Entrants' Sample Solutions

Beagle 0.9.47
CVC4 1.5.1
E 2.0
Geo-III 2016C
iProver 2.5
leanCoP 2.2
LEO-II 1.7.0
Leo-III 1.0
Leo+III 1.0
Princess 160606
Prover9 2011-11A
Satallax 2.8
Satallax 3.0
Vampire 4.0
Vampire 4.1
VampireZ3 1.0

Beagle 0.9.47

Sample solution for `DAT013=1`

% SZS status Theorem for DAT013=1.p

% SZS output start CNFRefutation for DAT013=1.p
%$ write > read > #nlpp > #skF_1

%Foreground sorts:
tff(array, type, array: $tType ).

%Background operators:
tff('#skE_1', type, '#skE_1': $int).
tff('#skF_4', type, '#skF_4': $int).
tff('#skF_2', type, '#skF_2': $int).
tff('#skF_3', type, '#skF_3': $int).

%Foreground operators:
tff(write, type, write: (array * $int * $int) > array).
tff('#nlpp', type, '#nlpp': ($real * $real) > $real).
tff('#skF_1', type, '#skF_1': array).
tff('#nlpp', type, '#nlpp': ($rat * $rat) > $rat).
tff('#nlpp', type, '#nlpp': ($int * $int) > $int).
tff(read, type, read: (array * $int) > $int).

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)) => $greater(read(U, Ya), 0))))), file('DAT013=1.p', co1)).
tff(c_7, plain, ($lesseq('#skF_4', '#skF_3')), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_35, plain, (~$less('#skF_3', '#skF_4')), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_7])).
tff(c_5, plain, (~$greater(read('#skF_1', '#skF_4'), 0)), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_39, plain, (~$less(0, read('#skF_1', '#skF_4'))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_5])).
tff(c_60, plain, (read('#skF_1', '#skF_4')='#skE_1'), inference(define, [status(thm), theory('equality')], [c_39])).
tff(c_57, plain, (~$less(0, read('#skF_1', '#skF_4'))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_5])).
tff(c_68, plain, (~$less(0, '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_60, c_57])).
tff(c_67, plain, (read('#skF_1', '#skF_4')='#skE_1'), inference(define, [status(thm), theory('equality')], [c_39])).
tff(c_11, plain, (![X_10a:$int]: ($greater(read('#skF_1', X_10a), 0) | ~$lesseq('#skF_2', X_10a) | ~$lesseq(X_10a, '#skF_3'))), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_119, plain, (![X_51a:$int]: ($less(0, read('#skF_1', X_51a)) | $less(X_51a, '#skF_2') | $less('#skF_3', X_51a))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_11])).
tff(c_122, plain, ($less(0, '#skE_1') | $less('#skF_4', '#skF_2') | $less('#skF_3', '#skF_4')), inference(superposition, [status(thm), theory('equality')], [c_67, c_119])).
tff(c_126, plain, ($less('#skF_4', '#skF_2') | $less('#skF_3', '#skF_4')), inference(negUnitSimplification, [status(thm)], [c_68, c_122])).
tff(c_128, plain, ($less('#skF_4', '#skF_2')), inference(negUnitSimplification, [status(thm)], [c_35, c_126])).
tff(c_9, plain, ($lesseq($sum('#skF_2', 3), '#skF_4')), inference(cnfTransformation, [status(thm)], [f_77])).
tff(c_34, plain, (~$less('#skF_4', $sum(3, '#skF_2'))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_9])).
tff(c_129, plain, $false, inference(close, [status(thm), theory('LIA')], [c_128, c_34])).
% SZS output end CNFRefutation for DAT013=1.p

CVC4 1.5.1

Andrew Reynolds
University of Iowa, USA

Sample solution for `DAT013=1`

------- cvc4-tfa casc j8 : DAT013=1.p at ...
--- Run --decision=internal --full-saturate-quant at 10...
% 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_VARIABLE_346))) (forall ((U array) (V Int) (W Int) (BOUND_VARIABLE_346 Int)) (or (not (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_346) 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`

------- cvc4-fof casc j8 : SEU140+2.p at ...
--- Run --relational-triggers --full-saturate-quant at 20...
% 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) (C $$unsorted)) (= (= C (set_union2 A B)) (forall ((D $$unsorted)) (= (in D C) (or (in D A) (in D B))) )) ) :
  ( skv_3, skv_4, (set_union2 skv_3 skv_4) )
  ( skv_3, (set_difference skv_4 skv_3), (set_union2 skv_3 (set_difference skv_4 skv_3)) )

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

Instantiations of (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (set_difference A B)) (forall ((D $$unsorted)) (= (in D C) (and (in D A) (not (in D B)))) )) ) :
  ( skv_3, skv_4, (set_difference skv_3 skv_4) )
  ( skv_4, skv_3, (set_difference 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)) (or (not (forall ((C $$unsorted)) (= (in C A) (in C B)) )) (= A B)) ) :
  ( empty_set, (set_intersection2 skv_3 skv_5) )
  ( empty_set, (set_difference skv_4 skv_3) )
  ( skv_3, skv_4 )

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_790 $$unsorted)) (or (not (disjoint A B)) (not (in BOUND_VARIABLE_790 A)) (not (in BOUND_VARIABLE_790 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_830 $$unsorted)) (or (not (in BOUND_VARIABLE_830 (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`

------- cvc4-fnt casc j8 : NLP042+1.p at ...
--- Run --finite-model-find --fmf-inst-engine --sort-inference --uf-ss-fair at 60...
% SZS status CounterSatisfiable for NLP042+1
% SZS output start FiniteModel for NLP042+1
(define-fun actual_world ((_ufmt_1 $$unsorted)) Bool true)
; cardinality of $$unsorted is 1
(declare-sort $$unsorted 0)
; rep: @uc___unsorted_0
; cardinality of it_2_$$unsorted is 4
(declare-sort it_2_$$unsorted 0)
; rep: @uc_it_2___unsorted_0
; rep: @uc_it_2___unsorted_1
; rep: @uc_it_2___unsorted_2
; rep: @uc_it_2___unsorted_3
(define-fun io_woman_1 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_0 $x2))
(define-fun io_female_2 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_0 $x2))
(define-fun io_human_person_3 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_0 $x2))
(define-fun io_animate_4 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_0 $x2))
(define-fun io_human_5 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_0 $x2))
(define-fun io_organism_6 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_0 $x2))
(define-fun io_living_7 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_0 $x2))
(define-fun io_impartial_8 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool true)
(define-fun io_entity_9 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (ite (= @uc_it_2___unsorted_0 $x2) true (= @uc_it_2___unsorted_2 $x2)))
(define-fun io_mia_forename_10 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_1 $x2))
(define-fun io_forename_11 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_1 $x2))
(define-fun io_abstraction_12 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_1 $x2))
(define-fun io_unisex_13 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (ite (= @uc_it_2___unsorted_3 $x2) true (ite (= @uc_it_2___unsorted_1 $x2) true (= @uc_it_2___unsorted_2 $x2))))
(define-fun io_general_14 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_1 $x2))
(define-fun io_nonhuman_15 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_1 $x2))
(define-fun io_thing_16 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool true)
(define-fun io_relation_17 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_1 $x2))
(define-fun io_relname_18 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_1 $x2))
(define-fun io_object_19 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_2 $x2))
(define-fun io_nonliving_20 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_2 $x2))
(define-fun io_existent_21 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (ite (= @uc_it_2___unsorted_0 $x2) true (= @uc_it_2___unsorted_2 $x2)))
(define-fun io_specific_22 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (ite (= @uc_it_2___unsorted_3 $x2) true (ite (= @uc_it_2___unsorted_0 $x2) true (= @uc_it_2___unsorted_2 $x2))))
(define-fun io_substance_matter_23 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_2 $x2))
(define-fun io_food_24 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_2 $x2))
(define-fun io_beverage_25 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_2 $x2))
(define-fun io_shake_beverage_26 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_2 $x2))
(define-fun io_order_27 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_3 $x2))
(define-fun io_event_28 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_3 $x2))
(define-fun io_eventuality_29 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_3 $x2))
(define-fun io_nonexistent_30 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_3 $x2))
(define-fun io_singleton_31 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool true)
(define-fun io_act_32 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_3 $x2))
(define-fun io_of_33 (($x1 $$unsorted) ($x2 it_2_$$unsorted) ($x3 it_2_$$unsorted)) Bool true)
(define-fun io_nonreflexive_34 (($x1 $$unsorted) ($x2 it_2_$$unsorted)) Bool (= @uc_it_2___unsorted_3 $x2))
(define-fun io_agent_35 (($x1 $$unsorted) ($x2 it_2_$$unsorted) ($x3 it_2_$$unsorted)) Bool (ite (and (= @uc_it_2___unsorted_3 $x2) (= @uc_it_2___unsorted_2 $x3)) false (ite (and (= @uc_it_2___unsorted_3 $x2) (= @uc_it_2___unsorted_1 $x3)) false (not (and (= @uc_it_2___unsorted_3 $x2) (= @uc_it_2___unsorted_3 $x3))))))
(define-fun io_patient_36 (($x1 $$unsorted) ($x2 it_2_$$unsorted) ($x3 it_2_$$unsorted)) Bool (not (and (= @uc_it_2___unsorted_3 $x2) (= @uc_it_2___unsorted_0 $x3))))
(define-fun io_past_37 ((_ufmt_1 $$unsorted) (_ufmt_2 it_2_$$unsorted)) Bool true)
% SZS output end FiniteModel for NLP042+1

