(X0_$i,X1_$i) | ~ object(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_501,plain,
    ( unisex(X0_$i,X1_$i) | ~ object(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_14]) ).

cnf(c_1016,plain,
    ( unisex(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_501,c_1013]) ).

cnf(c_1134,plain,
    ( ~ female(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_547,c_1016]) ).

cnf(c_36,plain,
    ( ~ entity(X0_$i,X1_$i)
    | ~ forename(X0_$i,X2_$i)
    | ~ forename(X0_$i,X3_$i)
    | ~ of(X0_$i,X2_$i,X1_$i)
    | ~ of(X0_$i,X3_$i,X1_$i)
    | X2_$i = X3_$i ),
    inference(cnf_transformation,[],[f238]) ).

cnf(c_572,plain,
    ( ~ entity(X0_$i,X1_$i)
    | ~ forename(X0_$i,X2_$i)
    | ~ forename(X0_$i,X3_$i)
    | ~ of(X0_$i,X2_$i,X1_$i)
    | ~ of(X0_$i,X3_$i,X1_$i)
    | X2_$i = X3_$i ),
    inference(subtyping,[status(esa)],[c_36]) ).

cnf(c_47,plain,( of(sK5,sK7,sK6) ),inference(cnf_transformation,[],[f240]) ).

cnf(c_570,plain,
    ( of(sK5,sK7,sK6) ),
    inference(subtyping,[status(esa)],[c_47]) ).

cnf(c_1039,plain,
    ( ~ entity(sK5,sK6)
    | ~ forename(sK5,sK7)
    | ~ forename(sK5,X0_$i)
    | ~ of(sK5,X0_$i,sK6)
    | X0_$i = sK7 ),
    inference(resolution,[status(thm)],[c_572,c_570]) ).

cnf(c_51,plain,
    ( forename(sK5,sK7) ),
    inference(subtyping,[status(esa)],[c_44]) ).

cnf(c_1040,plain,
    ( ~ entity(sK5,sK6)
    | ~ forename(sK5,X0_$i)
    | ~ of(sK5,X0_$i,sK6)
    | X0_$i = sK7 ),
    inference(global_propositional_subsumption,[status(thm)],[c_1039,c_51]) ).

cnf(c_18,plain,
    ( entity(X0_$i,X1_$i) | ~ object(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f220]) ).

cnf(c_502,plain,
    ( entity(X0_$i,X1_$i) | ~ object(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_18]) ).

cnf(c_1019,plain,
    ( entity(sK5,sK8) ),
    inference(resolution,[status(thm)],[c_502,c_1013]) ).

cnf(c_571,plain,
    ( of(X0_$i,X1_$i,X2_$i)
    | ~ of(X3_$i,X4_$i,X5_$i)
    | X0_$i != X3_$i
    | X1_$i != X4_$i
    | X2_$i != X5_$i ),
    theory(equality) ).

cnf(c_979,plain,
    ( of(X0_$i,X1_$i,X2_$i)
    | ~ of(X3_$i,X4_$i,X2_$i)
    | X0_$i != X3_$i
    | X1_$i != X4_$i ),
    inference(resolution,[status(thm)],[c_571,c_500]) ).

cnf(c_991,plain,
    ( of(X0_$i,X1_$i,X2_$i) | ~ of(X3_$i,X1_$i,X2_$i) | X0_$i != X3_$i ),
    inference(resolution,[status(thm)],[c_979,c_500]) ).

cnf(c_497,plain,
    ( patient(X0_$i,X1_$i,X2_$i)
    | ~ patient(X3_$i,X4_$i,X5_$i)
    | X0_$i != X3_$i
    | X1_$i != X4_$i
    | X2_$i != X5_$i ),
    theory(equality) ).

cnf(c_903,plain,
    ( patient(X0_$i,X1_$i,X2_$i)
    | ~ patient(X3_$i,X4_$i,X2_$i)
    | X0_$i != X3_$i
    | X1_$i != X4_$i ),
    inference(resolution,[status(thm)],[c_497,c_500]) ).

cnf(c_915,plain,
    ( patient(X0_$i,X1_$i,X2_$i)
    | ~ patient(X3_$i,X1_$i,X2_$i)
    | X0_$i != X3_$i ),
    inference(resolution,[status(thm)],[c_903,c_500]) ).

cnf(c_495,plain,
    ( agent(X0_$i,X1_$i,X2_$i)
    | ~ agent(X3_$i,X4_$i,X5_$i)
    | X0_$i != X3_$i
    | X1_$i != X4_$i
    | X2_$i != X5_$i ),
    theory(equality) ).

cnf(c_867,plain,
    ( agent(X0_$i,X1_$i,X2_$i)
    | ~ agent(X3_$i,X4_$i,X2_$i)
    | X0_$i != X3_$i
    | X1_$i != X4_$i ),
    inference(resolution,[status(thm)],[c_495,c_500]) ).

cnf(c_879,plain,
    ( agent(X0_$i,X1_$i,X2_$i)
    | ~ agent(X3_$i,X1_$i,X2_$i)
    | X0_$i != X3_$i ),
    inference(resolution,[status(thm)],[c_867,c_500]) ).

cnf(c_569,plain,
    ( forename(X0_$i,X1_$i)
    | ~ forename(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_843,plain,
    ( forename(X0_$i,X1_$i) | ~ forename(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_569,c_500]) ).

cnf(c_567,plain,
    ( mia_forename(X0_$i,X1_$i)
    | ~ mia_forename(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_822,plain,
    ( mia_forename(X0_$i,X1_$i)
    | ~ mia_forename(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_567,c_500]) ).

cnf(c_560,plain,
    ( woman(X0_$i,X1_$i)
    | ~ woman(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_801,plain,
    ( woman(X0_$i,X1_$i) | ~ woman(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_560,c_500]) ).

cnf(c_532,plain,
    ( order(X0_$i,X1_$i)
    | ~ order(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_754,plain,
    ( order(X0_$i,X1_$i) | ~ order(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_532,c_500]) ).

cnf(c_530,plain,
    ( event(X0_$i,X1_$i)
    | ~ event(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_733,plain,
    ( event(X0_$i,X1_$i) | ~ event(X2_$i,X1_$i) | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_530,c_500]) ).

cnf(c_513,plain,
    ( shake_beverage(X0_$i,X1_$i)
    | ~ shake_beverage(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_712,plain,
    ( shake_beverage(X0_$i,X1_$i)
    | ~ shake_beverage(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_513,c_500]) ).

cnf(c_493,plain,
    ( nonreflexive(X0_$i,X1_$i)
    | ~ nonreflexive(X2_$i,X3_$i)
    | X0_$i != X2_$i
    | X1_$i != X3_$i ),
    theory(equality) ).

cnf(c_691,plain,
    ( nonreflexive(X0_$i,X1_$i)
    | ~ nonreflexive(X2_$i,X1_$i)
    | X0_$i != X2_$i ),
    inference(resolution,[status(thm)],[c_493,c_500]) ).

cnf(c_37,plain,
    ( ~ nonreflexive(X0_$i,X1_$i)
    | ~ agent(X0_$i,X1_$i,X2_$i)
    | ~ patient(X0_$i,X1_$i,X2_$i) ),
    inference(cnf_transformation,[],[f239]) ).

cnf(c_498,plain,
    ( ~ nonreflexive(X0_$i,X1_$i)
    | ~ agent(X0_$i,X1_$i,X2_$i)
    | ~ patient(X0_$i,X1_$i,X2_$i) ),
    inference(subtyping,[status(esa)],[c_37]) ).

cnf(c_40,plain,
    ( patient(sK5,sK9,sK8) ),
    inference(cnf_transformation,[],[f247]) ).

cnf(c_496,plain,
    ( patient(sK5,sK9,sK8) ),
    inference(subtyping,[status(esa)],[c_40]) ).

cnf(c_676,plain,
    ( ~ nonreflexive(sK5,sK9) | ~ agent(sK5,sK9,sK8) ),
    inference(resolution,[status(thm)],[c_498,c_496]) ).

cnf(c_39,plain,
    ( nonreflexive(sK5,sK9) ),
    inference(cnf_transformation,[],[f248]) ).

cnf(c_56,plain,
    ( nonreflexive(sK5,sK9) ),
    inference(subtyping,[status(esa)],[c_39]) ).

cnf(c_677,plain,
    ( ~ agent(sK5,sK9,sK8) ),
    inference(global_propositional_subsumption,[status(thm)],[c_676,c_56]) ).

cnf(c_0,plain,
    ( female(X0_$i,X1_$i) | ~ woman(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f202]) ).

cnf(c_545,plain,
    ( female(X0_$i,X1_$i) | ~ woman(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_0]) ).

cnf(c_46,plain,( woman(sK5,sK6) ),inference(cnf_transformation,[],[f241]) ).

cnf(c_559,plain,
    ( woman(sK5,sK6) ),
    inference(subtyping,[status(esa)],[c_46]) ).

cnf(c_648,plain,
    ( female(sK5,sK6) ),
    inference(resolution,[status(thm)],[c_545,c_559]) ).

cnf(c_45,plain,
    ( mia_forename(sK5,sK7) ),
    inference(cnf_transformation,[],[f242]) ).

cnf(c_566,plain,
    ( mia_forename(sK5,sK7) ),
    inference(subtyping,[status(esa)],[c_45]) ).

cnf(c_41,plain,
    ( agent(sK5,sK9,sK6) ),
    inference(cnf_transformation,[],[f246]) ).

cnf(c_494,plain,
    ( agent(sK5,sK9,sK6) ),
    inference(subtyping,[status(esa)],[c_41]) ).

cnf(c_492,plain,
    ( nonreflexive(sK5,sK9) ),
    inference(subtyping,[status(esa)],[c_39]) ).

cnf(c_38,plain,( order(sK5,sK9) ),inference(cnf_transformation,[],[f249]) ).

cnf(c_531,plain,
    ( order(sK5,sK9) ),
    inference(subtyping,[status(esa)],[c_38]) ).

cnf(c_29,plain,
    ( ~ order(X0_$i,X1_$i) | act(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f231]) ).

cnf(c_527,plain,
    ( ~ order(X0_$i,X1_$i) | act(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_29]) ).

cnf(c_28,plain,
    ( event(X0_$i,X1_$i) | ~ act(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f230]) ).

cnf(c_529,plain,
    ( event(X0_$i,X1_$i) | ~ act(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_28]) ).

cnf(c_23,plain,
    ( event(X0_$i,X1_$i) | ~ order(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f225]) ).

cnf(c_533,plain,
    ( event(X0_$i,X1_$i) | ~ order(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_23]) ).

cnf(c_7,plain,
    ( forename(X0_$i,X1_$i) | ~ mia_forename(X0_$i,X1_$i) ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_568,plain,
    ( forename(X0_$i,X1_$i) | ~ mia_forename(X0_$i,X1_$i) ),
    inference(subtyping,[status(esa)],[c_7]) ).


% SZS output end Saturation

Sample finite model for NLP042+1

%------ The model is defined over ground terms (initial term algebra).
%------ Predicates are defined as (\forall x_1,..,x_n  ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) 
%------ where \phi is a formula over the term algebra.
%------ If we have equality in the problem then it is also defined as a predicate above, 
%------ with "=" on the right-hand-side of the definition interpreted over the term algebra $$term_algebra_type
%------ See help for --sat_out_model for different model outputs.
%------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
%------ where the first argument stands for the sort ($i in the unsorted case)
% SZS output start Model 

%------ Negative definition of $$equality_sorted 
fof(lit_def,axiom,
    (! [X0_$tType,X0_$i,X1_$i] : 
      ( ~($$equality_sorted(X0_$tType,X0_$i,X1_$i)) <=>
           (
              (
                ( X0_$tType=$i & X0_$i=sK9 )
               &
                ( X1_$i!=sK9 )
              )

             | 
              (
                ( X0_$tType=$i & X0_$i=sK8 )
               &
                ( X1_$i!=sK8 )
              )

             | 
              (
                ( X0_$tType=$i & X0_$i=sK6 )
               &
                ( X1_$i!=sK6 )
              )

             | 
              (
                ( X0_$tType=$i & X0_$i=sK7 )
               &
                ( X1_$i!=sK7 )
              )

             | 
              (
                ( X0_$tType=$i & X1_$i=sK9 )
               &
                ( X0_$i!=sK9 )
              )

             | 
              (
                ( X0_$tType=$i & X1_$i=sK8 )
               &
                ( X0_$i!=sK8 )
              )

             | 
              (
                ( X0_$tType=$i & X1_$i=sK6 )
               &
                ( X0_$i!=sK6 )
              )

             | 
              (
                ( X0_$tType=$i & X1_$i=sK7 )
               &
                ( X0_$i!=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of female 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( female(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of woman 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( woman(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of animate 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( animate(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of human_person 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( human_person(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of human 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( human(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of living 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( living(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of organism 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( organism(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of entity 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( entity(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of forename 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( forename(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of mia_forename 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( mia_forename(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of unisex 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( unisex(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of abstraction 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( abstraction(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of general 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( general(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of nonhuman 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( nonhuman(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of relation 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( relation(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of relname 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( relname(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 )
              )

             | 
              (
                ( X1_$i=sK7 )
              )

           )
      )
    )
   ).

%------ Positive definition of object 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( object(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

           )
      )
    )
   ).

%------ Positive definition of nonliving 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( nonliving(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

           )
      )
    )
   ).

%------ Positive definition of existent 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( existent(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of specific 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( specific(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X0_$i=sK5 & X1_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of substance_matter 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( substance_matter(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

           )
      )
    )
   ).

%------ Positive definition of food 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( food(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

           )
      )
    )
   ).

%------ Positive definition of beverage 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( beverage(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

           )
      )
    )
   ).

%------ Positive definition of shake_beverage 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( shake_beverage(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK8 )
              )

           )
      )
    )
   ).

%------ Positive definition of event 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( event(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

           )
      )
    )
   ).

%------ Positive definition of order 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( order(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

           )
      )
    )
   ).

%------ Positive definition of eventuality 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( eventuality(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

           )
      )
    )
   ).

%------ Positive definition of nonexistent 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( nonexistent(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

           )
      )
    )
   ).

%------ Positive definition of act 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( act(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

           )
      )
    )
   ).

%------ Positive definition of of 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i,X2_$i] : 
      ( of(X0_$i,X1_$i,X2_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK7 & X2_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK7 & X2_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of nonreflexive 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i] : 
      ( nonreflexive(X0_$i,X1_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 )
              )

             | 
              (
                ( X1_$i=sK9 )
              )

           )
      )
    )
   ).

%------ Positive definition of agent 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i,X2_$i] : 
      ( agent(X0_$i,X1_$i,X2_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 & X2_$i=sK6 )
              )

             | 
              (
                ( X1_$i=sK9 & X2_$i=sK6 )
              )

           )
      )
    )
   ).

%------ Positive definition of patient 
fof(lit_def,axiom,
    (! [X0_$i,X1_$i,X2_$i] : 
      ( patient(X0_$i,X1_$i,X2_$i) <=>
           (
              (
                ( X0_$i=sK5 & X1_$i=sK9 & X2_$i=sK8 )
              )

             | 
              (
                ( X1_$i=sK9 & X2_$i=sK8 )
              )

           )
      )
    )
   ).


% SZS output end Model 

Sample solution for SWV017+1

% SZS output start Saturation

fof(f168,plain,(
  ( ! [X0] : (~a_nonce(generate_key(X0))) )),
  inference(cnf_transformation,[],[f36])).

fof(f36,plain,(
  ! [X0] : ~a_nonce(generate_key(X0))),
  inference(flattening,[],[f27])).

fof(f27,axiom,(
  ! [X0] : ~a_nonce(generate_key(X0))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f160,plain,(
  ( ! [X0,X1] : (intruder_message(pair(X0,X1)) | ~intruder_message(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f123])).

fof(f123,plain,(
  ! [X0,X1] : (~intruder_message(X0) | ~intruder_message(X1) | intruder_message(pair(X0,X1)))),
  inference(flattening,[],[f122])).

fof(f122,plain,(
  ! [X0,X1] : ((~intruder_message(X0) | ~intruder_message(X1)) | intruder_message(pair(X0,X1)))),
  inference(ennf_transformation,[],[f19])).

fof(f19,axiom,(
  ! [X0,X1] : ((intruder_message(X0) & intruder_message(X1)) => intruder_message(pair(X0,X1)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f176,plain,(
  ( ! [X0] : (intruder_message(X0) | ~fresh_intruder_nonce(X0)) )),
  inference(cnf_transformation,[],[f138])).

fof(f138,plain,(
  ! [X0] : (~fresh_intruder_nonce(X0) | (fresh_to_b(X0) & intruder_message(X0)))),
  inference(ennf_transformation,[],[f33])).

fof(f33,axiom,(
  ! [X0] : (fresh_intruder_nonce(X0) => (fresh_to_b(X0) & intruder_message(X0)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f163,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X1) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(encrypt(X0,X1))) )),
  inference(cnf_transformation,[],[f129])).

fof(f129,plain,(
  ! [X0,X1,X2] : (~intruder_message(encrypt(X0,X1)) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2) | intruder_message(X1))),
  inference(flattening,[],[f128])).

fof(f128,plain,(
  ! [X0,X1,X2] : ((~intruder_message(encrypt(X0,X1)) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2)) | intruder_message(X1))),
  inference(ennf_transformation,[],[f22])).

fof(f22,axiom,(
  ! [X0,X1,X2] : ((intruder_message(encrypt(X0,X1)) & intruder_holds(key(X1,X2)) & party_of_protocol(X2)) => intruder_message(X1))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f156,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X0) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f121])).

fof(f121,plain,(
  ! [X0,X1,X2,X3] : (~intruder_message(quadruple(X0,X1,X2,X3)) | (intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)))),
  inference(ennf_transformation,[],[f18])).

fof(f18,axiom,(
  ! [X0,X1,X2,X3] : (intruder_message(quadruple(X0,X1,X2,X3)) => (intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f157,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X1) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f121])).

fof(f158,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X2) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f121])).

fof(f159,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(X3) | ~intruder_message(quadruple(X0,X1,X2,X3))) )),
  inference(cnf_transformation,[],[f121])).

fof(f153,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X0) | ~intruder_message(triple(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f120])).

fof(f120,plain,(
  ! [X0,X1,X2] : (~intruder_message(triple(X0,X1,X2)) | (intruder_message(X0) & intruder_message(X1) & intruder_message(X2)))),
  inference(ennf_transformation,[],[f17])).

fof(f17,axiom,(
  ! [X0,X1,X2] : (intruder_message(triple(X0,X1,X2)) => (intruder_message(X0) & intruder_message(X1) & intruder_message(X2)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f154,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X1) | ~intruder_message(triple(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f120])).

fof(f155,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X2) | ~intruder_message(triple(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f120])).

fof(f151,plain,(
  ( ! [X0,X1] : (intruder_message(X0) | ~intruder_message(pair(X0,X1))) )),
  inference(cnf_transformation,[],[f119])).

fof(f119,plain,(
  ! [X0,X1] : (~intruder_message(pair(X0,X1)) | (intruder_message(X0) & intruder_message(X1)))),
  inference(ennf_transformation,[],[f16])).

fof(f16,axiom,(
  ! [X0,X1] : (intruder_message(pair(X0,X1)) => (intruder_message(X0) & intruder_message(X1)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f152,plain,(
  ( ! [X0,X1] : (intruder_message(X1) | ~intruder_message(pair(X0,X1))) )),
  inference(cnf_transformation,[],[f119])).

fof(f150,plain,(
  ( ! [X2,X0,X1] : (intruder_message(X2) | ~message(sent(X0,X1,X2))) )),
  inference(cnf_transformation,[],[f118])).

fof(f118,plain,(
  ! [X0,X1,X2] : (~message(sent(X0,X1,X2)) | intruder_message(X2))),
  inference(ennf_transformation,[],[f15])).

fof(f15,axiom,(
  ! [X0,X1,X2] : (message(sent(X0,X1,X2)) => intruder_message(X2))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f161,plain,(
  ( ! [X2,X0,X1] : (intruder_message(triple(X0,X1,X2)) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f125])).

fof(f125,plain,(
  ! [X0,X1,X2] : (~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2) | intruder_message(triple(X0,X1,X2)))),
  inference(flattening,[],[f124])).

fof(f124,plain,(
  ! [X0,X1,X2] : ((~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2)) | intruder_message(triple(X0,X1,X2)))),
  inference(ennf_transformation,[],[f20])).

fof(f20,axiom,(
  ! [X0,X1,X2] : ((intruder_message(X0) & intruder_message(X1) & intruder_message(X2)) => intruder_message(triple(X0,X1,X2)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f162,plain,(
  ( ! [X2,X0,X3,X1] : (intruder_message(quadruple(X0,X1,X2,X3)) | ~intruder_message(X3) | ~intruder_message(X2) | ~intruder_message(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f127])).

fof(f127,plain,(
  ! [X0,X1,X2,X3] : (~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2) | ~intruder_message(X3) | intruder_message(quadruple(X0,X1,X2,X3)))),
  inference(flattening,[],[f126])).

fof(f126,plain,(
  ! [X0,X1,X2,X3] : ((~intruder_message(X0) | ~intruder_message(X1) | ~intruder_message(X2) | ~intruder_message(X3)) | intruder_message(quadruple(X0,X1,X2,X3)))),
  inference(ennf_transformation,[],[f21])).

fof(f21,axiom,(
  ! [X0,X1,X2,X3] : ((intruder_message(X0) & intruder_message(X1) & intruder_message(X2) & intruder_message(X3)) => intruder_message(quadruple(X0,X1,X2,X3)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f166,plain,(
  ( ! [X2,X0,X1] : (intruder_message(encrypt(X0,X1)) | ~party_of_protocol(X2) | ~intruder_holds(key(X1,X2)) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f135])).

fof(f135,plain,(
  ! [X0,X1,X2] : (~intruder_message(X0) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2) | intruder_message(encrypt(X0,X1)))),
  inference(flattening,[],[f134])).

fof(f134,plain,(
  ! [X0,X1,X2] : ((~intruder_message(X0) | ~intruder_holds(key(X1,X2)) | ~party_of_protocol(X2)) | intruder_message(encrypt(X0,X1)))),
  inference(ennf_transformation,[],[f25])).

fof(f25,axiom,(
  ! [X0,X1,X2] : ((intruder_message(X0) & intruder_holds(key(X1,X2)) & party_of_protocol(X2)) => intruder_message(encrypt(X0,X1)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f147,plain,(
  t_holds(key(bt,b))),
  inference(cnf_transformation,[],[f12])).

fof(f12,axiom,(
  t_holds(key(bt,b))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f146,plain,(
  t_holds(key(at,a))),
  inference(cnf_transformation,[],[f11])).

fof(f11,axiom,(
  t_holds(key(at,a))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f143,plain,(
  party_of_protocol(b)),
  inference(cnf_transformation,[],[f7])).

fof(f7,axiom,(
  party_of_protocol(b)),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f139,plain,(
  party_of_protocol(a)),
  inference(cnf_transformation,[],[f2])).

fof(f2,axiom,(
  party_of_protocol(a)),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f148,plain,(
  party_of_protocol(t)),
  inference(cnf_transformation,[],[f13])).

fof(f13,axiom,(
  party_of_protocol(t)),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f144,plain,(
  fresh_to_b(an_a_nonce)),
  inference(cnf_transformation,[],[f8])).

fof(f8,axiom,(
  fresh_to_b(an_a_nonce)),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f175,plain,(
  ( ! [X0] : (fresh_to_b(X0) | ~fresh_intruder_nonce(X0)) )),
  inference(cnf_transformation,[],[f138])).

fof(f174,plain,(
  ( ! [X0] : (fresh_intruder_nonce(generate_intruder_nonce(X0)) | ~fresh_intruder_nonce(X0)) )),
  inference(cnf_transformation,[],[f137])).

fof(f137,plain,(
  ! [X0] : (~fresh_intruder_nonce(X0) | fresh_intruder_nonce(generate_intruder_nonce(X0)))),
  inference(ennf_transformation,[],[f32])).

fof(f32,axiom,(
  ! [X0] : (fresh_intruder_nonce(X0) => fresh_intruder_nonce(generate_intruder_nonce(X0)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f173,plain,(
  fresh_intruder_nonce(an_intruder_nonce)),
  inference(cnf_transformation,[],[f31])).

fof(f31,axiom,(
  fresh_intruder_nonce(an_intruder_nonce)),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f141,plain,(
  a_stored(pair(b,an_a_nonce))),
  inference(cnf_transformation,[],[f4])).

fof(f4,axiom,(
  a_stored(pair(b,an_a_nonce))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f145,plain,(
  ( ! [X0,X1] : (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) | ~fresh_to_b(X1) | ~message(sent(X0,b,pair(X0,X1)))) )),
  inference(cnf_transformation,[],[f115])).

fof(f115,plain,(
  ! [X0,X1] : (~message(sent(X0,b,pair(X0,X1))) | ~fresh_to_b(X1) | message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))))),
  inference(flattening,[],[f114])).

fof(f114,plain,(
  ! [X0,X1] : ((~message(sent(X0,b,pair(X0,X1))) | ~fresh_to_b(X1)) | message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))))),
  inference(ennf_transformation,[],[f109])).

fof(f109,plain,(
  ! [X0,X1] : ((message(sent(X0,b,pair(X0,X1))) & fresh_to_b(X1)) => message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))))),
  inference(pure_predicate_removal,[],[f9])).

fof(f9,axiom,(
  ! [X0,X1] : ((message(sent(X0,b,pair(X0,X1))) & fresh_to_b(X1)) => (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) & b_stored(pair(X0,X1))))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f164,plain,(
  ( ! [X2,X0,X1] : (message(sent(X1,X2,X0)) | ~party_of_protocol(X2) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f131])).

fof(f131,plain,(
  ! [X0,X1,X2] : (~intruder_message(X0) | ~party_of_protocol(X1) | ~party_of_protocol(X2) | message(sent(X1,X2,X0)))),
  inference(flattening,[],[f130])).

fof(f130,plain,(
  ! [X0,X1,X2] : ((~intruder_message(X0) | ~party_of_protocol(X1) | ~party_of_protocol(X2)) | message(sent(X1,X2,X0)))),
  inference(ennf_transformation,[],[f23])).

fof(f23,axiom,(
  ! [X0,X1,X2] : ((intruder_message(X0) & party_of_protocol(X1) & party_of_protocol(X2)) => message(sent(X1,X2,X0)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f140,plain,(
  message(sent(a,b,pair(a,an_a_nonce)))),
  inference(cnf_transformation,[],[f3])).

fof(f3,axiom,(
  message(sent(a,b,pair(a,an_a_nonce)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f142,plain,(
  ( ! [X4,X2,X0,X5,X3,X1] : (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) | ~a_stored(pair(X4,X5)) | ~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0)))) )),
  inference(cnf_transformation,[],[f113])).

fof(f113,plain,(
  ! [X0,X1,X2,X3,X4,X5] : (~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) | ~a_stored(pair(X4,X5)) | message(sent(a,X4,pair(X3,encrypt(X0,X2)))))),
  inference(flattening,[],[f112])).

fof(f112,plain,(
  ! [X0,X1,X2,X3,X4,X5] : ((~message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) | ~a_stored(pair(X4,X5))) | message(sent(a,X4,pair(X3,encrypt(X0,X2)))))),
  inference(ennf_transformation,[],[f110])).

fof(f110,plain,(
  ! [X0,X1,X2,X3,X4,X5] : ((message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) & a_stored(pair(X4,X5))) => message(sent(a,X4,pair(X3,encrypt(X0,X2)))))),
  inference(pure_predicate_removal,[],[f5])).

fof(f5,axiom,(
  ! [X0,X1,X2,X3,X4,X5] : ((message(sent(t,a,triple(encrypt(quadruple(X4,X5,X2,X1),at),X3,X0))) & a_stored(pair(X4,X5))) => (message(sent(a,X4,pair(X3,encrypt(X0,X2)))) & a_holds(key(X2,X4))))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f149,plain,(
  ( ! [X6,X4,X2,X0,X5,X3,X1] : (message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))) | ~a_nonce(X3) | ~t_holds(key(X6,X2)) | ~t_holds(key(X5,X0)) | ~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5))))) )),
  inference(cnf_transformation,[],[f117])).

fof(f117,plain,(
  ! [X0,X1,X2,X3,X4,X5,X6] : (~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))) | ~t_holds(key(X5,X0)) | ~t_holds(key(X6,X2)) | ~a_nonce(X3) | message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
  inference(flattening,[],[f116])).

fof(f116,plain,(
  ! [X0,X1,X2,X3,X4,X5,X6] : ((~message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))) | ~t_holds(key(X5,X0)) | ~t_holds(key(X6,X2)) | ~a_nonce(X3)) | message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
  inference(ennf_transformation,[],[f14])).

fof(f14,axiom,(
  ! [X0,X1,X2,X3,X4,X5,X6] : ((message(sent(X0,t,triple(X0,X1,encrypt(triple(X2,X3,X4),X5)))) & t_holds(key(X5,X0)) & t_holds(key(X6,X2)) & a_nonce(X3)) => message(sent(t,X2,triple(encrypt(quadruple(X0,X3,generate_key(X3),X4),X6),encrypt(triple(X2,generate_key(X3),X4),X5),X1))))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f165,plain,(
  ( ! [X0,X1] : (intruder_holds(key(X0,X1)) | ~party_of_protocol(X1) | ~intruder_message(X0)) )),
  inference(cnf_transformation,[],[f133])).

fof(f133,plain,(
  ! [X0,X1] : (~intruder_message(X0) | ~party_of_protocol(X1) | intruder_holds(key(X0,X1)))),
  inference(flattening,[],[f132])).

fof(f132,plain,(
  ! [X0,X1] : ((~intruder_message(X0) | ~party_of_protocol(X1)) | intruder_holds(key(X0,X1)))),
  inference(ennf_transformation,[],[f35])).

fof(f35,plain,(
  ! [X0,X1] : ((intruder_message(X0) & party_of_protocol(X1)) => intruder_holds(key(X0,X1)))),
  inference(rectify,[],[f24])).

fof(f24,axiom,(
  ! [X1,X2] : ((intruder_message(X1) & party_of_protocol(X2)) => intruder_holds(key(X1,X2)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f171,plain,(
  ( ! [X0] : (~a_nonce(X0) | ~a_key(X0)) )),
  inference(cnf_transformation,[],[f136])).

fof(f136,plain,(
  ! [X0] : (~a_key(X0) | ~a_nonce(X0))),
  inference(ennf_transformation,[],[f29])).

fof(f29,axiom,(
  ! [X0] : ~(a_key(X0) & a_nonce(X0))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f172,plain,(
  ( ! [X0] : (a_key(generate_key(X0))) )),
  inference(cnf_transformation,[],[f30])).

fof(f30,axiom,(
  ! [X0] : a_key(generate_key(X0))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f170,plain,(
  ( ! [X0] : (a_nonce(generate_b_nonce(X0))) )),
  inference(cnf_transformation,[],[f28])).

fof(f28,axiom,(
  ! [X0] : (a_nonce(generate_expiration_time(X0)) & a_nonce(generate_b_nonce(X0)))),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

fof(f169,plain,(
  ( ! [X0] : (a_nonce(generate_expiration_time(X0))) )),
  inference(cnf_transformation,[],[f28])).

fof(f167,plain,(
  a_nonce(an_a_nonce)),
  inference(cnf_transformation,[],[f26])).

fof(f26,axiom,(
  a_nonce(an_a_nonce)),
  file('/Users/korovin/TPTP-v5.4.0/Problems/SWV/SWV017+1.p',unknown)).