Sample solution for `SWV017+1`

------- cvc4-fnt casc j8 : SWV017+1.p at ...
--- Run --finite-model-find --fmf-inst-engine --sort-inference --uf-ss-fair at 60...
% 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 a_holds (($x1 $$unsorted)) Bool true)
(define-fun a () $$unsorted @uc___unsorted_0)
(define-fun b () $$unsorted @uc___unsorted_0)
(define-fun an_a_nonce () $$unsorted @uc___unsorted_0)
(define-fun bt () $$unsorted @uc___unsorted_0)
(define-fun b_holds (($x1 $$unsorted)) Bool true)
(define-fun t_holds (($x1 $$unsorted)) Bool true)
(define-fun intruder_holds (($x1 $$unsorted)) Bool true)
(define-fun an_intruder_nonce () $$unsorted @uc___unsorted_0)
; cardinality of $$unsorted is 1
(declare-sort $$unsorted 0)
; rep: @uc___unsorted_0
; cardinality of it_4_$$unsorted is 2
(declare-sort it_4_$$unsorted 0)
; rep: @uc_it_4___unsorted_0
; rep: @uc_it_4___unsorted_1
(define-fun io_key_3 (($x1 it_4_$$unsorted) ($x2 it_4_$$unsorted)) $$unsorted @uc___unsorted_0)
(define-fun io_party_of_protocol_5 (($x1 it_4_$$unsorted)) Bool true)
; cardinality of it_19_$$unsorted is 1
(declare-sort it_19_$$unsorted 0)
; rep: @uc_it_19___unsorted_0
(define-fun io_pair_8 (($x1 it_4_$$unsorted) ($x2 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_0)
(define-fun io_sent_9 (($x1 it_4_$$unsorted) ($x2 it_4_$$unsorted) ($x3 it_4_$$unsorted)) it_19_$$unsorted @uc_it_19___unsorted_0)
(define-fun io_message_10 (($x1 it_19_$$unsorted)) Bool true)
(define-fun io_a_stored_11 (($x1 it_4_$$unsorted)) Bool true)
(define-fun io_quadruple_12 (($x1 it_4_$$unsorted) ($x2 it_4_$$unsorted) ($x3 it_4_$$unsorted) ($x4 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_0)
(define-fun io_encrypt_13 (($x1 it_4_$$unsorted) ($x2 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_0)
(define-fun io_triple_14 (($x1 it_4_$$unsorted) ($x2 it_4_$$unsorted) ($x3 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_0)
(define-fun io_fresh_to_b_16 (($x1 it_4_$$unsorted)) Bool true)
(define-fun io_generate_b_nonce_17 (($x1 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_0)
(define-fun io_generate_expiration_time_18 (($x1 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_0)
(define-fun io_b_stored_19 (($x1 it_4_$$unsorted)) Bool true)
(define-fun io_a_key_20 (($x1 it_4_$$unsorted)) Bool (= @uc_it_4___unsorted_1 $x1))
(define-fun io_a_nonce_21 (($x1 it_4_$$unsorted)) Bool (= @uc_it_4___unsorted_0 $x1))
(define-fun io_generate_key_22 (($x1 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_1)
(define-fun io_intruder_message_23 (($x1 it_4_$$unsorted)) Bool true)
(define-fun io_fresh_intruder_nonce_25 (($x1 it_4_$$unsorted)) Bool true)
(define-fun io_generate_intruder_nonce_26 (($x1 it_4_$$unsorted)) it_4_$$unsorted @uc_it_4___unsorted_0)
% SZS output end FiniteModel for SWV017+1

E 2.0

Stephan Schulz
DHBW Stuttgart, Germany

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.

Geo-III 2016C

Hans de Nivelle
University of Wrocław, Poland

Sample proof for `SEU140+2`

Couldn't solve it in 300s

Sample proof for `PUZ001+1`

% SZS output start Refutation for /tmp/SystemOnTPTP529/PUZ001+1.tptp

RuleSystem INPUT:

Initial Rules:
#0: input, references = 4, size of lhs = 1:
   P_agatha-{F}(V0) | EXISTS V1: pppp0-{T}(V1,V0)
      (used 0 times, uses = {})

#1: input, references = 6, size of lhs = 1:
   pppp0-{F}(V0,V1) | killed-{T}(V0,V1)
      (used 0 times, uses = {})

#2: input, references = 4, size of lhs = 1:
   pppp0-{F}(V0,V1) | lives-{T}(V0)
      (used 0 times, uses = {})

#3: input, references = 3, size of lhs = 1:
   P_agatha-{F}(V0) | lives-{T}(V0)
      (used 0 times, uses = {})

#4: input, references = 3, size of lhs = 2:
   P_agatha-{F}(V0), P_butler-{F}(V1) | lives-{T}(V1)
      (used 0 times, uses = {})

#5: input, references = 3, size of lhs = 3:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2) | lives-{T}(V2)
      (used 0 times, uses = {})

#6: input, references = 4, size of lhs = 7:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), lives-{F}(V3), V3 == V0, V3 == V1, V3 == V2 | FALSE
      (used 0 times, uses = {})

#7: input, references = 4, size of lhs = 4:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), killed-{F}(V3,V4) | hates-{T}(V3,V4)
      (used 0 times, uses = {})

#8: input, references = 4, size of lhs = 5:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), killed-{F}(V3,V4), richer-{F}(V3,V4) | FALSE
      (used 0 times, uses = {})

#9: input, references = 4, size of lhs = 5:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), hates-{F}(V0,V3), hates-{F}(V2,V3) | FALSE
      (used 0 times, uses = {})

#10: input, references = 5, size of lhs = 5:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), #-{F} V3, V3 == V1 | hates-{T}(V0,V3)
      (used 0 times, uses = {})

#11: input, references = 5, size of lhs = 4:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), #-{F} V3 | richer-{T}(V3,V0), hates-{T}(V1,V3)
      (used 0 times, uses = {})

#12: input, references = 4, size of lhs = 4:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), hates-{F}(V0,V3) | hates-{T}(V1,V3)
      (used 0 times, uses = {})

#13: input, references = 4, size of lhs = 4:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), #-{F} V3 | EXISTS V4: pppp1-{T}(V3,V4)
      (used 0 times, uses = {})

#14: input, references = 4, size of lhs = 2:
   pppp1-{F}(V0,V1), hates-{F}(V0,V1) | FALSE
      (used 0 times, uses = {})

#15: input, references = 4, size of lhs = 3:
   P_agatha-{F}(V1), P_butler-{F}(V1), P_charles-{F}(V2) | FALSE
      (used 0 times, uses = {})

#16: input, references = 4, size of lhs = 4:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), killed-{F}(V0,V0) | FALSE
      (used 0 times, uses = {})

#17: input, references = 4, size of lhs = 0:
   FALSE | EXISTS V0: P_agatha-{T}(V0)
      (used 0 times, uses = {})

#18: input, references = 4, size of lhs = 0:
   FALSE | EXISTS V0: P_butler-{T}(V0)
      (used 0 times, uses = {})

#19: input, references = 5, size of lhs = 0:
   FALSE | EXISTS V0: P_charles-{T}(V0)
      (used 0 times, uses = {})

number of initial rules = 20

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

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

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

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

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

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

#26: unsound, references = 3, size of lhs = 3:
   pppp0-{F}(V0,V1), pppp0-{F}(V2,V1), V0 == V2 | FALSE
      (used 0 times, uses = {})

#27: unsound, references = 3, size of lhs = 3:
   pppp0-{F}(V0,V1), pppp0-{F}(V2,V3), V1 == V3 | FALSE
      (used 0 times, uses = {})

#28: unsound, references = 3, size of lhs = 3:
   pppp1-{F}(V0,V1), pppp1-{F}(V0,V3), V1 == V3 | FALSE
      (used 0 times, uses = {})

number of simplifiers = 9

Learnt:
#30: exists( #19, #15 ), references = 2, size of lhs = 2:
   P_agatha-{F}(V0), P_butler-{F}(V0) | FALSE
      (used 0 times, uses = {})

#38: mergings( V0 == V4, V1 == V5, V2 == V6; #34 ), references = 1, size of lhs = 4:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), killed-{F}(V3,V0) | hates-{T}(V1,V3)
      (used 0 times, uses = {})

#47: mergings( V0 == V7, V1 == V5, V5 == V3, V2 == V6, V6 == V8; #41 ), references = 1, size of lhs = 3:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2) | pppp1-{T}(V1,V1)
      (used 0 times, uses = {})

#49: disj( #11, input ), references = 1, size of lhs = 4:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2), pppp1-{F}(V1,V3) | richer-{T}(V3,V0)
      (used 0 times, uses = {})

#53: mergings( V0 == V2; #51 ), references = 1, size of lhs = 3:
   P_agatha-{F}(V0), P_butler-{F}(V1), P_charles-{F}(V2) | pppp0-{T}(V0,V0), pppp0-{T}(V1,V0), pppp0-{T}(V2,V0)
      (used 0 times, uses = {})

#65: mergings( V0 == V5, V5 == V8, V1 == V3, V3 == V6, V6 == V9, V4 == V7, V7 == V2; #57 ), references = 1, size of lhs = 4:
   P_agatha-{F}(V0), hates-{F}(V0,V0), P_butler-{F}(V1), P_charles-{F}(V2) | pppp0-{T}(V1,V0)
      (used 0 times, uses = {})

#84: mergings( V2 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V13, V1 == V3, V3 == V5, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14; #71 ), references = 1, size of lhs = 3:
   P_agatha-{F}(V0), P_butler-{F}(V1), V0 == V1 | FALSE
      (used 0 times, uses = {})

#91: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #85 ), references = 1, size of lhs = 1:
   P_agatha-{F}(V0) | P_butler-{T}(V0)
      (used 0 times, uses = {})

#94: exists( #17, #92 ), references = 1, size of lhs = 0:
   FALSE | FALSE
      (used 0 times, uses = {})

number of learnt formulas = 9


% SZS output end Refutation for /tmp/SystemOnTPTP529/PUZ001+1.tptp

Sample proof for `NLP042+1`

% SZS output start Model for /tmp/SystemOnTPTP436/NLP042+1.tptp

Interpretation 3:
Guesses:
0 : guesser 1, 0, ( | 1, 0 ), 0, 0s old, 0 lemmas
1 : guesser 4, 2, ( | 1, 2, 0 ), 0, 0s old, 0 lemmas
2 : guesser 17, 15, ( 1 | 2, 0 ), 0, 0s old, 1 lemmas
3 : guesser 29, 26, ( 2, 1 | 3, 0 ), 1, 0s old, 2 lemmas
4 : guesser 45, 41, ( | 0, 3, 2, 4, 1 ), 3, 0s old, 0 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,E1)                     { 0, 1 }
5 : pppp3-{T}(E1,E1)                     { 0, 1 }
6 : order-{T}(E1,E1)                     { 0, 1 }
7 : nonreflexive-{T}(E1,E1)                     { 0, 1 }
8 : past-{T}(E1,E1)                     { 0, 1 }
9 : event-{T}(E1,E1)                     { 0, 1 }
10 : act-{T}(E1,E1)                     { 0, 1 }
11 : eventuality-{T}(E1,E1)                     { 0, 1 }
12 : unisex-{T}(E1,E1)                     { 0, 1 }
13 : nonexistent-{T}(E1,E1)                     { 0, 1 }
14 : specific-{T}(E1,E1)                     { 0, 1 }
15 : thing-{T}(E1,E1)                     { 0, 1 }
16 : singleton-{T}(E1,E1)                     { 0, 1 }
17 : #-{T} E2                     { 0, 1, 2 }
18 : pppp2-{T}(E1,E2,E1)                     { 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 : #-{T} E3                     { 0, 1, 3 }
30 : pppp0-{T}(E1,E3,E1)                     { 0, 1, 3 }
31 : patient-{T}(E1,E1,E3)                     { 0, 1, 3 }
32 : shake_beverage-{T}(E1,E3)                     { 0, 1, 3 }
33 : beverage-{T}(E1,E3)                     { 0, 1, 3 }
34 : food-{T}(E1,E3)                     { 0, 1, 3 }
35 : substance_matter-{T}(E1,E3)                     { 0, 1, 3 }
36 : object-{T}(E1,E3)                     { 0, 1, 3 }
37 : unisex-{T}(E1,E3)                     { 0, 1, 3 }
38 : impartial-{T}(E1,E3)                     { 0, 1, 3 }
39 : nonliving-{T}(E1,E3)                     { 0, 1, 3 }
40 : entity-{T}(E1,E3)                     { 0, 1, 3 }
41 : existent-{T}(E1,E3)                     { 0, 1, 3 }
42 : specific-{T}(E1,E3)                     { 0, 1, 3 }
43 : thing-{T}(E1,E3)                     { 0, 1, 3 }
44 : singleton-{T}(E1,E3)                     { 0, 1, 3 }
45 : pppp1-{T}(E1,E0,E2,E1)                     { 0, 1, 2, 4 }
46 : agent-{T}(E1,E1,E0)                     { 0, 1, 2, 4 }
47 : woman-{T}(E1,E0)                     { 0, 1, 2, 4 }
48 : of-{T}(E1,E2,E0)                     { 0, 1, 2, 4 }
49 : female-{T}(E1,E0)                     { 0, 1, 2, 4 }
50 : human_person-{T}(E1,E0)                     { 0, 1, 2, 4 }
51 : animate-{T}(E1,E0)                     { 0, 1, 2, 4 }
52 : human-{T}(E1,E0)                     { 0, 1, 2, 4 }
53 : organism-{T}(E1,E0)                     { 0, 1, 2, 4 }
54 : living-{T}(E1,E0)                     { 0, 1, 2, 4 }
55 : impartial-{T}(E1,E0)                     { 0, 1, 2, 4 }
56 : entity-{T}(E1,E0)                     { 0, 1, 2, 4 }
57 : existent-{T}(E1,E0)                     { 0, 1, 2, 4 }
58 : specific-{T}(E1,E0)                     { 0, 1, 2, 4 }
59 : thing-{T}(E1,E0)                     { 0, 1, 2, 4 }
60 : singleton-{T}(E1,E0)                     { 0, 1, 2, 4 }


% SZS output end Model for /tmp/SystemOnTPTP436/NLP042+1.tptp

Sample proof for `SWV017+1`

% SZS output start Model for /tmp/SystemOnTPTP484/SWV017+1.tptp

Interpretation 18:
Guesses:
0 : guesser 1, 0, ( | 1, 0 ), 0, 1s old, 0 lemmas
1 : guesser 3, 1, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
2 : guesser 4, 2, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
3 : guesser 5, 3, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
4 : guesser 6, 4, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
5 : guesser 7, 5, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
6 : guesser 8, 6, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
7 : guesser 9, 7, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
8 : guesser 10, 8, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
9 : guesser 11, 9, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
10 : guesser 12, 10, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
11 : guesser 13, 11, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
12 : guesser 14, 12, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
13 : guesser 15, 13, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
14 : guesser 16, 14, ( | 0, 2, 1 ), 0, 1s old, 0 lemmas
15 : guesser 17, 15, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
16 : guesser 18, 16, ( | 1, 2, 0 ), 0, 1s old, 0 lemmas
17 : guesser 19, 17, ( 1 | 2, 0 ), 0, 1s old, 2 lemmas
18 : guesser 21, 18, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
19 : guesser 22, 19, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
20 : guesser 23, 20, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
21 : guesser 24, 21, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
22 : guesser 25, 22, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
23 : guesser 26, 23, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
24 : guesser 27, 24, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
25 : guesser 28, 25, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
26 : guesser 29, 26, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
27 : guesser 30, 27, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
28 : guesser 33, 30, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
29 : guesser 34, 31, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
30 : guesser 35, 32, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
31 : guesser 36, 33, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
32 : guesser 37, 34, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
33 : guesser 38, 35, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
34 : guesser 39, 36, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
35 : guesser 40, 37, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
36 : guesser 41, 38, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
37 : guesser 42, 39, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
38 : guesser 43, 40, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
39 : guesser 44, 41, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
40 : guesser 45, 42, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
41 : guesser 46, 43, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
42 : guesser 47, 44, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
43 : guesser 48, 45, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
44 : guesser 49, 46, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
45 : guesser 50, 47, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
46 : guesser 51, 48, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
47 : guesser 52, 49, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
48 : guesser 53, 50, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
49 : guesser 54, 51, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
50 : guesser 55, 52, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
51 : guesser 56, 53, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
52 : guesser 57, 54, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
53 : guesser 58, 55, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
54 : guesser 59, 56, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
55 : guesser 60, 57, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
56 : guesser 61, 58, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
57 : guesser 62, 59, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
58 : guesser 63, 60, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
59 : guesser 64, 61, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
60 : guesser 65, 62, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
61 : guesser 66, 63, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
62 : guesser 67, 64, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
63 : guesser 68, 65, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
64 : guesser 69, 66, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
65 : guesser 70, 67, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
66 : guesser 71, 68, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
67 : guesser 72, 69, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
68 : guesser 73, 70, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
69 : guesser 74, 71, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
70 : guesser 75, 72, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
71 : guesser 76, 73, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
72 : guesser 77, 74, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
73 : guesser 78, 75, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
74 : guesser 79, 76, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
75 : guesser 80, 77, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
76 : guesser 81, 78, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
77 : guesser 82, 79, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
78 : guesser 83, 80, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
79 : guesser 84, 81, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
80 : guesser 85, 82, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
81 : guesser 86, 83, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
82 : guesser 87, 84, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
83 : guesser 88, 85, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
84 : guesser 89, 86, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
85 : guesser 90, 87, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
86 : guesser 91, 88, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
87 : guesser 92, 89, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
88 : guesser 93, 90, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
89 : guesser 94, 91, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
90 : guesser 95, 92, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
91 : guesser 96, 93, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
92 : guesser 122, 119, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
93 : guesser 123, 120, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
94 : guesser 126, 123, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
95 : guesser 127, 124, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
96 : guesser 128, 125, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
97 : guesser 129, 126, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
98 : guesser 130, 127, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
99 : guesser 131, 128, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
100 : guesser 132, 129, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
101 : guesser 133, 130, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
102 : guesser 134, 131, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
103 : guesser 135, 132, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
104 : guesser 136, 133, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
105 : guesser 137, 134, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
106 : guesser 138, 135, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
107 : guesser 139, 136, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
108 : guesser 140, 137, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
109 : guesser 141, 138, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
110 : guesser 142, 139, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
111 : guesser 143, 140, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
112 : guesser 144, 141, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
113 : guesser 145, 142, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
114 : guesser 146, 143, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
115 : guesser 147, 144, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
116 : guesser 148, 145, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
117 : guesser 150, 147, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
118 : guesser 151, 148, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
119 : guesser 152, 149, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
120 : guesser 153, 150, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
121 : guesser 154, 151, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
122 : guesser 155, 152, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
123 : guesser 156, 153, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
124 : guesser 157, 154, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
125 : guesser 158, 155, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
126 : guesser 159, 156, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
127 : guesser 160, 157, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
128 : guesser 161, 158, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
129 : guesser 162, 159, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
130 : guesser 163, 160, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
131 : guesser 164, 161, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
132 : guesser 165, 162, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
133 : guesser 166, 163, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
134 : guesser 167, 164, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
135 : guesser 168, 165, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
136 : guesser 169, 166, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
137 : guesser 170, 167, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
138 : guesser 172, 169, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
139 : guesser 173, 170, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
140 : guesser 174, 171, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
141 : guesser 175, 172, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
142 : guesser 176, 173, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
143 : guesser 177, 174, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
144 : guesser 178, 175, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
145 : guesser 179, 176, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
146 : guesser 180, 177, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
147 : guesser 181, 178, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
148 : guesser 182, 179, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
149 : guesser 183, 180, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
150 : guesser 184, 181, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
151 : guesser 185, 182, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
152 : guesser 186, 183, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
153 : guesser 187, 184, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
154 : guesser 188, 185, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
155 : guesser 189, 186, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
156 : guesser 190, 187, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
157 : guesser 191, 188, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
158 : guesser 192, 189, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
159 : guesser 193, 190, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
160 : guesser 194, 191, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
161 : guesser 195, 192, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
162 : guesser 196, 193, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
163 : guesser 197, 194, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
164 : guesser 198, 195, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
165 : guesser 199, 196, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
166 : guesser 200, 197, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
167 : guesser 201, 198, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
168 : guesser 202, 199, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
169 : guesser 203, 200, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
170 : guesser 204, 201, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
171 : guesser 205, 202, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
172 : guesser 206, 203, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
173 : guesser 207, 204, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
174 : guesser 208, 205, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
175 : guesser 209, 206, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
176 : guesser 210, 207, ( | 1, 0, 3, 2 ), 18, 0s old, 0 lemmas
177 : guesser 211, 208, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
178 : guesser 212, 209, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas
179 : guesser 213, 210, ( | 2, 1, 3, 0 ), 18, 0s old, 0 lemmas
180 : guesser 214, 211, ( | 0, 2, 3, 1 ), 18, 0s old, 0 lemmas