cnf(c_29,plain,
    ( ~ a_nonce(generate_key(X0_$i)) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_291,plain,
    ( ~ a_nonce(generate_key(X0_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_29]) ).

cnf(c_21,plain,
    ( intruder_message(pair(X0_$i,X1_$i))
    | ~ intruder_message(X0_$i)
    | ~ intruder_message(X1_$i) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_298,plain,
    ( intruder_message(pair(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1))
    | ~ intruder_message(X0_$$iProver_key_$i_1)
    | ~ intruder_message(X1_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_21]) ).

cnf(c_36,plain,
    ( intruder_message(X0_$i) | ~ fresh_intruder_nonce(X0_$i) ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_285,plain,
    ( intruder_message(X0_$$iProver_key_$i_1)
    | ~ fresh_intruder_nonce(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_36]) ).

cnf(c_24,plain,
    ( ~ party_of_protocol(X0_$i)
    | ~ intruder_message(encrypt(X1_$i,X2_$i))
    | intruder_message(X2_$i)
    | ~ intruder_holds(key(X2_$i,X0_$i)) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_295,plain,
    ( ~ party_of_protocol(X0_$$iProver_key_$i_1)
    | ~ intruder_message(encrypt(X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | intruder_message(X2_$$iProver_key_$i_1)
    | ~ intruder_holds(key(X2_$$iProver_key_$i_1,X0_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_24]) ).

cnf(c_20,plain,
    ( ~ intruder_message(quadruple(X0_$i,X1_$i,X2_$i,X3_$i))
    | intruder_message(X0_$i) ),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_299,plain,
    ( ~ intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_$i_1))
    | intruder_message(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_20]) ).

cnf(c_19,plain,
    ( ~ intruder_message(quadruple(X0_$i,X1_$i,X2_$i,X3_$i))
    | intruder_message(X1_$i) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_300,plain,
    ( ~ intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_$i_1))
    | intruder_message(X1_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_19]) ).

cnf(c_18,plain,
    ( ~ intruder_message(quadruple(X0_$i,X1_$i,X2_$i,X3_$i))
    | intruder_message(X2_$i) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_301,plain,
    ( ~ intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_$i_1))
    | intruder_message(X2_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_18]) ).

cnf(c_17,plain,
    ( ~ intruder_message(quadruple(X0_$i,X1_$i,X2_$i,X3_$i))
    | intruder_message(X3_$i) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_302,plain,
    ( ~ intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_$i_1))
    | intruder_message(X3_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_17]) ).

cnf(c_16,plain,
    ( ~ intruder_message(triple(X0_$i,X1_$i,X2_$i))
    | intruder_message(X0_$i) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_303,plain,
    ( ~ intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | intruder_message(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_16]) ).

cnf(c_15,plain,
    ( ~ intruder_message(triple(X0_$i,X1_$i,X2_$i))
    | intruder_message(X1_$i) ),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_304,plain,
    ( ~ intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | intruder_message(X1_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_15]) ).

cnf(c_14,plain,
    ( ~ intruder_message(triple(X0_$i,X1_$i,X2_$i))
    | intruder_message(X2_$i) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_305,plain,
    ( ~ intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | intruder_message(X2_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_14]) ).

cnf(c_13,plain,
    ( ~ intruder_message(pair(X0_$i,X1_$i)) | intruder_message(X0_$i) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_306,plain,
    ( ~ intruder_message(pair(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1))
    | intruder_message(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_13]) ).

cnf(c_12,plain,
    ( ~ intruder_message(pair(X0_$i,X1_$i)) | intruder_message(X1_$i) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_307,plain,
    ( ~ intruder_message(pair(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1))
    | intruder_message(X1_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_12]) ).

cnf(c_11,plain,
    ( ~ message(sent(X0_$i,X1_$i,X2_$i)) | intruder_message(X2_$i) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_308,plain,
    ( ~ message(sent(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | intruder_message(X2_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_11]) ).

cnf(c_22,plain,
    ( intruder_message(triple(X0_$i,X1_$i,X2_$i))
    | ~ intruder_message(X0_$i)
    | ~ intruder_message(X1_$i)
    | ~ intruder_message(X2_$i) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_297,plain,
    ( intruder_message(triple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | ~ intruder_message(X0_$$iProver_key_$i_1)
    | ~ intruder_message(X1_$$iProver_key_$i_1)
    | ~ intruder_message(X2_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_22]) ).

cnf(c_23,plain,
    ( intruder_message(quadruple(X0_$i,X1_$i,X2_$i,X3_$i))
    | ~ intruder_message(X0_$i)
    | ~ intruder_message(X1_$i)
    | ~ intruder_message(X2_$i)
    | ~ intruder_message(X3_$i) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_296,plain,
    ( intruder_message(quadruple(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_$i_1))
    | ~ intruder_message(X0_$$iProver_key_$i_1)
    | ~ intruder_message(X1_$$iProver_key_$i_1)
    | ~ intruder_message(X2_$$iProver_key_$i_1)
    | ~ intruder_message(X3_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_23]) ).

cnf(c_27,plain,
    ( ~ party_of_protocol(X0_$i)
    | intruder_message(encrypt(X1_$i,X2_$i))
    | ~ intruder_message(X1_$i)
    | ~ intruder_holds(key(X2_$i,X0_$i)) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_292,plain,
    ( ~ party_of_protocol(X0_$$iProver_key_$i_1)
    | intruder_message(encrypt(X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | ~ intruder_message(X1_$$iProver_key_$i_1)
    | ~ intruder_holds(key(X2_$$iProver_key_$i_1,X0_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_27]) ).

cnf(c_8,plain,
    ( t_holds(key(bt,b)) ),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_280,plain,
    ( t_holds(key(bt,b)) ),
    inference(subtyping,[status(esa)],[c_8]) ).

cnf(c_7,plain,
    ( t_holds(key(at,a)) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_279,plain,
    ( t_holds(key(at,a)) ),
    inference(subtyping,[status(esa)],[c_7]) ).

cnf(c_4,plain,
    ( party_of_protocol(b) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_277,plain,
    ( party_of_protocol(b) ),
    inference(subtyping,[status(esa)],[c_4]) ).

cnf(c_0,plain,
    ( party_of_protocol(a) ),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_274,plain,
    ( party_of_protocol(a) ),
    inference(subtyping,[status(esa)],[c_0]) ).

cnf(c_9,plain,
    ( party_of_protocol(t) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_281,plain,
    ( party_of_protocol(t) ),
    inference(subtyping,[status(esa)],[c_9]) ).

cnf(c_5,plain,
    ( fresh_to_b(an_a_nonce) ),
    inference(cnf_transformation,[],[f144]) ).

cnf(c_278,plain,
    ( fresh_to_b(an_a_nonce) ),
    inference(subtyping,[status(esa)],[c_5]) ).

cnf(c_37,plain,
    ( fresh_to_b(X0_$i) | ~ fresh_intruder_nonce(X0_$i) ),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_284,plain,
    ( fresh_to_b(X0_$$iProver_key_$i_1)
    | ~ fresh_intruder_nonce(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_37]) ).

cnf(c_35,plain,
    ( fresh_intruder_nonce(generate_intruder_nonce(X0_$i))
    | ~ fresh_intruder_nonce(X0_$i) ),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_286,plain,
    ( fresh_intruder_nonce(generate_intruder_nonce(X0_$$iProver_key_$i_1))
    | ~ fresh_intruder_nonce(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_35]) ).

cnf(c_34,plain,
    ( fresh_intruder_nonce(an_intruder_nonce) ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_283,plain,
    ( fresh_intruder_nonce(an_intruder_nonce) ),
    inference(subtyping,[status(esa)],[c_34]) ).

cnf(c_2,plain,
    ( a_stored(pair(b,an_a_nonce)) ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_276,plain,
    ( a_stored(pair(b,an_a_nonce)) ),
    inference(subtyping,[status(esa)],[c_2]) ).

cnf(c_6,plain,
    ( message(sent(b,t,triple(b,generate_b_nonce(X0_$i),encrypt(triple(X1_$i,X0_$i,generate_expiration_time(X0_$i)),bt))))
    | ~ message(sent(X1_$i,b,pair(X1_$i,X0_$i)))
    | ~ fresh_to_b(X0_$i) ),
    inference(cnf_transformation,[],[f145]) ).

cnf(c_310,plain,
    ( message(sent(b,t,triple(b,generate_b_nonce(X0_$$iProver_key_$i_1),encrypt(triple(X1_$$iProver_key_$i_1,X0_$$iProver_key_$i_1,generate_expiration_time(X0_$$iProver_key_$i_1)),bt))))
    | ~ message(sent(X1_$$iProver_key_$i_1,b,pair(X1_$$iProver_key_$i_1,X0_$$iProver_key_$i_1)))
    | ~ fresh_to_b(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_6]) ).

cnf(c_25,plain,
    ( ~ party_of_protocol(X0_$i)
    | ~ party_of_protocol(X1_$i)
    | message(sent(X0_$i,X1_$i,X2_$i))
    | ~ intruder_message(X2_$i) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_294,plain,
    ( ~ party_of_protocol(X0_$$iProver_key_$i_1)
    | ~ party_of_protocol(X1_$$iProver_key_$i_1)
    | message(sent(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1))
    | ~ intruder_message(X2_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_25]) ).

cnf(c_1,plain,
    ( message(sent(a,b,pair(a,an_a_nonce))) ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_275,plain,
    ( message(sent(a,b,pair(a,an_a_nonce))) ),
    inference(subtyping,[status(esa)],[c_1]) ).

cnf(c_3,plain,
    ( message(sent(a,X0_$i,pair(X1_$i,encrypt(X2_$i,X3_$i))))
    | ~ message(sent(t,a,triple(encrypt(quadruple(X0_$i,X4_$i,X3_$i,X5_$i),at),X1_$i,X2_$i)))
    | ~ a_stored(pair(X0_$i,X4_$i)) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_311,plain,
    ( message(sent(a,X0_$$iProver_key_$i_1,pair(X1_$$iProver_key_$i_1,encrypt(X2_$$iProver_key_$i_1,X3_$$iProver_key_$i_1))))
    | ~ message(sent(t,a,triple(encrypt(quadruple(X0_$$iProver_key_$i_1,X4_$$iProver_key_$i_1,X3_$$iProver_key_$i_1,X5_$$iProver_key_$i_1),at),X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1)))
    | ~ a_stored(pair(X0_$$iProver_key_$i_1,X4_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_3]) ).

cnf(c_10,plain,
    ( message(sent(t,X0_$i,triple(encrypt(quadruple(X1_$i,X2_$i,generate_key(X2_$i),X3_$i),X4_$i),encrypt(triple(X0_$i,generate_key(X2_$i),X3_$i),X5_$i),X6_$i)))
    | ~ message(sent(X1_$i,t,triple(X1_$i,X6_$i,encrypt(triple(X0_$i,X2_$i,X3_$i),X5_$i))))
    | ~ t_holds(key(X5_$i,X1_$i))
    | ~ t_holds(key(X4_$i,X0_$i))
    | ~ a_nonce(X2_$i) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_309,plain,
    ( message(sent(t,X0_$$iProver_key_$i_1,triple(encrypt(quadruple(X1_$$iProver_key_$i_1,X2_$$iProver_key_$i_1,generate_key(X2_$$iProver_key_$i_1),X3_$$iProver_key_$i_1),X4_$$iProver_key_$i_1),encrypt(triple(X0_$$iProver_key_$i_1,generate_key(X2_$$iProver_key_$i_1),X3_$$iProver_key_$i_1),X5_$$iProver_key_$i_1),X6_$$iProver_key_$i_1)))
    | ~ message(sent(X1_$$iProver_key_$i_1,t,triple(X1_$$iProver_key_$i_1,X6_$$iProver_key_$i_1,encrypt(triple(X0_$$iProver_key_$i_1,X2_$$iProver_key_$i_1,X3_$$iProver_key_$i_1),X5_$$iProver_key_$i_1))))
    | ~ t_holds(key(X5_$$iProver_key_$i_1,X1_$$iProver_key_$i_1))
    | ~ t_holds(key(X4_$$iProver_key_$i_1,X0_$$iProver_key_$i_1))
    | ~ a_nonce(X2_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_10]) ).

cnf(c_26,plain,
    ( ~ party_of_protocol(X0_$i)
    | ~ intruder_message(X1_$i)
    | intruder_holds(key(X1_$i,X0_$i)) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_293,plain,
    ( ~ party_of_protocol(X0_$$iProver_key_$i_1)
    | ~ intruder_message(X1_$$iProver_key_$i_1)
    | intruder_holds(key(X1_$$iProver_key_$i_1,X0_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_26]) ).

cnf(c_32,plain,
    ( ~ a_nonce(X0_$i) | ~ a_key(X0_$i) ),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_321,plain,
    ( ~ a_nonce(X0_$$iProver_key_$i_1) | ~ a_key(X0_$$iProver_key_$i_1) ),
    inference(subtyping,[status(esa)],[c_32]) ).

cnf(c_33,plain,
    ( a_key(generate_key(X0_$i)) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_320,plain,
    ( a_key(generate_key(X0_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_33]) ).

cnf(c_338,plain,
    ( ~ a_nonce(generate_key(X0_$$iProver_key_$i_1)) ),
    inference(resolution,[status(thm)],[c_321,c_320]) ).

cnf(c_30,plain,
    ( a_nonce(generate_b_nonce(X0_$i)) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_319,plain,
    ( a_nonce(generate_b_nonce(X0_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_30]) ).

cnf(c_31,plain,
    ( a_nonce(generate_expiration_time(X0_$i)) ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_318,plain,
    ( a_nonce(generate_expiration_time(X0_$$iProver_key_$i_1)) ),
    inference(subtyping,[status(esa)],[c_31]) ).

cnf(c_28,plain,
    ( a_nonce(an_a_nonce) ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_317,plain,
    ( a_nonce(an_a_nonce) ),
    inference(subtyping,[status(esa)],[c_28]) ).


% SZS output end Saturation

Sample finite model for SWV017+1

%------ The model is defined over ground terms (initial term algebra).
%------ Predicates are defined as (\forall x_1,..,x_n  ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) 
%------ where \phi is a formula over the term algebra.
%------ If we have equality in the problem then it is also defined as a predicate above, 
%------ with "=" on the right-hand-side of the definition interpreted over the term algebra $$term_algebra_type
%------ See help for --sat_out_model for different model outputs.
%------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
%------ where the first argument stands for the sort ($i in the unsorted case)

% SZS output start Model 
%------ Negative definition of party_of_protocol 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( ~(party_of_protocol(X0_$$iProver_key_$i_1)) <=>
          $false
      )
    )
   ).

%------ Negative definition of message 
fof(lit_def,axiom,
    (! [X0_$$iProver_message_$i_1] : 
      ( ~(message(X0_$$iProver_message_$i_1)) <=>
          $false
      )
    )
   ).

%------ Negative definition of a_stored 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( ~(a_stored(X0_$$iProver_key_$i_1)) <=>
          $false
      )
    )
   ).

%------ Positive definition of fresh_to_b 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( fresh_to_b(X0_$$iProver_key_$i_1) <=>
          $true
      )
    )
   ).

%------ Negative definition of t_holds 
fof(lit_def,axiom,
    (! [X0_$$iProver_intruder_holds_$i_1] : 
      ( ~(t_holds(X0_$$iProver_intruder_holds_$i_1)) <=>
          $false
      )
    )
   ).

%------ Positive definition of a_nonce 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( a_nonce(X0_$$iProver_key_$i_1) <=>
           (
              (
                ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_1 )
              )

           )
      )
    )
   ).

%------ Positive definition of intruder_message 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( intruder_message(X0_$$iProver_key_$i_1) <=>
          $true
      )
    )
   ).

%------ Negative definition of intruder_holds 
fof(lit_def,axiom,
    (! [X0_$$iProver_intruder_holds_$i_1] : 
      ( ~(intruder_holds(X0_$$iProver_intruder_holds_$i_1)) <=>
          $false
      )
    )
   ).

%------ Positive definition of a_key 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( a_key(X0_$$iProver_key_$i_1) <=>
           (
              (
                ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_2 )
              )

           )
      )
    )
   ).

%------ Negative definition of fresh_intruder_nonce 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( ~(fresh_intruder_nonce(X0_$$iProver_key_$i_1)) <=>
          $false
      )
    )
   ).

%------ Positive definition of $$iProver_Flat_an_a_nonce 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1] : 
      ( $$iProver_Flat_an_a_nonce(X0_$$iProver_key_$i_1) <=>
           (
              (
                ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_1 )
              )

           )
      )
    )
   ).

%------ Positive definition of $$iProver_Flat_generate_b_nonce 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1] : 
      ( $$iProver_Flat_generate_b_nonce(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1) <=>
           (
              (
                ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_1 )
              )

           )
      )
    )
   ).

%------ Positive definition of $$iProver_Flat_generate_expiration_time 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1] : 
      ( $$iProver_Flat_generate_expiration_time(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1) <=>
           (
              (
                ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_1 )
              )

           )
      )
    )
   ).

%------ Positive definition of $$iProver_Flat_generate_key 
fof(lit_def,axiom,
    (! [X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1] : 
      ( $$iProver_Flat_generate_key(X0_$$iProver_key_$i_1,X1_$$iProver_key_$i_1) <=>
           (
              (
                ( X0_$$iProver_key_$i_1=$$iProver_Domain_$$iProver_key_$i_1_2 )
              )

           )
      )
    )
   ).


% SZS output end Model 

iProver 2.0

Sample proof for SEU140+2

% SZS status Theorem


% SZS output start CNFRefutation

fof(f43,axiom,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  file('/Users/korovin/TPTP-v6.1.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f70,plain,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  inference(rectify,[],[f43])).

fof(f71,plain,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  inference(flattening,[],[f70])).

fof(f131,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | (in(sK8(X1,X0),X0) & in(sK8(X1,X0),X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
  inference(skolemisation,[status(esa)],[f92])).
fof(f92,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | ? [X3] : (in(X3,X0) & in(X3,X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f71])).

fof(f198,plain,(
  ( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
  inference(cnf_transformation,[],[f131])).

fof(f8,axiom,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  file('/Users/korovin/TPTP-v6.1.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f77,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))),
  inference(ennf_transformation,[],[f8])).

fof(f113,plain,(
  ! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))),
  inference(nnf_transformation,[],[f77])).

fof(f115,plain,(
  ! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & ((in(sK2(X1,X0),X0) & ~in(sK2(X1,X0),X1)) | subset(X0,X1)))),
  inference(skolemisation,[status(esa)],[f114])).
fof(f114,plain,(
  ! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))),
  inference(rectify,[],[f113])).

fof(f149,plain,(
  ( ! [X0,X3,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
  inference(cnf_transformation,[],[f115])).

fof(f197,plain,(
  ( ! [X0,X1] : (in(sK8(X1,X0),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f131])).

fof(f196,plain,(
  ( ! [X0,X1] : (in(sK8(X1,X0),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f131])).

fof(f51,conjecture,(
  ! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  file('/Users/korovin/TPTP-v6.1.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f52,negated_conjecture,(
  ~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).

fof(f97,plain,(
  ? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
  inference(ennf_transformation,[],[f52])).

fof(f133,plain,(
  subset(sK10,sK11) & disjoint(sK11,sK12) & ~disjoint(sK10,sK12)),
  inference(skolemisation,[status(esa)],[f98])).
fof(f98,plain,(
  ? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
  inference(flattening,[],[f97])).

fof(f209,plain,(
  ~disjoint(sK10,sK12)),
  inference(cnf_transformation,[],[f133])).

fof(f208,plain,(
  disjoint(sK11,sK12)),
  inference(cnf_transformation,[],[f133])).

fof(f207,plain,(
  subset(sK10,sK11)),
  inference(cnf_transformation,[],[f133])).

cnf(c_414,plain,
    ( ~ in(X0_$i,X1_$i) | ~ in(X0_$i,X2_$i) | ~ disjoint(X1_$i,X2_$i) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_563,plain,
    ( ~ in(X0_$i,X1_$i) | ~ in(X0_$i,X2_$i) | ~ disjoint(X1_$i,X2_$i) ),
    inference(subtyping,[status(esa)],[c_414]) ).

cnf(c_1466,plain,
    ( ~ in(sK8(sK12,sK10),sK11)
    | ~ in(sK8(sK12,sK10),X0_$i)
    | ~ disjoint(sK11,X0_$i) ),
    inference(instantiation,[status(thm)],[c_563]) ).

cnf(c_2229,plain,
    ( ~ in(sK8(sK12,sK10),sK12)
    | ~ in(sK8(sK12,sK10),sK11)
    | ~ disjoint(sK11,sK12) ),
    inference(instantiation,[status(thm)],[c_1466]) ).

cnf(c_372,plain,
    ( ~ in(X0_$i,X1_$i) | in(X0_$i,X2_$i) | ~ subset(X1_$i,X2_$i) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_614,plain,
    ( ~ in(X0_$i,X1_$i) | in(X0_$i,X2_$i) | ~ subset(X1_$i,X2_$i) ),
    inference(subtyping,[status(esa)],[c_372]) ).

cnf(c_653,plain,
    ( ~ in(sK8(sK12,sK10),sK10)
    | in(sK8(sK12,sK10),X0_$i)
    | ~ subset(sK10,X0_$i) ),
    inference(instantiation,[status(thm)],[c_614]) ).

cnf(c_1127,plain,
    ( ~ in(sK8(sK12,sK10),sK10)
    | in(sK8(sK12,sK10),sK11)
    | ~ subset(sK10,sK11) ),
    inference(instantiation,[status(thm)],[c_653]) ).

cnf(c_415,plain,
    ( in(sK8(X0_$i,X1_$i),X0_$i) | disjoint(X1_$i,X0_$i) ),
    inference(cnf_transformation,[],[f197]) ).

cnf(c_562,plain,
    ( in(sK8(X0_$i,X1_$i),X0_$i) | disjoint(X1_$i,X0_$i) ),
    inference(subtyping,[status(esa)],[c_415]) ).

cnf(c_630,plain,
    ( in(sK8(sK12,sK10),sK12) | disjoint(sK10,sK12) ),
    inference(instantiation,[status(thm)],[c_562]) ).

cnf(c_416,plain,
    ( in(sK8(X0_$i,X1_$i),X1_$i) | disjoint(X1_$i,X0_$i) ),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_561,plain,
    ( in(sK8(X0_$i,X1_$i),X1_$i) | disjoint(X1_$i,X0_$i) ),
    inference(subtyping,[status(esa)],[c_416]) ).

cnf(c_629,plain,
    ( in(sK8(sK12,sK10),sK10) | disjoint(sK10,sK12) ),
    inference(instantiation,[status(thm)],[c_561]) ).

cnf(c_72,plain,
    ( ~ disjoint(sK10,sK12) ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_73,plain,
    ( disjoint(sK11,sK12) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_74,plain,
    ( subset(sK10,sK11) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(contradiction,plain,
    ( $false ),
    inference(minisat,
              [status(thm)],
              [c_2229,c_1127,c_630,c_629,c_72,c_73,c_74]) ).

% SZS output end CNFRefutation

Sample model for NLP042+1

% SZS status CounterSatisfiable

------ Building Model...Done

%------ The model is defined over ground terms (initial term algebra).
%------ Predicates are defined as (\forall x_1,..,x_n  ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) 
%------ where \phi is a formula over the term algebra.
%------ If we have equality in the problem then it is also defined as a predicate above, 
%------ with "=" on the right-hand-side of the definition interpreted over the term algebra $$term_algebra_type
%------ See help for --sat_out_model for different model outputs.
%------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
%------ where the first argument stands for the sort ($i in the unsorted case)


% SZS output start Model 


%------ Positive definition of $$equality_sorted 
fof(lit_def,axiom,
    (! [X0_$tType,X0_$$iProver_of_2_$i,X1_$$iProver_of_2_$i] : 
      ( $$equality_sorted(X0_$tType,X0_$$iProver_of_2_$i,X1_$$iProver_of_2_$i) <=>
           (
              (
                ( X0_$tType=$$iProver_of_2_$i )
               &
                ( X0_$$iProver_of_2_$i!=esk5_0 | X1_$$iProver_of_2_$i!=esk4_0 )
               &
                ( X0_$$iProver_of_2_$i!=esk4_0 )
               &
                ( X0_$$iProver_of_2_$i!=esk4_0 | X1_$$iProver_of_2_$i!=esk2_0 )
               &
                ( X0_$$iProver_of_2_$i!=esk2_0 )
               &
                ( X0_$$iProver_of_2_$i!=esk2_0 | X1_$$iProver_of_2_$i!=esk5_0 )
               &
                ( X0_$$iProver_of_2_$i!=esk3_0 )
               &
                ( X1_$$iProver_of_2_$i!=esk4_0 )
               &
                ( X1_$$iProver_of_2_$i!=esk2_0 )
               &
                ( X1_$$iProver_of_2_$i!=esk3_0 )
              )

             | 
              (
                ( X0_$tType=$$iProver_of_2_$i & X0_$$iProver_of_2_$i=esk4_0 & X1_$$iProver_of_2_$i=esk4_0 )
              )

             | 
              (
                ( X0_$tType=$$iProver_of_2_$i & X0_$$iProver_of_2_$i=esk2_0 & X1_$$iProver_of_2_$i=esk2_0 )
              )

             | 
              (
                ( X0_$tType=$$iProver_of_2_$i & X0_$$iProver_of_2_$i=esk3_0 & X1_$$iProver_of_2_$i=esk3_0 )
              )

             | 
              (
                ( X0_$tType=$$iProver_of_2_$i & X1_$$iProver_of_2_$i=X0_$$iProver_of_2_$i )
               &
                ( X0_$$iProver_of_2_$i!=esk4_0 )
               &
                ( X0_$$iProver_of_2_$i!=esk2_0 )
               &
                ( X0_$$iProver_of_2_$i!=esk3_0 )
              )

           )
      )
    )
   ).

%------ Positive definition of forename 
fof(lit_def,axiom,
    (! [X0_$$iProver_of_1_$i,X0_$$iProver_of_2_$i] : 
      ( forename(X0_$$iProver_of_1_$i,X0_$$iProver_of_2_$i) <=>
           (
              (
                ( X0_$$iProver_of_1_$i=esk1_0 & X0_$$iProver_of_2_$i=esk3_0 )
              )

           )
      )
    )
   ).

%------ Positive definition of of 
fof(lit_def,axiom,
    (! [X0_$$iProver_of_1_$i,X0_$$iProver_of_2_$i,X1_$$iProver_of_2_$i] : 
      ( of(X0_$$iProver_of_1_$i,X0_$$iProver_of_2_$i,X1_$$iProver_of_2_$i) <=>
           (
              (
                ( X0_$$iProver_of_1_$i=esk1_0 & X0_$$iProver_of_2_$i=esk3_0 & X1_$$iProver_of_2_$i=esk2_0 )
              )

           )
      )
    )
   ).


% SZS output end Model 

Sample model for SWV017+1

% SZS status Satisfiable

------ Building Model...Done

%------ The model is defined over ground terms (initial term algebra).
%------ Predicates are defined as (\forall x_1,..,x_n  ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) 
%------ where \phi is a formula over the term algebra.
%------ If we have equality in the problem then it is also defined as a predicate above, 
%------ with "=" on the right-hand-side of the definition interpreted over the term algebra $$term_algebra_type
%------ See help for --sat_out_model for different model outputs.
%------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
%------ where the first argument stands for the sort ($i in the unsorted case)


% SZS output start Model 


%------ Negative definition of message 
fof(lit_def,axiom,
    (! [X0_$$iProver_message_1_$i] : 
      ( ~(message(X0_$$iProver_message_1_$i)) <=>
          $false
      )
    )
   ).

%------ Negative definition of t_holds 
fof(lit_def,axiom,
    (! [X0_$$iProver_t_holds_1_$i] : 
      ( ~(t_holds(X0_$$iProver_t_holds_1_$i)) <=>
          $false
      )
    )
   ).

%------ Positive definition of intruder_message 
fof(lit_def,axiom,
    (! [X0_$$iProver_sent_2_$i] : 
      ( intruder_message(X0_$$iProver_sent_2_$i) <=>
          $true
      )
    )
   ).

%------ Negative definition of party_of_protocol 
fof(lit_def,axiom,
    (! [X0_$$iProver_sent_2_$i] : 
      ( ~(party_of_protocol(X0_$$iProver_sent_2_$i)) <=>
          $false
      )
    )
   ).

%------ Negative definition of fresh_intruder_nonce 
fof(lit_def,axiom,
    (! [X0_$$iProver_sent_2_$i] : 
      ( ~(fresh_intruder_nonce(X0_$$iProver_sent_2_$i)) <=>
          $false
      )
    )
   ).

%------ Positive definition of sP0_iProver_split 
fof(lit_def,axiom,
      ( sP0_iProver_split <=>
          $false
      )
   ).

%------ Positive definition of sP1_iProver_split 
fof(lit_def,axiom,
      ( sP1_iProver_split <=>
          $true
      )
   ).