Elements:
   { E0, E1, E2 }

Atoms:
0 : #-{T} E0                     { }
1 : #-{T} E1                     { 0 }
2 : P_at-{T}(E1)                     { 0 }
3 : P_t-{T}(E1)                     { 1 }
4 : P_a-{T}(E1)                     { 2 }
5 : P_b-{T}(E1)                     { 3 }
6 : P_an_a_nonce-{T}(E0)                     { 4 }
7 : P_bt-{T}(E0)                     { 5 }
8 : P_an_intruder_nonce-{T}(E0)                     { 6 }
9 : P_generate_b_nonce-{T}(E0,E0)                     { 7 }
10 : P_generate_expiration_time-{T}(E0,E0)                     { 8 }
11 : P_generate_key-{T}(E0,E1)                     { 9 }
12 : P_generate_intruder_nonce-{T}(E0,E1)                     { 10 }
13 : P_key-{T}(E0,E0,E0)                     { 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,E1)                     { 16 }
19 : #-{T} E2                     { 0, 17 }
20 : P_generate_b_nonce-{T}(E1,E2)                     { 0, 17 }
21 : P_generate_expiration_time-{T}(E1,E0)                     { 0, 18 }
22 : P_generate_key-{T}(E1,E1)                     { 0, 19 }
23 : P_generate_intruder_nonce-{T}(E1,E2)                     { 0, 20 }
24 : P_key-{T}(E0,E1,E2)                     { 0, 21 }
25 : P_pair-{T}(E0,E1,E0)                     { 0, 22 }
26 : P_encrypt-{T}(E0,E1,E0)                     { 0, 23 }
27 : P_key-{T}(E1,E0,E1)                     { 0, 24 }
28 : P_pair-{T}(E1,E0,E2)                     { 0, 25 }
29 : P_encrypt-{T}(E1,E0,E2)                     { 0, 26 }
30 : P_key-{T}(E1,E1,E1)                     { 0, 27 }
31 : a_holds-{T}(E1)                     { 0, 1, 27 }
32 : party_of_protocol-{T}(E1)                     { 0, 1, 2, 27 }
33 : P_pair-{T}(E1,E1,E2)                     { 0, 28 }
34 : P_encrypt-{T}(E1,E1,E2)                     { 0, 29 }
35 : P_sent-{T}(E0,E0,E1,E2)                     { 0, 30 }
36 : P_sent-{T}(E0,E1,E0,E0)                     { 0, 31 }
37 : P_triple-{T}(E0,E0,E1,E0)                     { 0, 32 }
38 : P_quadruple-{T}(E0,E0,E0,E1,E1)                     { 0, 33 }
39 : P_sent-{T}(E0,E1,E1,E1)                     { 0, 34 }
40 : P_triple-{T}(E0,E1,E0,E0)                     { 0, 35 }
41 : P_quadruple-{T}(E0,E0,E1,E0,E1)                     { 0, 36 }
42 : P_sent-{T}(E1,E0,E0,E2)                     { 0, 37 }
43 : P_triple-{T}(E0,E1,E1,E2)                     { 0, 38 }
44 : P_quadruple-{T}(E0,E0,E1,E1,E0)                     { 0, 39 }
45 : P_sent-{T}(E1,E0,E1,E0)                     { 0, 40 }
46 : P_triple-{T}(E1,E0,E0,E1)                     { 0, 41 }
47 : P_quadruple-{T}(E0,E1,E0,E0,E1)                     { 0, 42 }
48 : P_sent-{T}(E1,E1,E0,E0)                     { 0, 43 }
49 : P_triple-{T}(E1,E0,E1,E0)                     { 0, 44 }
50 : P_quadruple-{T}(E0,E1,E0,E1,E1)                     { 0, 45 }
51 : P_sent-{T}(E1,E1,E1,E1)                     { 0, 46 }
52 : P_triple-{T}(E1,E1,E0,E2)                     { 0, 47 }
53 : P_quadruple-{T}(E0,E1,E1,E0,E2)                     { 0, 48 }
54 : P_triple-{T}(E1,E1,E1,E1)                     { 0, 49 }
55 : P_quadruple-{T}(E0,E1,E1,E1,E2)                     { 0, 50 }
56 : P_generate_b_nonce-{T}(E2,E0)                     { 0, 17, 51 }
57 : P_quadruple-{T}(E1,E0,E0,E0,E1)                     { 0, 52 }
58 : P_generate_expiration_time-{T}(E2,E0)                     { 0, 17, 53 }
59 : P_generate_key-{T}(E2,E1)                     { 0, 17, 54 }
60 : P_quadruple-{T}(E1,E0,E0,E1,E2)                     { 0, 55 }
61 : P_generate_intruder_nonce-{T}(E2,E2)                     { 0, 17, 56 }
62 : P_key-{T}(E0,E2,E1)                     { 0, 17, 57 }
63 : P_quadruple-{T}(E1,E0,E1,E0,E0)                     { 0, 58 }
64 : P_key-{T}(E1,E2,E0)                     { 0, 17, 59 }
65 : P_pair-{T}(E0,E2,E0)                     { 0, 17, 60 }
66 : P_quadruple-{T}(E1,E0,E1,E1,E1)                     { 0, 61 }
67 : P_key-{T}(E2,E0,E2)                     { 0, 17, 62 }
68 : P_pair-{T}(E1,E2,E1)                     { 0, 17, 63 }
69 : P_quadruple-{T}(E1,E1,E0,E0,E0)                     { 0, 64 }
70 : P_key-{T}(E2,E1,E0)                     { 0, 17, 65 }
71 : P_pair-{T}(E2,E0,E0)                     { 0, 17, 66 }
72 : P_quadruple-{T}(E1,E1,E0,E1,E2)                     { 0, 67 }
73 : P_key-{T}(E2,E2,E0)                     { 0, 17, 68 }
74 : P_pair-{T}(E2,E1,E2)                     { 0, 17, 69 }
75 : P_quadruple-{T}(E1,E1,E1,E0,E0)                     { 0, 70 }
76 : P_pair-{T}(E2,E2,E0)                     { 0, 17, 71 }
77 : P_encrypt-{T}(E0,E2,E0)                     { 0, 17, 72 }
78 : P_quadruple-{T}(E1,E1,E1,E1,E2)                     { 0, 73 }
79 : P_encrypt-{T}(E1,E2,E0)                     { 0, 17, 74 }
80 : P_sent-{T}(E0,E0,E2,E1)                     { 0, 17, 75 }
81 : P_encrypt-{T}(E2,E0,E2)                     { 0, 17, 76 }
82 : P_sent-{T}(E0,E1,E2,E1)                     { 0, 17, 77 }
83 : P_triple-{T}(E0,E0,E2,E2)                     { 0, 17, 78 }
84 : P_encrypt-{T}(E2,E1,E0)                     { 0, 17, 79 }
85 : P_sent-{T}(E0,E2,E0,E1)                     { 0, 17, 80 }
86 : P_triple-{T}(E0,E1,E2,E1)                     { 0, 17, 81 }
87 : P_encrypt-{T}(E2,E2,E1)                     { 0, 17, 82 }
88 : P_sent-{T}(E0,E2,E1,E1)                     { 0, 17, 83 }
89 : P_triple-{T}(E0,E2,E0,E0)                     { 0, 17, 84 }
90 : P_sent-{T}(E0,E2,E2,E0)                     { 0, 17, 85 }
91 : P_triple-{T}(E0,E2,E1,E0)                     { 0, 17, 86 }
92 : P_quadruple-{T}(E0,E0,E0,E2,E0)                     { 0, 17, 87 }
93 : P_sent-{T}(E1,E0,E2,E2)                     { 0, 17, 88 }
94 : P_triple-{T}(E0,E2,E2,E2)                     { 0, 17, 89 }
95 : P_quadruple-{T}(E0,E0,E1,E2,E2)                     { 0, 17, 90 }
96 : P_sent-{T}(E1,E1,E2,E0)                     { 0, 17, 91 }
97 : message-{T}(E0)                     { 0, 1, 2, 3, 4, 17, 25, 27, 91 }
98 : a_stored-{T}(E2)                     { 0, 1, 2, 3, 4, 17, 25, 27, 91 }
99 : b_holds-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
100 : fresh_to_b-{T}(E0)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
101 : t_holds-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
102 : t_holds-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
103 : a_nonce-{T}(E0)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
104 : intruder_message-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
105 : fresh_intruder_nonce-{T}(E0)                     { 0, 1, 2, 3, 4, 5, 6, 17, 21, 25, 27, 91 }
106 : intruder_message-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
107 : intruder_message-{T}(E0)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
108 : intruder_holds-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
109 : a_key-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 9, 17, 21, 25, 27, 91 }
110 : fresh_intruder_nonce-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 6, 10, 17, 21, 25, 27, 91 }
111 : intruder_holds-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 91 }
112 : fresh_to_b-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 6, 10, 17, 21, 25, 27, 91 }
113 : a_nonce-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 17, 18, 21, 25, 27, 91 }
114 : fresh_intruder_nonce-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 6, 10, 17, 20, 21, 25, 27, 91 }
115 : message-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 46, 91 }
116 : fresh_to_b-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 6, 10, 17, 20, 21, 25, 27, 91 }
117 : a_holds-{T}(E2)                     { 0, 1, 2, 3, 4, 13, 17, 21, 23, 25, 27, 28, 35, 43, 64, 91 }
118 : intruder_holds-{T}(E0)                     { 0, 1, 2, 3, 4, 5, 17, 21, 25, 27, 65, 91 }
119 : message-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 9, 15, 17, 21, 25, 27, 31, 32, 35, 36, 37, 62, 72, 74, 91 }
120 : b_stored-{T}(E0)                     { 0, 1, 2, 3, 4, 5, 6, 10, 13, 17, 20, 21, 25, 27, 31, 41, 46, 51, 53, 60, 84, 91 }
121 : b_holds-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 17, 20, 21, 23, 24, 25, 27, 31, 34, 35, 41, 46, 51, 53, 60, 84, 91 }
122 : P_sent-{T}(E1,E2,E0,E2)                     { 0, 17, 92 }
123 : P_triple-{T}(E1,E0,E2,E0)                     { 0, 17, 93 }
124 : b_stored-{T}(E2)                     { 0, 1, 2, 3, 4, 5, 7, 8, 17, 21, 25, 26, 27, 41, 43, 91, 93 }
125 : b_stored-{T}(E1)                     { 0, 1, 2, 3, 4, 5, 7, 8, 12, 15, 17, 21, 25, 26, 27, 34, 43, 46, 91, 93 }
126 : P_sent-{T}(E1,E2,E1,E2)                     { 0, 17, 94 }
127 : P_triple-{T}(E1,E1,E2,E1)                     { 0, 17, 95 }
128 : P_quadruple-{T}(E0,E0,E2,E0,E0)                     { 0, 17, 96 }
129 : P_sent-{T}(E1,E2,E2,E2)                     { 0, 17, 97 }
130 : P_triple-{T}(E1,E2,E0,E2)                     { 0, 17, 98 }
131 : P_quadruple-{T}(E0,E0,E2,E1,E1)                     { 0, 17, 99 }
132 : P_sent-{T}(E2,E0,E0,E0)                     { 0, 17, 100 }
133 : P_triple-{T}(E1,E2,E1,E2)                     { 0, 17, 101 }
134 : P_quadruple-{T}(E0,E0,E2,E2,E2)                     { 0, 17, 102 }
135 : P_sent-{T}(E2,E0,E1,E0)                     { 0, 17, 103 }
136 : P_triple-{T}(E1,E2,E2,E1)                     { 0, 17, 104 }
137 : P_quadruple-{T}(E0,E1,E0,E2,E0)                     { 0, 17, 105 }
138 : P_sent-{T}(E2,E0,E2,E1)                     { 0, 17, 106 }
139 : P_triple-{T}(E2,E0,E0,E2)                     { 0, 17, 107 }
140 : P_quadruple-{T}(E0,E1,E1,E2,E0)                     { 0, 17, 108 }
141 : P_sent-{T}(E2,E1,E0,E2)                     { 0, 17, 109 }
142 : P_triple-{T}(E2,E0,E1,E2)                     { 0, 17, 110 }
143 : P_quadruple-{T}(E0,E1,E2,E0,E0)                     { 0, 17, 111 }
144 : P_sent-{T}(E2,E1,E1,E0)                     { 0, 17, 112 }
145 : P_triple-{T}(E2,E0,E2,E2)                     { 0, 17, 113 }
146 : P_quadruple-{T}(E0,E1,E2,E1,E1)                     { 0, 17, 114 }
147 : P_sent-{T}(E2,E1,E2,E1)                     { 0, 17, 115 }
148 : P_triple-{T}(E2,E1,E0,E2)                     { 0, 17, 116 }
149 : b_holds-{T}(E0)                     { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 17, 20, 21, 23, 25, 27, 31, 32, 35, 36, 37, 41, 46, 51, 53, 59, 60, 62, 66, 72, 74, 76, 84, 91, 109, 116 }
150 : P_sent-{T}(E2,E2,E0,E0)                     { 0, 17, 117 }
151 : P_triple-{T}(E2,E1,E1,E2)                     { 0, 17, 118 }
152 : P_quadruple-{T}(E0,E1,E2,E2,E0)                     { 0, 17, 119 }
153 : P_sent-{T}(E2,E2,E1,E1)                     { 0, 17, 120 }
154 : P_triple-{T}(E2,E1,E2,E2)                     { 0, 17, 121 }
155 : P_quadruple-{T}(E0,E2,E0,E0,E0)                     { 0, 17, 122 }
156 : P_sent-{T}(E2,E2,E2,E0)                     { 0, 17, 123 }
157 : P_triple-{T}(E2,E2,E0,E2)                     { 0, 17, 124 }
158 : P_quadruple-{T}(E0,E2,E0,E1,E2)                     { 0, 17, 125 }
159 : P_triple-{T}(E2,E2,E1,E2)                     { 0, 17, 126 }
160 : P_quadruple-{T}(E0,E2,E0,E2,E0)                     { 0, 17, 127 }
161 : P_triple-{T}(E2,E2,E2,E2)                     { 0, 17, 128 }
162 : P_quadruple-{T}(E0,E2,E1,E0,E1)                     { 0, 17, 129 }
163 : P_quadruple-{T}(E0,E2,E1,E1,E2)                     { 0, 17, 130 }
164 : P_quadruple-{T}(E0,E2,E1,E2,E0)                     { 0, 17, 131 }
165 : P_quadruple-{T}(E0,E2,E2,E0,E0)                     { 0, 17, 132 }
166 : P_quadruple-{T}(E0,E2,E2,E1,E0)                     { 0, 17, 133 }
167 : P_quadruple-{T}(E0,E2,E2,E2,E2)                     { 0, 17, 134 }
168 : P_quadruple-{T}(E1,E0,E0,E2,E2)                     { 0, 17, 135 }
169 : P_quadruple-{T}(E1,E0,E1,E2,E1)                     { 0, 17, 136 }
170 : P_quadruple-{T}(E1,E0,E2,E0,E1)                     { 0, 17, 137 }
171 : a_holds-{T}(E0)                     { 0, 1, 2, 3, 4, 12, 17, 25, 27, 29, 46, 65, 72, 91, 107, 137 }
172 : P_quadruple-{T}(E1,E0,E2,E1,E1)                     { 0, 17, 138 }
173 : P_quadruple-{T}(E1,E0,E2,E2,E2)                     { 0, 17, 139 }
174 : P_quadruple-{T}(E1,E1,E0,E2,E0)                     { 0, 17, 140 }
175 : P_quadruple-{T}(E1,E1,E1,E2,E2)                     { 0, 17, 141 }
176 : P_quadruple-{T}(E1,E1,E2,E0,E0)                     { 0, 17, 142 }
177 : P_quadruple-{T}(E1,E1,E2,E1,E0)                     { 0, 17, 143 }
178 : P_quadruple-{T}(E1,E1,E2,E2,E0)                     { 0, 17, 144 }
179 : P_quadruple-{T}(E1,E2,E0,E0,E1)                     { 0, 17, 145 }
180 : P_quadruple-{T}(E1,E2,E0,E1,E0)                     { 0, 17, 146 }
181 : P_quadruple-{T}(E1,E2,E0,E2,E0)                     { 0, 17, 147 }
182 : P_quadruple-{T}(E1,E2,E1,E0,E1)                     { 0, 17, 148 }
183 : P_quadruple-{T}(E1,E2,E1,E1,E2)                     { 0, 17, 149 }
184 : P_quadruple-{T}(E1,E2,E1,E2,E1)                     { 0, 17, 150 }
185 : P_quadruple-{T}(E1,E2,E2,E0,E0)                     { 0, 17, 151 }
186 : P_quadruple-{T}(E1,E2,E2,E1,E2)                     { 0, 17, 152 }
187 : P_quadruple-{T}(E1,E2,E2,E2,E1)                     { 0, 17, 153 }
188 : P_quadruple-{T}(E2,E0,E0,E0,E0)                     { 0, 17, 154 }
189 : P_quadruple-{T}(E2,E0,E0,E1,E0)                     { 0, 17, 155 }
190 : P_quadruple-{T}(E2,E0,E0,E2,E1)                     { 0, 17, 156 }
191 : P_quadruple-{T}(E2,E0,E1,E0,E2)                     { 0, 17, 157 }
192 : P_quadruple-{T}(E2,E0,E1,E1,E0)                     { 0, 17, 158 }
193 : P_quadruple-{T}(E2,E0,E1,E2,E1)                     { 0, 17, 159 }
194 : P_quadruple-{T}(E2,E0,E2,E0,E1)                     { 0, 17, 160 }
195 : P_quadruple-{T}(E2,E0,E2,E1,E0)                     { 0, 17, 161 }
196 : P_quadruple-{T}(E2,E0,E2,E2,E2)                     { 0, 17, 162 }
197 : P_quadruple-{T}(E2,E1,E0,E0,E2)                     { 0, 17, 163 }
198 : P_quadruple-{T}(E2,E1,E0,E1,E2)                     { 0, 17, 164 }
199 : P_quadruple-{T}(E2,E1,E0,E2,E2)                     { 0, 17, 165 }
200 : P_quadruple-{T}(E2,E1,E1,E0,E0)                     { 0, 17, 166 }
201 : P_quadruple-{T}(E2,E1,E1,E1,E1)                     { 0, 17, 167 }
202 : P_quadruple-{T}(E2,E1,E1,E2,E0)                     { 0, 17, 168 }
203 : P_quadruple-{T}(E2,E1,E2,E0,E0)                     { 0, 17, 169 }
204 : P_quadruple-{T}(E2,E1,E2,E1,E0)                     { 0, 17, 170 }
205 : P_quadruple-{T}(E2,E1,E2,E2,E1)                     { 0, 17, 171 }
206 : P_quadruple-{T}(E2,E2,E0,E0,E2)                     { 0, 17, 172 }
207 : P_quadruple-{T}(E2,E2,E0,E1,E0)                     { 0, 17, 173 }
208 : P_quadruple-{T}(E2,E2,E0,E2,E1)                     { 0, 17, 174 }
209 : P_quadruple-{T}(E2,E2,E1,E0,E1)                     { 0, 17, 175 }
210 : P_quadruple-{T}(E2,E2,E1,E1,E1)                     { 0, 17, 176 }
211 : P_quadruple-{T}(E2,E2,E1,E2,E0)                     { 0, 17, 177 }
212 : P_quadruple-{T}(E2,E2,E2,E0,E0)                     { 0, 17, 178 }
213 : P_quadruple-{T}(E2,E2,E2,E1,E2)                     { 0, 17, 179 }
214 : P_quadruple-{T}(E2,E2,E2,E2,E0)                     { 0, 17, 180 }


% SZS output end Model for /tmp/SystemOnTPTP484/SWV017+1.tptp

iProver 2.5

Kontantin Korovin
University of Manchester, United Kingdom

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

leanCoP 2.2

Jens Otten
University of Potsdam, Germany

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 1.7.0

Max Wisniewski
Freie Universität Berlin, Germany

Sample solution for `SET014^4`

 No.of.Axioms: 0

 Length.of.Defs: 2223

 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:7,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 /home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p : (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:7,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('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',complement)).
 thf(disjoint,definition,(disjoint = (^[X:($i>$o),Y:($i>$o)]: (((intersection@X)@Y) = emptyset))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',disjoint)).
 thf(emptyset,definition,(emptyset = (^[X:$i]: $false)),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',emptyset)).
 thf(excl_union,definition,(excl_union = (^[X:($i>$o),Y:($i>$o),U:$i]: (((X@U) & (~ (Y@U))) | ((~ (X@U)) & (Y@U))))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',excl_union)).
 thf(in,definition,(in = (^[X:$i,M:($i>$o)]: (M@X))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',in)).
 thf(intersection,definition,(intersection = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (Y@U)))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',intersection)).
 thf(is_a,definition,(is_a = (^[X:$i,M:($i>$o)]: (M@X))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',is_a)).
 thf(meets,definition,(meets = (^[X:($i>$o),Y:($i>$o)]: (?[U:$i]: ((X@U) & (Y@U))))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',meets)).
 thf(misses,definition,(misses = (^[X:($i>$o),Y:($i>$o)]: (~ (?[U:$i]: ((X@U) & (Y@U)))))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',misses)).
 thf(setminus,definition,(setminus = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) & (~ (Y@U))))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',setminus)).
 thf(singleton,definition,(singleton = (^[X:$i,U:$i]: (U = X))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',singleton)).
 thf(subset,definition,(subset = (^[X:($i>$o),Y:($i>$o)]: (![U:$i]: ((X@U) => (Y@U))))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',subset)).
 thf(union,definition,(union = (^[X:($i>$o),Y:($i>$o),U:$i]: ((X@U) | (Y@U)))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',union)).
 thf(unord_pair,definition,(unord_pair = (^[X:$i,Y:$i,U:$i]: ((U = X) | (U = Y)))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',unord_pair)).
 thf(1,conjecture,(![X:($i>$o),Y:($i>$o),A:($i>$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',thm)).
 thf(2,negated_conjecture,(((![X:($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 /home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p : (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:7,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)

Leo-III 1.0 and Leo+III 1.0

Max Wisniewski
Freie Universität Berlin, Germany

Sample solution for `SET014^4`

% Configuration: problem(TPTP-v6.3.0/Problems/SET/SET014^4.p),time(60),proofObject(true),sos(false)

% (1) No. of processed clauses: 6
% (1) No. of generated clauses: 4
% (1) No. of forward subsumed clauses: 0
% (1) No. of units in store: 1