% SZS output end Model 

iProverModulo 0.7-0.3

Sample solution for SEU140+2

% SZS output start CNFRefutation
% Axioms transformation by autotheo
# Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
# Orienting axioms whose shape is orientable
fof(t6_boole,axiom,![A]:(empty(A)=>A=empty_set),input).
fof(t6_boole_0,plain,![A]:(~empty(A)
   |A=empty_set),inference(orientation, [status(thm)], [t6_boole]))
fof(t4_boole,axiom,![A]:set_difference(empty_set,A)=empty_set,input).
fof(t4_boole_0,plain,![A]:(set_difference(empty_set,A)=empty_set
   |$false),inference(orientation, [status(thm)], [t4_boole]))
fof(t3_boole,axiom,![A]:set_difference(A,empty_set)=A,input).
fof(t3_boole_0,plain,![A]:(set_difference(A,empty_set)=A
   |$false),inference(orientation, [status(thm)], [t3_boole]))
fof(t2_tarski,axiom,![A,B]:(![C]:(in(C,A)<=>in(C,B))=>A=B),input).
fof(t2_tarski_0,plain,![A,B]:(A=B
   |~![C]:(in(C,A)
   <=>in(C,B))),inference(orientation, [status(thm)], [t2_tarski]))
fof(t2_boole,axiom,![A]:set_intersection2(A,empty_set)=empty_set,input).
fof(t2_boole_0,plain,![A]:(set_intersection2(A,empty_set)=empty_set
   |$false),inference(orientation, [status(thm)], [t2_boole]))
fof(t1_boole,axiom,![A]:set_union2(A,empty_set)=A,input).
fof(t1_boole_0,plain,![A]:(set_union2(A,empty_set)=A
   |$false),inference(orientation, [status(thm)], [t1_boole]))
fof(symmetry_r1_xboole_0,axiom,![A,B]:(disjoint(A,B)=>disjoint(B,A)),input).
fof(symmetry_r1_xboole_0_0,plain,![A,B]:(~disjoint(A,B)
   |disjoint(B,A)),inference(orientation, [status(thm)], [symmetry_r1_xboole_0]))
fof(reflexivity_r1_tarski,axiom,![A,B]:subset(A,A),input).
fof(reflexivity_r1_tarski_0,plain,![A]:(subset(A,A)
   |$false),inference(orientation, [status(thm)], [reflexivity_r1_tarski]))
fof(irreflexivity_r2_xboole_0,axiom,![A,B]:~proper_subset(A,A),input).
fof(irreflexivity_r2_xboole_0_0,plain,![A]:(~proper_subset(A,A)
   |$false),inference(orientation, [status(thm)], [irreflexivity_r2_xboole_0]))
fof(idempotence_k3_xboole_0,axiom,![A,B]:set_intersection2(A,A)=A,input).
fof(idempotence_k3_xboole_0_0,plain,![A]:(set_intersection2(A,A)=A
   |$false),inference(orientation, [status(thm)], [idempotence_k3_xboole_0]))
fof(idempotence_k2_xboole_0,axiom,![A,B]:set_union2(A,A)=A,input).
fof(idempotence_k2_xboole_0_0,plain,![A]:(set_union2(A,A)=A
   |$false),inference(orientation, [status(thm)], [idempotence_k2_xboole_0]))
fof(fc3_xboole_0,axiom,![A,B]:(~empty(A)=>~empty(set_union2(B,A))),input).
fof(fc3_xboole_0_0,plain,![A,B]:(empty(A)
   |~empty(set_union2(B,A))),inference(orientation, [status(thm)], [fc3_xboole_0]))
fof(fc2_xboole_0,axiom,![A,B]:(~empty(A)=>~empty(set_union2(A,B))),input).
fof(fc2_xboole_0_0,plain,![A,B]:(empty(A)
   |~empty(set_union2(A,B))),inference(orientation, [status(thm)], [fc2_xboole_0]))
fof(fc1_xboole_0,axiom,empty(empty_set),input).
fof(fc1_xboole_0_0,plain,![]:(empty(empty_set)
   |$false),inference(orientation, [status(thm)], [fc1_xboole_0]))
fof(dt_k4_xboole_0,axiom,$true,input).
fof(dt_k4_xboole_0_0,plain,![]:($true
   |$false),inference(orientation, [status(thm)], [dt_k4_xboole_0]))
fof(dt_k3_xboole_0,axiom,$true,input).
fof(dt_k3_xboole_0_0,plain,![]:($true
   |$false),inference(orientation, [status(thm)], [dt_k3_xboole_0]))
fof(dt_k2_xboole_0,axiom,$true,input).
fof(dt_k2_xboole_0_0,plain,![]:($true
   |$false),inference(orientation, [status(thm)], [dt_k2_xboole_0]))
fof(dt_k1_xboole_0,axiom,$true,input).
fof(dt_k1_xboole_0_0,plain,![]:($true
   |$false),inference(orientation, [status(thm)], [dt_k1_xboole_0]))
fof(d8_xboole_0,axiom,![A,B]:(proper_subset(A,B)<=>(subset(A,B)&A!=B)),input).
fof(d8_xboole_0_0,plain,![A,B]:(proper_subset(A,B)
   |~(subset(A,B)
   &A!=B)),inference(orientation, [status(thm)], [d8_xboole_0]))
fof(d8_xboole_0_1,plain,![A,B]:(~proper_subset(A,B)
   |(subset(A,B)
   &A!=B)),inference(orientation, [status(thm)], [d8_xboole_0]))
fof(d7_xboole_0,axiom,![A,B]:(disjoint(A,B)<=>set_intersection2(A,B)=empty_set),input).
fof(d7_xboole_0_0,plain,![A,B]:(disjoint(A,B)
   |~set_intersection2(A,B)=empty_set),inference(orientation, [status(thm)], [d7_xboole_0]))
fof(d7_xboole_0_1,plain,![A,B]:(~disjoint(A,B)
   |set_intersection2(A,B)=empty_set),inference(orientation, [status(thm)], [d7_xboole_0]))
fof(d4_xboole_0,axiom,![A,B,C]:(C=set_difference(A,B)<=>![D]:(in(D,C)<=>(in(D,A)&~in(D,B)))),input).
fof(d4_xboole_0_0,plain,![A,B,C]:(C=set_difference(A,B)
   |~![D]:(in(D,C)
   <=>(in(D,A)
   &~in(D,B)))),inference(orientation, [status(thm)], [d4_xboole_0]))
fof(d4_xboole_0_1,plain,![A,B,C]:(~C=set_difference(A,B)
   |![D]:(in(D,C)
   <=>(in(D,A)
   &~in(D,B)))),inference(orientation, [status(thm)], [d4_xboole_0]))
fof(d3_xboole_0,axiom,![A,B,C]:(C=set_intersection2(A,B)<=>![D]:(in(D,C)<=>(in(D,A)&in(D,B)))),input).
fof(d3_xboole_0_0,plain,![A,B,C]:(C=set_intersection2(A,B)
   |~![D]:(in(D,C)
   <=>(in(D,A)
   &in(D,B)))),inference(orientation, [status(thm)], [d3_xboole_0]))
fof(d3_xboole_0_1,plain,![A,B,C]:(~C=set_intersection2(A,B)
   |![D]:(in(D,C)
   <=>(in(D,A)
   &in(D,B)))),inference(orientation, [status(thm)], [d3_xboole_0]))
fof(d3_tarski,axiom,![A,B]:(subset(A,B)<=>![C]:(in(C,A)=>in(C,B))),input).
fof(d3_tarski_0,plain,![A,B]:(subset(A,B)
   |~![C]:(in(C,A)
   =>in(C,B))),inference(orientation, [status(thm)], [d3_tarski]))
fof(d3_tarski_1,plain,![A,B]:(~subset(A,B)
   |![C]:(in(C,A)
   =>in(C,B))),inference(orientation, [status(thm)], [d3_tarski]))
fof(d2_xboole_0,axiom,![A,B,C]:(C=set_union2(A,B)<=>![D]:(in(D,C)<=>(in(D,A)|in(D,B)))),input).
fof(d2_xboole_0_0,plain,![A,B,C]:(C=set_union2(A,B)
   |~![D]:(in(D,C)
   <=>(in(D,A)
   |in(D,B)))),inference(orientation, [status(thm)], [d2_xboole_0]))
fof(d2_xboole_0_1,plain,![A,B,C]:(~C=set_union2(A,B)
   |![D]:(in(D,C)
   <=>(in(D,A)
   |in(D,B)))),inference(orientation, [status(thm)], [d2_xboole_0]))
fof(d1_xboole_0,axiom,![A]:(A=empty_set<=>![B]:~in(B,A)),input).
fof(d1_xboole_0_0,plain,![A]:(A=empty_set
   |~![B]:~in(B,A)),inference(orientation, [status(thm)], [d1_xboole_0]))
fof(d1_xboole_0_1,plain,![A]:(~A=empty_set
   |![B]:~in(B,A)),inference(orientation, [status(thm)], [d1_xboole_0]))
fof(d10_xboole_0,axiom,![A,B]:(A=B<=>(subset(A,B)&subset(B,A))),input).
fof(d10_xboole_0_0,plain,![A,B]:(A=B
   |~(subset(A,B)
   &subset(B,A))),inference(orientation, [status(thm)], [d10_xboole_0]))
fof(d10_xboole_0_1,plain,![A,B]:(~A=B
   |(subset(A,B)
   &subset(B,A))),inference(orientation, [status(thm)], [d10_xboole_0]))
fof(commutativity_k3_xboole_0,axiom,![A,B]:set_intersection2(A,B)=set_intersection2(B,A),input).
fof(commutativity_k3_xboole_0_0,plain,![A,B]:(set_intersection2(A,B)=set_intersection2(B,A)
   |$false),inference(orientation, [status(thm)], [commutativity_k3_xboole_0]))
fof(commutativity_k2_xboole_0,axiom,![A,B]:set_union2(A,B)=set_union2(B,A),input).
fof(commutativity_k2_xboole_0_0,plain,![A,B]:(set_union2(A,B)=set_union2(B,A)
   |$false),inference(orientation, [status(thm)], [commutativity_k2_xboole_0]))
fof(antisymmetry_r2_xboole_0,axiom,![A,B]:(proper_subset(A,B)=>~proper_subset(B,A)),input).
fof(antisymmetry_r2_xboole_0_0,plain,![A,B]:(~proper_subset(A,B)
   |~proper_subset(B,A)),inference(orientation, [status(thm)], [antisymmetry_r2_xboole_0]))
fof(antisymmetry_r2_hidden,axiom,![A,B]:(in(A,B)=>~in(B,A)),input).
fof(antisymmetry_r2_hidden_0,plain,![A,B]:(~in(A,B)
   |~in(B,A)),inference(orientation, [status(thm)], [antisymmetry_r2_hidden]))
fof(def_lhs_atom1, axiom, ![B,A]: lhs_atom1(B,A) <=> ~in(A,B), inference(definition,[],[]))
fof(to_be_clausified_0, plain, ![A,B]: (lhs_atom1(B,A)
   |~in(B,A)), inference(fold_definition,[status(thm)],[antisymmetry_r2_hidden_0, def_lhs_atom1]))
fof(def_lhs_atom2, axiom, ![B,A]: lhs_atom2(B,A) <=> ~proper_subset(A,B), inference(definition,[],[]))
fof(to_be_clausified_1, plain, ![A,B]: (lhs_atom2(B,A)
   |~proper_subset(B,A)), inference(fold_definition,[status(thm)],[antisymmetry_r2_xboole_0_0, def_lhs_atom2]))
fof(def_lhs_atom3, axiom, ![B,A]: lhs_atom3(B,A) <=> set_union2(A,B)=set_union2(B,A), inference(definition,[],[]))
fof(to_be_clausified_2, plain, ![A,B]: (lhs_atom3(B,A)
   |$false), inference(fold_definition,[status(thm)],[commutativity_k2_xboole_0_0, def_lhs_atom3]))
fof(def_lhs_atom4, axiom, ![B,A]: lhs_atom4(B,A) <=> set_intersection2(A,B)=set_intersection2(B,A), inference(definition,[],[]))
fof(to_be_clausified_3, plain, ![A,B]: (lhs_atom4(B,A)
   |$false), inference(fold_definition,[status(thm)],[commutativity_k3_xboole_0_0, def_lhs_atom4]))
fof(def_lhs_atom5, axiom, ![B,A]: lhs_atom5(B,A) <=> ~A=B, inference(definition,[],[]))
fof(to_be_clausified_4, plain, ![A,B]: (lhs_atom5(B,A)
   |(subset(A,B)
   &subset(B,A))), inference(fold_definition,[status(thm)],[d10_xboole_0_1, def_lhs_atom5]))
fof(def_lhs_atom6, axiom, ![B,A]: lhs_atom6(B,A) <=> A=B, inference(definition,[],[]))
fof(to_be_clausified_5, plain, ![A,B]: (lhs_atom6(B,A)
   |~(subset(A,B)
   &subset(B,A))), inference(fold_definition,[status(thm)],[d10_xboole_0_0, def_lhs_atom6]))
fof(def_lhs_atom7, axiom, ![A]: lhs_atom7(A) <=> ~A=empty_set, inference(definition,[],[]))
fof(to_be_clausified_6, plain, ![A]: (lhs_atom7(A)
   |![B]:~in(B,A)), inference(fold_definition,[status(thm)],[d1_xboole_0_1, def_lhs_atom7]))
fof(def_lhs_atom8, axiom, ![A]: lhs_atom8(A) <=> A=empty_set, inference(definition,[],[]))
fof(to_be_clausified_7, plain, ![A]: (lhs_atom8(A)
   |~![B]:~in(B,A)), inference(fold_definition,[status(thm)],[d1_xboole_0_0, def_lhs_atom8]))
fof(def_lhs_atom9, axiom, ![C,B,A]: lhs_atom9(C,B,A) <=> ~C=set_union2(A,B), inference(definition,[],[]))
fof(to_be_clausified_8, plain, ![A,B,C]: (lhs_atom9(C,B,A)
   |![D]:(in(D,C)
   <=>(in(D,A)
   |in(D,B)))), inference(fold_definition,[status(thm)],[d2_xboole_0_1, def_lhs_atom9]))
fof(def_lhs_atom10, axiom, ![C,B,A]: lhs_atom10(C,B,A) <=> C=set_union2(A,B), inference(definition,[],[]))
fof(to_be_clausified_9, plain, ![A,B,C]: (lhs_atom10(C,B,A)
   |~![D]:(in(D,C)
   <=>(in(D,A)
   |in(D,B)))), inference(fold_definition,[status(thm)],[d2_xboole_0_0, def_lhs_atom10]))
fof(def_lhs_atom11, axiom, ![B,A]: lhs_atom11(B,A) <=> ~subset(A,B), inference(definition,[],[]))
fof(to_be_clausified_10, plain, ![A,B]: (lhs_atom11(B,A)
   |![C]:(in(C,A)
   =>in(C,B))), inference(fold_definition,[status(thm)],[d3_tarski_1, def_lhs_atom11]))
fof(def_lhs_atom12, axiom, ![B,A]: lhs_atom12(B,A) <=> subset(A,B), inference(definition,[],[]))
fof(to_be_clausified_11, plain, ![A,B]: (lhs_atom12(B,A)
   |~![C]:(in(C,A)
   =>in(C,B))), inference(fold_definition,[status(thm)],[d3_tarski_0, def_lhs_atom12]))
fof(def_lhs_atom13, axiom, ![C,B,A]: lhs_atom13(C,B,A) <=> ~C=set_intersection2(A,B), inference(definition,[],[]))
fof(to_be_clausified_12, plain, ![A,B,C]: (lhs_atom13(C,B,A)
   |![D]:(in(D,C)
   <=>(in(D,A)
   &in(D,B)))), inference(fold_definition,[status(thm)],[d3_xboole_0_1, def_lhs_atom13]))
fof(def_lhs_atom14, axiom, ![C,B,A]: lhs_atom14(C,B,A) <=> C=set_intersection2(A,B), inference(definition,[],[]))
fof(to_be_clausified_13, plain, ![A,B,C]: (lhs_atom14(C,B,A)
   |~![D]:(in(D,C)
   <=>(in(D,A)
   &in(D,B)))), inference(fold_definition,[status(thm)],[d3_xboole_0_0, def_lhs_atom14]))
fof(def_lhs_atom15, axiom, ![C,B,A]: lhs_atom15(C,B,A) <=> ~C=set_difference(A,B), inference(definition,[],[]))
fof(to_be_clausified_14, plain, ![A,B,C]: (lhs_atom15(C,B,A)
   |![D]:(in(D,C)
   <=>(in(D,A)
   &~in(D,B)))), inference(fold_definition,[status(thm)],[d4_xboole_0_1, def_lhs_atom15]))
fof(def_lhs_atom16, axiom, ![C,B,A]: lhs_atom16(C,B,A) <=> C=set_difference(A,B), inference(definition,[],[]))
fof(to_be_clausified_15, plain, ![A,B,C]: (lhs_atom16(C,B,A)
   |~![D]:(in(D,C)
   <=>(in(D,A)
   &~in(D,B)))), inference(fold_definition,[status(thm)],[d4_xboole_0_0, def_lhs_atom16]))
fof(def_lhs_atom17, axiom, ![B,A]: lhs_atom17(B,A) <=> ~disjoint(A,B), inference(definition,[],[]))
fof(to_be_clausified_16, plain, ![A,B]: (lhs_atom17(B,A)
   |set_intersection2(A,B)=empty_set), inference(fold_definition,[status(thm)],[d7_xboole_0_1, def_lhs_atom17]))
fof(def_lhs_atom18, axiom, ![B,A]: lhs_atom18(B,A) <=> disjoint(A,B), inference(definition,[],[]))
fof(to_be_clausified_17, plain, ![A,B]: (lhs_atom18(B,A)
   |~set_intersection2(A,B)=empty_set), inference(fold_definition,[status(thm)],[d7_xboole_0_0, def_lhs_atom18]))
fof(to_be_clausified_18, plain, ![A,B]: (lhs_atom2(B,A)
   |(subset(A,B)
   &A!=B)), inference(fold_definition,[status(thm)],[d8_xboole_0_1, def_lhs_atom2]))
fof(def_lhs_atom19, axiom, ![B,A]: lhs_atom19(B,A) <=> proper_subset(A,B), inference(definition,[],[]))
fof(to_be_clausified_19, plain, ![A,B]: (lhs_atom19(B,A)
   |~(subset(A,B)
   &A!=B)), inference(fold_definition,[status(thm)],[d8_xboole_0_0, def_lhs_atom19]))
fof(def_lhs_atom20, axiom, ![]: lhs_atom20() <=> $true, inference(definition,[],[]))
fof(to_be_clausified_20, plain, ![]: (lhs_atom20
   |$false), inference(fold_definition,[status(thm)],[dt_k1_xboole_0_0, def_lhs_atom20]))
fof(to_be_clausified_21, plain, ![]: (lhs_atom20
   |$false), inference(fold_definition,[status(thm)],[dt_k2_xboole_0_0, def_lhs_atom20]))
fof(to_be_clausified_22, plain, ![]: (lhs_atom20
   |$false), inference(fold_definition,[status(thm)],[dt_k3_xboole_0_0, def_lhs_atom20]))
fof(to_be_clausified_23, plain, ![]: (lhs_atom20
   |$false), inference(fold_definition,[status(thm)],[dt_k4_xboole_0_0, def_lhs_atom20]))
fof(def_lhs_atom21, axiom, ![]: lhs_atom21() <=> empty(empty_set), inference(definition,[],[]))
fof(to_be_clausified_24, plain, ![]: (lhs_atom21
   |$false), inference(fold_definition,[status(thm)],[fc1_xboole_0_0, def_lhs_atom21]))
fof(def_lhs_atom22, axiom, ![A]: lhs_atom22(A) <=> empty(A), inference(definition,[],[]))
fof(to_be_clausified_25, plain, ![A,B]: (lhs_atom22(A)
   |~empty(set_union2(A,B))), inference(fold_definition,[status(thm)],[fc2_xboole_0_0, def_lhs_atom22]))
fof(to_be_clausified_26, plain, ![A,B]: (lhs_atom22(A)
   |~empty(set_union2(B,A))), inference(fold_definition,[status(thm)],[fc3_xboole_0_0, def_lhs_atom22]))
fof(def_lhs_atom23, axiom, ![A]: lhs_atom23(A) <=> set_union2(A,A)=A, inference(definition,[],[]))
fof(to_be_clausified_27, plain, ![A]: (lhs_atom23(A)
   |$false), inference(fold_definition,[status(thm)],[idempotence_k2_xboole_0_0, def_lhs_atom23]))
fof(def_lhs_atom24, axiom, ![A]: lhs_atom24(A) <=> set_intersection2(A,A)=A, inference(definition,[],[]))
fof(to_be_clausified_28, plain, ![A]: (lhs_atom24(A)
   |$false), inference(fold_definition,[status(thm)],[idempotence_k3_xboole_0_0, def_lhs_atom24]))
fof(def_lhs_atom25, axiom, ![A]: lhs_atom25(A) <=> ~proper_subset(A,A), inference(definition,[],[]))
fof(to_be_clausified_29, plain, ![A]: (lhs_atom25(A)
   |$false), inference(fold_definition,[status(thm)],[irreflexivity_r2_xboole_0_0, def_lhs_atom25]))
fof(def_lhs_atom26, axiom, ![A]: lhs_atom26(A) <=> subset(A,A), inference(definition,[],[]))
fof(to_be_clausified_30, plain, ![A]: (lhs_atom26(A)
   |$false), inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0, def_lhs_atom26]))
fof(to_be_clausified_31, plain, ![A,B]: (lhs_atom17(B,A)
   |disjoint(B,A)), inference(fold_definition,[status(thm)],[symmetry_r1_xboole_0_0, def_lhs_atom17]))
fof(def_lhs_atom27, axiom, ![A]: lhs_atom27(A) <=> set_union2(A,empty_set)=A, inference(definition,[],[]))
fof(to_be_clausified_32, plain, ![A]: (lhs_atom27(A)
   |$false), inference(fold_definition,[status(thm)],[t1_boole_0, def_lhs_atom27]))
fof(def_lhs_atom28, axiom, ![A]: lhs_atom28(A) <=> set_intersection2(A,empty_set)=empty_set, inference(definition,[],[]))
fof(to_be_clausified_33, plain, ![A]: (lhs_atom28(A)
   |$false), inference(fold_definition,[status(thm)],[t2_boole_0, def_lhs_atom28]))
fof(to_be_clausified_34, plain, ![A,B]: (lhs_atom6(B,A)
   |~![C]:(in(C,A)
   <=>in(C,B))), inference(fold_definition,[status(thm)],[t2_tarski_0, def_lhs_atom6]))
fof(def_lhs_atom29, axiom, ![A]: lhs_atom29(A) <=> set_difference(A,empty_set)=A, inference(definition,[],[]))
fof(to_be_clausified_35, plain, ![A]: (lhs_atom29(A)
   |$false), inference(fold_definition,[status(thm)],[t3_boole_0, def_lhs_atom29]))
fof(def_lhs_atom30, axiom, ![A]: lhs_atom30(A) <=> set_difference(empty_set,A)=empty_set, inference(definition,[],[]))
fof(to_be_clausified_36, plain, ![A]: (lhs_atom30(A)
   |$false), inference(fold_definition,[status(thm)],[t4_boole_0, def_lhs_atom30]))
fof(def_lhs_atom31, axiom, ![A]: lhs_atom31(A) <=> ~empty(A), inference(definition,[],[]))
fof(to_be_clausified_37, plain, ![A]: (lhs_atom31(A)
   |A=empty_set), inference(fold_definition,[status(thm)],[t6_boole_0, def_lhs_atom31]))
# Start CNF derivation
fof(c_0_0, axiom, (![X3]:![X1]:![X2]:(lhs_atom14(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1)))))), file('', to_be_clausified_13)).
fof(c_0_1, axiom, (![X3]:![X1]:![X2]:(lhs_atom16(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&~(in(X4,X1))))))), file('', to_be_clausified_15)).
fof(c_0_2, axiom, (![X3]:![X1]:![X2]:(lhs_atom10(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1)))))), file('', to_be_clausified_9)).
fof(c_0_3, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~(![X3]:(in(X3,X2)<=>in(X3,X1))))), file('', to_be_clausified_34)).
fof(c_0_4, axiom, (![X3]:![X1]:![X2]:(lhs_atom13(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1))))), file('', to_be_clausified_12)).
fof(c_0_5, axiom, (![X3]:![X1]:![X2]:(lhs_atom15(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&~(in(X4,X1)))))), file('', to_be_clausified_14)).
fof(c_0_6, axiom, (![X3]:![X1]:![X2]:(lhs_atom9(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1))))), file('', to_be_clausified_8)).
fof(c_0_7, axiom, (![X1]:![X2]:(lhs_atom12(X1,X2)|~(![X3]:(in(X3,X2)=>in(X3,X1))))), file('', to_be_clausified_11)).
fof(c_0_8, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~((subset(X2,X1)&subset(X1,X2))))), file('', to_be_clausified_5)).
fof(c_0_9, axiom, (![X1]:![X2]:(lhs_atom22(X2)|~(empty(set_union2(X1,X2))))), file('', to_be_clausified_26)).
fof(c_0_10, axiom, (![X1]:![X2]:(lhs_atom22(X2)|~(empty(set_union2(X2,X1))))), file('', to_be_clausified_25)).
fof(c_0_11, axiom, (![X1]:![X2]:(lhs_atom11(X1,X2)|![X3]:(in(X3,X2)=>in(X3,X1)))), file('', to_be_clausified_10)).
fof(c_0_12, axiom, (![X1]:![X2]:(lhs_atom19(X1,X2)|~((subset(X2,X1)&X2!=X1)))), file('', to_be_clausified_19)).
fof(c_0_13, axiom, (![X1]:![X2]:(lhs_atom18(X1,X2)|~(set_intersection2(X2,X1)=empty_set))), file('', to_be_clausified_17)).
fof(c_0_14, axiom, (![X1]:![X2]:(lhs_atom2(X1,X2)|~(proper_subset(X1,X2)))), file('', to_be_clausified_1)).
fof(c_0_15, axiom, (![X1]:![X2]:(lhs_atom1(X1,X2)|~(in(X1,X2)))), file('', to_be_clausified_0)).
fof(c_0_16, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|disjoint(X1,X2))), file('', to_be_clausified_31)).
fof(c_0_17, axiom, (![X1]:![X2]:(lhs_atom2(X1,X2)|(subset(X2,X1)&X2!=X1))), file('', to_be_clausified_18)).
fof(c_0_18, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|set_intersection2(X2,X1)=empty_set)), file('', to_be_clausified_16)).
fof(c_0_19, axiom, (![X1]:![X2]:(lhs_atom5(X1,X2)|(subset(X2,X1)&subset(X1,X2)))), file('', to_be_clausified_4)).
fof(c_0_20, axiom, (![X2]:(lhs_atom7(X2)|![X1]:~(in(X1,X2)))), file('', to_be_clausified_6)).
fof(c_0_21, axiom, (![X2]:(lhs_atom8(X2)|~(![X1]:~(in(X1,X2))))), file('', to_be_clausified_7)).
fof(c_0_22, axiom, (![X1]:![X2]:(lhs_atom4(X1,X2)|~$true)), file('', to_be_clausified_3)).
fof(c_0_23, axiom, (![X1]:![X2]:(lhs_atom3(X1,X2)|~$true)), file('', to_be_clausified_2)).
fof(c_0_24, axiom, (![X2]:(lhs_atom31(X2)|X2=empty_set)), file('', to_be_clausified_37)).
fof(c_0_25, axiom, (![X2]:(lhs_atom30(X2)|~$true)), file('', to_be_clausified_36)).
fof(c_0_26, axiom, (![X2]:(lhs_atom29(X2)|~$true)), file('', to_be_clausified_35)).
fof(c_0_27, axiom, (![X2]:(lhs_atom28(X2)|~$true)), file('', to_be_clausified_33)).
fof(c_0_28, axiom, (![X2]:(lhs_atom27(X2)|~$true)), file('', to_be_clausified_32)).
fof(c_0_29, axiom, (![X2]:(lhs_atom26(X2)|~$true)), file('', to_be_clausified_30)).
fof(c_0_30, axiom, (![X2]:(lhs_atom25(X2)|~$true)), file('', to_be_clausified_29)).
fof(c_0_31, axiom, (![X2]:(lhs_atom24(X2)|~$true)), file('', to_be_clausified_28)).
fof(c_0_32, axiom, (![X2]:(lhs_atom23(X2)|~$true)), file('', to_be_clausified_27)).
fof(c_0_33, axiom, ((lhs_atom21|~$true)), file('', to_be_clausified_24)).
fof(c_0_34, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_23)).
fof(c_0_35, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_22)).
fof(c_0_36, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_21)).
fof(c_0_37, axiom, ((lhs_atom20|~$true)), file('', to_be_clausified_20)).
fof(c_0_38, axiom, (![X3]:![X1]:![X2]:(lhs_atom14(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1)))))), c_0_0).
fof(c_0_39, plain, (![X3]:![X1]:![X2]:(lhs_atom16(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)&~in(X4,X1)))))), inference(fof_simplification,[status(thm)],[c_0_1])).
fof(c_0_40, axiom, (![X3]:![X1]:![X2]:(lhs_atom10(X3,X1,X2)|~(![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1)))))), c_0_2).
fof(c_0_41, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~(![X3]:(in(X3,X2)<=>in(X3,X1))))), c_0_3).
fof(c_0_42, axiom, (![X3]:![X1]:![X2]:(lhs_atom13(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&in(X4,X1))))), c_0_4).
fof(c_0_43, plain, (![X3]:![X1]:![X2]:(lhs_atom15(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)&~in(X4,X1))))), inference(fof_simplification,[status(thm)],[c_0_5])).
fof(c_0_44, axiom, (![X3]:![X1]:![X2]:(lhs_atom9(X3,X1,X2)|![X4]:(in(X4,X3)<=>(in(X4,X2)|in(X4,X1))))), c_0_6).
fof(c_0_45, axiom, (![X1]:![X2]:(lhs_atom12(X1,X2)|~(![X3]:(in(X3,X2)=>in(X3,X1))))), c_0_7).
fof(c_0_46, axiom, (![X1]:![X2]:(lhs_atom6(X1,X2)|~((subset(X2,X1)&subset(X1,X2))))), c_0_8).
fof(c_0_47, plain, (![X1]:![X2]:(lhs_atom22(X2)|~empty(set_union2(X1,X2)))), inference(fof_simplification,[status(thm)],[c_0_9])).
fof(c_0_48, plain, (![X1]:![X2]:(lhs_atom22(X2)|~empty(set_union2(X2,X1)))), inference(fof_simplification,[status(thm)],[c_0_10])).
fof(c_0_49, axiom, (![X1]:![X2]:(lhs_atom11(X1,X2)|![X3]:(in(X3,X2)=>in(X3,X1)))), c_0_11).
fof(c_0_50, axiom, (![X1]:![X2]:(lhs_atom19(X1,X2)|~((subset(X2,X1)&X2!=X1)))), c_0_12).
fof(c_0_51, plain, (![X1]:![X2]:(lhs_atom18(X1,X2)|set_intersection2(X2,X1)!=empty_set)), inference(fof_simplification,[status(thm)],[c_0_13])).
fof(c_0_52, plain, (![X1]:![X2]:(lhs_atom2(X1,X2)|~proper_subset(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_14])).
fof(c_0_53, plain, (![X1]:![X2]:(lhs_atom1(X1,X2)|~in(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_15])).
fof(c_0_54, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|disjoint(X1,X2))), c_0_16).
fof(c_0_55, axiom, (![X1]:![X2]:(lhs_atom2(X1,X2)|(subset(X2,X1)&X2!=X1))), c_0_17).
fof(c_0_56, axiom, (![X1]:![X2]:(lhs_atom17(X1,X2)|set_intersection2(X2,X1)=empty_set)), c_0_18).
fof(c_0_57, axiom, (![X1]:![X2]:(lhs_atom5(X1,X2)|(subset(X2,X1)&subset(X1,X2)))), c_0_19).
fof(c_0_58, plain, (![X2]:(lhs_atom7(X2)|![X1]:~in(X1,X2))), inference(fof_simplification,[status(thm)],[c_0_20])).
fof(c_0_59, plain, (![X2]:(lhs_atom8(X2)|~(![X1]:~in(X1,X2)))), inference(fof_simplification,[status(thm)],[c_0_21])).
fof(c_0_60, plain, (![X1]:![X2]:lhs_atom4(X1,X2)), inference(fof_simplification,[status(thm)],[c_0_22])).
fof(c_0_61, plain, (![X1]:![X2]:lhs_atom3(X1,X2)), inference(fof_simplification,[status(thm)],[c_0_23])).
fof(c_0_62, axiom, (![X2]:(lhs_atom31(X2)|X2=empty_set)), c_0_24).
fof(c_0_63, plain, (![X2]:lhs_atom30(X2)), inference(fof_simplification,[status(thm)],[c_0_25])).
fof(c_0_64, plain, (![X2]:lhs_atom29(X2)), inference(fof_simplification,[status(thm)],[c_0_26])).
fof(c_0_65, plain, (![X2]:lhs_atom28(X2)), inference(fof_simplification,[status(thm)],[c_0_27])).
fof(c_0_66, plain, (![X2]:lhs_atom27(X2)), inference(fof_simplification,[status(thm)],[c_0_28])).
fof(c_0_67, plain, (![X2]:lhs_atom26(X2)), inference(fof_simplification,[status(thm)],[c_0_29])).
fof(c_0_68, plain, (![X2]:lhs_atom25(X2)), inference(fof_simplification,[status(thm)],[c_0_30])).
fof(c_0_69, plain, (![X2]:lhs_atom24(X2)), inference(fof_simplification,[status(thm)],[c_0_31])).
fof(c_0_70, plain, (![X2]:lhs_atom23(X2)), inference(fof_simplification,[status(thm)],[c_0_32])).
fof(c_0_71, plain, (lhs_atom21), inference(fof_simplification,[status(thm)],[c_0_33])).
fof(c_0_72, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_34])).
fof(c_0_73, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_35])).
fof(c_0_74, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_36])).
fof(c_0_75, plain, (lhs_atom20), inference(fof_simplification,[status(thm)],[c_0_37])).
fof(c_0_76, plain, (![X5]:![X6]:![X7]:(((~in(esk4_3(X5,X6,X7),X5)|(~in(esk4_3(X5,X6,X7),X7)|~in(esk4_3(X5,X6,X7),X6)))|lhs_atom14(X5,X6,X7))&(((in(esk4_3(X5,X6,X7),X7)|in(esk4_3(X5,X6,X7),X5))|lhs_atom14(X5,X6,X7))&((in(esk4_3(X5,X6,X7),X6)|in(esk4_3(X5,X6,X7),X5))|lhs_atom14(X5,X6,X7))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])).
fof(c_0_77, plain, (![X5]:![X6]:![X7]:(((~in(esk5_3(X5,X6,X7),X5)|(~in(esk5_3(X5,X6,X7),X7)|in(esk5_3(X5,X6,X7),X6)))|lhs_atom16(X5,X6,X7))&(((in(esk5_3(X5,X6,X7),X7)|in(esk5_3(X5,X6,X7),X5))|lhs_atom16(X5,X6,X7))&((~in(esk5_3(X5,X6,X7),X6)|in(esk5_3(X5,X6,X7),X5))|lhs_atom16(X5,X6,X7))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])).
fof(c_0_78, plain, (![X5]:![X6]:![X7]:((((~in(esk2_3(X5,X6,X7),X7)|~in(esk2_3(X5,X6,X7),X5))|lhs_atom10(X5,X6,X7))&((~in(esk2_3(X5,X6,X7),X6)|~in(esk2_3(X5,X6,X7),X5))|lhs_atom10(X5,X6,X7)))&((in(esk2_3(X5,X6,X7),X5)|(in(esk2_3(X5,X6,X7),X7)|in(esk2_3(X5,X6,X7),X6)))|lhs_atom10(X5,X6,X7)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])).
fof(c_0_79, plain, (![X4]:![X5]:(((~in(esk6_2(X4,X5),X5)|~in(esk6_2(X4,X5),X4))|lhs_atom6(X4,X5))&((in(esk6_2(X4,X5),X5)|in(esk6_2(X4,X5),X4))|lhs_atom6(X4,X5)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])).
fof(c_0_80, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:((((in(X8,X7)|~in(X8,X5))|lhs_atom13(X5,X6,X7))&((in(X8,X6)|~in(X8,X5))|lhs_atom13(X5,X6,X7)))&(((~in(X9,X7)|~in(X9,X6))|in(X9,X5))|lhs_atom13(X5,X6,X7)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])])).
fof(c_0_81, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:((((in(X8,X7)|~in(X8,X5))|lhs_atom15(X5,X6,X7))&((~in(X8,X6)|~in(X8,X5))|lhs_atom15(X5,X6,X7)))&(((~in(X9,X7)|in(X9,X6))|in(X9,X5))|lhs_atom15(X5,X6,X7)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])])).
fof(c_0_82, plain, (![X5]:![X6]:![X7]:![X8]:![X9]:(((~in(X8,X5)|(in(X8,X7)|in(X8,X6)))|lhs_atom9(X5,X6,X7))&(((~in(X9,X7)|in(X9,X5))|lhs_atom9(X5,X6,X7))&((~in(X9,X6)|in(X9,X5))|lhs_atom9(X5,X6,X7))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])])).
fof(c_0_83, plain, (![X4]:![X5]:((in(esk3_2(X4,X5),X5)|lhs_atom12(X4,X5))&(~in(esk3_2(X4,X5),X4)|lhs_atom12(X4,X5)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])).
fof(c_0_84, plain, (![X3]:![X4]:(lhs_atom6(X3,X4)|(~subset(X4,X3)|~subset(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])).
fof(c_0_85, plain, (![X3]:![X4]:(lhs_atom22(X4)|~empty(set_union2(X3,X4)))), inference(variable_rename,[status(thm)],[c_0_47])).
fof(c_0_86, plain, (![X3]:![X4]:(lhs_atom22(X4)|~empty(set_union2(X4,X3)))), inference(variable_rename,[status(thm)],[c_0_48])).
fof(c_0_87, plain, (![X4]:![X5]:![X6]:(lhs_atom11(X4,X5)|(~in(X6,X5)|in(X6,X4)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])).
fof(c_0_88, plain, (![X3]:![X4]:(lhs_atom19(X3,X4)|(~subset(X4,X3)|X4=X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])).
fof(c_0_89, plain, (![X3]:![X4]:(lhs_atom18(X3,X4)|set_intersection2(X4,X3)!=empty_set)), inference(variable_rename,[status(thm)],[c_0_51])).
fof(c_0_90, plain, (![X3]:![X4]:(lhs_atom2(X3,X4)|~proper_subset(X3,X4))), inference(variable_rename,[status(thm)],[c_0_52])).
fof(c_0_91, plain, (![X3]:![X4]:(lhs_atom1(X3,X4)|~in(X3,X4))), inference(variable_rename,[status(thm)],[c_0_53])).
fof(c_0_92, plain, (![X3]:![X4]:(lhs_atom17(X3,X4)|disjoint(X3,X4))), inference(variable_rename,[status(thm)],[c_0_54])).
fof(c_0_93, plain, (![X3]:![X4]:((subset(X4,X3)|lhs_atom2(X3,X4))&(X4!=X3|lhs_atom2(X3,X4)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_55])])).
fof(c_0_94, plain, (![X3]:![X4]:(lhs_atom17(X3,X4)|set_intersection2(X4,X3)=empty_set)), inference(variable_rename,[status(thm)],[c_0_56])).
fof(c_0_95, plain, (![X3]:![X4]:((subset(X4,X3)|lhs_atom5(X3,X4))&(subset(X3,X4)|lhs_atom5(X3,X4)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_57])])).
fof(c_0_96, plain, (![X3]:![X4]:(lhs_atom7(X3)|~in(X4,X3))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_58])])).
fof(c_0_97, plain, (![X3]:(lhs_atom8(X3)|in(esk1_1(X3),X3))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])).
fof(c_0_98, plain, (![X3]:![X4]:lhs_atom4(X3,X4)), inference(variable_rename,[status(thm)],[c_0_60])).
fof(c_0_99, plain, (![X3]:![X4]:lhs_atom3(X3,X4)), inference(variable_rename,[status(thm)],[c_0_61])).
fof(c_0_100, plain, (![X3]:(lhs_atom31(X3)|X3=empty_set)), inference(variable_rename,[status(thm)],[c_0_62])).
fof(c_0_101, plain, (![X3]:lhs_atom30(X3)), inference(variable_rename,[status(thm)],[c_0_63])).
fof(c_0_102, plain, (![X3]:lhs_atom29(X3)), inference(variable_rename,[status(thm)],[c_0_64])).
fof(c_0_103, plain, (![X3]:lhs_atom28(X3)), inference(variable_rename,[status(thm)],[c_0_65])).
fof(c_0_104, plain, (![X3]:lhs_atom27(X3)), inference(variable_rename,[status(thm)],[c_0_66])).
fof(c_0_105, plain, (![X3]:lhs_atom26(X3)), inference(variable_rename,[status(thm)],[c_0_67])).
fof(c_0_106, plain, (![X3]:lhs_atom25(X3)), inference(variable_rename,[status(thm)],[c_0_68])).
fof(c_0_107, plain, (![X3]:lhs_atom24(X3)), inference(variable_rename,[status(thm)],[c_0_69])).
fof(c_0_108, plain, (![X3]:lhs_atom23(X3)), inference(variable_rename,[status(thm)],[c_0_70])).
fof(c_0_109, plain, (lhs_atom21), c_0_71).
fof(c_0_110, plain, (lhs_atom20), c_0_72).
fof(c_0_111, plain, (lhs_atom20), c_0_73).
fof(c_0_112, plain, (lhs_atom20), c_0_74).
fof(c_0_113, plain, (lhs_atom20), c_0_75).
cnf(c_0_114,plain,(lhs_atom14(X1,X2,X3)|~in(esk4_3(X1,X2,X3),X2)|~in(esk4_3(X1,X2,X3),X3)|~in(esk4_3(X1,X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_115,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X2)|~in(esk5_3(X1,X2,X3),X3)|~in(esk5_3(X1,X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_77])).
cnf(c_0_116,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_78])).
cnf(c_0_117,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_78])).
cnf(c_0_118,plain,(lhs_atom10(X1,X2,X3)|in(esk2_3(X1,X2,X3),X2)|in(esk2_3(X1,X2,X3),X3)|in(esk2_3(X1,X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_78])).
cnf(c_0_119,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|~in(esk5_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_77])).
cnf(c_0_120,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|in(esk5_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_77])).
cnf(c_0_121,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_122,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_123,plain,(lhs_atom6(X1,X2)|~in(esk6_2(X1,X2),X1)|~in(esk6_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_79])).
cnf(c_0_124,plain,(lhs_atom13(X1,X2,X3)|in(X4,X1)|~in(X4,X2)|~in(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_125,plain,(lhs_atom15(X1,X2,X3)|in(X4,X1)|in(X4,X2)|~in(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_126,plain,(lhs_atom9(X1,X2,X3)|in(X4,X2)|in(X4,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_82])).
cnf(c_0_127,plain,(lhs_atom15(X1,X2,X3)|~in(X4,X1)|~in(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_128,plain,(lhs_atom6(X1,X2)|in(esk6_2(X1,X2),X1)|in(esk6_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_79])).
cnf(c_0_129,plain,(lhs_atom15(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_130,plain,(lhs_atom13(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_131,plain,(lhs_atom13(X1,X2,X3)|in(X4,X2)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_132,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_82])).
cnf(c_0_133,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_82])).
cnf(c_0_134,plain,(lhs_atom12(X1,X2)|~in(esk3_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_135,plain,(lhs_atom6(X1,X2)|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_84])).
cnf(c_0_136,plain,(lhs_atom12(X1,X2)|in(esk3_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_137,plain,(lhs_atom22(X2)|~empty(set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_85])).
cnf(c_0_138,plain,(lhs_atom22(X1)|~empty(set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_86])).
cnf(c_0_139,plain,(in(X1,X2)|lhs_atom11(X2,X3)|~in(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_87])).
cnf(c_0_140,plain,(X1=X2|lhs_atom19(X2,X1)|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_88])).
cnf(c_0_141,plain,(lhs_atom18(X2,X1)|set_intersection2(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_89])).
cnf(c_0_142,plain,(lhs_atom2(X1,X2)|~proper_subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_90])).
cnf(c_0_143,plain,(lhs_atom1(X1,X2)|~in(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_91])).
cnf(c_0_144,plain,(disjoint(X1,X2)|lhs_atom17(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_92])).
cnf(c_0_145,plain,(lhs_atom2(X1,X2)|subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_93])).
cnf(c_0_146,plain,(set_intersection2(X1,X2)=empty_set|lhs_atom17(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_94])).
cnf(c_0_147,plain,(lhs_atom5(X1,X2)|subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_95])).
cnf(c_0_148,plain,(lhs_atom5(X1,X2)|subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_95])).
cnf(c_0_149,plain,(lhs_atom7(X2)|~in(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_96])).
cnf(c_0_150,plain,(in(esk1_1(X1),X1)|lhs_atom8(X1)), inference(split_conjunct,[status(thm)],[c_0_97])).
cnf(c_0_151,plain,(lhs_atom2(X1,X2)|X2!=X1), inference(split_conjunct,[status(thm)],[c_0_93])).
cnf(c_0_152,plain,(lhs_atom4(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_98])).
cnf(c_0_153,plain,(lhs_atom3(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_99])).
cnf(c_0_154,plain,(X1=empty_set|lhs_atom31(X1)), inference(split_conjunct,[status(thm)],[c_0_100])).
cnf(c_0_155,plain,(lhs_atom30(X1)), inference(split_conjunct,[status(thm)],[c_0_101])).
cnf(c_0_156,plain,(lhs_atom29(X1)), inference(split_conjunct,[status(thm)],[c_0_102])).
cnf(c_0_157,plain,(lhs_atom28(X1)), inference(split_conjunct,[status(thm)],[c_0_103])).
cnf(c_0_158,plain,(lhs_atom27(X1)), inference(split_conjunct,[status(thm)],[c_0_104])).
cnf(c_0_159,plain,(lhs_atom26(X1)), inference(split_conjunct,[status(thm)],[c_0_105])).
cnf(c_0_160,plain,(lhs_atom25(X1)), inference(split_conjunct,[status(thm)],[c_0_106])).
cnf(c_0_161,plain,(lhs_atom24(X1)), inference(split_conjunct,[status(thm)],[c_0_107])).
cnf(c_0_162,plain,(lhs_atom23(X1)), inference(split_conjunct,[status(thm)],[c_0_108])).
cnf(c_0_163,plain,(lhs_atom21), inference(split_conjunct,[status(thm)],[c_0_109])).
cnf(c_0_164,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_110])).
cnf(c_0_165,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_111])).
cnf(c_0_166,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_112])).
cnf(c_0_167,plain,(lhs_atom20), inference(split_conjunct,[status(thm)],[c_0_113])).
cnf(c_0_168,plain,(lhs_atom14(X1,X2,X3)|~in(esk4_3(X1,X2,X3),X2)|~in(esk4_3(X1,X2,X3),X3)|~in(esk4_3(X1,X2,X3),X1)), c_0_114, ['final']).
cnf(c_0_169,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X2)|~in(esk5_3(X1,X2,X3),X3)|~in(esk5_3(X1,X2,X3),X1)), c_0_115, ['final']).
cnf(c_0_170,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X3)), c_0_116, ['final']).
cnf(c_0_171,plain,(lhs_atom10(X1,X2,X3)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X2)), c_0_117, ['final']).
cnf(c_0_172,plain,(lhs_atom10(X1,X2,X3)|in(esk2_3(X1,X2,X3),X2)|in(esk2_3(X1,X2,X3),X3)|in(esk2_3(X1,X2,X3),X1)), c_0_118, ['final']).
cnf(c_0_173,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|~in(esk5_3(X1,X2,X3),X2)), c_0_119, ['final']).
cnf(c_0_174,plain,(lhs_atom16(X1,X2,X3)|in(esk5_3(X1,X2,X3),X1)|in(esk5_3(X1,X2,X3),X3)), c_0_120, ['final']).
cnf(c_0_175,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X3)), c_0_121, ['final']).
cnf(c_0_176,plain,(lhs_atom14(X1,X2,X3)|in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X2)), c_0_122, ['final']).
cnf(c_0_177,plain,(lhs_atom6(X1,X2)|~in(esk6_2(X1,X2),X1)|~in(esk6_2(X1,X2),X2)), c_0_123, ['final']).
cnf(c_0_178,plain,(lhs_atom13(X1,X2,X3)|in(X4,X1)|~in(X4,X2)|~in(X4,X3)), c_0_124, ['final']).
cnf(c_0_179,plain,(lhs_atom15(X1,X2,X3)|in(X4,X1)|in(X4,X2)|~in(X4,X3)), c_0_125, ['final']).
cnf(c_0_180,plain,(lhs_atom9(X1,X2,X3)|in(X4,X2)|in(X4,X3)|~in(X4,X1)), c_0_126, ['final']).
cnf(c_0_181,plain,(lhs_atom15(X1,X2,X3)|~in(X4,X1)|~in(X4,X2)), c_0_127, ['final']).
cnf(c_0_182,plain,(lhs_atom6(X1,X2)|in(esk6_2(X1,X2),X1)|in(esk6_2(X1,X2),X2)), c_0_128, ['final']).
cnf(c_0_183,plain,(lhs_atom15(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), c_0_129, ['final']).
cnf(c_0_184,plain,(lhs_atom13(X1,X2,X3)|in(X4,X3)|~in(X4,X1)), c_0_130, ['final']).
cnf(c_0_185,plain,(lhs_atom13(X1,X2,X3)|in(X4,X2)|~in(X4,X1)), c_0_131, ['final']).
cnf(c_0_186,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X3)), c_0_132, ['final']).
cnf(c_0_187,plain,(lhs_atom9(X1,X2,X3)|in(X4,X1)|~in(X4,X2)), c_0_133, ['final']).
cnf(c_0_188,plain,(lhs_atom12(X1,X2)|~in(esk3_2(X1,X2),X1)), c_0_134, ['final']).
cnf(c_0_189,plain,(lhs_atom6(X1,X2)|~subset(X1,X2)|~subset(X2,X1)), c_0_135, ['final']).
cnf(c_0_190,plain,(lhs_atom12(X1,X2)|in(esk3_2(X1,X2),X2)), c_0_136, ['final']).
cnf(c_0_191,plain,(lhs_atom22(X2)|~empty(set_union2(X1,X2))), c_0_137, ['final']).
cnf(c_0_192,plain,(lhs_atom22(X1)|~empty(set_union2(X1,X2))), c_0_138, ['final']).
cnf(c_0_193,plain,(in(X1,X2)|lhs_atom11(X2,X3)|~in(X1,X3)), c_0_139, ['final']).
cnf(c_0_194,plain,(X1=X2|lhs_atom19(X2,X1)|~subset(X1,X2)), c_0_140, ['final']).
cnf(c_0_195,plain,(lhs_atom18(X2,X1)|set_intersection2(X1,X2)!=empty_set), c_0_141, ['final']).
cnf(c_0_196,plain,(lhs_atom2(X1,X2)|~proper_subset(X1,X2)), c_0_142, ['final']).
cnf(c_0_197,plain,(lhs_atom1(X1,X2)|~in(X1,X2)), c_0_143, ['final']).
cnf(c_0_198,plain,(disjoint(X1,X2)|lhs_atom17(X1,X2)), c_0_144, ['final']).
cnf(c_0_199,plain,(lhs_atom2(X1,X2)|subset(X2,X1)), c_0_145, ['final']).
cnf(c_0_200,plain,(set_intersection2(X1,X2)=empty_set|lhs_atom17(X2,X1)), c_0_146, ['final']).
cnf(c_0_201,plain,(lhs_atom5(X1,X2)|subset(X2,X1)), c_0_147, ['final']).
cnf(c_0_202,plain,(lhs_atom5(X1,X2)|subset(X1,X2)), c_0_148, ['final']).
cnf(c_0_203,plain,(lhs_atom7(X2)|~in(X1,X2)), c_0_149, ['final']).
cnf(c_0_204,plain,(in(esk1_1(X1),X1)|lhs_atom8(X1)), c_0_150, ['final']).
cnf(c_0_205,plain,(lhs_atom2(X1,X2)|X2!=X1), c_0_151, ['final']).
cnf(c_0_206,plain,(lhs_atom4(X1,X2)), c_0_152, ['final']).
cnf(c_0_207,plain,(lhs_atom3(X1,X2)), c_0_153, ['final']).
cnf(c_0_208,plain,(X1=empty_set|lhs_atom31(X1)), c_0_154, ['final']).
cnf(c_0_209,plain,(lhs_atom30(X1)), c_0_155, ['final']).
cnf(c_0_210,plain,(lhs_atom29(X1)), c_0_156, ['final']).
cnf(c_0_211,plain,(lhs_atom28(X1)), c_0_157, ['final']).
cnf(c_0_212,plain,(lhs_atom27(X1)), c_0_158, ['final']).
cnf(c_0_213,plain,(lhs_atom26(X1)), c_0_159, ['final']).
cnf(c_0_214,plain,(lhs_atom25(X1)), c_0_160, ['final']).
cnf(c_0_215,plain,(lhs_atom24(X1)), c_0_161, ['final']).
cnf(c_0_216,plain,(lhs_atom23(X1)), c_0_162, ['final']).
cnf(c_0_217,plain,(lhs_atom21), c_0_163, ['final']).
cnf(c_0_218,plain,(lhs_atom20), c_0_164, ['final']).
cnf(c_0_219,plain,(lhs_atom20), c_0_165, ['final']).
cnf(c_0_220,plain,(lhs_atom20), c_0_166, ['final']).
cnf(c_0_221,plain,(lhs_atom20), c_0_167, ['final']).
# End CNF derivation
cnf(c_0_168_0,axiom,X1=set_intersection2(X3,X2)|~in(sk1_esk4_3(X1,X2,X3),X2)|~in(sk1_esk4_3(X1,X2,X3),X3)|~in(sk1_esk4_3(X1,X2,X3),X1),inference(unfold_definition, [status(thm)], [c_0_168, def_lhs_atom14])).
cnf(c_0_169_0,axiom,X1=set_difference(X3,X2)|in(sk1_esk5_3(X1,X2,X3),X2)|~in(sk1_esk5_3(X1,X2,X3),X3)|~in(sk1_esk5_3(X1,X2,X3),X1),inference(unfold_definition, [status(thm)], [c_0_169, def_lhs_atom16])).
cnf(c_0_170_0,axiom,X1=set_union2(X3,X2)|~in(sk1_esk2_3(X1,X2,X3),X1)|~in(sk1_esk2_3(X1,X2,X3),X3),inference(unfold_definition, [status(thm)], [c_0_170, def_lhs_atom10])).
cnf(c_0_171_0,axiom,X1=set_union2(X3,X2)|~in(sk1_esk2_3(X1,X2,X3),X1)|~in(sk1_esk2_3(X1,X2,X3),X2),inference(unfold_definition, [status(thm)], [c_0_171, def_lhs_atom10])).
cnf(c_0_172_0,axiom,X1=set_union2(X3,X2)|in(sk1_esk2_3(X1,X2,X3),X2)|in(sk1_esk2_3(X1,X2,X3),X3)|in(sk1_esk2_3(X1,X2,X3),X1),inference(unfold_definition, [status(thm)], [c_0_172, def_lhs_atom10])).
cnf(c_0_173_0,axiom,X1=set_difference(X3,X2)|in(sk1_esk5_3(X1,X2,X3),X1)|~in(sk1_esk5_3(X1,X2,X3),X2),inference(unfold_definition, [status(thm)], [c_0_173, def_lhs_atom16])).
cnf(c_0_174_0,axiom,X1=set_difference(X3,X2)|in(sk1_esk5_3(X1,X2,X3),X1)|in(sk1_esk5_3(X1,X2,X3),X3),inference(unfold_definition, [status(thm)], [c_0_174, def_lhs_atom16])).
cnf(c_0_175_0,axiom,X1=set_intersection2(X3,X2)|in(sk1_esk4_3(X1,X2,X3),X1)|in(sk1_esk4_3(X1,X2,X3),X3),inference(unfold_definition, [status(thm)], [c_0_175, def_lhs_atom14])).
cnf(c_0_176_0,axiom,X1=set_intersection2(X3,X2)|in(sk1_esk4_3(X1,X2,X3),X1)|in(sk1_esk4_3(X1,X2,X3),X2),inference(unfold_definition, [status(thm)], [c_0_176, def_lhs_atom14])).
cnf(c_0_177_0,axiom,X2=X1|~in(sk1_esk6_2(X1,X2),X1)|~in(sk1_esk6_2(X1,X2),X2),inference(unfold_definition, [status(thm)], [c_0_177, def_lhs_atom6])).
cnf(c_0_178_0,axiom,~X1=set_intersection2(X3,X2)|in(X4,X1)|~in(X4,X2)|~in(X4,X3),inference(unfold_definition, [status(thm)], [c_0_178, def_lhs_atom13])).
cnf(c_0_179_0,axiom,~X1=set_difference(X3,X2)|in(X4,X1)|in(X4,X2)|~in(X4,X3),inference(unfold_definition, [status(thm)], [c_0_179, def_lhs_atom15])).
cnf(c_0_180_0,axiom,~X1=set_union2(X3,X2)|in(X4,X2)|in(X4,X3)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_180, def_lhs_atom9])).
cnf(c_0_181_0,axiom,~X1=set_difference(X3,X2)|~in(X4,X1)|~in(X4,X2),inference(unfold_definition, [status(thm)], [c_0_181, def_lhs_atom15])).
cnf(c_0_182_0,axiom,X2=X1|in(sk1_esk6_2(X1,X2),X1)|in(sk1_esk6_2(X1,X2),X2),inference(unfold_definition, [status(thm)], [c_0_182, def_lhs_atom6])).
cnf(c_0_183_0,axiom,~X1=set_difference(X3,X2)|in(X4,X3)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_183, def_lhs_atom15])).
cnf(c_0_184_0,axiom,~X1=set_intersection2(X3,X2)|in(X4,X3)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_184, def_lhs_atom13])).
cnf(c_0_185_0,axiom,~X1=set_intersection2(X3,X2)|in(X4,X2)|~in(X4,X1),inference(unfold_definition, [status(thm)], [c_0_185, def_lhs_atom13])).
cnf(c_0_186_0,axiom,~X1=set_union2(X3,X2)|in(X4,X1)|~in(X4,X3),inference(unfold_definition, [status(thm)], [c_0_186, def_lhs_atom9])).
cnf(c_0_187_0,axiom,~X1=set_union2(X3,X2)|in(X4,X1)|~in(X4,X2),inference(unfold_definition, [status(thm)], [c_0_187, def_lhs_atom9])).
cnf(c_0_188_0,axiom,subset(X2,X1)|~in(sk1_esk3_2(X1,X2),X1),inference(unfold_definition, [status(thm)], [c_0_188, def_lhs_atom12])).
cnf(c_0_189_0,axiom,X2=X1|~subset(X1,X2)|~subset(X2,X1),inference(unfold_definition, [status(thm)], [c_0_189, def_lhs_atom6])).
cnf(c_0_190_0,axiom,subset(X2,X1)|in(sk1_esk3_2(X1,X2),X2),inference(unfold_definition, [status(thm)], [c_0_190, def_lhs_atom12])).
cnf(c_0_191_0,axiom,empty(X2)|~empty(set_union2(X1,X2)),inference(unfold_definition, [status(thm)], [c_0_191, def_lhs_atom22])).
cnf(c_0_192_0,axiom,empty(X1)|~empty(set_union2(X1,X2)),inference(unfold_definition, [status(thm)], [c_0_192, def_lhs_atom22])).
cnf(c_0_193_0,axiom,~subset(X3,X2)|in(X1,X2)|~in(X1,X3),inference(unfold_definition, [status(thm)], [c_0_193, def_lhs_atom11])).
cnf(c_0_194_0,axiom,proper_subset(X1,X2)|X1=X2|~subset(X1,X2),inference(unfold_definition, [status(thm)], [c_0_194, def_lhs_atom19])).
cnf(c_0_195_0,axiom,disjoint(X1,X2)|set_intersection2(X1,X2)!=empty_set,inference(unfold_definition, [status(thm)], [c_0_195, def_lhs_atom18])).
cnf(c_0_196_0,axiom,~proper_subset(X2,X1)|~proper_subset(X1,X2),inference(unfold_definition, [status(thm)], [c_0_196, def_lhs_atom2])).
cnf(c_0_197_0,axiom,~in(X2,X1)|~in(X1,X2),inference(unfold_definition, [status(thm)], [c_0_197, def_lhs_atom1])).
cnf(c_0_198_0,axiom,~disjoint(X2,X1)|disjoint(X1,X2),inference(unfold_definition, [status(thm)], [c_0_198, def_lhs_atom17])).
cnf(c_0_199_0,axiom,~proper_subset(X2,X1)|subset(X2,X1),inference(unfold_definition, [status(thm)], [c_0_199, def_lhs_atom2])).
cnf(c_0_200_0,axiom,~disjoint(X1,X2)|set_intersection2(X1,X2)=empty_set,inference(unfold_definition, [status(thm)], [c_0_200, def_lhs_atom17])).
cnf(c_0_201_0,axiom,~X2=X1|subset(X2,X1),inference(unfold_definition, [status(thm)], [c_0_201, def_lhs_atom5])).
cnf(c_0_202_0,axiom,~X2=X1|subset(X1,X2),inference(unfold_definition, [status(thm)], [c_0_202, def_lhs_atom5])).
cnf(c_0_203_0,axiom,~X2=empty_set|~in(X1,X2),inference(unfold_definition, [status(thm)], [c_0_203, def_lhs_atom7])).
cnf(c_0_204_0,axiom,X1=empty_set|in(sk1_esk1_1(X1),X1),inference(unfold_definition, [status(thm)], [c_0_204, def_lhs_atom8])).
cnf(c_0_205_0,axiom,~proper_subset(X2,X1)|X2!=X1,inference(unfold_definition, [status(thm)], [c_0_205, def_lhs_atom2])).
cnf(c_0_208_0,axiom,~empty(X1)|X1=empty_set,inference(unfold_definition, [status(thm)], [c_0_208, def_lhs_atom31])).
cnf(c_0_206_0,axiom,set_intersection2(X2,X1)=set_intersection2(X1,X2),inference(unfold_definition, [status(thm)], [c_0_206, def_lhs_atom4])).
cnf(c_0_207_0,axiom,set_union2(X2,X1)=set_union2(X1,X2),inference(unfold_definition, [status(thm)], [c_0_207, def_lhs_atom3])).
cnf(c_0_209_0,axiom,set_difference(empty_set,X1)=empty_set,inference(unfold_definition, [status(thm)], [c_0_209, def_lhs_atom30])).
cnf(c_0_210_0,axiom,set_difference(X1,empty_set)=X1,inference(unfold_definition, [status(thm)], [c_0_210, def_lhs_atom29])).
cnf(c_0_211_0,axiom,set_intersection2(X1,empty_set)=empty_set,inference(unfold_definition, [status(thm)], [c_0_211, def_lhs_atom28])).
cnf(c_0_212_0,axiom,set_union2(X1,empty_set)=X1,inference(unfold_definition, [status(thm)], [c_0_212, def_lhs_atom27])).
cnf(c_0_213_0,axiom,subset(X1,X1),inference(unfold_definition, [status(thm)], [c_0_213, def_lhs_atom26])).
cnf(c_0_214_0,axiom,~proper_subset(X1,X1),inference(unfold_definition, [status(thm)], [c_0_214, def_lhs_atom25])).
cnf(c_0_215_0,axiom,set_intersection2(X1,X1)=X1,inference(unfold_definition, [status(thm)], [c_0_215, def_lhs_atom24])).
cnf(c_0_216_0,axiom,set_union2(X1,X1)=X1,inference(unfold_definition, [status(thm)], [c_0_216, def_lhs_atom23])).
cnf(c_0_217_0,axiom,empty(empty_set),inference(unfold_definition, [status(thm)], [c_0_217, def_lhs_atom21])).
cnf(c_0_218_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_218, def_lhs_atom20])).
cnf(c_0_219_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_219, def_lhs_atom20])).
cnf(c_0_220_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_220, def_lhs_atom20])).
cnf(c_0_221_0,axiom,$true,inference(unfold_definition, [status(thm)], [c_0_221, def_lhs_atom20])).
# Orienting (remaining) axiom formulas using strategy ClausalAll
# CNF of (remaining) axioms:
# Start CNF derivation
fof(c_0_0, axiom, (![X1]:![X2]:~((in(X1,X2)&empty(X2)))), file('', t7_boole)).
fof(c_0_1, axiom, (![X1]:![X2]:~((empty(X1)&(X1!=X2&empty(X2))))), file('', t8_boole)).
fof(c_0_2, axiom, (?[X1]:~(empty(X1))), file('', rc2_xboole_0)).
fof(c_0_3, axiom, (?[X1]:empty(X1)), file('', rc1_xboole_0)).
fof(c_0_4, axiom, (![X1]:![X2]:~((in(X1,X2)&empty(X2)))), c_0_0).
fof(c_0_5, axiom, (![X1]:![X2]:~((empty(X1)&(X1!=X2&empty(X2))))), c_0_1).
fof(c_0_6, plain, (?[X1]:~empty(X1)), inference(fof_simplification,[status(thm)],[c_0_2])).
fof(c_0_7, axiom, (?[X1]:empty(X1)), c_0_3).
fof(c_0_8, plain, (![X3]:![X4]:(~in(X3,X4)|~empty(X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])).
fof(c_0_9, plain, (![X3]:![X4]:(~empty(X3)|(X3=X4|~empty(X4)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])).
fof(c_0_10, plain, (~empty(esk1_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])).
fof(c_0_11, plain, (empty(esk2_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])).
cnf(c_0_12,plain,(~empty(X1)|~in(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8])).
cnf(c_0_13,plain,(X2=X1|~empty(X1)|~empty(X2)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_14,plain,(~empty(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_15,plain,(empty(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_16,plain,(~empty(X1)|~in(X2,X1)), c_0_12, ['final']).
cnf(c_0_17,plain,(X2=X1|~empty(X1)|~empty(X2)), c_0_13, ['final']).
cnf(c_0_18,plain,(~empty(esk1_0)), c_0_14, ['final']).
cnf(c_0_19,plain,(empty(esk2_0)), c_0_15, ['final']).
# End CNF derivation
# Generating one_way clauses for all literals in the CNF.
cnf(c_0_16_0, axiom, (~empty(X1)
   |~in(X2,X1)), inference(literals_permutation, [status(thm)], [c_0_16]))
cnf(c_0_16_1, axiom, (~in(X2,X1)
   |~empty(X1)), inference(literals_permutation, [status(thm)], [c_0_16]))
cnf(c_0_17_0, axiom, (X2=X1
   |(~empty(X1)
   |~empty(X2))), inference(literals_permutation, [status(thm)], [c_0_17]))
cnf(c_0_17_1, axiom, ((~empty(X1)
   |X2=X1)
   |~empty(X2)), inference(literals_permutation, [status(thm)], [c_0_17]))
cnf(c_0_17_2, axiom, (~empty(X2)
   |(~empty(X1)
   |X2=X1)), inference(literals_permutation, [status(thm)], [c_0_17]))
cnf(c_0_18_0, axiom, ~empty(sk2_esk1_0), inference(literals_permutation, [status(thm)], [c_0_18]))
cnf(c_0_19_0, axiom, empty(sk2_esk2_0), inference(literals_permutation, [status(thm)], [c_0_19]))
# CNF of non-axioms
# Start CNF derivation
fof(c_0_0, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_difference(X1,X3),set_difference(X2,X3)))), file('', t33_xboole_1)).
fof(c_0_1, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_intersection2(X1,X3),set_intersection2(X2,X3)))), file('', t26_xboole_1)).
fof(c_0_2, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2))))), file('', t4_xboole_0)).
fof(c_0_3, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X3,X2))=>subset(set_union2(X1,X3),X2))), file('', t8_xboole_1)).
fof(c_0_4, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X1,X3))=>subset(X1,set_intersection2(X2,X3)))), file('', t19_xboole_1)).
fof(c_0_5, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('', t3_xboole_0)).
fof(c_0_6, lemma, (![X1]:![X2]:(subset(X1,X2)=>X2=set_union2(X1,set_difference(X2,X1)))), file('', t45_xboole_1)).
fof(c_0_7, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3))), file('', t1_xboole_1)).
fof(c_0_8, lemma, (![X1]:![X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), file('', t48_xboole_1)).
fof(c_0_9, lemma, (![X1]:![X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), file('', t40_xboole_1)).
fof(c_0_10, lemma, (![X1]:![X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), file('', t39_xboole_1)).
fof(c_0_11, lemma, (![X1]:![X2]:~((subset(X1,X2)&proper_subset(X2,X1)))), file('', t60_xboole_1)).
fof(c_0_12, lemma, (![X1]:![X2]:subset(X1,set_union2(X1,X2))), file('', t7_xboole_1)).
fof(c_0_13, lemma, (![X1]:![X2]:subset(set_difference(X1,X2),X1)), file('', t36_xboole_1)).
fof(c_0_14, lemma, (![X1]:![X2]:subset(set_intersection2(X1,X2),X1)), file('', t17_xboole_1)).
fof(c_0_15, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_intersection2(X1,X2)=X1)), file('', t28_xboole_1)).
fof(c_0_16, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2)), file('', t12_xboole_1)).
fof(c_0_17, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('', t37_xboole_1)).
fof(c_0_18, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('', l32_xboole_1)).
fof(c_0_19, lemma, (![X1]:(subset(X1,empty_set)=>X1=empty_set)), file('', t3_xboole_1)).
fof(c_0_20, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('', t63_xboole_1)).
fof(c_0_21, lemma, (![X1]:subset(empty_set,X1)), file('', t2_xboole_1)).
fof(c_0_22, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_difference(X1,X3),set_difference(X2,X3)))), c_0_0).
fof(c_0_23, lemma, (![X1]:![X2]:![X3]:(subset(X1,X2)=>subset(set_intersection2(X1,X3),set_intersection2(X2,X3)))), c_0_1).
fof(c_0_24, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~in(X3,set_intersection2(X1,X2))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_2])).
fof(c_0_25, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X3,X2))=>subset(set_union2(X1,X3),X2))), c_0_3).
fof(c_0_26, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X1,X3))=>subset(X1,set_intersection2(X2,X3)))), c_0_4).
fof(c_0_27, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_5])).
fof(c_0_28, lemma, (![X1]:![X2]:(subset(X1,X2)=>X2=set_union2(X1,set_difference(X2,X1)))), c_0_6).
fof(c_0_29, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3))), c_0_7).
fof(c_0_30, lemma, (![X1]:![X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), c_0_8).
fof(c_0_31, lemma, (![X1]:![X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), c_0_9).
fof(c_0_32, lemma, (![X1]:![X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), c_0_10).
fof(c_0_33, lemma, (![X1]:![X2]:~((subset(X1,X2)&proper_subset(X2,X1)))), c_0_11).
fof(c_0_34, lemma, (![X1]:![X2]:subset(X1,set_union2(X1,X2))), c_0_12).
fof(c_0_35, lemma, (![X1]:![X2]:subset(set_difference(X1,X2),X1)), c_0_13).
fof(c_0_36, lemma, (![X1]:![X2]:subset(set_intersection2(X1,X2),X1)), c_0_14).
fof(c_0_37, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_intersection2(X1,X2)=X1)), c_0_15).
fof(c_0_38, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2)), c_0_16).
fof(c_0_39, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), c_0_17).
fof(c_0_40, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), c_0_18).
fof(c_0_41, lemma, (![X1]:(subset(X1,empty_set)=>X1=empty_set)), c_0_19).
fof(c_0_42, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_20])).
fof(c_0_43, lemma, (![X1]:subset(empty_set,X1)), c_0_21).
fof(c_0_44, lemma, (![X4]:![X5]:![X6]:(~subset(X4,X5)|subset(set_difference(X4,X6),set_difference(X5,X6)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])).
fof(c_0_45, lemma, (![X4]:![X5]:![X6]:(~subset(X4,X5)|subset(set_intersection2(X4,X6),set_intersection2(X5,X6)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])).
fof(c_0_46, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:((disjoint(X4,X5)|in(esk2_2(X4,X5),set_intersection2(X4,X5)))&(~in(X9,set_intersection2(X7,X8))|~disjoint(X7,X8)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])])).
fof(c_0_47, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X6,X5))|subset(set_union2(X4,X6),X5))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])).
fof(c_0_48, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X4,X6))|subset(X4,set_intersection2(X5,X6)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])).
fof(c_0_49, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk1_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk1_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])])])).
fof(c_0_50, lemma, (![X3]:![X4]:(~subset(X3,X4)|X4=set_union2(X3,set_difference(X4,X3)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])).
fof(c_0_51, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X5,X6))|subset(X4,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])).
fof(c_0_52, lemma, (![X3]:![X4]:set_difference(X3,set_difference(X3,X4))=set_intersection2(X3,X4)), inference(variable_rename,[status(thm)],[c_0_30])).
fof(c_0_53, lemma, (![X3]:![X4]:set_difference(set_union2(X3,X4),X4)=set_difference(X3,X4)), inference(variable_rename,[status(thm)],[c_0_31])).
fof(c_0_54, lemma, (![X3]:![X4]:set_union2(X3,set_difference(X4,X3))=set_union2(X3,X4)), inference(variable_rename,[status(thm)],[c_0_32])).
fof(c_0_55, lemma, (![X3]:![X4]:(~subset(X3,X4)|~proper_subset(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])).
fof(c_0_56, lemma, (![X3]:![X4]:subset(X3,set_union2(X3,X4))), inference(variable_rename,[status(thm)],[c_0_34])).
fof(c_0_57, lemma, (![X3]:![X4]:subset(set_difference(X3,X4),X3)), inference(variable_rename,[status(thm)],[c_0_35])).
fof(c_0_58, lemma, (![X3]:![X4]:subset(set_intersection2(X3,X4),X3)), inference(variable_rename,[status(thm)],[c_0_36])).
fof(c_0_59, lemma, (![X3]:![X4]:(~subset(X3,X4)|set_intersection2(X3,X4)=X3)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])).
fof(c_0_60, lemma, (![X3]:![X4]:(~subset(X3,X4)|set_union2(X3,X4)=X4)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])).
fof(c_0_61, lemma, (![X3]:![X4]:![X5]:![X6]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X5,X6)|set_difference(X5,X6)=empty_set))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])).
fof(c_0_62, lemma, (![X3]:![X4]:![X5]:![X6]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X5,X6)|set_difference(X5,X6)=empty_set))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])).
fof(c_0_63, lemma, (![X2]:(~subset(X2,empty_set)|X2=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])).
fof(c_0_64, negated_conjecture, (((subset(esk3_0,esk4_0)&disjoint(esk4_0,esk5_0))&~disjoint(esk3_0,esk5_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])).
fof(c_0_65, lemma, (![X2]:subset(empty_set,X2)), inference(variable_rename,[status(thm)],[c_0_43])).
cnf(c_0_66,lemma,(subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_67,lemma,(subset(set_intersection2(X1,X2),set_intersection2(X3,X2))|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_68,lemma,(~disjoint(X1,X2)|~in(X3,set_intersection2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_69,lemma,(subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_70,lemma,(subset(X1,set_intersection2(X2,X3))|~subset(X1,X3)|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_71,lemma,(in(esk2_2(X1,X2),set_intersection2(X1,X2))|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_72,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_73,lemma,(X1=set_union2(X2,set_difference(X1,X2))|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_74,lemma,(subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_75,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_76,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_77,lemma,(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_52])).
cnf(c_0_78,lemma,(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_79,lemma,(set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54])).
cnf(c_0_80,lemma,(~proper_subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_55])).
cnf(c_0_81,lemma,(subset(X1,set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_56])).
cnf(c_0_82,lemma,(subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_57])).
cnf(c_0_83,lemma,(subset(set_intersection2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_58])).
cnf(c_0_84,lemma,(set_intersection2(X1,X2)=X1|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59])).
cnf(c_0_85,lemma,(set_union2(X1,X2)=X2|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_60])).
cnf(c_0_86,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_61])).
cnf(c_0_87,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_61])).
cnf(c_0_88,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_62])).
cnf(c_0_89,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62])).
cnf(c_0_90,lemma,(X1=empty_set|~subset(X1,empty_set)), inference(split_conjunct,[status(thm)],[c_0_63])).
cnf(c_0_91,negated_conjecture,(~disjoint(esk3_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
cnf(c_0_92,lemma,(subset(empty_set,X1)), inference(split_conjunct,[status(thm)],[c_0_65])).
cnf(c_0_93,negated_conjecture,(subset(esk3_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
cnf(c_0_94,negated_conjecture,(disjoint(esk4_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
cnf(c_0_95,lemma,(subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3)), c_0_66, ['final']).
cnf(c_0_96,lemma,(subset(set_intersection2(X1,X2),set_intersection2(X3,X2))|~subset(X1,X3)), c_0_67, ['final']).
cnf(c_0_97,lemma,(~disjoint(X1,X2)|~in(X3,set_intersection2(X1,X2))), c_0_68, ['final']).
cnf(c_0_98,lemma,(subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3)), c_0_69, ['final']).
cnf(c_0_99,lemma,(subset(X1,set_intersection2(X2,X3))|~subset(X1,X3)|~subset(X1,X2)), c_0_70, ['final']).
cnf(c_0_100,lemma,(in(esk2_2(X1,X2),set_intersection2(X1,X2))|disjoint(X1,X2)), c_0_71, ['final']).
cnf(c_0_101,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_72, ['final']).
cnf(c_0_102,lemma,(set_union2(X2,set_difference(X1,X2))=X1|~subset(X2,X1)), c_0_73, ['final']).
cnf(c_0_103,lemma,(subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3)), c_0_74, ['final']).
cnf(c_0_104,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X1)), c_0_75, ['final']).
cnf(c_0_105,lemma,(disjoint(X1,X2)|in(esk1_2(X1,X2),X2)), c_0_76, ['final']).
cnf(c_0_106,lemma,(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), c_0_77, ['final']).
cnf(c_0_107,lemma,(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), c_0_78, ['final']).
cnf(c_0_108,lemma,(set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), c_0_79, ['final']).
cnf(c_0_109,lemma,(~proper_subset(X1,X2)|~subset(X2,X1)), c_0_80, ['final']).
cnf(c_0_110,lemma,(subset(X1,set_union2(X1,X2))), c_0_81, ['final']).
cnf(c_0_111,lemma,(subset(set_difference(X1,X2),X1)), c_0_82, ['final']).
cnf(c_0_112,lemma,(subset(set_intersection2(X1,X2),X1)), c_0_83, ['final']).
cnf(c_0_113,lemma,(set_intersection2(X1,X2)=X1|~subset(X1,X2)), c_0_84, ['final']).
cnf(c_0_114,lemma,(set_union2(X1,X2)=X2|~subset(X1,X2)), c_0_85, ['final']).
cnf(c_0_115,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), c_0_86, ['final']).
cnf(c_0_116,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), c_0_87, ['final']).
cnf(c_0_117,lemma,(subset(X1,X2)|set_difference(X1,X2)!=empty_set), c_0_88, ['final']).
cnf(c_0_118,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), c_0_89, ['final']).
cnf(c_0_119,lemma,(X1=empty_set|~subset(X1,empty_set)), c_0_90, ['final']).
cnf(c_0_120,negated_conjecture,(~disjoint(esk3_0,esk5_0)), c_0_91, ['final']).
cnf(c_0_121,lemma,(subset(empty_set,X1)), c_0_92, ['final']).
cnf(c_0_122,negated_conjecture,(subset(esk3_0,esk4_0)), c_0_93, ['final']).
cnf(c_0_123,negated_conjecture,(disjoint(esk4_0,esk5_0)), c_0_94, ['final']).
# End CNF derivation