% SZS status Theorem for TPTP-v6.3.0/Problems/SET/SET014^4.p : 5075 ms resp. 390 ms w/o parsing
% SZS output start CNFRefutation for TPTP-v6.3.0/Problems/SET/SET014^4.p
thf(in_type, type, in: ($i > (($i > $o) > $o))).
thf(is_a_type, type, is_a: ($i > (($i > $o) > $o))).
thf(emptyset_type, type, emptyset: ($i > $o)).
thf(unord_pair_type, type, unord_pair: ($i > ($i > ($i > $o)))).
thf(singleton_type, type, singleton: ($i > ($i > $o))).
thf(union_type, type, union: (($i > $o) > (($i > $o) > ($i > $o)))).
thf(excl_union_type, type, excl_union: (($i > $o) > (($i > $o) > ($i > $o)))).
thf(intersection_type, type, intersection: (($i > $o) > (($i > $o) > ($i > $o)))).
thf(setminus_type, type, setminus: (($i > $o) > (($i > $o) > ($i > $o)))).
thf(complement_type, type, complement: (($i > $o) > ($i > $o))).
thf(disjoint_type, type, disjoint: (($i > $o) > (($i > $o) > $o))).
thf(subset_type, type, subset: (($i > $o) > (($i > $o) > $o))).
thf(meets_type, type, meets: (($i > $o) > (($i > $o) > $o))).
thf(misses_type, type, misses: (($i > $o) > (($i > $o) > $o))).
thf(sk1_type, type, sk1: ($i > $o)).
thf(sk2_type, type, sk2: ($i > $o)).
thf(sk3_type, type, sk3: ($i > $o)).
thf(sk4_type, type, sk4: ($i > ($i > $i))).
thf(1, conjecture, ((! [A:($i > $o),B:($i > $o),C:($i > $o)]: (((((((subset) @ (A)) @ (C))) & ((((subset) @ (B)) @ (C)))) => ((((subset) @ ((((union) @ (A)) @ (B)))) @ (C))))))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',thm)).
thf(2, negated_conjecture, ((~ ((! [A:($i > $o),B:($i > $o),C:($i > $o)]: (((((((subset) @ (A)) @ (C))) & ((((subset) @ (B)) @ (C)))) => ((((subset) @ ((((union) @ (A)) @ (B)))) @ (C))))))))),inference(neg_conjecture,[status(cth)],[1])).
thf(3, plain, ((~ ((! [A:($i > $o),B:($i > $o),C:($i > $o)]: ((((! [D:$i]: (((((A) @ (D))) => (((C) @ (D)))))) & (! [D:$i]: (((((B) @ (D))) => (((C) @ (D))))))) => (! [D:$i]: ((((((A) @ (D))) | (((B) @ (D)))) => (((C) @ (D)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(4, plain, ((? [A:($i > $o),B:($i > $o),C:($i > $o)]: ((((! [D:$i]: (((~ ((((A) @ (D))))) | (((C) @ (D)))))) & (! [D:$i]: (((~ ((((B) @ (D))))) | (((C) @ (D))))))) & (? [D:$i]: ((((((A) @ (D))) | (((B) @ (D)))) & (~ ((((C) @ (D)))))))))))),inference(negation_normal,[status(thm)],[3])).
thf(6, plain, ((! [A:$i,B:$i]: (((((sk1) @ ((((sk4) @ (A)) @ (B))))) | (((sk2) @ ((((sk4) @ (A)) @ (B))))))))),inference(cnf,[status(thm)],[4])).
thf(7, plain, ((! [A:$i]: (((~ ((((sk2) @ (A))))) | (((sk3) @ (A))))))),inference(cnf,[status(thm)],[4])).
thf(9, plain, ((! [A:$i]: (((~ ((((sk2) @ (A))))) | (((sk3) @ (A))))))),inference(simp,[status(thm)],[7])).
thf(5, plain, ((! [A:$i,B:$i]: ((~ ((((sk3) @ ((((sk4) @ (A)) @ (B)))))))))),inference(cnf,[status(thm)],[4])).
thf(14, plain, ((! [A:$i,B:$i,C:$i]: (((~ ((((sk2) @ (C))))) | (~ (((((sk3) @ ((((sk4) @ (A)) @ (B))))) = (((sk3) @ (C)))))))))),inference(paramod_ordered,[status(thm)],[9,5])).
thf(15, plain, ((! [A:$i,B:$i]: ((~ ((((sk2) @ ((((sk4) @ (A)) @ (B)))))))))),inference(pre_uni,[status(esa)],[14])).
thf(17, plain, ((! [A:$i,B:$i]: ((~ ((((sk2) @ ((((sk4) @ (A)) @ (B)))))))))),inference(rewrite,[status(thm)],[15])).
thf(18, plain, ((! [A:$i,B:$i,C:$i,D:$i]: (((((sk1) @ ((((sk4) @ (C)) @ (D))))) | (~ (((((sk2) @ ((((sk4) @ (C)) @ (D))))) = (((sk2) @ ((((sk4) @ (A)) @ (B)))))))))))),inference(paramod_ordered,[status(thm)],[6,17])).
thf(19, plain, ((! [A:$i,B:$i]: ((((sk1) @ ((((sk4) @ (A)) @ (B)))))))),inference(pre_uni,[status(esa)],[18])).
thf(21, plain, ((! [A:$i,B:$i]: ((((sk1) @ ((((sk4) @ (A)) @ (B)))))))),inference(rewrite,[status(thm)],[19])).
thf(8, plain, ((! [A:$i]: (((~ ((((sk1) @ (A))))) | (((sk3) @ (A))))))),inference(cnf,[status(thm)],[4])).
thf(10, plain, ((! [A:$i,B:$i,C:$i]: (((~ ((((sk1) @ (C))))) | (~ (((((sk3) @ ((((sk4) @ (A)) @ (B))))) = (((sk3) @ (C)))))))))),inference(paramod_ordered,[status(thm)],[8,5])).
thf(11, plain, ((! [A:$i,B:$i]: ((~ ((((sk1) @ ((((sk4) @ (A)) @ (B)))))))))),inference(pre_uni,[status(esa)],[10])).
thf(13, plain, ((! [A:$i,B:$i]: ((~ ((((sk1) @ ((((sk4) @ (A)) @ (B)))))))))),inference(rewrite,[status(thm)],[11])).
thf(22, plain, ((! [A:$i,B:$i,C:$i,D:$i]: ((~ (((((sk1) @ ((((sk4) @ (C)) @ (D))))) = (((sk1) @ ((((sk4) @ (A)) @ (B))))))))))),inference(paramod_ordered,[status(thm)],[21,13])).
thf(23, plain, (($false)),inference(pre_uni,[status(esa)],[22])).
thf(25, plain, (($false)),inference(rewrite,[status(thm)],[23])).
% SZS output end CNFRefutation for TPTP-v6.3.0/Problems/SET/SET014^4.p

Princess 160606

Philipp Rümmer
Uppsala University, Sweden

Sample solution for `DAT013=1`

% SZS status Theorem for DAT013=1
% SZS output start Proof for DAT013=1
Assumptions after simplification:
---------------------------------

  (co1)
   ? [v0: $int] :  ? [v1: $int] :  ? [v2: $int] : (in_array(v0) &  ! [v3: $int] :
     ! [v4: $int] : ( ~ ($lesseq(v4, 0) |  ~ ($lesseq(v3, v2)) |  ~ ($lesseq(v1,
            v3)) |  ~ (read(v0, v3) = v4)) &  ? [v3: $int] :  ? [v4: $int] :
      ($lesseq(v4, 0)$lesseq(v3, v2) & $lesseq(3, $difference(v3, v1)) & read(v0,
          v3) = v4))

Further assumptions not needed in the proof:
--------------------------------------------
ax1, ax2

Those formulas are unsatisfiable:
---------------------------------

Begin of proof
|
| DELTA: instantiating (co1) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
|   (1)  in_array(all_4_2) &  ! [v0: $int] :  ! [v1: $int] : ( ~ ($lesseq(v1, 0)
|            |  ~ ($lesseq(v0, all_4_0)) |  ~ ($lesseq(all_4_1, v0)) |  ~
|            (read(all_4_2, v0) = v1)) &  ? [v0: $int] :  ? [v1: $int] :
|          ($lesseq(v1, 0)$lesseq(v0, all_4_0) & $lesseq(3, $difference(v0,
|                all_4_1)) & read(all_4_2, v0) = v1)
|
| ALPHA: (1) implies:
|   (2)   ! [v0: $int] :  ! [v1: $int] : ( ~ ($lesseq(v1, 0) |  ~ ($lesseq(v0,
|                all_4_0)) |  ~ ($lesseq(all_4_1, v0)) |  ~ (read(all_4_2, v0) =
|              v1))
|   (3)   ? [v0: $int] :  ? [v1: $int] : ($lesseq(v1, 0)$lesseq(v0, all_4_0) &
|          $lesseq(3, $difference(v0, all_4_1)) & read(all_4_2, v0) = v1)
|
| DELTA: instantiating (3) with fresh symbols all_9_0, all_9_1 gives:
|   (4)  $lesseq(all_9_0, 0)$lesseq(all_9_1, all_4_0) & $lesseq(3,
|          $difference(all_9_1, all_4_1)) & read(all_4_2, all_9_1) = all_9_0
|
| ALPHA: (4) implies:
|   (5)  $lesseq(3, $difference(all_9_1, all_4_1))
|   (6)  $lesseq(all_9_1, all_4_0)
|   (7)  $lesseq(all_9_0, 0)
|   (8)  read(all_4_2, all_9_1) = all_9_0
|
| GROUND_INST: instantiating (2) with all_9_0, all_9_1, simplifying with (8)
|              gives:
|   (9)   ~ ($lesseq(all_9_0, 0) |  ~ ($lesseq(all_9_1, all_4_0)) |  ~
|          ($lesseq(all_4_1, all_9_1))
|
| BETA: splitting (9) gives:
|
| Case 1:
| |
| |   (10)  $lesseq(1, all_9_0)
| |
| | COMBINE_INEQS: (7), (10) imply:
| |   (11)  $lesseq(0, -1)
| |
| | CLOSE: (11) is inconsistent.
| |
| Case 2:
| |
| |   (12)   ~ ($lesseq(all_9_1, all_4_0)) |  ~ ($lesseq(all_4_1, all_9_1))
| |
| | BETA: splitting (12) gives:
| |
| | Case 1:
| | |
| | |   (13)  $lesseq(1, $difference(all_9_1, all_4_0))
| | |
| | | COMBINE_INEQS: (6), (13) imply:
| | |   (14)  $lesseq(0, -1)
| | |
| | | CLOSE: (14) is inconsistent.
| | |
| | Case 2:
| | |
| | |   (15)  $lesseq(1, $difference(all_4_1, all_9_1))
| | |
| | | COMBINE_INEQS: (5), (15) imply:
| | |   (16)  $lesseq(0, -1)
| | |
| | | CLOSE: (16) is inconsistent.
| | |
| | End of split
| |
| End of split
|
End of proof
% SZS output end Proof for DAT013=1

Prover9 2009-11A

William McCune, Bob Veroff
University of New Mexico, USA

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)].

Satallax 2.8

Nik Sultana
Cambridge University, United Kingdom

Sample solution for `SET014^4`

thf(ty$i, type, $i : $tType).
thf(tyeigen__1, type, eigen__1 : ($i>$o)).
thf(tyeigen__2, type, eigen__2 : ($i>$o)).
thf(tyeigen__3, type, eigen__3 : $i).
thf(tyeigen__0, type, eigen__0 : ($i>$o)).
thf(thm,conjecture,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:(((![X3:$i]:((eigen__0 @ X3) => (X2 @ X3))) & (![X3:$i]:((X1 @ X3) => (X2 @ X3)))) => (![X3:$i]:(((eigen__0 @ X3) | (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:$i>$o]:(((![X2:$i]:((eigen__0 @ X2) => (X1 @ X2))) & (![X2:$i]:((eigen__1 @ X2) => (X1 @ X2)))) => (![X2:$i]:(((eigen__0 @ X2) | (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~((((![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))) & (![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1)))) => (![X1:$i]:(((eigen__0 @ X1) | (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,((![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))) & (![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1)))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:$i]:(((eigen__0 @ X1) | (eigen__1 @ X1)) => (eigen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,(~((((eigen__0 @ eigen__3) | (eigen__1 @ eigen__3)) => (eigen__2 @ eigen__3)))),introduced(assumption,[])).
thf(h7,assumption,((eigen__0 @ eigen__3) | (eigen__1 @ eigen__3)),introduced(assumption,[])).
thf(h8,assumption,(~((eigen__2 @ eigen__3))),introduced(assumption,[])).
thf(h9,assumption,(![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(assumption,[])).
thf(h10,assumption,(![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduced(assumption,[])).
thf(h11,assumption,((eigen__1 @ eigen__3) => (eigen__2 @ eigen__3)),introduced(assumption,[])).
thf(h12,assumption,((eigen__0 @ eigen__3) => (eigen__2 @ eigen__3)),introduced(assumption,[])).
thf(h13,assumption,(~((eigen__1 @ eigen__3))),introduced(assumption,[])).
thf(h14,assumption,(eigen__2 @ eigen__3),introduced(assumption,[])).
thf(h15,assumption,(~((eigen__0 @ eigen__3))),introduced(assumption,[])).
thf(h16,assumption,(eigen__0 @ eigen__3),introduced(assumption,[])).
thf(h17,assumption,(eigen__1 @ eigen__3),introduced(assumption,[])).
thf(13,plain,$false,inference(tab_conflict,[status(thm),assumptions([h16,h15,h13,h12,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[h16,h15])).
thf(14,plain,$false,inference(tab_conflict,[status(thm),assumptions([h17,h15,h13,h12,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[h17,h13])).
thf(12,plain,$false,inference(tab_or,[status(thm),assumptions([h15,h13,h12,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_or(discharge,[h16]),tab_or(discharge,[h17])],[h7,13,14,h16,h17])).
thf(15,plain,$false,inference(tab_conflict,[status(thm),assumptions([h14,h13,h12,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[h14,h8])).
thf(11,plain,$false,inference(tab_imp,[status(thm),assumptions([h13,h12,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h14])],[h12,12,15,h15,h14])).
thf(16,plain,$false,inference(tab_conflict,[status(thm),assumptions([h14,h12,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[h14,h8])).
thf(10,plain,$false,inference(tab_imp,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h11,11,16,h13,h14])).
thf(9,plain,$false,inference(tab_all,[status(thm),assumptions([h11,h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_all(discharge,[h12])],[h9:[bind(X1,$thf(eigen__3))],10,h12])).
thf(8,plain,$false,inference(tab_all,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_all(discharge,[h11])],[h10:[bind(X1,$thf(eigen__3))],9,h11])).
thf(7,plain,$false,inference(tab_and,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_and(discharge,[h9,h10])],[h4,8,h9,h10])).
thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,7,h7,h8])).
thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,6,h6])).
thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,5,h4,h5])).
thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,4,h3])).
thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2])).
thf(1,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1])).
thf(0,theorem,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% SZS output end Proof