%-------------------------------------------------------------
% Dedukti proof by iprover
#NAME iprover_sig.
builtin_eq : (FOL.i -> (FOL.i -> Type)).
True : Type.
disjoint : (FOL.i -> (FOL.i -> Type)).
empty : (FOL.i -> Type).
empty_set : FOL.i.
in : (FOL.i -> (FOL.i -> Type)).
proper_subset : (FOL.i -> (FOL.i -> Type)).
set_difference : (FOL.i -> (FOL.i -> FOL.i)).
set_intersection2 : (FOL.i -> (FOL.i -> FOL.i)).
set_union2 : (FOL.i -> (FOL.i -> FOL.i)).
sk1_esk1_1 : (FOL.i -> FOL.i).
sk1_esk2_3 : (FOL.i -> (FOL.i -> (FOL.i -> FOL.i))).
sk1_esk3_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk1_esk4_3 : (FOL.i -> (FOL.i -> (FOL.i -> FOL.i))).
sk1_esk5_3 : (FOL.i -> (FOL.i -> (FOL.i -> FOL.i))).
sk1_esk6_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk2_esk1_0 : FOL.i.
sk2_esk2_0 : FOL.i.
sk3_esk1_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk3_esk2_2 : (FOL.i -> (FOL.i -> FOL.i)).
sk3_esk3_0 : FOL.i.
sk3_esk4_0 : FOL.i.
sk3_esk5_0 : FOL.i.
subset :
(FOL.i -> (FOL.i -> Type)).
[X0 : FOL.i] set_intersection2 X0 X0 -->  X0
[X0 : FOL.i] set_intersection2 X0 empty_set -->  empty_set.
[X0 : FOL.i] set_union2 X0 X0 -->  X0
[X0 : FOL.i] set_union2 X0 empty_set -->  X0.
[X0 : FOL.i] set_difference X0 empty_set -->  X0
[X0 : FOL.i] set_difference empty_set X0 -->
empty_set.
#NAME iprover_prf.
clause2 :
(((iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
   FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_).
clause5 :
((iprover_sig.disjoint iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0 ->
  FOL.proof FOL.bot_) -> FOL.proof FOL.bot_).
clause6 :
(X0 : FOL.i ->
 (X1 : FOL.i ->
  (((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_)
   ->
   ((iprover_sig.disjoint X1 X0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_)))).
{clause4} :
((iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 ->
  FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) :=
(lit1 :
 (iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 ->
  FOL.proof FOL.bot_) => clause5
 (tp : iprover_sig.disjoint iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0 =>
  clause6 iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0
  (tn :
   (iprover_sig.disjoint iprover_sig.sk3_esk4_0 iprover_sig.sk3_esk5_0 ->
    FOL.proof FOL.bot_) => tn tp) lit1)).
clause9 :
(X0 : FOL.i ->
 (X1 : FOL.i ->
  ((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) ->
   ((iprover_sig.in (iprover_sig.sk3_esk1_2 X0 X1) X0 -> FOL.proof FOL.bot_)
    -> FOL.proof FOL.bot_)))).
clause11 :
((iprover_sig.subset iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk4_0 ->
  FOL.proof FOL.bot_) -> FOL.proof FOL.bot_).
clause12 :
(X1 : FOL.i ->
 (X2 : FOL.i ->
  (X0 : FOL.i ->
   (((iprover_sig.subset X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_)
    ->
    ((iprover_sig.in X2 X1 -> FOL.proof FOL.bot_) ->
     (((iprover_sig.in X2 X0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) ->
      FOL.proof FOL.bot_)))))).
{clause10} :
(X0 : FOL.i ->
 (((iprover_sig.in X0 iprover_sig.sk3_esk3_0 -> FOL.proof FOL.bot_) ->
   FOL.proof FOL.bot_) ->
  ((iprover_sig.in X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) ->
   FOL.proof FOL.bot_))) :=
(X0 : FOL.i =>
 (lit3 :
  ((iprover_sig.in X0 iprover_sig.sk3_esk3_0 -> FOL.proof FOL.bot_) ->
   FOL.proof FOL.bot_) =>
  (lit2 : (iprover_sig.in X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) =>
   clause11
   (tp : iprover_sig.subset iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk4_0 =>
    clause12 iprover_sig.sk3_esk4_0 X0 iprover_sig.sk3_esk3_0
    (tn :
     (iprover_sig.subset iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk4_0 ->
      FOL.proof FOL.bot_) => tn tp) lit2 lit3)))).
{clause8} :
(X0 : FOL.i ->
 ((iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) ->
  ((iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
    iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_))) :=
(X0 : FOL.i =>
 (lit5 :
  (iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) =>
  (lit4 :
   (iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
    iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) => clause9
   iprover_sig.sk3_esk3_0 X0 lit5
   (tp : iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
    iprover_sig.sk3_esk3_0 => clause10
    (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
    (tn :
     (iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
      iprover_sig.sk3_esk3_0 -> FOL.proof FOL.bot_) => tn tp) lit4)))).
clause14 :
(X1 : FOL.i ->
 (X0 : FOL.i ->
  ((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) ->
   ((iprover_sig.in (iprover_sig.sk3_esk1_2 X0 X1) X1 -> FOL.proof FOL.bot_)
    -> FOL.proof FOL.bot_)))).
clause15 :
(X1 : FOL.i ->
 (X2 : FOL.i ->
  (X0 : FOL.i ->
   (((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof
     FOL.bot_) ->
    (((iprover_sig.in X2 X1 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) ->
     (((iprover_sig.in X2 X0 -> FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) ->
      FOL.proof FOL.bot_)))))).
{clause13} :
(X1 : FOL.i ->
 (X0 : FOL.i ->
  (X2 : FOL.i ->
   (((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof
     FOL.bot_) ->
    (((iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X1 -> FOL.proof
       FOL.bot_) -> FOL.proof FOL.bot_) ->
     ((iprover_sig.disjoint X2 X0 -> FOL.proof FOL.bot_) -> FOL.proof
      FOL.bot_)))))) :=
(X1 : FOL.i =>
 (X0 : FOL.i =>
  (X2 : FOL.i =>
   (lit6 :
    ((iprover_sig.disjoint X0 X1 -> FOL.proof FOL.bot_) -> FOL.proof
     FOL.bot_) =>
    (lit7 :
     ((iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X1 -> FOL.proof
       FOL.bot_) -> FOL.proof FOL.bot_) =>
     (lit8 : (iprover_sig.disjoint X2 X0 -> FOL.proof FOL.bot_) => clause14
      X0 X2 lit8
      (tp : iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X0 => clause15 X1
       (iprover_sig.sk3_esk1_2 X2 X0) X0 lit6 lit7
       (tn :
        (iprover_sig.in (iprover_sig.sk3_esk1_2 X2 X0) X0 -> FOL.proof
         FOL.bot_) => tn tp)))))))).
{clause7} :
(X0 : FOL.i ->
 (((iprover_sig.disjoint X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) ->
   FOL.proof FOL.bot_) ->
  ((iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) ->
   FOL.proof FOL.bot_))) :=
(X0 : FOL.i =>
 (lit9 :
  ((iprover_sig.disjoint X0 iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) ->
   FOL.proof FOL.bot_) =>
  (lit5 :
   (iprover_sig.disjoint iprover_sig.sk3_esk3_0 X0 -> FOL.proof FOL.bot_) =>
   clause8 X0 lit5
   (tp : iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
    iprover_sig.sk3_esk4_0 => clause13 iprover_sig.sk3_esk4_0 X0
    iprover_sig.sk3_esk3_0 lit9
    (tn :
     (iprover_sig.in (iprover_sig.sk3_esk1_2 iprover_sig.sk3_esk3_0 X0)
      iprover_sig.sk3_esk4_0 -> FOL.proof FOL.bot_) => tn tp) lit5)))).
{clause3} :
((iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
  FOL.proof FOL.bot_) -> FOL.proof FOL.bot_) :=
(lit10 :
 (iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
  FOL.proof FOL.bot_) => clause4
 (tp : iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 =>
  clause7 iprover_sig.sk3_esk5_0
  (tn :
   (iprover_sig.disjoint iprover_sig.sk3_esk5_0 iprover_sig.sk3_esk4_0 ->
    FOL.proof FOL.bot_) => tn tp) lit10)).
{clause1} : FOL.proof FOL.bot_ := clause2
(tnl1 :
 (iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 ->
  FOL.proof FOL.bot_) => clause3
 (tl1 : iprover_sig.disjoint iprover_sig.sk3_esk3_0 iprover_sig.sk3_esk5_0 =>
  tnl1 tl1)).
{empty_clause} : FOL.proof FOL.bot_ :=
clause1.
% SZS output end CNFRefutation

leanCoP 2.2

Sample solution for SEU140+2

% SZS status Theorem for SEU140+2.p
% SZS output start Proof for SEU140+2.p

%-----------------------------------------------------
fof(t63_xboole_1,conjecture,! [_63308,_63311,_63314] : (subset(_63308,_63311) & disjoint(_63311,_63314) => disjoint(_63308,_63314)),file('SEU140+2.p',t63_xboole_1)).
fof(d3_tarski,axiom,! [_63543,_63546] : (subset(_63543,_63546) <=> ! [_63564] : (in(_63564,_63543) => in(_63564,_63546))),file('SEU140+2.p',d3_tarski)).
fof(t3_xboole_0,lemma,! [_63793,_63796] : (~ (~ disjoint(_63793,_63796) & ! [_63818] : ~ (in(_63818,_63793) & in(_63818,_63796))) & ~ (? [_63818] : (in(_63818,_63793) & in(_63818,_63796)) & disjoint(_63793,_63796))),file('SEU140+2.p',t3_xboole_0)).

cnf(1,plain,[-(subset(11^[],12^[]))],clausify(t63_xboole_1)).
cnf(2,plain,[-(disjoint(12^[],13^[]))],clausify(t63_xboole_1)).
cnf(3,plain,[disjoint(11^[],13^[])],clausify(t63_xboole_1)).
cnf(4,plain,[subset(_29177,_29233),in(_29347,_29177),-(in(_29347,_29233))],clausify(d3_tarski)).
cnf(5,plain,[-(disjoint(_40265,_40352)),-(in(9^[_40352,_40265],_40265))],clausify(t3_xboole_0)).
cnf(6,plain,[-(disjoint(_40265,_40352)),-(in(9^[_40352,_40265],_40352))],clausify(t3_xboole_0)).
cnf(7,plain,[disjoint(_40265,_40352),in(_40769,_40265),in(_40769,_40352)],clausify(t3_xboole_0)).

cnf('1',plain,[disjoint(12^[],13^[]),in(9^[13^[],11^[]],12^[]),in(9^[13^[],11^[]],13^[])],start(7,bind([[_40265,_40769,_40352],[12^[],9^[13^[],11^[]],13^[]]]))).
cnf('1.1',plain,[-(disjoint(12^[],13^[]))],extension(2)).
cnf('1.2',plain,[-(in(9^[13^[],11^[]],12^[])),subset(11^[],12^[]),in(9^[13^[],11^[]],11^[])],extension(4,bind([[_29233,_29347,_29177],[12^[],9^[13^[],11^[]],11^[]]]))).
cnf('1.2.1',plain,[-(subset(11^[],12^[]))],extension(1)).
cnf('1.2.2',plain,[-(in(9^[13^[],11^[]],11^[])),-(disjoint(11^[],13^[]))],extension(5,bind([[_40265,_40352],[11^[],13^[]]]))).
cnf('1.2.2.1',plain,[disjoint(11^[],13^[])],extension(3)).
cnf('1.3',plain,[-(in(9^[13^[],11^[]],13^[])),-(disjoint(11^[],13^[]))],extension(6,bind([[_40265,_40352],[11^[],13^[]]]))).
cnf('1.3.1',plain,[disjoint(11^[],13^[])],extension(3)).
%-----------------------------------------------------

% SZS output end Proof for SEU140+2.p

LEO-II 1.6.2

Sample solution for SET014^4

 No.of.Axioms: 0

 Length.of.Defs: 1901

 Contains.Choice.Funs: false
(rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:3,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)
********************************
*   All subproblems solved!    *
********************************
% SZS status Theorem for /tmp/SystemOnTPTP42612/SET014^4.tptp : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:3,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)

%**** Beginning of derivation protocol ****
% SZS output start CNFRefutation
 thf(tp_complement,type,(complement: (($i>$o)>($i>$o)))).
 thf(tp_disjoint,type,(disjoint: (($i>$o)>(($i>$o)>$o)))).
 thf(tp_emptyset,type,(emptyset: ($i>$o))).
 thf(tp_excl_union,type,(excl_union: (($i>$o)>(($i>$o)>($i>$o))))).
 thf(tp_in,type,(in: ($i>(($i>$o)>$o)))).
 thf(tp_intersection,type,(intersection: (($i>$o)>(($i>$o)>($i>$o))))).
 thf(tp_is_a,type,(is_a: ($i>(($i>$o)>$o)))).
 thf(tp_meets,type,(meets: (($i>$o)>(($i>$o)>$o)))).
 thf(tp_misses,type,(misses: (($i>$o)>(($i>$o)>$o)))).
 thf(tp_sK1_X,type,(sK1_X: ($i>$o))).
 thf(tp_sK2_SY0,type,(sK2_SY0: ($i>$o))).
 thf(tp_sK3_SY2,type,(sK3_SY2: ($i>$o))).
 thf(tp_sK4_SX0,type,(sK4_SX0: $i)).
 thf(tp_setminus,type,(setminus: (($i>$o)>(($i>$o)>($i>$o))))).
 thf(tp_singleton,type,(singleton: ($i>($i>$o)))).
 thf(tp_subset,type,(subset: (($i>$o)>(($i>$o)>$o)))).
 thf(tp_union,type,(union: (($i>$o)>(($i>$o)>($i>$o))))).
 thf(tp_unord_pair,type,(unord_pair: ($i>($i>($i>$o))))).
 thf(complement,definition,(complement = (^[X:($i>$o),U:$i]: (~ (X@U)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',complement)).
 thf(disjoint,definition,(disjoint = (^[X:($i>$o),Y:($i>$o)]: (((intersection@X)@Y) = emptyset))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',disjoint)).
 thf(emptyset,definition,(emptyset = (^[X:$i]: $false)),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',emptyset)).
 thf(excl_union,definition,(excl_union = (^[X:($i>$o),Y:($i>$o),U:$i]: (((X@U) & (~ (Y@U))) | ((~ (X@U)) & (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',excl_union)).
 thf(in,definition,(in = (^[X:$i,M:($i>$o)]: (M@X))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',in)).
 thf(intersection,definition,(intersection = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (Y@U)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',intersection)).
 thf(is_a,definition,(is_a = (^[X:$i,M:($i>$o)]: (M@X))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',is_a)).
 thf(meets,definition,(meets = (^[X:($i>$o),Y:($i>$o)]: (?[U:$i]: ((X@U) & (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',meets)).
 thf(misses,definition,(misses = (^[X:($i>$o),Y:($i>$o)]: (~ (?[U:$i]: ((X@U) & (Y@U)))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',misses)).
 thf(setminus,definition,(setminus = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (~ (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',setminus)).
 thf(singleton,definition,(singleton = (^[X:$i,U:$i]: (U = X))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',singleton)).
 thf(subset,definition,(subset = (^[X:($i>$o),Y:($i>$o)]: (![U:$i]: ((X@U) => (Y@U))))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',subset)).
 thf(union,definition,(union = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) | (Y@U)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',union)).
 thf(unord_pair,definition,(unord_pair = (^[X:$i,Y:$i,U:$i]: ((U = X) | (U = Y)))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',unord_pair)).
 thf(1,conjecture,(![X:($i>$o),Y:($i>$o),A:($i>$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A))),file('/tmp/SystemOnTPTP42612/SET014^4.tptp',thm)).
 thf(2,negated_conjecture,(((![X:($i>$o),Y:($i>$o),A:($i>$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A)))=$false)),inference(negate_conjecture,[status(cth)],[1])).
 thf(3,plain,(((![SY0:($i>$o),SY1:($i>$o)]: ((((subset@sK1_X)@SY1) & ((subset@SY0)@SY1)) => ((subset@((union@sK1_X)@SY0))@SY1)))=$false)),inference(extcnf_forall_neg,[status(esa)],[2])).
 thf(4,plain,(((![SY2:($i>$o)]: ((((subset@sK1_X)@SY2) & ((subset@sK2_SY0)@SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@SY2)))=$false)),inference(extcnf_forall_neg,[status(esa)],[3])).
 thf(5,plain,((((((subset@sK1_X)@sK3_SY2) & ((subset@sK2_SY0)@sK3_SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$false)),inference(extcnf_forall_neg,[status(esa)],[4])).
 thf(6,plain,((((subset@sK1_X)@sK3_SY2)=$true)),inference(standard_cnf,[status(thm)],[5])).
 thf(7,plain,((((subset@sK2_SY0)@sK3_SY2)=$true)),inference(standard_cnf,[status(thm)],[5])).
 thf(8,plain,((((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2)=$false)),inference(standard_cnf,[status(thm)],[5])).
 thf(9,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$true)),inference(polarity_switch,[status(thm)],[8])).
 thf(10,plain,((((subset@sK2_SY0)@sK3_SY2)=$true)),inference(copy,[status(thm)],[7])).
 thf(11,plain,((((subset@sK1_X)@sK3_SY2)=$true)),inference(copy,[status(thm)],[6])).
 thf(12,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=$true)),inference(copy,[status(thm)],[9])).
 thf(13,plain,(((~ (![SX0:$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0))))=$true)),inference(unfold_def,[status(thm)],[12,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
 thf(14,plain,(((![SX0:$i]: ((~ (sK1_X@SX0)) | (sK3_SY2@SX0)))=$true)),inference(unfold_def,[status(thm)],[11,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
 thf(15,plain,(((![SX0:$i]: ((~ (sK2_SY0@SX0)) | (sK3_SY2@SX0)))=$true)),inference(unfold_def,[status(thm)],[10,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
 thf(16,plain,(((![SX0:$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0)))=$false)),inference(extcnf_not_pos,[status(thm)],[13])).
 thf(17,plain,(![SV1:$i]: ((((~ (sK1_X@SV1)) | (sK3_SY2@SV1))=$true))),inference(extcnf_forall_pos,[status(thm)],[14])).
 thf(18,plain,(![SV2:$i]: ((((~ (sK2_SY0@SV2)) | (sK3_SY2@SV2))=$true))),inference(extcnf_forall_pos,[status(thm)],[15])).
 thf(19,plain,((((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))) | (sK3_SY2@sK4_SX0))=$false)),inference(extcnf_forall_neg,[status(esa)],[16])).
 thf(20,plain,(![SV1:$i]: (((~ (sK1_X@SV1))=$true) | ((sK3_SY2@SV1)=$true))),inference(extcnf_or_pos,[status(thm)],[17])).
 thf(21,plain,(![SV2:$i]: (((~ (sK2_SY0@SV2))=$true) | ((sK3_SY2@SV2)=$true))),inference(extcnf_or_pos,[status(thm)],[18])).
 thf(22,plain,(((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0)))=$false)),inference(extcnf_or_neg,[status(thm)],[19])).
 thf(23,plain,(((sK3_SY2@sK4_SX0)=$false)),inference(extcnf_or_neg,[status(thm)],[19])).
 thf(24,plain,(![SV1:$i]: (((sK1_X@SV1)=$false) | ((sK3_SY2@SV1)=$true))),inference(extcnf_not_pos,[status(thm)],[20])).
 thf(25,plain,(![SV2:$i]: (((sK2_SY0@SV2)=$false) | ((sK3_SY2@SV2)=$true))),inference(extcnf_not_pos,[status(thm)],[21])).
 thf(26,plain,((((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))=$true)),inference(extcnf_not_neg,[status(thm)],[22])).
 thf(27,plain,(((sK1_X@sK4_SX0)=$true) | ((sK2_SY0@sK4_SX0)=$true)),inference(extcnf_or_pos,[status(thm)],[26])).
 thf(28,plain,((($false)=$true)),inference(fo_atp_e,[status(thm)],[23,27,25,24])).
 thf(29,plain,($false),inference(solved_all_splits,[solved_all_splits(join,[])],[28])).
% SZS output end CNFRefutation