Satallax 3.0

Michael Färber
Universität Innsbruck, Austria

Sample solution for `SET014^4`

% SZS output start Proof
thf(ty$i, type, $i : $tType).
thf(tyeigen__3, type, eigen__3 : $i).
thf(tyeigen__2, type, eigen__2 : ($i>$o)).
thf(tyeigen__1, type, eigen__1 : ($i>$o)).
thf(tyeigen__0, type, eigen__0 : ($i>$o)).
thf(thm,conjecture,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:(((![X3:$i]:((eigen__0 @ X3) => (X2 @ X3))) & (![X3:$i]:((X1 @ X3) => (X2 @ X3)))) => (![X3:$i]:(((eigen__0 @ X3) | (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:$i>$o]:(((![X2:$i]:((eigen__0 @ X2) => (X1 @ X2))) & (![X2:$i]:((eigen__1 @ X2) => (X1 @ X2)))) => (![X2:$i]:(((eigen__0 @ X2) | (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~((((![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))) & (![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1)))) => (![X1:$i]:(((eigen__0 @ X1) | (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,((![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))) & (![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1)))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:$i]:(((eigen__0 @ X1) | (eigen__1 @ X1)) => (eigen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,(![X1:$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(assumption,[])).
thf(h7,assumption,(![X1:$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduced(assumption,[])).
thf(h8,assumption,(~((((eigen__0 @ eigen__3) | (eigen__1 @ eigen__3)) => (eigen__2 @ eigen__3)))),introduced(assumption,[])).
thf(h9,assumption,((eigen__0 @ eigen__3) | (eigen__1 @ eigen__3)),introduced(assumption,[])).
thf(h10,assumption,(~((eigen__2 @ eigen__3))),introduced(assumption,[])).
thf(h11,assumption,(eigen__0 @ eigen__3),introduced(assumption,[])).
thf(h12,assumption,(eigen__1 @ eigen__3),introduced(assumption,[])).
thf(h13,assumption,((eigen__0 @ eigen__3) => (eigen__2 @ eigen__3)),introduced(assumption,[])).
thf(h14,assumption,(~((eigen__0 @ eigen__3))),introduced(assumption,[])).
thf(h15,assumption,(eigen__2 @ eigen__3),introduced(assumption,[])).
thf(11,plain,$false,inference(tab_conflict,[status(thm),assumptions([h14,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h11,h14])).
thf(12,plain,$false,inference(tab_conflict,[status(thm),assumptions([h15,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h15,h10])).
thf(10,plain,$false,inference(tab_imp,[status(thm),assumptions([h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h13,11,12,h14,h15])).
thf(9,plain,$false,inference(tab_all,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_all(discharge,[h13])],[h6:[bind(X1,$thf(eigen__3))],10,h13])).
thf(h16,assumption,((eigen__1 @ eigen__3) => (eigen__2 @ eigen__3)),introduced(assumption,[])).
thf(h17,assumption,(~((eigen__1 @ eigen__3))),introduced(assumption,[])).
thf(15,plain,$false,inference(tab_conflict,[status(thm),assumptions([h17,h16,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h12,h17])).
thf(16,plain,$false,inference(tab_conflict,[status(thm),assumptions([h15,h16,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[h15,h10])).
thf(14,plain,$false,inference(tab_imp,[status(thm),assumptions([h16,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h17]),tab_imp(discharge,[h15])],[h16,15,16,h17,h15])).
thf(13,plain,$false,inference(tab_all,[status(thm),assumptions([h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_all(discharge,[h16])],[h7:[bind(X1,$thf(eigen__3))],14,h16])).
thf(8,plain,$false,inference(tab_or,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_or(discharge,[h11]),tab_or(discharge,[h12])],[h9,9,13,h11,h12])).
thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10])).
thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,7,h8])).
thf(5,plain,$false,inference(tab_and,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_and(discharge,[h6,h7])],[h4,6,h6,h7])).
thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,5,h4,h5])).
thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,4,h3])).
thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2])).
thf(1,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1])).
thf(0,theorem,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:(((![X4:$i]:((X1 @ X4) => (X3 @ X4))) & (![X4:$i]:((X2 @ X4) => (X3 @ X4)))) => (![X4:$i]:(((X1 @ X4) | (X2 @ X4)) => (X3 @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% SZS output end Proof

Sample solution for `SYO553^1`

% SZS output start Proof
thf(ty$i, type, $i : $tType).
thf(tyeigen__2, type, eigen__2 : $i).
thf(claim,conjecture,(?[X1:$i>$i>$i]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) = X3))))).
thf(h0,negated_conjecture,(~(?[X1:$i>$i>$i]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) = X3))))),inference(assume_negation,[status(cth)],[claim])).
thf(h1,assumption,(~((![X1:$i]:(![X2:$i]:(X2 = X2))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:$i]:(X1 = X1)))),introduced(assumption,[])).
thf(h3,assumption,(~((eigen__2 = eigen__2))),introduced(assumption,[])).
thf(4,plain,$false,inference(tab_refl,[status(thm),assumptions([h3,h2,h1,h0])],[h3])).
thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,4,h3])).
thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2])).
thf(1,plain,$false,inference(tab_negex,[status(thm),assumptions([h0]),tab_negex(discharge,[h1])],[h0:[bind(X1,$thf((^[X1:$i]:(^[X2:$i]:X2))))],2,h1])).
thf(0,theorem,(?[X1:$i>$i>$i]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) = X3)))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% SZS output end Proof

Vampire 4.0

Giles Reger
University of Manchester, United Kingdom

Sample solution for `SEU140+2`

% SZS status Theorem for SEU140+2
% SZS output start Proof for SEU140+2
fof(f6,axiom,(
  ! [X0] : (empty_set = X0 <=> ! [X1] : ~in(X1,X0))),
  file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d1_xboole_0)).
fof(f8,axiom,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
  file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d3_tarski)).
fof(f9,axiom,(
  ! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X0) & in(X3,X1))))),
  file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d3_xboole_0)).
fof(f11,axiom,(
  ! [X0,X1] : (disjoint(X0,X1) <=> set_intersection2(X0,X1) = empty_set)),
  file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',d7_xboole_0)).
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('/tmp/SystemOnTPTP11775/SEU140+2.tptp',t3_xboole_0)).
fof(f51,conjecture,(
  ! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  file('/tmp/SystemOnTPTP11775/SEU140+2.tptp',t63_xboole_1)).
fof(f52,negated_conjecture,(
  ~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).
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(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(f63,plain,(
  ! [X0] : (empty_set = X0 <=> ! [X1] : ~in(X1,X0))),
  inference(flattening,[],[f6])).
fof(f74,plain,(
  ? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
  inference(ennf_transformation,[],[f52])).
fof(f75,plain,(
  ? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
  inference(flattening,[],[f74])).
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(f96,plain,(
  ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))),
  inference(ennf_transformation,[],[f8])).
fof(f101,plain,(
  subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f75])).
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(f106,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | set_intersection2(X0,X1) = empty_set) & (set_intersection2(X0,X1) != empty_set | disjoint(X0,X1)))),
  inference(nnf_transformation,[],[f11])).
fof(f109,plain,(
  ! [X0] : ((empty_set != X0 | ! [X1] : ~in(X1,X0)) & (? [X1] : in(X1,X0) | empty_set = X0))),
  inference(nnf_transformation,[],[f63])).
fof(f110,plain,(
  ! [X0] : ((empty_set != X0 | ! [X2] : ~in(X2,X0)) & (? [X1] : in(X1,X0) | empty_set = X0))),
  inference(rectify,[],[f109])).
fof(f111,plain,(
  ! [X0] : ((empty_set != X0 | ! [X2] : ~in(X2,X0)) & (in(sK5(X0),X0) | empty_set = X0))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f110])).
fof(f116,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(f117,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,[],[f116])).
fof(f118,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,[],[f117])).
fof(f119,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(sK7(X2,X1,X0),X2) | (in(sK7(X2,X1,X0),X0) & in(sK7(X2,X1,X0),X1))) & (~in(sK7(X2,X1,X0),X2) | ~in(sK7(X2,X1,X0),X0) | ~in(sK7(X2,X1,X0),X1))) | set_intersection2(X0,X1) = X2))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f118])).
fof(f124,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,[],[f96])).
fof(f125,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,[],[f124])).
fof(f126,plain,(
  ! [X0,X1] : ((~subset(X0,X1) | ! [X3] : (~in(X3,X0) | in(X3,X1))) & ((in(sK9(X1,X0),X0) & ~in(sK9(X1,X0),X1)) | subset(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f125])).
fof(f133,plain,(
  subset(sK0,sK1)),
  inference(cnf_transformation,[],[f101])).
fof(f134,plain,(
  disjoint(sK1,sK2)),
  inference(cnf_transformation,[],[f101])).
fof(f135,plain,(
  ~disjoint(sK0,sK2)),
  inference(cnf_transformation,[],[f101])).
fof(f146,plain,(
  ( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f103])).
fof(f147,plain,(
  ( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f103])).
fof(f162,plain,(
  ( ! [X0,X1] : (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f106])).
fof(f169,plain,(
  ( ! [X2,X0] : (~in(X2,X0) | empty_set != X0) )),
  inference(cnf_transformation,[],[f111])).
fof(f189,plain,(
  ( ! [X4,X2,X0,X1] : (in(X4,X2) | ~in(X4,X1) | ~in(X4,X0) | set_intersection2(X0,X1) != X2) )),
  inference(cnf_transformation,[],[f119])).
fof(f202,plain,(
  ( ! [X0,X3,X1] : (~subset(X0,X1) | ~in(X3,X0) | in(X3,X1)) )),
  inference(cnf_transformation,[],[f126])).
fof(f218,plain,(
  ( ! [X2] : (~in(X2,empty_set)) )),
  inference(equality_resolution,[],[f169])).
fof(f222,plain,(
  ( ! [X4,X0,X1] : (in(X4,set_intersection2(X0,X1)) | ~in(X4,X1) | ~in(X4,X0)) )),
  inference(equality_resolution,[],[f189])).
fof(f234,plain,(
  set_intersection2(sK1,sK2) = empty_set),
  inference(unit_resulting_resolution,[],[f134,f162])).
fof(f467,plain,(
  in(sK4(sK2,sK0),sK0)),
  inference(unit_resulting_resolution,[],[f135,f146])).
fof(f480,plain,(
  in(sK4(sK2,sK0),sK1)),
  inference(unit_resulting_resolution,[],[f133,f467,f202])).
fof(f513,plain,(
  in(sK4(sK2,sK0),sK2)),
  inference(unit_resulting_resolution,[],[f135,f147])).
fof(f857,plain,(
  in(sK4(sK2,sK0),set_intersection2(sK1,sK2))),
  inference(unit_resulting_resolution,[],[f513,f480,f222])).
fof(f865,plain,(
  in(sK4(sK2,sK0),empty_set)),
  inference(forward_demodulation,[],[f857,f234])).
fof(f866,plain,(
  $false),
  inference(subsumption_resolution,[],[f865,f218])).
% 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