%**** End of derivation protocol ****
%**** no. of clauses in derivation: 29 ****
%**** clause counter: 28 ****

% SZS status Theorem for /tmp/SystemOnTPTP42612/SET014^4.tptp : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:3,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)

MaLARea 0.5

Sample solution for SEU140+2

# SZS status Theorem
# SZS output start CNFRefutation.
fof(c_0_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', symmetry_r1_xboole_0)).
fof(c_0_1, lemma, (![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(c_0_2, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(c_0_3, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), file('/Users/schulz/EPROVER/TPTP_5.4.0_FLAT/SEU140+2.p', d3_tarski)).
fof(c_0_4, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), c_0_0).
fof(c_0_5, lemma, (![X1]:![X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2))))), inference(fof_simplification,[status(thm)],[c_0_1])).
fof(c_0_6, negated_conjecture, (~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)))), inference(assume_negation,[status(cth)],[c_0_2])).
fof(c_0_7, plain, (![X3]:![X4]:(~disjoint(X3,X4)|disjoint(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])).
fof(c_0_8, lemma, (![X4]:![X5]:![X7]:![X8]:![X9]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X9,X7)|~in(X9,X8))|~disjoint(X7,X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])).
fof(c_0_9, negated_conjecture, (((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])).
cnf(c_0_10,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), inference(split_conjunct,[status((null))],[c_0_7])).
cnf(c_0_11,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status((null))],[c_0_8])).
fof(c_0_12, axiom, (![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2)))), c_0_3).
cnf(c_0_13,lemma,(~in(X3,X2)|~in(X3,X1)|~disjoint(X1,X2)), inference(split_conjunct,[status((null))],[c_0_8])).
cnf(c_0_14,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status((null))],[c_0_9])).
cnf(c_0_15,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status((null))],[c_0_9])).
cnf(c_0_16,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_10).
cnf(c_0_17,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_11).
fof(c_0_18, plain, (![X4]:![X5]:![X6]:![X7]:![X8]:((~subset(X4,X5)|(~in(X6,X4)|in(X6,X5)))&((in(esk3_2(X7,X8),X7)|subset(X7,X8))&(~in(esk3_2(X7,X8),X8)|subset(X7,X8))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])])])).
cnf(c_0_19,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status((null))],[c_0_8])).
cnf(c_0_20,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_13).
cnf(c_0_21,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_14).
cnf(c_0_22,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_15).
cnf(c_0_23,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), c_0_16).
cnf(c_0_24,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), c_0_17).
cnf(c_0_25,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)), inference(split_conjunct,[status((null))],[c_0_18])).
cnf(c_0_26,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status((null))],[c_0_9])).
cnf(c_0_27,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_19).
cnf(c_0_28,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), c_0_20).
cnf(c_0_29,negated_conjecture,(disjoint(esk12_0,esk13_0)), c_0_21).
cnf(c_0_30,negated_conjecture,(~disjoint(esk11_0,esk13_0)), c_0_22).
cnf(c_0_31,lemma,(disjoint(X1,X2)|in(esk9_2(X2,X1),X2)), inference(spm,[status(thm)],[c_0_23, c_0_24, theory(equality)]])).
cnf(c_0_32,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_25).
cnf(c_0_33,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_26).
cnf(c_0_34,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), c_0_27).
cnf(c_0_35,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_28, c_0_29, theory(equality)]])).
cnf(c_0_36,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk13_0)), inference(spm,[status(thm)],[c_0_30, c_0_31, theory(equality)]])).
cnf(c_0_37,plain,(in(X1,X2)|~subset(X3,X2)|~in(X1,X3)), c_0_32).
cnf(c_0_38,negated_conjecture,(subset(esk11_0,esk12_0)), c_0_33).
cnf(c_0_39,lemma,(disjoint(X1,X2)|in(esk9_2(X2,X1),X1)), inference(spm,[status(thm)],[c_0_23, c_0_34, theory(equality)]])).
cnf(c_0_40,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk12_0)), inference(spm,[status(thm)],[c_0_35, c_0_36, theory(equality)]])).
cnf(c_0_41,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)), inference(spm,[status(thm)],[c_0_37, c_0_38, theory(equality)]])).
cnf(c_0_42,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk11_0)), inference(spm,[status(thm)],[c_0_30, c_0_39, theory(equality)]])).
cnf(c_0_43,negated_conjecture,($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41, theory(equality)]]), c_0_42, theory(equality)]]), theory(equality,[symmetry])]]), ['proof']).
# SZS output end CNFRefutation.

Muscadet 4.5

Sample solution for SEU140+2

SZS status Theorem for SEU140+2.p

SZS output start Proof for SEU140+2.p

* * * * * * * * * * * * * * * * * * * * * * * *
in the following, N is the number of a (sub)theorem
       E is the current step
         or the step when a hypothesis or conclusion has been added or modified
hyp(N,H,E) means that H is an hypothesis of (sub)theorem N
concl(N,C,E) means that C is the conclusion of (sub)theorem N
obj_ct(N,C) means that C is a created object or a given constant
addhyp(N,H,E) means add H as a new hypothesis for N
newconcl(N,C,E) means that the new conclusion of N is C
           (C replaces the precedent conclusion)
a subtheorem N-i or N+i is a subtheorem of the (sub)theorem N
   N is proved if all N-i have been proved (&-node)
             or if one N+i have been proved (|-node)
the initial theorem is numbered 0

* * * theorem to be proved
![A,B,C]: (subset(A,B)&disjoint(B,C)=>disjoint(A,C))

* * * proof :

* * * * * * theoreme 0 * * * * * *
*** newconcl(0,![A,B,C]: (subset(A,B)&disjoint(B,C)=>disjoint(A,C)),1)
*** explanation : initial theorem
------------------------------------------------------- action ini
create object(s) z3 z2 z1
*** newconcl(0,subset(z1,z2)&disjoint(z2,z3)=>disjoint(z1,z3),2)
*** because concl((0,![A,B,C]: (subset(A,B)&disjoint(B,C)=>disjoint(A,C))),1)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** addhyp(0,subset(z1,z2),3)
*** addhyp(0,disjoint(z2,z3),3)
*** newconcl(0,disjoint(z1,z3),3)
*** because concl(0,subset(z1,z2)&disjoint(z2,z3)=>disjoint(z1,z3),2)
*** explanation : to prove H=>C, assume H and prove C
------------------------------------------------------- rule =>
*** addhyp(0,set_intersection2(z2,z3)::empty_set,4)
*** because hyp(0,disjoint(z2,z3),3)
*** explanation : rule if hyp(A,disjoint(B,C),_)then addhyp(A,set_intersection2(B,C)::empty_set,_)
built from the definition of disjoint (fof axiom:d7_xboole_0 )
------------------------------------------------------- rule disjoint
*** addhyp(0,set_difference(z1,z2)::empty_set,21)
*** because hyp(0,subset(z1,z2),3),obj_ct(0,z1),obj_ct(0,z2)
*** explanation : rule if (hyp(A,subset(B,C),_),obj_ct(A,B),obj_ct(A,C))then addhyp(A,set_difference(B,C)::empty_set,_)
built from the axiom lemma:l32_xboole_1
------------------------------------------------------- rule lemma:l32_xboole_1_1
*** newconcl(0,set_intersection2(z1,z3)::empty_set,109)
*** because concl(0,disjoint(z1,z3),3)
*** explanation : the conclusion  disjoint(z1,z3) is replaced by its definition(fof axiom:d7_xboole_0 )
------------------------------------------------------- rule def_concl_pred
*** newconcl(0,seul(set_intersection2(z1,z3)::A,A=empty_set),110)
*** because concl(0,set_intersection2(z1,z3)::empty_set,109)
*** explanation :  FX::Y is rewriten only(FX::Z, Z=Y)
------------------------------------------------------- rule concl2pts
*** addhyp(0,set_intersection2(z1,z3)::z4,111),newconcl(0,z4=empty_set,111)
*** because concl(0,seul(set_intersection2(z1,z3)::A,A=empty_set),110)
*** explanation : creation of object z4 and of its definition
------------------------------------------------------- rule concl_only
*** addhyp(0,set_intersection2(z3,z1)::z4,113)
*** because hyp(0,set_intersection2(z1,z3)::z4,111),obj_ct(0,z1),obj_ct(0,z3)
*** explanation : rule if (hyp(A,set_intersection2(B,C)::D,_),obj_ct(A,B),obj_ct(A,C))then addhyp(A,set_intersection2(C,B)::D,_)
built from the axiom axiom:commutativity_k3_xboole_0
------------------------------------------------------- rule axiom:commutativity_k3_xboole_0_1
*** newconcl(0,![A]: ~in(A,z4),114)
*** because concl(0,z4=empty_set,111)
*** explanation : sufficient condition (rule :  axiom:d1_xboole_0_1 (fof axiom:d1_xboole_0 )
------------------------------------------------------- rule axiom:d1_xboole_0_1_cs
create object(s) z5
*** newconcl(0,~in(z5,z4),115)
*** because concl((0,![A]: ~in(A,z4)),114)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** addhyp(0,in(z5,z4),116),newconcl(0,false,116)
*** because concl(0,~in(z5,z4),115)
*** explanation : assume in(z5,z4) and search for a contradiction
------------------------------------------------------- rule concl_not
*** addhyp(0,in(z5,z1),118)
*** because hyp(0,set_intersection2(z1,z3)::z4,111),hyp(0,in(z5,z4),116),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_intersection2(D,_)::B,_),hyp(A,in(C,B),_),obj_ct(A,C))then addhyp(A,in(C,D),_)
built from the definition of set_intersection2 (fof axiom:d3_xboole_0 )
------------------------------------------------------- rule set_intersection2_
*** addhyp(0,in(z5,z2),119)
*** because hyp(0,subset(z1,z2),3),hyp(0,in(z5,z1),118),obj_ct(0,z5)
*** explanation : rule if (hyp(A,subset(B,D),_),hyp(A,in(C,B),_),obj_ct(A,C))then addhyp(A,in(C,D),_)
built from the definition of subset (fof axiom:d3_tarski )
------------------------------------------------------- rule subset
*** addhyp(0,in(z5,z3),120)
*** because hyp(0,set_intersection2(z3,z1)::z4,113),hyp(0,in(z5,z4),116),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_intersection2(D,_)::B,_),hyp(A,in(C,B),_),obj_ct(A,C))then addhyp(A,in(C,D),_)
built from the definition of set_intersection2 (fof axiom:d3_xboole_0 )
------------------------------------------------------- rule set_intersection2_
*** addhyp(0,in(z5,empty_set),121)
*** because hyp(0,set_intersection2(z2,z3)::empty_set,4),hyp(0,in(z5,z2),119),hyp(0,in(z5,z3),120),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_intersection2(B,D)::E,_),hyp(A,in(C,B),_),hyp(A,in(C,D),_),obj_ct(A,C))then addhyp(A,in(C,E),_)
built from the definition of set_intersection2 (fof axiom:d3_xboole_0 )
------------------------------------------------------- rule set_intersection2_2
*** addhyp(0,false,123)
*** because hyp(0,set_difference(z1,z2)::empty_set,21),hyp(0,in(z5,empty_set),121),hyp(0,in(z5,z2),119),obj_ct(0,z5)
*** explanation : rule if (hyp(A,set_difference(_,D)::B,_),hyp(A,in(C,B),_),hyp(A,in(C,D),_),obj_ct(A,C))then addhyp(A,false,_)
built from the definition of set_difference (fof axiom:d4_xboole_0 )
------------------------------------------------------- rule set_difference1
*** newconcl(0,true,124)
*** because hyp(0,false,123),concl(0,false,116)
*** explanation : the conclusion false to be proved is a hypothesis
------------------------------------------------------- rule stop_hyp_concl
then the initial theorem is proved
* * * * * * * * * * * * * * * * * * * * * * * *

SZS output end Proof for SEU140+2.p

Prover9 2009-11A

Sample solution for SEU140+2

8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
42 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
55 -(all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(negated_conjecture) # label(non_clause).  [assumption].
60 subset(c3,c4) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
61 disjoint(c4,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
75 disjoint(A,B) | in(f7(A,B),A) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
76 disjoint(A,B) | in(f7(A,B),B) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
92 -disjoint(c3,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
101 -in(A,B) | -in(A,C) | -disjoint(B,C) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
109 -disjoint(A,B) | disjoint(B,A) # label(symmetry_r1_xboole_0) # label(axiom).  [clausify(26)].
123 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom).  [clausify(8)].
273 -disjoint(c5,c3).  [ur(109,b,92,a)].
300 -in(A,c3) | in(A,c4).  [resolve(123,a,60,a)].
959 in(f7(c5,c3),c3).  [resolve(273,a,76,a)].
960 in(f7(c5,c3),c5).  [resolve(273,a,75,a)].
1084 -in(f7(c5,c3),c4).  [ur(101,b,960,a,c,61,a)].
1292 $F.  [resolve(300,a,959,a),unit_del(a,1084)].

SPASS+T 2.2.22

Sample solution for DAT013=1

SPASS V 2.2.22  in combination with yices.
SPASS beiseite: Proof found by SPASS.
Problem: DAT013=1+tff2fof.dfgt
SPASS derived 36 clauses, backtracked 5 clauses and kept 67 clauses.
SPASS backtracked 2 times (0 times due to theory inconsistency).
SPASS allocated 6259 KBytes.
SPASS spent     0:00:00.01 on the problem.
                0:00:00.00 for the input.
                0:00:00.00 for the FLOTTER CNF translation.
                0:00:00.00 for inferences.
                0:00:00.00 for the backtracking.
                0:00:00.00 for the reduction.
                0:00:00.00 for interacting with the SMT procedure.


% SZS output start CNFRefutation for DAT013=1+tff2fof.dfgt

% Here is a proof with depth 3, length 19 :
4[0:Inp] ||  -> lesseq(skc8,skc6)*.
5[0:Inp] ||  -> lesseq(plus(skc7,3),skc8)*.
6[0:Inp] || greater(read(skc5,skc8),0)* -> .
9[0:Inp] || lesseq(U,skc6) lesseq(skc7,U) -> greater(read(skc5,U),0)*.
18[0:ThA] ||  -> equal(plus(U,0),U)**.
25[0:ThA] ||  -> lesseq(U,V) less(plus(W,V),plus(W,U))*.
42[0:ArS:6.0] || less(0,read(skc5,skc8))* -> .
43[0:TOC:42.0] ||  -> lesseq(read(skc5,skc8),0)*.
44[0:ArS:9.2] || lesseq(U,skc6) lesseq(skc7,U) -> less(0,read(skc5,U))*.
45[0:TOC:44.1] ||  -> less(U,skc7) less(skc6,U) less(0,read(skc5,U))*.
49[0:OCh:5.0,25.1] ||  -> lesseq(3,U) less(plus(skc7,U),skc8)*.
51[0:SpR:18.0,49.1] ||  -> lesseq(3,0) less(skc7,skc8)*.
57[0:ArS:51.0] ||  -> less(skc7,skc8)*.
77(e)[0:OCE:45.2,43.0] ||  -> less(skc8,skc7)* less(skc6,skc8).
80[1:Spt:77.0] ||  -> less(skc8,skc7)*.
81(e)[1:OCE:80.0,57.0] ||  -> .
84[1:Spt:81.0,77.0,80.0] || less(skc8,skc7)* -> .
85[1:Spt:81.0,77.1] ||  -> less(skc6,skc8)*.
89(e)[1:OCE:85.0,4.0] ||  -> .

% SZS output end CNFRefutation for DAT013=1+tff2fof.dfgt

Formulae used in the proof : fof_co1 fof_ax1

Vampire 2.6

Sample solution for SEU140+2

% SZS output start Proof for SEU140+2
fof(f1738,plain,(
  $false),
  inference(subsumption_resolution,[],[f1737,f136])).
fof(f136,plain,(
  ~disjoint(sK0,sK2)),
  inference(cnf_transformation,[],[f104])).
fof(f104,plain,(
  subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
  inference(skolemisation,[status(esa)],[f76])).
fof(f76,plain,(
  ? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
  inference(flattening,[],[f75])).
fof(f75,plain,(
  ? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
  inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
  ~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
  ! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  file('Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f1737,plain,(
  disjoint(sK0,sK2)),
  inference(duplicate_literal_removal,[],[f1736])).
fof(f1736,plain,(
  disjoint(sK0,sK2) | disjoint(sK0,sK2)),
  inference(resolution,[],[f1707,f378])).
fof(f378,plain,(
  ( ! [X1] : (~in(sK4(sK2,X1),sK1) | disjoint(X1,sK2)) )),
  inference(resolution,[],[f372,f148])).
fof(f148,plain,(
  ( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f106])).
fof(f106,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
  inference(skolemisation,[status(esa)],[f79])).
fof(f79,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | ? [X3] : (in(X3,X0) & in(X3,X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f61])).
fof(f61,plain,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  inference(flattening,[],[f60])).
fof(f60,plain,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  inference(rectify,[],[f43])).
fof(f43,axiom,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  file('Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f372,plain,(
  ( ! [X0] : (~in(X0,sK2) | ~in(X0,sK1)) )),
  inference(resolution,[],[f149,f135])).
fof(f135,plain,(
  disjoint(sK1,sK2)),
  inference(cnf_transformation,[],[f104])).
fof(f149,plain,(
  ( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
  inference(cnf_transformation,[],[f106])).
fof(f1707,plain,(
  ( ! [X0] : (in(sK4(X0,sK0),sK1) | disjoint(sK0,X0)) )),
  inference(resolution,[],[f1706,f147])).
fof(f147,plain,(
  ( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f106])).
fof(f1706,plain,(
  ( ! [X78] : (~in(X78,sK0) | in(X78,sK1)) )),
  inference(resolution,[],[f1661,f134])).
fof(f134,plain,(
  subset(sK0,sK1)),
  inference(cnf_transformation,[],[f104])).
fof(f1661,plain,(
  ( ! [X6,X7,X5] : (~subset(X5,X6) | in(X7,X6) | ~in(X7,X5)) )),
  inference(superposition,[],[f236,f218])).
fof(f218,plain,(
  ( ! [X0,X1] : (set_difference(X0,set_difference(X0,X1)) = X0 | ~subset(X0,X1)) )),
  inference(definition_unfolding,[],[f150,f144])).
fof(f144,plain,(
  ( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
  inference(cnf_transformation,[],[f47])).
fof(f47,axiom,(
  ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
  file('Problems/SEU/SEU140+2.p',t48_xboole_1)).
fof(f150,plain,(
  ( ! [X0,X1] : (set_intersection2(X0,X1) = X0 | ~subset(X0,X1)) )),
  inference(cnf_transformation,[],[f80])).
fof(f80,plain,(
  ! [X0,X1] : (~subset(X0,X1) | set_intersection2(X0,X1) = X0)),
  inference(ennf_transformation,[],[f34])).
fof(f34,axiom,(
  ! [X0,X1] : (subset(X0,X1) => set_intersection2(X0,X1) = X0)),
  file('Problems/SEU/SEU140+2.p',t28_xboole_1)).
fof(f236,plain,(
  ( ! [X4,X0,X1] : (~in(X4,set_difference(X0,set_difference(X0,X1))) | in(X4,X1)) )),
  inference(equality_resolution,[],[f230])).
fof(f230,plain,(
  ( ! [X4,X2,X0,X1] : (in(X4,X1) | ~in(X4,X2) | set_difference(X0,set_difference(X0,X1)) != X2) )),
  inference(definition_unfolding,[],[f196,f144])).
fof(f196,plain,(
  ( ! [X4,X2,X0,X1] : (in(X4,X1) | ~in(X4,X2) | set_intersection2(X0,X1) != X2) )),
  inference(cnf_transformation,[],[f123])).
fof(f123,plain,(
  ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X4] : ((~in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X0) | ~in(X4,X1) | in(X4,X2)))) & (((in(sK8(X2,X1,X0),X2) | (in(sK8(X2,X1,X0),X0) & in(sK8(X2,X1,X0),X1))) & (~in(sK8(X2,X1,X0),X2) | ~in(sK8(X2,X1,X0),X0) | ~in(sK8(X2,X1,X0),X1))) | set_intersection2(X0,X1) = X2))),
  inference(skolemisation,[status(esa)],[f122])).
fof(f122,plain,(
  ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X4] : ((~in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X0) | ~in(X4,X1) | in(X4,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))),
  inference(rectify,[],[f121])).
fof(f121,plain,(
  ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))),
  inference(flattening,[],[f120])).
fof(f120,plain,(
  ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & ((~in(X3,X0) | ~in(X3,X1)) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | (~in(X3,X0) | ~in(X3,X1)))) | set_intersection2(X0,X1) = X2))),
  inference(nnf_transformation,[],[f9])).
fof(f9,axiom,(
  ! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X0) & in(X3,X1))))),
  file('Problems/SEU/SEU140+2.p',d3_xboole_0)).
% SZS output end Proof for SEU140+2

ZenonArith 0.1.0

Sample solution for DAT013=1

Add LoadPath "/usr/local/lib".
Require Import zenon.
Require Import zenon_arith.
Parameter zenon_U : Set.
Parameter zenon_E : zenon_U.
Parameter array : Type.
Parameter read : ((array) -> (Z) -> (Z)).
Axiom read_proper : Proper ( eq ==>eq ==>eq) read.
Parameter write : ((array) -> (Z) -> (Z) -> (array)).
Axiom write_proper : Proper ( eq ==>eq ==>eq ==>eq) write.
Parameter ax1 : (forall v_U:(array),(forall v_V:(Z),(forall v_W:(Z),(((
read (write v_U (v_V)%Z (v_W)%Z) (v_V)%Z))%Z = (v_W)%Z)))).
Parameter ax2 : (forall v_X:(array),(forall v_Y:(Z),(forall v_Z:(Z),(
forall v_X1:(Z),(((v_Y)%Z = (v_Z)%Z)\/(((read (write v_X (v_Y)%Z (v_X1)
%Z) (v_Z)%Z))%Z = ((read v_X (v_Z)%Z))%Z)))))).
Theorem co1 : (forall v_U : (array), (forall v_V : (Z), (forall v_W : (Z), ((forall v_X : (Z), ((((((v_V)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((v_V)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)))))).
Proof.
apply NNPP. intro zenon_G.
apply (zenon_notallex_s (fun v_U : (array) => (forall v_V : (Z), (forall v_W : (Z), ((forall v_X : (Z), ((((((v_V)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((v_V)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read v_U (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)))))) zenon_G); [ zenon_intro zenon_Hd; idtac ].
elim zenon_Hd. zenon_intro zenon_Tv_U_a. zenon_intro zenon_He.
apply (zenon_notallex_s (fun v_V : (Z) => (forall v_W : (Z), ((forall v_X : (Z), ((((((v_V)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((v_V)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))))) zenon_He); [ zenon_intro zenon_Hf; idtac ].
elim zenon_Hf. zenon_intro zenon_Tv_V_b. zenon_intro zenon_H10.
apply (zenon_notallex_s (fun v_W : (Z) => ((forall v_X : (Z), ((((((zenon_Tv_V_b)%Z # (1)) <= ((v_X)%Z # (1))))%Q/\((((v_X)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_X)%Z))%Z # (1)) > ((0)%Z # (1))))%Q))->(forall v_Y : (Z), ((((((((zenon_Tv_V_b)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((v_W)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
elim zenon_H11. zenon_intro zenon_Tv_W_c. zenon_intro zenon_H12.
apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H4. zenon_intro zenon_H13.
apply (zenon_notallex_s (fun v_Y : (Z) => ((((((((zenon_Tv_V_b)%Z + (3)%Z))%Z # (1)) <= ((v_Y)%Z # (1))))%Q/\((((v_Y)%Z # (1)) <= ((zenon_Tv_W_c)%Z # (1))))%Q)->(((((read zenon_Tv_U_a (v_Y)%Z))%Z # (1)) > ((0)%Z # (1))))%Q)) zenon_H13); [ zenon_intro zenon_H14; idtac ].
elim zenon_H14. zenon_intro zenon_Tv_Y_d. zenon_intro zenon_H15.
apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H19. zenon_intro zenon_H18.
(* ARITH -- 'var' : ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q : '(Prop)', ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)',
 * ->((((((zenon_Tv_V_b)%Z + (3)%Z))%Z # (1)) <= ((zenon_Tv_Y_d)%Z # (1))))%Q,
 * |- ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q, ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z), *)
pose (zenon_Vi := (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z).
  pose proof (Z.eq_refl zenon_Vi) as zenon_H1a; change zenon_Vi with (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z in zenon_H1a at 2.
  cut ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q; [zenon_intro zenon_H1b | subst zenon_Vi; arith_omega zenon_H19 ].
generalize (zenon_H4 (zenon_Tv_Y_d)%Z). zenon_intro zenon_H1c.
apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
(* ARITH -- 'neg2_$lesseq' : (zenon_Tv_V_b)%Z : '(Z)', (zenon_Tv_Y_d)%Z : '(Z)',
 * ->(~((((zenon_Tv_V_b)%Z # (1)) <= ((zenon_Tv_Y_d)%Z # (1))))%Q),
 * |- ((((zenon_Tv_V_b)%Z # (1)) > ((zenon_Tv_Y_d)%Z # (1))))%Q, *)
apply (arith_refut _ _ (arith_neg_leq ((zenon_Tv_V_b)%Z # (1)) ((zenon_Tv_Y_d)%Z # (1)))); [zenon_intro zenon_H21 | exact zenon_H20].
(* ARITH -- 'int_gt' : (zenon_Tv_V_b)%Z : '(Z)', (zenon_Tv_Y_d)%Z : '(Z)',
 * ->((((zenon_Tv_V_b)%Z # (1)) > ((zenon_Tv_Y_d)%Z # (1))))%Q,
 * |- ((((((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z # (1)) >= ((1)%Z # (1))))%Q, *)
cut ((((((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z # (1)) >= ((1)%Z # (1))))%Q; [ zenon_intro zenon_H22 | arith_omega zenon_H21 ].
(* ARITH -- 'var' : ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q : '(Prop)', ((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)',
 * ->((((((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z # (1)) >= ((1)%Z # (1))))%Q,
 * |- ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q, ((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z), *)
pose (zenon_Vw := (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z).
  pose proof (Z.eq_refl zenon_Vw) as zenon_H23; change zenon_Vw with (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z in zenon_H23 at 2.
  cut ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q; [zenon_intro zenon_H24 | subst zenon_Vw; arith_omega zenon_H22 ].
(* ARITH -- 'simplex_lin' : ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z) : '(Prop)', ((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)', ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z) : '(Prop)',
 * ->((zenon_Vw)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z), ((zenon_Vi)%Z = (((zenon_Tv_V_b)%Z - (zenon_Tv_Y_d)%Z))%Z),
 * |- ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z), *)
cut ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z); [ zenon_intro zenon_H25 | subst zenon_Vw; subst zenon_Vi; arith_norm; apply eq_refl ].
(* ARITH -- 'simplex_bound' : (zenon_Vw)%Z : '(Z)', ((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z) : '(Prop)', ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q : '(Prop)',
 * ->((((zenon_Vi)%Z - (zenon_Vw)%Z))%Z = (0)%Z), ((((zenon_Vi)%Z # (1)) <= ((-3)%Z # (1))))%Q,
 * |- ((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q, *)
cut (((zenon_Vw)%Z = (zenon_Vi)%Z)); [ zenon_intro zenon_H26 | arith_simpl ((-1)%Z # (1)) zenon_H25 ].
Qle_mult ((1)%Z # (1)) zenon_H1b zenon_H1b_zenon_H25.
pose proof (zenon_H1b_zenon_H25) as zenon_H27_pre.
cut ((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q; [ zenon_intro zenon_H27 | rewrite -> zenon_H26; arith_simpl 1 zenon_H27_pre ].
(* ARITH -- 'conflict' : ((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q : '(Prop)', ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q : '(Prop)',
 * ->((((zenon_Vw)%Z # (1)) <= ((-3)%Z # (1))))%Q, ((((zenon_Vw)%Z # (1)) >= ((1)%Z # (1))))%Q,
 * |- *)
arith_trans_simpl zenon_H27 zenon_H24.
exact (zenon_H1f zenon_H18).
exact (zenon_H16 zenon_H1d).
Qed.

Vampire 4.0

Sample solution for DAT013=1

% SZS output start Proof for DAT013=1
fof(f2288,plain,(
  $false),
  inference(subsumption_resolution,[],[f2287,f2273])).
fof(f2273,plain,(
  $lesseq(sK1,sK3)),
  inference(evaluation,[],[f2269])).
fof(f2269,plain,(
  $lesseq(sK1,sK3) | ~$lesseq(0,3)),
  inference(superposition,[],[f2092,f36])).
fof(f36,plain,(
  ( ! [X0:$int] : ($sum(0,X0) = X0) )),
  inference(superposition,[],[f8,f10])).
fof(f10,plain,(
  ( ! [X0:$int] : ($sum(X0,0) = X0) )),
  introduced(theory_axiom,[])).
fof(f8,plain,(
  ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) )),
  introduced(theory_axiom,[])).
fof(f2092,plain,(
  ( ! [X2:$int] : ($lesseq($sum(X2,sK1),sK3) | ~$lesseq(X2,3)) )),
  inference(resolution,[],[f79,f16])).
fof(f16,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($lesseq($sum(X0,X2),$sum(X1,X2)) | ~$lesseq(X0,X1)) )),
  introduced(theory_axiom,[])).
fof(f79,plain,(
  ( ! [X11:$int] : (~$lesseq(X11,$sum(3,sK1)) | $lesseq(X11,sK3)) )),
  inference(resolution,[],[f14,f34])).
fof(f34,plain,(
  $lesseq($sum(3,sK1),sK3)),
  inference(forward_demodulation,[],[f31,f8])).
fof(f31,plain,(
  $lesseq($sum(sK1,3),sK3)),
  inference(cnf_transformation,[],[f25])).
fof(f25,plain,(
  ! [X4 : $int] : (~$lesseq(sK1,X4) | ~$lesseq(X4,sK2) | ~$lesseq(read(sK0,X4),0)) & ($lesseq($sum(sK1,3),sK3) & $lesseq(sK3,sK2) & $lesseq(read(sK0,sK3),0))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24])).
fof(f24,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (! [X4 : $int] : (~$lesseq(X1,X4) | ~$lesseq(X4,X2) | ~$lesseq(read(X0,X4),0)) & ? [X3 : $int] : ($lesseq($sum(X1,3),X3) & $lesseq(X3,X2) & $lesseq(read(X0,X3),0)))),
  inference(rectify,[],[f23])).
fof(f23,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (~$lesseq(X1,X3) | ~$lesseq(X3,X2) | ~$lesseq(read(X0,X3),0)) & ? [X4 : $int] : ($lesseq($sum(X1,3),X4) & $lesseq(X4,X2) & $lesseq(read(X0,X4),0)))),
  inference(flattening,[],[f22])).
fof(f22,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$lesseq(X1,X3) | ~$lesseq(X3,X2)) | ~$lesseq(read(X0,X3),0)) & ? [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) & $lesseq(read(X0,X4),0)))),
  inference(ennf_transformation,[],[f7])).
fof(f7,plain,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => ~$lesseq(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) => ~$lesseq(read(X0,X4),0)))),
  inference(evaluation,[],[f4])).
fof(f4,negated_conjecture,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) => $greater(read(X0,X4),0)))),
  inference(negated_conjecture,[],[f3])).
fof(f3,conjecture,(
  ! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) => $greater(read(X0,X4),0)))),
  file('Problems/DAT/DAT013=1.p',unknown)).
fof(f14,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X1,X2) | ~$lesseq(X0,X1) | $lesseq(X0,X2)) )),
  introduced(theory_axiom,[])).
fof(f2287,plain,(
  ~$lesseq(sK1,sK3)),
  inference(subsumption_resolution,[],[f2282,f32])).
fof(f32,plain,(
  $lesseq(sK3,sK2)),
  inference(cnf_transformation,[],[f25])).
fof(f2282,plain,(
  ~$lesseq(sK3,sK2) | ~$lesseq(sK1,sK3)),
  inference(resolution,[],[f33,f30])).
fof(f30,plain,(
  ( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) )),
  inference(cnf_transformation,[],[f25])).
fof(f33,plain,(
  $lesseq(read(sK0,sK3),0)),
  inference(cnf_transformation,[],[f25])).
% SZS output end Proof for DAT013=1

Sample solution for SEU140+2

% SZS output start Proof for SEU140+2
fof(f926,plain,(
  $false),
  inference(subsumption_resolution,[],[f901,f501])).
fof(f501,plain,(
  in(sK4(sK2,sK0),sK1)),
  inference(unit_resulting_resolution,[],[f133,f323,f190])).
fof(f190,plain,(
  ( ! [X0,X3,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
  inference(cnf_transformation,[],[f118])).
fof(f118,plain,(
  ! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & ((in(sK7(X1,X0),X0) & ~in(sK7(X1,X0),X1)) | subset(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f117])).
fof(f117,plain,(
  ! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))),
  inference(rectify,[],[f116])).
fof(f116,plain,(
  ! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))),
  inference(nnf_transformation,[],[f98])).
fof(f98,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))),
  inference(ennf_transformation,[],[f8])).
fof(f8,axiom,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  file('Problems/SEU/SEU140+2.p',d3_tarski)).
fof(f323,plain,(
  in(sK4(sK2,sK0),sK0)),
  inference(unit_resulting_resolution,[],[f135,f146])).
fof(f146,plain,(
  ( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f103])).
fof(f103,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78])).
fof(f78,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | ? [X3] : (in(X3,X0) & in(X3,X1))) & (! [X2] : (~in(X2,X0) | ~in(X2,X1)) | ~disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f61])).
fof(f61,plain,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  inference(flattening,[],[f60])).
fof(f60,plain,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X3] : ~(in(X3,X0) & in(X3,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  inference(rectify,[],[f43])).
fof(f43,axiom,(
  ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
  file('Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f135,plain,(
  ~disjoint(sK0,sK2)),
  inference(cnf_transformation,[],[f101])).
fof(f101,plain,(
  subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f75])).
fof(f75,plain,(
  ? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
  inference(flattening,[],[f74])).
fof(f74,plain,(
  ? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
  inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
  ~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
  ! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  file('Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f133,plain,(
  subset(sK0,sK1)),
  inference(cnf_transformation,[],[f101])).
fof(f901,plain,(
  ~in(sK4(sK2,sK0),sK1)),
  inference(unit_resulting_resolution,[],[f134,f326,f148])).
fof(f148,plain,(
  ( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
  inference(cnf_transformation,[],[f103])).
fof(f326,plain,(
  in(sK4(sK2,sK0),sK2)),
  inference(unit_resulting_resolution,[],[f135,f147])).
fof(f147,plain,(
  ( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f103])).
fof(f134,plain,(
  disjoint(sK1,sK2)),
  inference(cnf_transformation,[],[f101])).
% SZS output end Proof for SEU140+2

Sample solution for NLP042+1

% # SZS output start Saturation.
cnf(u110,negated_conjecture,
    past(sK0,sK4)).

cnf(u101,negated_conjecture,
    actual_world(sK0)).

cnf(u109,negated_conjecture,
    patient(sK0,sK4,sK3)).

cnf(u184,negated_conjecture,
    ~patient(sK0,sK4,X0) | ~agent(sK0,sK4,X0)).

cnf(u108,negated_conjecture,
    agent(sK0,sK4,sK1)).

cnf(u203,negated_conjecture,
    ~agent(sK0,sK4,sK3)).

cnf(u111,negated_conjecture,
    nonreflexive(sK0,sK4)).

cnf(u157,axiom,
    ~nonreflexive(X0,X1) | ~agent(X0,X1,X3) | ~patient(X0,X1,X3)).

cnf(u102,negated_conjecture,
    of(sK0,sK2,sK1)).

cnf(u193,negated_conjecture,
    ~of(sK0,X0,sK1) | sK2 = X0 | ~forename(sK0,X0)).

cnf(u155,axiom,
    ~of(X0,X2,X1) | X2 = X3 | ~forename(X0,X3) | ~of(X0,X3,X1) | ~forename(X0,X2) | ~entity(X0,X1)).

cnf(u125,axiom,
    act(X0,X1) | ~order(X0,X1)).

cnf(u120,axiom,
    ~act(X0,X1) | event(X0,X1)).

cnf(u152,axiom,
    singleton(X0,X1) | ~thing(X0,X1)).

cnf(u181,negated_conjecture,
    nonexistent(sK0,sK4)).

cnf(u122,axiom,
    ~nonexistent(X0,X1) | ~existent(X0,X1)).

cnf(u175,negated_conjecture,
    eventuality(sK0,sK4)).

cnf(u135,axiom,
    ~eventuality(X0,X1) | nonexistent(X0,X1)).

cnf(u140,axiom,
    ~eventuality(X0,X1) | specific(X0,X1)).

cnf(u142,axiom,
    ~eventuality(X0,X1) | unisex(X0,X1)).

cnf(u144,axiom,
    ~eventuality(X0,X1) | thing(X0,X1)).

cnf(u127,axiom,
    event(X0,X1) | ~order(X0,X1)).

cnf(u107,negated_conjecture,
    event(sK0,sK4)).

cnf(u153,axiom,
    ~event(X0,X1) | eventuality(X0,X1)).

cnf(u112,negated_conjecture,
    order(sK0,sK4)).

cnf(u176,axiom,
    ~order(X0,X1) | eventuality(X0,X1)).

cnf(u106,negated_conjecture,
    shake_beverage(sK0,sK3)).

cnf(u113,axiom,
    ~shake_beverage(X0,X1) | beverage(X0,X1)).

cnf(u158,negated_conjecture,
    beverage(sK0,sK3)).

cnf(u114,axiom,
    ~beverage(X0,X1) | food(X0,X1)).

cnf(u159,negated_conjecture,
    food(sK0,sK3)).

cnf(u115,axiom,
    ~food(X0,X1) | substance_matter(X0,X1)).

cnf(u160,negated_conjecture,
    substance_matter(sK0,sK3)).

cnf(u117,axiom,
    ~substance_matter(X0,X1) | object(X0,X1)).

cnf(u180,negated_conjecture,
    specific(sK0,sK4)).

cnf(u150,axiom,
    specific(X0,X1) | ~entity(X0,X1)).

cnf(u147,axiom,
    ~specific(X0,X1) | ~general(X0,X1)).

cnf(u149,axiom,
    existent(X0,X1) | ~entity(X0,X1)).

cnf(u183,negated_conjecture,
    ~existent(sK0,sK4)).

cnf(u163,negated_conjecture,
    nonliving(sK0,sK3)).

cnf(u123,axiom,
    ~nonliving(X0,X1) | ~animate(X0,X1)).

cnf(u128,axiom,
    ~nonliving(X0,X1) | ~living(X0,X1)).

cnf(u161,negated_conjecture,
    object(sK0,sK3)).

cnf(u138,axiom,
    ~object(X0,X1) | nonliving(X0,X1)).

cnf(u139,axiom,
    ~object(X0,X1) | impartial(X0,X1)).

cnf(u141,axiom,
    ~object(X0,X1) | entity(X0,X1)).

cnf(u146,axiom,
    ~object(X0,X1) | unisex(X0,X1)).

cnf(u148,axiom,
    relname(X0,X1) | ~forename(X0,X1)).

cnf(u116,axiom,
    ~relname(X0,X1) | relation(X0,X1)).

cnf(u173,axiom,
    relation(X0,X1) | ~forename(X0,X1)).

cnf(u118,axiom,
    ~relation(X0,X1) | abstraction(X0,X1)).

cnf(u178,negated_conjecture,
    thing(sK0,sK4)).

cnf(u145,axiom,
    thing(X0,X1) | ~abstraction(X0,X1)).

cnf(u151,axiom,
    thing(X0,X1) | ~entity(X0,X1)).

cnf(u207,negated_conjecture,
    nonhuman(sK0,sK2)).

cnf(u121,axiom,
    ~nonhuman(X0,X1) | ~human(X0,X1)).

cnf(u136,axiom,
    general(X0,X1) | ~abstraction(X0,X1)).

cnf(u174,axiom,
    ~general(X0,X1) | ~entity(X0,X1)).

cnf(u182,negated_conjecture,
    ~general(sK0,sK4)).

cnf(u179,negated_conjecture,
    unisex(sK0,sK4)).

cnf(u172,negated_conjecture,
    unisex(sK0,sK3)).

cnf(u143,axiom,
    unisex(X0,X1) | ~abstraction(X0,X1)).

cnf(u202,negated_conjecture,
    ~unisex(sK0,sK1)).

cnf(u205,negated_conjecture,
    abstraction(sK0,sK2)).

cnf(u204,negated_conjecture,
    ~abstraction(sK0,sK1)).

cnf(u185,negated_conjecture,
    ~abstraction(sK0,sK4)).

cnf(u137,axiom,
    ~abstraction(X0,X1) | nonhuman(X0,X1)).

cnf(u200,axiom,
    ~abstraction(X0,X1) | ~entity(X0,X1)).

cnf(u119,axiom,
    forename(X0,X1) | ~mia_forename(X0,X1)).

cnf(u105,negated_conjecture,
    forename(sK0,sK2)).

cnf(u199,axiom,
    ~forename(X0,X1) | abstraction(X0,X1)).

cnf(u104,negated_conjecture,
    mia_forename(sK0,sK2)).

cnf(u206,axiom,
    ~mia_forename(X0,X1) | abstraction(X0,X1)).

cnf(u191,negated_conjecture,
    entity(sK0,sK1)).

cnf(u171,negated_conjecture,
    entity(sK0,sK3)).

cnf(u134,axiom,
    entity(X0,X1) | ~organism(X0,X1)).

cnf(u212,negated_conjecture,
    ~entity(sK0,sK2)).

cnf(u186,negated_conjecture,
    ~entity(sK0,sK4)).

cnf(u166,negated_conjecture,
    impartial(sK0,sK3)).

cnf(u133,axiom,
    impartial(X0,X1) | ~organism(X0,X1)).

cnf(u131,axiom,
    living(X0,X1) | ~organism(X0,X1)).

cnf(u164,negated_conjecture,
    ~living(sK0,sK3)).

cnf(u132,axiom,
    organism(X0,X1) | ~human_person(X0,X1)).

cnf(u214,negated_conjecture,
    ~organism(sK0,sK2)).

cnf(u187,negated_conjecture,
    ~organism(sK0,sK4)).

cnf(u167,negated_conjecture,
    ~organism(sK0,sK3)).

cnf(u130,axiom,
    human(X0,X1) | ~human_person(X0,X1)).

cnf(u209,negated_conjecture,
    ~human(sK0,sK2)).

cnf(u129,axiom,
    animate(X0,X1) | ~human_person(X0,X1)).

cnf(u165,negated_conjecture,
    ~animate(sK0,sK3)).

cnf(u126,axiom,
    human_person(X0,X1) | ~woman(X0,X1)).

cnf(u210,negated_conjecture,
    ~human_person(sK0,sK2)).

cnf(u188,negated_conjecture,
    ~human_person(sK0,sK4)).

cnf(u168,negated_conjecture,
    ~human_person(sK0,sK3)).

cnf(u124,axiom,
    female(X0,X1) | ~woman(X0,X1)).

cnf(u154,axiom,
    ~female(X0,X1) | ~unisex(X0,X1)).

cnf(u103,negated_conjecture,
    woman(sK0,sK1)).

cnf(u177,axiom,
    ~woman(X0,X1) | ~unisex(X0,X1)).

cnf(u211,negated_conjecture,
    ~woman(sK0,sK2)).

cnf(u198,negated_conjecture,
    ~woman(sK0,sK4)).

cnf(u170,negated_conjecture,
    ~woman(sK0,sK3)).

% # SZS output end Saturation.

Sample solution for SWV017+1

% SZS output start FiniteModel for SWV017+1 
fof(domain,interpretation_domain,
      ! [X] : (
         X = fmb1 | X = fmb2
      ) ).

fof(distinct_domain,interpreted_domain,
         fmb1 != fmb2
).

fof(constant_at,functors,at = fmb1).
fof(constant_t,functors,t = fmb2).
fof(constant_a,functors,a = fmb1).
fof(constant_b,functors,b = fmb1).
fof(constant_an_a_nonce,functors,an_a_nonce = fmb1).
fof(constant_bt,functors,bt = fmb1).
fof(constant_an_intruder_nonce,functors,an_intruder_nonce = fmb1).

fof(function_key,functors,
         key(fmb1,fmb1) = fmb1 & 
         key(fmb1,fmb2) = fmb2 & 
         key(fmb2,fmb1) = fmb2 & 
         key(fmb2,fmb2) = fmb2
).

fof(function_pair,functors,
         pair(fmb1,fmb1) = fmb2 & 
         pair(fmb1,fmb2) = fmb1 & 
         pair(fmb2,fmb1) = fmb1 & 
         pair(fmb2,fmb2) = fmb1
).

fof(function_sent,functors,
         sent(fmb1,fmb1,fmb1) = fmb1 & 
         sent(fmb1,fmb1,fmb2) = fmb1 & 
         sent(fmb1,fmb2,fmb1) = fmb1 & 
         sent(fmb1,fmb2,fmb2) = fmb1 & 
         sent(fmb2,fmb1,fmb1) = fmb1 & 
         sent(fmb2,fmb1,fmb2) = fmb1 & 
         sent(fmb2,fmb2,fmb1) = fmb1 & 
         sent(fmb2,fmb2,fmb2) = fmb1
).

fof(function_quadruple,functors,
         quadruple(fmb1,fmb1,fmb1,fmb1) = fmb2 & 
         quadruple(fmb1,fmb1,fmb1,fmb2) = fmb2 & 
         quadruple(fmb1,fmb1,fmb2,fmb1) = fmb2 & 
         quadruple(fmb1,fmb1,fmb2,fmb2) = fmb2 & 
         quadruple(fmb1,fmb2,fmb1,fmb1) = fmb2 & 
         quadruple(fmb1,fmb2,fmb1,fmb2) = fmb1 & 
         quadruple(fmb1,fmb2,fmb2,fmb1) = fmb1 & 
         quadruple(fmb1,fmb2,fmb2,fmb2) = fmb1 & 
         quadruple(fmb2,fmb1,fmb1,fmb1) = fmb2 & 
         quadruple(fmb2,fmb1,fmb1,fmb2) = fmb1 & 
         quadruple(fmb2,fmb1,fmb2,fmb1) = fmb1 & 
         quadruple(fmb2,fmb1,fmb2,fmb2) = fmb1 & 
         quadruple(fmb2,fmb2,fmb1,fmb1) = fmb1 & 
         quadruple(fmb2,fmb2,fmb1,fmb2) = fmb1 & 
         quadruple(fmb2,fmb2,fmb2,fmb1) = fmb1 & 
         quadruple(fmb2,fmb2,fmb2,fmb2) = fmb1
).

fof(function_encrypt,functors,
         encrypt(fmb1,fmb1) = fmb2 & 
         encrypt(fmb1,fmb2) = fmb2 & 
         encrypt(fmb2,fmb1) = fmb1 & 
         encrypt(fmb2,fmb2) = fmb1
).

fof(function_triple,functors,
         triple(fmb1,fmb1,fmb1) = fmb2 & 
         triple(fmb1,fmb1,fmb2) = fmb2 & 
         triple(fmb1,fmb2,fmb1) = fmb2 & 
         triple(fmb1,fmb2,fmb2) = fmb1 & 
         triple(fmb2,fmb1,fmb1) = fmb2 & 
         triple(fmb2,fmb1,fmb2) = fmb1 & 
         triple(fmb2,fmb2,fmb1) = fmb1 & 
         triple(fmb2,fmb2,fmb2) = fmb1
).

fof(function_generate_b_nonce,functors,
         generate_b_nonce(fmb1) = fmb1 & 
         generate_b_nonce(fmb2) = fmb1
).

fof(function_generate_expiration_time,functors,
         generate_expiration_time(fmb1) = fmb1 & 
         generate_expiration_time(fmb2) = fmb1
).

fof(function_generate_key,functors,
         generate_key(fmb1) = fmb2 & 
         generate_key(fmb2) = fmb2
).

fof(function_generate_intruder_nonce,functors,
         generate_intruder_nonce(fmb1) = fmb1 & 
         generate_intruder_nonce(fmb2) = fmb1
).


fof(predicate_a_holds,predicates,
         ~a_holds(fmb1)  & 
         ~a_holds(fmb2) 
).

fof(predicate_party_of_protocol,predicates,
         party_of_protocol(fmb1)  & 
         party_of_protocol(fmb2) 
).

fof(predicate_message,predicates,
         message(fmb1)  & 
         ~message(fmb2) 
).

fof(predicate_a_stored,predicates,
         a_stored(fmb1)  & 
         a_stored(fmb2) 
).

fof(predicate_b_holds,predicates,
         ~b_holds(fmb1)  & 
         ~b_holds(fmb2) 
).

fof(predicate_fresh_to_b,predicates,
         fresh_to_b(fmb1)  & 
         ~fresh_to_b(fmb2) 
).

fof(predicate_b_stored,predicates,
         ~b_stored(fmb1)  & 
         ~b_stored(fmb2) 
).

fof(predicate_a_key,predicates,
         ~a_key(fmb1)  & 
         a_key(fmb2) 
).

fof(predicate_t_holds,predicates,
         t_holds(fmb1)  & 
         ~t_holds(fmb2) 
).

fof(predicate_a_nonce,predicates,
         a_nonce(fmb1)  & 
         ~a_nonce(fmb2) 
).

fof(predicate_intruder_message,predicates,
         intruder_message(fmb1)  & 
         intruder_message(fmb2) 
).

fof(predicate_intruder_holds,predicates,
         intruder_holds(fmb1)  & 
         intruder_holds(fmb2) 
).

fof(predicate_fresh_intruder_nonce,predicates,
         fresh_intruder_nonce(fmb1)  & 
         ~fresh_intruder_nonce(fmb2) 
).
% SZS output end FiniteModel for SWV017+1 

VampireZ3 1.0

Sample solution for DAT013=1

% SZS output start Proof for DAT013=1
fof(f208,plain,(
  $false),
  inference(sat_splitting_refutation,[],[f20,f34,f19,f35,f18,f36,f16,f37,f15,f38,f14,f39,f13,f40,f12,f41,f11,f42,f10,f43,f9,f44,f8,f45,f28,f46,f29,f47,f33,f49,f32,f51,f31,f53,f30,f54,f55,f57,f59,f60,f61,f62,f63,f70,f71,f73,f72,f74,f76,f83,f77,f78,f84,f79,f85,f80,f81,f86,f82,f87,f89,f90,f95,f92,f93,f96,f101,f102,f98,f99,f103,f107,f114,f109,f118,f116,f110,f122,f120,f111,f123,f112,f124,f113,f128,f126,f132,f133,f141,f134,f142,f136,f143,f137,f144,f138,f145,f139,f146,f140,f147,f152,f164,f153,f165,f155,f167,f156,f157,f168,f158,f169,f160,f171,f161,f162,f172,f163,f173,f177,f178,f180,f189,f181,f190,f182,f183,f186,f203,f205,f200,f206,f201,f202,f207])).
fof(f207,plain,(
  ( ! [X1:$int] : (~$lesseq(X1,sK2) | ~$lesseq(sK1,X1) | $lesseq(0,read(sK0,X1))) ) | $spl120),
  inference(cnf_transformation,[],[f207_D])).
fof(f207_D,plain,(
  ( ! [X1:$int] : (~$lesseq(X1,sK2) | ~$lesseq(sK1,X1) | $lesseq(0,read(sK0,X1))) ) <=> ~$spl120),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl120])])).
fof(f202,plain,(
  ( ! [X2:$int] : (~$lesseq(X2,sK2) | ~$lesseq(sK1,X2) | $lesseq(0,read(sK0,X2))) ) | ($spl8 | $spl34)),
  inference(resolution,[],[f54,f38])).
fof(f201,plain,(
  ( ! [X1:$int] : (~$lesseq(X1,sK2) | ~$lesseq(sK1,X1) | $lesseq(0,read(sK0,X1))) ) | ($spl8 | $spl34)),
  inference(resolution,[],[f54,f38])).
fof(f206,plain,(
  ( ! [X0:$int] : (~$lesseq(X0,sK2) | ~$lesseq(sK1,X0) | $lesseq(1,read(sK0,X0))) ) | $spl118),
  inference(cnf_transformation,[],[f206_D])).
fof(f206_D,plain,(
  ( ! [X0:$int] : (~$lesseq(X0,sK2) | ~$lesseq(sK1,X0) | $lesseq(1,read(sK0,X0))) ) <=> ~$spl118),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl118])])).
fof(f200,plain,(
  ( ! [X0:$int] : (~$lesseq(X0,sK2) | ~$lesseq(sK1,X0) | $lesseq(1,read(sK0,X0))) ) | ($spl34 | $spl42)),
  inference(resolution,[],[f54,f74])).
fof(f205,plain,(
  ~$lesseq(sK1,sK3) | $spl117),
  inference(cnf_transformation,[],[f205_D])).
fof(f205_D,plain,(
  ~$lesseq(sK1,sK3) <=> ~$spl117),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl117])])).
fof(f203,plain,(
  ~$lesseq(sK1,sK3) | ($spl28 | $spl30 | $spl34)),
  inference(subsumption_resolution,[],[f199,f51])).
fof(f199,plain,(
  ~$lesseq(sK3,sK2) | ~$lesseq(sK1,sK3) | ($spl28 | $spl34)),
  inference(resolution,[],[f54,f49])).
fof(f186,plain,(
  ( ! [X4:$int,X3:$int] : ($sum($uminus(X4),$uminus(X3)) = $uminus($sum(X4,X3))) ) | $spl110),
  inference(cnf_transformation,[],[f186_D])).
fof(f186_D,plain,(
  ( ! [X4:$int,X3:$int] : ($sum($uminus(X4),$uminus(X3)) = $uminus($sum(X4,X3))) ) <=> ~$spl110),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl110])])).
fof(f183,plain,(
  ( ! [X10:$int,X9:$int] : ($sum($uminus(X10),$uminus(X9)) = $uminus($sum(X10,X9))) ) | ($spl16 | $spl22)),
  inference(superposition,[],[f45,f42])).
fof(f182,plain,(
  ( ! [X8:$int,X7:$int] : ($sum($uminus(X8),$uminus(X7)) = $uminus($sum(X8,X7))) ) | ($spl16 | $spl22)),
  inference(superposition,[],[f45,f42])).
fof(f190,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($uminus($sum(X5,X4)),$sum(X6,$uminus(X5))) | ~$lesseq($uminus(X4),X6)) ) | $spl114),
  inference(cnf_transformation,[],[f190_D])).
fof(f190_D,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($uminus($sum(X5,X4)),$sum(X6,$uminus(X5))) | ~$lesseq($uminus(X4),X6)) ) <=> ~$spl114),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl114])])).
fof(f181,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($uminus($sum(X5,X4)),$sum(X6,$uminus(X5))) | ~$lesseq($uminus(X4),X6)) ) | ($spl6 | $spl16)),
  inference(superposition,[],[f37,f42])).
fof(f189,plain,(
  ( ! [X2:$int,X3:$int,X1:$int] : ($lesseq($sum(X3,$uminus(X2)),$uminus($sum(X2,X1))) | ~$lesseq(X3,$uminus(X1))) ) | $spl112),
  inference(cnf_transformation,[],[f189_D])).
fof(f189_D,plain,(
  ( ! [X2:$int,X3:$int,X1:$int] : ($lesseq($sum(X3,$uminus(X2)),$uminus($sum(X2,X1))) | ~$lesseq(X3,$uminus(X1))) ) <=> ~$spl112),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl112])])).
fof(f180,plain,(
  ( ! [X2:$int,X3:$int,X1:$int] : ($lesseq($sum(X3,$uminus(X2)),$uminus($sum(X2,X1))) | ~$lesseq(X3,$uminus(X1))) ) | ($spl6 | $spl16)),
  inference(superposition,[],[f37,f42])).
fof(f178,plain,(
  ( ! [X6:$int,X5:$int] : ($sum($uminus(X6),$uminus(X5)) = $uminus($sum(X6,X5))) ) | ($spl16 | $spl22)),
  inference(superposition,[],[f42,f45])).
fof(f177,plain,(
  ( ! [X4:$int,X3:$int] : ($sum($uminus(X4),$uminus(X3)) = $uminus($sum(X4,X3))) ) | ($spl16 | $spl22)),
  inference(superposition,[],[f42,f45])).
fof(f173,plain,(
  ( ! [X10:$int,X11:$int] : ($lesseq($sum(X11,X10),X10) | ~$lesseq(X11,0)) ) | $spl108),
  inference(cnf_transformation,[],[f173_D])).
fof(f173_D,plain,(
  ( ! [X10:$int,X11:$int] : ($lesseq($sum(X11,X10),X10) | ~$lesseq(X11,0)) ) <=> ~$spl108),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl108])])).
fof(f163,plain,(
  ( ! [X10:$int,X11:$int] : ($lesseq($sum(X11,X10),X10) | ~$lesseq(X11,0)) ) | ($spl6 | $spl38)),
  inference(superposition,[],[f37,f63])).
fof(f172,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X6,X5),$sum(X5,X4)) | ~$lesseq(X6,X4)) ) | $spl106),
  inference(cnf_transformation,[],[f172_D])).
fof(f172_D,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X6,X5),$sum(X5,X4)) | ~$lesseq(X6,X4)) ) <=> ~$spl106),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl106])])).
fof(f162,plain,(
  ( ! [X8:$int,X7:$int,X9:$int] : ($lesseq($sum(X9,X8),$sum(X8,X7)) | ~$lesseq(X9,X7)) ) | ($spl6 | $spl22)),
  inference(superposition,[],[f37,f45])).
fof(f161,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X6,X5),$sum(X5,X4)) | ~$lesseq(X6,X4)) ) | ($spl6 | $spl22)),
  inference(superposition,[],[f37,f45])).
fof(f171,plain,(
  ( ! [X2:$int,X3:$int] : ($lesseq($sum(X3,$uminus(X2)),0) | ~$lesseq(X3,X2)) ) | $spl104),
  inference(cnf_transformation,[],[f171_D])).
fof(f171_D,plain,(
  ( ! [X2:$int,X3:$int] : ($lesseq($sum(X3,$uminus(X2)),0) | ~$lesseq(X3,X2)) ) <=> ~$spl104),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl104])])).
fof(f160,plain,(
  ( ! [X2:$int,X3:$int] : ($lesseq($sum(X3,$uminus(X2)),0) | ~$lesseq(X3,X2)) ) | ($spl6 | $spl14)),
  inference(superposition,[],[f37,f41])).
fof(f169,plain,(
  ( ! [X10:$int,X11:$int] : ($lesseq(X10,$sum(X11,X10)) | ~$lesseq(0,X11)) ) | $spl102),
  inference(cnf_transformation,[],[f169_D])).
fof(f169_D,plain,(
  ( ! [X10:$int,X11:$int] : ($lesseq(X10,$sum(X11,X10)) | ~$lesseq(0,X11)) ) <=> ~$spl102),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl102])])).
fof(f158,plain,(
  ( ! [X10:$int,X11:$int] : ($lesseq(X10,$sum(X11,X10)) | ~$lesseq(0,X11)) ) | ($spl6 | $spl38)),
  inference(superposition,[],[f37,f63])).
fof(f168,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X5,X4),$sum(X6,X5)) | ~$lesseq(X4,X6)) ) | $spl100),
  inference(cnf_transformation,[],[f168_D])).
fof(f168_D,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X5,X4),$sum(X6,X5)) | ~$lesseq(X4,X6)) ) <=> ~$spl100),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl100])])).
fof(f157,plain,(
  ( ! [X8:$int,X7:$int,X9:$int] : ($lesseq($sum(X8,X7),$sum(X9,X8)) | ~$lesseq(X7,X9)) ) | ($spl6 | $spl22)),
  inference(superposition,[],[f37,f45])).
fof(f156,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($lesseq($sum(X5,X4),$sum(X6,X5)) | ~$lesseq(X4,X6)) ) | ($spl6 | $spl22)),
  inference(superposition,[],[f37,f45])).
fof(f167,plain,(
  ( ! [X2:$int,X3:$int] : ($lesseq(0,$sum(X3,$uminus(X2))) | ~$lesseq(X2,X3)) ) | $spl98),
  inference(cnf_transformation,[],[f167_D])).
fof(f167_D,plain,(
  ( ! [X2:$int,X3:$int] : ($lesseq(0,$sum(X3,$uminus(X2))) | ~$lesseq(X2,X3)) ) <=> ~$spl98),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl98])])).
fof(f155,plain,(
  ( ! [X2:$int,X3:$int] : ($lesseq(0,$sum(X3,$uminus(X2))) | ~$lesseq(X2,X3)) ) | ($spl6 | $spl14)),
  inference(superposition,[],[f37,f41])).
fof(f165,plain,(
  ( ! [X8:$int,X7:$int,X9:$int] : (~$lesseq(X7,X8) | ~$lesseq($sum(X8,X9),$sum(X7,X9)) | $sum(X7,X9) = $sum(X8,X9)) ) | $spl96),
  inference(cnf_transformation,[],[f165_D])).
fof(f165_D,plain,(
  ( ! [X8:$int,X7:$int,X9:$int] : (~$lesseq(X7,X8) | ~$lesseq($sum(X8,X9),$sum(X7,X9)) | $sum(X7,X9) = $sum(X8,X9)) ) <=> ~$spl96),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl96])])).
fof(f153,plain,(
  ( ! [X8:$int,X7:$int,X9:$int] : (~$lesseq(X7,X8) | ~$lesseq($sum(X8,X9),$sum(X7,X9)) | $sum(X7,X9) = $sum(X8,X9)) ) | ($spl2 | $spl6)),
  inference(resolution,[],[f37,f35])).
fof(f164,plain,(
  ( ! [X6:$int,X4:$int,X5:$int,X3:$int] : (~$lesseq(X3,X4) | ~$lesseq(X5,$sum(X3,X6)) | $lesseq(X5,$sum(X4,X6))) ) | $spl94),
  inference(cnf_transformation,[],[f164_D])).
fof(f164_D,plain,(
  ( ! [X6:$int,X4:$int,X5:$int,X3:$int] : (~$lesseq(X3,X4) | ~$lesseq(X5,$sum(X3,X6)) | $lesseq(X5,$sum(X4,X6))) ) <=> ~$spl94),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl94])])).
fof(f152,plain,(
  ( ! [X6:$int,X4:$int,X5:$int,X3:$int] : (~$lesseq(X3,X4) | ~$lesseq(X5,$sum(X3,X6)) | $lesseq(X5,$sum(X4,X6))) ) | ($spl6 | $spl10)),
  inference(resolution,[],[f37,f39])).
fof(f147,plain,(
  ( ! [X19:$int] : (~$lesseq(X19,sK3) | $lesseq(X19,sK2)) ) | $spl92),
  inference(cnf_transformation,[],[f147_D])).
fof(f147_D,plain,(
  ( ! [X19:$int] : (~$lesseq(X19,sK3) | $lesseq(X19,sK2)) ) <=> ~$spl92),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl92])])).
fof(f140,plain,(
  ( ! [X19:$int] : (~$lesseq(X19,sK3) | $lesseq(X19,sK2)) ) | ($spl10 | $spl30)),
  inference(resolution,[],[f39,f51])).
fof(f146,plain,(
  ( ! [X17:$int,X18:$int] : (~$lesseq(X17,1) | $lesseq(X17,X18) | $lesseq(X18,0)) ) | $spl90),
  inference(cnf_transformation,[],[f146_D])).
fof(f146_D,plain,(
  ( ! [X17:$int,X18:$int] : (~$lesseq(X17,1) | $lesseq(X17,X18) | $lesseq(X18,0)) ) <=> ~$spl90),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl90])])).
fof(f139,plain,(
  ( ! [X17:$int,X18:$int] : (~$lesseq(X17,1) | $lesseq(X17,X18) | $lesseq(X18,0)) ) | ($spl10 | $spl42)),
  inference(resolution,[],[f39,f74])).
fof(f145,plain,(
  ( ! [X14:$int,X15:$int,X16:$int] : (~$lesseq(X14,$sum(X15,1)) | $lesseq(X14,X16) | $lesseq(X16,X15)) ) | $spl88),
  inference(cnf_transformation,[],[f145_D])).
fof(f145_D,plain,(
  ( ! [X14:$int,X15:$int,X16:$int] : (~$lesseq(X14,$sum(X15,1)) | $lesseq(X14,X16) | $lesseq(X16,X15)) ) <=> ~$spl88),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl88])])).
fof(f138,plain,(
  ( ! [X14:$int,X15:$int,X16:$int] : (~$lesseq(X14,$sum(X15,1)) | $lesseq(X14,X16) | $lesseq(X16,X15)) ) | ($spl0 | $spl10)),
  inference(resolution,[],[f39,f34])).
fof(f144,plain,(
  ( ! [X13:$int] : (~$lesseq(X13,$sum(3,sK1)) | $lesseq(X13,sK3)) ) | $spl86),
  inference(cnf_transformation,[],[f144_D])).
fof(f144_D,plain,(
  ( ! [X13:$int] : (~$lesseq(X13,$sum(3,sK1)) | $lesseq(X13,sK3)) ) <=> ~$spl86),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl86])])).
fof(f137,plain,(
  ( ! [X13:$int] : (~$lesseq(X13,$sum(3,sK1)) | $lesseq(X13,sK3)) ) | ($spl10 | $spl36)),
  inference(resolution,[],[f39,f57])).
fof(f143,plain,(
  ( ! [X12:$int] : (~$lesseq(X12,read(sK0,sK3)) | $lesseq(X12,0)) ) | $spl84),
  inference(cnf_transformation,[],[f143_D])).
fof(f143_D,plain,(
  ( ! [X12:$int] : (~$lesseq(X12,read(sK0,sK3)) | $lesseq(X12,0)) ) <=> ~$spl84),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl84])])).
fof(f136,plain,(
  ( ! [X12:$int] : (~$lesseq(X12,read(sK0,sK3)) | $lesseq(X12,0)) ) | ($spl10 | $spl28)),
  inference(resolution,[],[f39,f49])).
fof(f142,plain,(
  ( ! [X8:$int,X9:$int] : (~$lesseq(X8,X9) | $lesseq(X8,0) | $lesseq(1,X9)) ) | $spl82),
  inference(cnf_transformation,[],[f142_D])).
fof(f142_D,plain,(
  ( ! [X8:$int,X9:$int] : (~$lesseq(X8,X9) | $lesseq(X8,0) | $lesseq(1,X9)) ) <=> ~$spl82),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl82])])).
fof(f134,plain,(
  ( ! [X8:$int,X9:$int] : (~$lesseq(X8,X9) | $lesseq(X8,0) | $lesseq(1,X9)) ) | ($spl10 | $spl42)),
  inference(resolution,[],[f39,f74])).
fof(f141,plain,(
  ( ! [X4:$int,X2:$int,X3:$int] : (~$lesseq(X2,X3) | $lesseq(X2,X4) | $lesseq(X4,X3)) ) | $spl80),
  inference(cnf_transformation,[],[f141_D])).
fof(f141_D,plain,(
  ( ! [X4:$int,X2:$int,X3:$int] : (~$lesseq(X2,X3) | $lesseq(X2,X4) | $lesseq(X4,X3)) ) <=> ~$spl80),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl80])])).
fof(f133,plain,(
  ( ! [X6:$int,X7:$int,X5:$int] : (~$lesseq(X5,X6) | $lesseq(X5,X7) | $lesseq(X7,X6)) ) | ($spl8 | $spl10)),
  inference(resolution,[],[f39,f38])).
fof(f132,plain,(
  ( ! [X4:$int,X2:$int,X3:$int] : (~$lesseq(X2,X3) | $lesseq(X2,X4) | $lesseq(X4,X3)) ) | ($spl8 | $spl10)),
  inference(resolution,[],[f39,f38])).
fof(f126,plain,(
  sK2 = sK3 | $spl76),
  inference(cnf_transformation,[],[f126_D])).
fof(f126_D,plain,(
  sK2 = sK3 <=> ~$spl76),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl76])])).
fof(f128,plain,(
  ~$lesseq(sK2,sK3) | $spl79),
  inference(cnf_transformation,[],[f128_D])).
fof(f128_D,plain,(
  ~$lesseq(sK2,sK3) <=> ~$spl79),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl79])])).
fof(f113,plain,(
  ~$lesseq(sK2,sK3) | sK2 = sK3 | ($spl2 | $spl30)),
  inference(resolution,[],[f35,f51])).
fof(f124,plain,(
  ( ! [X9:$int] : (~$lesseq(X9,1) | 1 = X9 | $lesseq(X9,0)) ) | $spl74),
  inference(cnf_transformation,[],[f124_D])).
fof(f124_D,plain,(
  ( ! [X9:$int] : (~$lesseq(X9,1) | 1 = X9 | $lesseq(X9,0)) ) <=> ~$spl74),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl74])])).
fof(f112,plain,(
  ( ! [X9:$int] : (~$lesseq(X9,1) | 1 = X9 | $lesseq(X9,0)) ) | ($spl2 | $spl42)),
  inference(resolution,[],[f35,f74])).
fof(f123,plain,(
  ( ! [X8:$int,X7:$int] : (~$lesseq(X7,$sum(X8,1)) | $sum(X8,1) = X7 | $lesseq(X7,X8)) ) | $spl72),
  inference(cnf_transformation,[],[f123_D])).
fof(f123_D,plain,(
  ( ! [X8:$int,X7:$int] : (~$lesseq(X7,$sum(X8,1)) | $sum(X8,1) = X7 | $lesseq(X7,X8)) ) <=> ~$spl72),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl72])])).
fof(f111,plain,(
  ( ! [X8:$int,X7:$int] : (~$lesseq(X7,$sum(X8,1)) | $sum(X8,1) = X7 | $lesseq(X7,X8)) ) | ($spl0 | $spl2)),
  inference(resolution,[],[f35,f34])).
fof(f120,plain,(
  $sum(3,sK1) = sK3 | $spl68),
  inference(cnf_transformation,[],[f120_D])).
fof(f120_D,plain,(
  $sum(3,sK1) = sK3 <=> ~$spl68),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl68])])).
fof(f122,plain,(
  ~$lesseq(sK3,$sum(3,sK1)) | $spl71),
  inference(cnf_transformation,[],[f122_D])).
fof(f122_D,plain,(
  ~$lesseq(sK3,$sum(3,sK1)) <=> ~$spl71),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl71])])).
fof(f110,plain,(
  ~$lesseq(sK3,$sum(3,sK1)) | $sum(3,sK1) = sK3 | ($spl2 | $spl36)),
  inference(resolution,[],[f35,f57])).
fof(f116,plain,(
  read(sK0,sK3) = 0 | $spl64),
  inference(cnf_transformation,[],[f116_D])).
fof(f116_D,plain,(
  read(sK0,sK3) = 0 <=> ~$spl64),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl64])])).
fof(f118,plain,(
  ~$lesseq(0,read(sK0,sK3)) | $spl67),
  inference(cnf_transformation,[],[f118_D])).
fof(f118_D,plain,(
  ~$lesseq(0,read(sK0,sK3)) <=> ~$spl67),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl67])])).
fof(f109,plain,(
  ~$lesseq(0,read(sK0,sK3)) | read(sK0,sK3) = 0 | ($spl2 | $spl28)),
  inference(resolution,[],[f35,f49])).
fof(f114,plain,(
  ( ! [X5:$int] : (~$lesseq(0,X5) | 0 = X5 | $lesseq(1,X5)) ) | $spl62),
  inference(cnf_transformation,[],[f114_D])).
fof(f114_D,plain,(
  ( ! [X5:$int] : (~$lesseq(0,X5) | 0 = X5 | $lesseq(1,X5)) ) <=> ~$spl62),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl62])])).
fof(f107,plain,(
  ( ! [X5:$int] : (~$lesseq(0,X5) | 0 = X5 | $lesseq(1,X5)) ) | ($spl2 | $spl42)),
  inference(resolution,[],[f35,f74])).
fof(f103,plain,(
  ( ! [X0:$int] : ($lesseq(X0,$sum(1,X0))) ) | $spl60),
  inference(cnf_transformation,[],[f103_D])).
fof(f103_D,plain,(
  ( ! [X0:$int] : ($lesseq(X0,$sum(1,X0))) ) <=> ~$spl60),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl60])])).
fof(f99,plain,(
  ( ! [X1:$int] : ($lesseq(X1,$sum(1,X1))) ) | ($spl22 | $spl54)),
  inference(superposition,[],[f95,f45])).
fof(f98,plain,(
  ( ! [X0:$int] : ($lesseq(X0,$sum(1,X0))) ) | ($spl22 | $spl54)),
  inference(superposition,[],[f95,f45])).
fof(f102,plain,(
  ( ! [X0:$int] : (~$lesseq($sum(1,$sum(X0,1)),X0)) ) | $spl58),
  inference(cnf_transformation,[],[f102_D])).
fof(f102_D,plain,(
  ( ! [X0:$int] : (~$lesseq($sum(1,$sum(X0,1)),X0)) ) <=> ~$spl58),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl58])])).
fof(f101,plain,(
  ( ! [X0:$int] : (~$lesseq($sum(1,$sum(X0,1)),X0)) ) | ($spl4 | $spl22 | $spl54)),
  inference(forward_demodulation,[],[f97,f45])).
fof(f97,plain,(
  ( ! [X0:$int] : (~$lesseq($sum($sum(X0,1),1),X0)) ) | ($spl4 | $spl54)),
  inference(resolution,[],[f95,f36])).
fof(f96,plain,(
  ( ! [X0:$int] : (~$lesseq($sum(1,X0),X0)) ) | $spl56),
  inference(cnf_transformation,[],[f96_D])).
fof(f96_D,plain,(
  ( ! [X0:$int] : (~$lesseq($sum(1,X0),X0)) ) <=> ~$spl56),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl56])])).
fof(f93,plain,(
  ( ! [X1:$int] : (~$lesseq($sum(1,X1),X1)) ) | ($spl22 | $spl44)),
  inference(superposition,[],[f83,f45])).
fof(f92,plain,(
  ( ! [X0:$int] : (~$lesseq($sum(1,X0),X0)) ) | ($spl22 | $spl44)),
  inference(superposition,[],[f83,f45])).
fof(f95,plain,(
  ( ! [X1:$int] : ($lesseq(X1,$sum(X1,1))) ) | $spl54),
  inference(cnf_transformation,[],[f95_D])).
fof(f95_D,plain,(
  ( ! [X1:$int] : ($lesseq(X1,$sum(X1,1))) ) <=> ~$spl54),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl54])])).
fof(f90,plain,(
  ( ! [X2:$int] : ($lesseq(X2,$sum(X2,1))) ) | ($spl8 | $spl44)),
  inference(resolution,[],[f83,f38])).
fof(f89,plain,(
  ( ! [X1:$int] : ($lesseq(X1,$sum(X1,1))) ) | ($spl8 | $spl44)),
  inference(resolution,[],[f83,f38])).
fof(f87,plain,(
  ( ! [X4:$int] : (~$lesseq(1,X4) | ~$lesseq(X4,0)) ) | $spl52),
  inference(cnf_transformation,[],[f87_D])).
fof(f87_D,plain,(
  ( ! [X4:$int] : (~$lesseq(1,X4) | ~$lesseq(X4,0)) ) <=> ~$spl52),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl52])])).
fof(f82,plain,(
  ( ! [X4:$int] : (~$lesseq(1,X4) | ~$lesseq(X4,0)) ) | ($spl4 | $spl38)),
  inference(superposition,[],[f36,f63])).
fof(f86,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq($sum(1,X0),X1) | ~$lesseq(X1,X0)) ) | $spl50),
  inference(cnf_transformation,[],[f86_D])).
fof(f86_D,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq($sum(1,X0),X1) | ~$lesseq(X1,X0)) ) <=> ~$spl50),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl50])])).
fof(f81,plain,(
  ( ! [X2:$int,X3:$int] : (~$lesseq($sum(1,X2),X3) | ~$lesseq(X3,X2)) ) | ($spl4 | $spl22)),
  inference(superposition,[],[f36,f45])).
fof(f80,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq($sum(1,X0),X1) | ~$lesseq(X1,X0)) ) | ($spl4 | $spl22)),
  inference(superposition,[],[f36,f45])).
fof(f85,plain,(
  ( ! [X7:$int] : (~$lesseq(0,X7) | $lesseq(1,$sum(X7,1))) ) | $spl48),
  inference(cnf_transformation,[],[f85_D])).
fof(f85_D,plain,(
  ( ! [X7:$int] : (~$lesseq(0,X7) | $lesseq(1,$sum(X7,1))) ) <=> ~$spl48),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl48])])).
fof(f79,plain,(
  ( ! [X7:$int] : (~$lesseq(0,X7) | $lesseq(1,$sum(X7,1))) ) | ($spl4 | $spl42)),
  inference(resolution,[],[f36,f74])).
fof(f84,plain,(
  ( ! [X4:$int,X3:$int] : (~$lesseq(X3,X4) | $lesseq(X3,$sum(X4,1))) ) | $spl46),
  inference(cnf_transformation,[],[f84_D])).
fof(f84_D,plain,(
  ( ! [X4:$int,X3:$int] : (~$lesseq(X3,X4) | $lesseq(X3,$sum(X4,1))) ) <=> ~$spl46),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl46])])).
fof(f78,plain,(
  ( ! [X6:$int,X5:$int] : (~$lesseq(X5,X6) | $lesseq(X5,$sum(X6,1))) ) | ($spl4 | $spl8)),
  inference(resolution,[],[f36,f38])).
fof(f77,plain,(
  ( ! [X4:$int,X3:$int] : (~$lesseq(X3,X4) | $lesseq(X3,$sum(X4,1))) ) | ($spl4 | $spl8)),
  inference(resolution,[],[f36,f38])).
fof(f83,plain,(
  ( ! [X2:$int] : (~$lesseq($sum(X2,1),X2)) ) | $spl44),
  inference(cnf_transformation,[],[f83_D])).
fof(f83_D,plain,(
  ( ! [X2:$int] : (~$lesseq($sum(X2,1),X2)) ) <=> ~$spl44),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl44])])).
fof(f76,plain,(
  ( ! [X2:$int] : (~$lesseq($sum(X2,1),X2)) ) | ($spl4 | $spl12)),
  inference(resolution,[],[f36,f40])).
fof(f74,plain,(
  ( ! [X4:$int] : ($lesseq(1,X4) | $lesseq(X4,0)) ) | $spl42),
  inference(cnf_transformation,[],[f74_D])).
fof(f74_D,plain,(
  ( ! [X4:$int] : ($lesseq(1,X4) | $lesseq(X4,0)) ) <=> ~$spl42),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl42])])).
fof(f72,plain,(
  ( ! [X4:$int] : ($lesseq(1,X4) | $lesseq(X4,0)) ) | ($spl0 | $spl38)),
  inference(superposition,[],[f34,f63])).
fof(f73,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq($sum(1,X0),X1) | $lesseq(X1,X0)) ) | $spl40),
  inference(cnf_transformation,[],[f73_D])).
fof(f73_D,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq($sum(1,X0),X1) | $lesseq(X1,X0)) ) <=> ~$spl40),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl40])])).
fof(f71,plain,(
  ( ! [X2:$int,X3:$int] : ($lesseq($sum(1,X2),X3) | $lesseq(X3,X2)) ) | ($spl0 | $spl22)),
  inference(superposition,[],[f34,f45])).
fof(f70,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq($sum(1,X0),X1) | $lesseq(X1,X0)) ) | ($spl0 | $spl22)),
  inference(superposition,[],[f34,f45])).
fof(f63,plain,(
  ( ! [X0:$int] : ($sum(0,X0) = X0) ) | $spl38),
  inference(cnf_transformation,[],[f63_D])).
fof(f63_D,plain,(
  ( ! [X0:$int] : ($sum(0,X0) = X0) ) <=> ~$spl38),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl38])])).
fof(f62,plain,(
  ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)),
  inference(superposition,[],[f43,f45])).
fof(f61,plain,(
  ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)),
  inference(superposition,[],[f43,f45])).
fof(f60,plain,(
  ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)),
  inference(superposition,[],[f45,f43])).
fof(f59,plain,(
  ( ! [X0:$int] : ($sum(0,X0) = X0) ) | ($spl18 | $spl22)),
  inference(superposition,[],[f45,f43])).
fof(f57,plain,(
  $lesseq($sum(3,sK1),sK3) | $spl36),
  inference(cnf_transformation,[],[f57_D])).
fof(f57_D,plain,(
  $lesseq($sum(3,sK1),sK3) <=> ~$spl36),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl36])])).
fof(f55,plain,(
  $lesseq($sum(3,sK1),sK3) | ($spl22 | $spl32)),
  inference(backward_demodulation,[],[f45,f53])).
fof(f54,plain,(
  ( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) ) | $spl34),
  inference(cnf_transformation,[],[f54_D])).
fof(f54_D,plain,(
  ( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) ) <=> ~$spl34),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl34])])).
fof(f30,plain,(
  ( ! [X4:$int] : (~$lesseq(read(sK0,X4),0) | ~$lesseq(X4,sK2) | ~$lesseq(sK1,X4)) )),
  inference(cnf_transformation,[],[f25])).
fof(f25,plain,(
  ! [X4 : $int] : (~$lesseq(sK1,X4) | ~$lesseq(X4,sK2) | ~$lesseq(read(sK0,X4),0)) & ($lesseq($sum(sK1,3),sK3) & $lesseq(sK3,sK2) & $lesseq(read(sK0,sK3),0))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24])).
fof(f24,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (! [X4 : $int] : (~$lesseq(X1,X4) | ~$lesseq(X4,X2) | ~$lesseq(read(X0,X4),0)) & ? [X3 : $int] : ($lesseq($sum(X1,3),X3) & $lesseq(X3,X2) & $lesseq(read(X0,X3),0)))),
  inference(rectify,[],[f23])).
fof(f23,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (~$lesseq(X1,X3) | ~$lesseq(X3,X2) | ~$lesseq(read(X0,X3),0)) & ? [X4 : $int] : ($lesseq($sum(X1,3),X4) & $lesseq(X4,X2) & $lesseq(read(X0,X4),0)))),
  inference(flattening,[],[f22])).
fof(f22,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$lesseq(X1,X3) | ~$lesseq(X3,X2)) | ~$lesseq(read(X0,X3),0)) & ? [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) & $lesseq(read(X0,X4),0)))),
  inference(ennf_transformation,[],[f7])).
fof(f7,plain,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => ~$lesseq(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) => ~$lesseq(read(X0,X4),0)))),
  inference(evaluation,[],[f4])).
fof(f4,negated_conjecture,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) => $greater(read(X0,X4),0)))),
  inference(negated_conjecture,[],[f3])).
fof(f3,conjecture,(
  ! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq($sum(X1,3),X4) & $lesseq(X4,X2)) => $greater(read(X0,X4),0)))),
  file('Problems/DAT/DAT013=1.p',unknown)).
fof(f53,plain,(
  $lesseq($sum(sK1,3),sK3) | $spl32),
  inference(cnf_transformation,[],[f53_D])).
fof(f53_D,plain,(
  $lesseq($sum(sK1,3),sK3) <=> ~$spl32),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl32])])).
fof(f31,plain,(
  $lesseq($sum(sK1,3),sK3)),
  inference(cnf_transformation,[],[f25])).
fof(f51,plain,(
  $lesseq(sK3,sK2) | $spl30),
  inference(cnf_transformation,[],[f51_D])).
fof(f51_D,plain,(
  $lesseq(sK3,sK2) <=> ~$spl30),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl30])])).
fof(f32,plain,(
  $lesseq(sK3,sK2)),
  inference(cnf_transformation,[],[f25])).
fof(f49,plain,(
  $lesseq(read(sK0,sK3),0) | $spl28),
  inference(cnf_transformation,[],[f49_D])).
fof(f49_D,plain,(
  $lesseq(read(sK0,sK3),0) <=> ~$spl28),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl28])])).
fof(f33,plain,(
  $lesseq(read(sK0,sK3),0)),
  inference(cnf_transformation,[],[f25])).
fof(f47,plain,(
  ( ! [X2:$int,X0,X3:$int,X1:$int] : (read(X0,X2) = read(write(X0,X1,X3),X2) | X1 = X2) ) | $spl26),
  inference(cnf_transformation,[],[f47_D])).
fof(f47_D,plain,(
  ( ! [X2:$int,X0,X3:$int,X1:$int] : (read(X0,X2) = read(write(X0,X1,X3),X2) | X1 = X2) ) <=> ~$spl26),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl26])])).
fof(f29,plain,(
  ( ! [X2:$int,X0,X3:$int,X1:$int] : (read(X0,X2) = read(write(X0,X1,X3),X2) | X1 = X2) )),
  inference(cnf_transformation,[],[f21])).
fof(f21,plain,(
  ! [X0 : array,X1 : $int,X2 : $int,X3 : $int] : (X1 = X2 | read(X0,X2) = read(write(X0,X1,X3),X2))),
  inference(rectify,[],[f2])).
fof(f2,axiom,(
  ! [X3 : array,X4 : $int,X5 : $int,X6 : $int] : (X4 = X5 | read(X3,X5) = read(write(X3,X4,X6),X5))),
  file('Problems/DAT/DAT013=1.p',unknown)).
fof(f46,plain,(
  ( ! [X2:$int,X0,X1:$int] : (read(write(X0,X1,X2),X1) = X2) ) | $spl24),
  inference(cnf_transformation,[],[f46_D])).
fof(f46_D,plain,(
  ( ! [X2:$int,X0,X1:$int] : (read(write(X0,X1,X2),X1) = X2) ) <=> ~$spl24),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl24])])).
fof(f28,plain,(
  ( ! [X2:$int,X0,X1:$int] : (read(write(X0,X1,X2),X1) = X2) )),
  inference(cnf_transformation,[],[f1])).
fof(f1,axiom,(
  ! [X0 : array,X1 : $int,X2 : $int] : read(write(X0,X1,X2),X1) = X2),
  file('Problems/DAT/DAT013=1.p',unknown)).
fof(f45,plain,(
  ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) ) | $spl22),
  inference(cnf_transformation,[],[f45_D])).
fof(f45_D,plain,(
  ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) ) <=> ~$spl22),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl22])])).
fof(f8,plain,(
  ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) )),
  introduced(theory_axiom,[])).
fof(f44,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) ) | $spl20),
  inference(cnf_transformation,[],[f44_D])).
fof(f44_D,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) ) <=> ~$spl20),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl20])])).
fof(f9,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
  introduced(theory_axiom,[])).
fof(f43,plain,(
  ( ! [X0:$int] : ($sum(X0,0) = X0) ) | $spl18),
  inference(cnf_transformation,[],[f43_D])).
fof(f43_D,plain,(
  ( ! [X0:$int] : ($sum(X0,0) = X0) ) <=> ~$spl18),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl18])])).
fof(f10,plain,(
  ( ! [X0:$int] : ($sum(X0,0) = X0) )),
  introduced(theory_axiom,[])).
fof(f42,plain,(
  ( ! [X0:$int,X1:$int] : ($sum($uminus(X1),$uminus(X0)) = $uminus($sum(X0,X1))) ) | $spl16),
  inference(cnf_transformation,[],[f42_D])).
fof(f42_D,plain,(
  ( ! [X0:$int,X1:$int] : ($sum($uminus(X1),$uminus(X0)) = $uminus($sum(X0,X1))) ) <=> ~$spl16),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl16])])).
fof(f11,plain,(
  ( ! [X0:$int,X1:$int] : ($sum($uminus(X1),$uminus(X0)) = $uminus($sum(X0,X1))) )),
  introduced(theory_axiom,[])).
fof(f41,plain,(
  ( ! [X0:$int] : (0 = $sum(X0,$uminus(X0))) ) | $spl14),
  inference(cnf_transformation,[],[f41_D])).
fof(f41_D,plain,(
  ( ! [X0:$int] : (0 = $sum(X0,$uminus(X0))) ) <=> ~$spl14),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl14])])).
fof(f12,plain,(
  ( ! [X0:$int] : (0 = $sum(X0,$uminus(X0))) )),
  introduced(theory_axiom,[])).
fof(f40,plain,(
  ( ! [X0:$int] : ($lesseq(X0,X0)) ) | $spl12),
  inference(cnf_transformation,[],[f40_D])).
fof(f40_D,plain,(
  ( ! [X0:$int] : ($lesseq(X0,X0)) ) <=> ~$spl12),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl12])])).
fof(f13,plain,(
  ( ! [X0:$int] : ($lesseq(X0,X0)) )),
  introduced(theory_axiom,[])).
fof(f39,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X1,X2) | ~$lesseq(X0,X1) | $lesseq(X0,X2)) ) | $spl10),
  inference(cnf_transformation,[],[f39_D])).
fof(f39_D,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X1,X2) | ~$lesseq(X0,X1) | $lesseq(X0,X2)) ) <=> ~$spl10),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl10])])).
fof(f14,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X0,X1) | ~$lesseq(X1,X2) | $lesseq(X0,X2)) )),
  introduced(theory_axiom,[])).
fof(f38,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq(X0,X1) | $lesseq(X1,X0)) ) | $spl8),
  inference(cnf_transformation,[],[f38_D])).
fof(f38_D,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq(X0,X1) | $lesseq(X1,X0)) ) <=> ~$spl8),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl8])])).
fof(f15,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq(X0,X1) | $lesseq(X1,X0)) )),
  introduced(theory_axiom,[])).
fof(f37,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($lesseq($sum(X0,X2),$sum(X1,X2)) | ~$lesseq(X0,X1)) ) | $spl6),
  inference(cnf_transformation,[],[f37_D])).
fof(f37_D,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($lesseq($sum(X0,X2),$sum(X1,X2)) | ~$lesseq(X0,X1)) ) <=> ~$spl6),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl6])])).
fof(f16,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : (~$lesseq(X0,X1) | $lesseq($sum(X0,X2),$sum(X1,X2))) )),
  introduced(theory_axiom,[])).
fof(f36,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq($sum(X0,1),X1) | ~$lesseq(X1,X0)) ) | $spl4),
  inference(cnf_transformation,[],[f36_D])).
fof(f36_D,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq($sum(X0,1),X1) | ~$lesseq(X1,X0)) ) <=> ~$spl4),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl4])])).
fof(f18,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq($sum(X0,1),X1)) )),
  introduced(theory_axiom,[])).
fof(f35,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq(X0,X1) | X0 = X1) ) | $spl2),
  inference(cnf_transformation,[],[f35_D])).
fof(f35_D,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq(X0,X1) | X0 = X1) ) <=> ~$spl2),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl2])])).
fof(f19,plain,(
  ( ! [X0:$int,X1:$int] : (~$lesseq(X1,X0) | ~$lesseq(X0,X1) | X0 = X1) )),
  introduced(theory_axiom,[])).
fof(f34,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq($sum(X0,1),X1) | $lesseq(X1,X0)) ) | $spl0),
  inference(cnf_transformation,[],[f34_D])).
fof(f34_D,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq($sum(X0,1),X1) | $lesseq(X1,X0)) ) <=> ~$spl0),
  introduced(sat_splitting_component,[new_symbols(naming,[$spl0])])).
fof(f20,plain,(
  ( ! [X0:$int,X1:$int] : ($lesseq(X1,X0) | $lesseq($sum(X0,1),X1)) )),
  introduced(theory_axiom,[])).
% SZS output end Proof for DAT013=1