Vampire 4.1

Giles Reger
University of Manchester, United Kingdom

Sample solution for `DAT013=1`

tff(type_def_6, type, array: $tType).
tff(func_def_0, type, read: (array * $int) > $int).
tff(func_def_1, type, write: (array * $int * $int) > array).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: $int).
tff(func_def_9, type, sK2: $int).
tff(func_def_10, type, sK3: $int).
tff(f3,conjecture,(
  ! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/DAT/DAT013=1.p',unknown)).
tff(f4,negated_conjecture,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
  inference(negated_conjecture,[],[f3])).
tff(f6,plain,(
  ~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
  inference(evaluation,[],[f4])).
tff(f7,plain,(
  ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) )),
  introduced(theory_axiom,[])).
tff(f9,plain,(
  ( ! [X0:$int] : ($sum(X0,0) = X0) )),
  introduced(theory_axiom,[])).
tff(f12,plain,(
  ( ! [X0:$int] : (~$less(X0,X0)) )),
  introduced(theory_axiom,[])).
tff(f13,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
  introduced(theory_axiom,[])).
tff(f14,plain,(
  ( ! [X0:$int,X1:$int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
  introduced(theory_axiom,[])).
tff(f15,plain,(
  ( ! [X2:$int,X0:$int,X1:$int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
  introduced(theory_axiom,[])).
tff(f20,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X2,X4) & ~$less(X4,$sum(X1,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X2,X3) | $less(X3,X1))))),
  inference(ennf_transformation,[],[f6])).
tff(f21,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X2,X4) & ~$less(X4,$sum(X1,3))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | $less(X2,X3) | $less(X3,X1)))),
  inference(flattening,[],[f20])).
tff(f22,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1)))),
  inference(rectify,[],[f21])).
tff(f23,plain,(
  ? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1))) => (? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)))),
  introduced(choice_axiom,[])).
tff(f24,plain,(
  ( ! [X2:$int,X0:array,X1:$int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) => (~$less(0,read(X0,sK3)) & ~$less(X2,sK3) & ~$less(sK3,$sum(X1,3)))) )),
  introduced(choice_axiom,[])).
tff(f25,plain,(
  (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f22,f24,f23])).
tff(f29,plain,(
  ( ! [X4:$int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)) )),
  inference(cnf_transformation,[],[f25])).
tff(f30,plain,(
  ~$less(sK3,$sum(sK1,3))),
  inference(cnf_transformation,[],[f25])).
tff(f31,plain,(
  ~$less(sK2,sK3)),
  inference(cnf_transformation,[],[f25])).
tff(f32,plain,(
  ~$less(0,read(sK0,sK3))),
  inference(cnf_transformation,[],[f25])).
tff(f33,plain,(
  ~$less(sK3,$sum(3,sK1))),
  inference(forward_demodulation,[],[f30,f7])).
tff(f98,plain,(
  $less($sum(3,sK1),sK3) | $sum(3,sK1) = sK3),
  inference(resolution,[],[f14,f33])).
tff(f131,plain,(
  spl4_8 <=> $sum(3,sK1) = sK3),
  introduced(AVATAR_definition,[new_symbols(naming,[spl4_8])])).
tff(f132,plain,(
  $sum(3,sK1) = sK3 | ~spl4_8),
  inference(AVATAR_component_clause,[],[f131])).
tff(f137,plain,(
  spl4_10 <=> $less($sum(3,sK1),sK3)),
  introduced(AVATAR_definition,[new_symbols(naming,[spl4_10])])).
tff(f138,plain,(
  $less($sum(3,sK1),sK3) | ~spl4_10),
  inference(AVATAR_component_clause,[],[f137])).
tff(f142,plain,(
  spl4_8 | spl4_10),
  inference(AVATAR_split_clause,[],[f98,f137,f131])).
tff(f172,plain,(
  ( ! [X6:$int,X4:$int,X5:$int] : ($less($sum(X5,X4),$sum(X6,X5)) | ~$less(X4,X6)) )),
  inference(superposition,[],[f15,f7])).
tff(f489,plain,(
  ( ! [X6:$int,X7:$int] : ($less(X6,$sum(X7,X6)) | ~$less(0,X7)) )),
  inference(superposition,[],[f172,f9])).
tff(f659,plain,(
  $less(sK2,sK3) | $less(sK3,sK1)),
  inference(resolution,[],[f29,f32])).
tff(f662,plain,(
  $less(sK3,sK1)),
  inference(subsumption_resolution,[],[f659,f31])).
tff(f664,plain,(
  ( ! [X0:$int] : (~$less(X0,sK3) | $less(X0,sK1)) )),
  inference(resolution,[],[f662,f13])).
tff(f673,plain,(
  ( ! [X4:$int] : ($less($sum(sK1,X4),sK3) | ~$less(X4,3)) ) | ~spl4_8),
  inference(superposition,[],[f172,f132])).
tff(f2473,plain,(
  $less(sK1,sK3) | ~$less(0,3) | ~spl4_8),
  inference(superposition,[],[f673,f9])).
tff(f2478,plain,(
  $less(sK1,sK3) | ~spl4_8),
  inference(evaluation,[],[f2473])).
tff(f2480,plain,(
  $less(sK1,sK1) | ~spl4_8),
  inference(resolution,[],[f2478,f664])).
tff(f2484,plain,(
  $false | ~spl4_8),
  inference(subsumption_resolution,[],[f2480,f12])).
tff(f2485,plain,(
  ~spl4_8),
  inference(AVATAR_contradiction_clause,[],[f2484,f131])).
tff(f2513,plain,(
  ( ! [X2:$int] : (~$less(X2,$sum(3,sK1)) | $less(X2,sK3)) ) | ~spl4_10),
  inference(resolution,[],[f138,f13])).
tff(f2962,plain,(
  ~$less(0,3) | $less(sK1,sK3) | ~spl4_10),
  inference(resolution,[],[f489,f2513])).
tff(f2989,plain,(
  $less(sK1,sK3) | ~spl4_10),
  inference(evaluation,[],[f2962])).
tff(f2991,plain,(
  $less(sK1,sK1) | ~spl4_10),
  inference(resolution,[],[f2989,f664])).
tff(f2995,plain,(
  $false | ~spl4_10),
  inference(subsumption_resolution,[],[f2991,f12])).
tff(f2996,plain,(
  ~spl4_10),
  inference(AVATAR_contradiction_clause,[],[f2995,f137])).
tff(f2997,plain,(
  $false),
  inference(AVATAR_sat_refutation,[],[f142,f2485,f2996])).

Sample solution for `SEU140+2`

fof(f3,axiom,(
  ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f4,axiom,(
  ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f5,axiom,(
  ! [X0,X1] : (X0 = X1 <=> (subset(X1,X0) & subset(X0,X1)))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f10,axiom,(
  ! [X0,X1,X2] : (set_difference(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (~in(X3,X1) & in(X3,X0))))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f11,axiom,(
  ! [X0,X1] : (disjoint(X0,X1) <=> set_intersection2(X0,X1) = empty_set)),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f20,axiom,(
  ! [X0,X1] : set_union2(X0,X0) = X0),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f23,axiom,(
  ! [X0,X1] : (empty_set = set_difference(X0,X1) <=> subset(X0,X1))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f27,axiom,(
  ! [X0,X1] : (disjoint(X0,X1) => disjoint(X1,X0))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f28,axiom,(
  ! [X0,X1] : (subset(X0,X1) => set_union2(X0,X1) = X1)),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f39,axiom,(
  ! [X0,X1] : subset(set_difference(X0,X1),X0)),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f41,axiom,(
  ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f42,axiom,(
  ! [X0] : set_difference(X0,empty_set) = X0),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f43,axiom,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f45,axiom,(
  ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f47,axiom,(
  ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f51,conjecture,(
  ! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f52,negated_conjecture,(
  ~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
  inference(negated_conjecture,[],[f51])).
fof(f55,axiom,(
  ! [X0,X1] : subset(X0,set_union2(X0,X1))),
  file('/Users/giles/TPTP/TPTP-v6.2.0/Problems/SEU/SEU140+2.p',unknown)).
fof(f58,plain,(
  ! [X0] : set_union2(X0,X0) = X0),
  inference(rectify,[],[f20])).
fof(f62,plain,(
  ! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
  inference(rectify,[],[f43])).
fof(f72,plain,(
  ! [X0,X1] : (disjoint(X1,X0) | ~disjoint(X0,X1))),
  inference(ennf_transformation,[],[f27])).
fof(f73,plain,(
  ! [X0,X1] : (set_union2(X0,X1) = X1 | ~subset(X0,X1))),
  inference(ennf_transformation,[],[f28])).
fof(f82,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
  inference(ennf_transformation,[],[f62])).
fof(f87,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
  inference(ennf_transformation,[],[f52])).
fof(f88,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
  inference(flattening,[],[f87])).
fof(f94,plain,(
  ! [X0,X1] : ((X0 = X1 | (~subset(X1,X0) | ~subset(X0,X1))) & ((subset(X1,X0) & subset(X0,X1)) | X0 != X1))),
  inference(nnf_transformation,[],[f5])).
fof(f95,plain,(
  ! [X0,X1] : ((X0 = X1 | ~subset(X1,X0) | ~subset(X0,X1)) & ((subset(X1,X0) & subset(X0,X1)) | X0 != X1))),
  inference(flattening,[],[f94])).
fof(f114,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : (((in(X3,X1) | ~in(X3,X0)) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (in(X3,X1) | ~in(X3,X0))) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
  inference(nnf_transformation,[],[f10])).
fof(f115,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | in(X3,X1) | ~in(X3,X0)) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
  inference(flattening,[],[f114])).
fof(f116,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
  inference(rectify,[],[f115])).
fof(f117,plain,(
  ! [X2,X1,X0] : (? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2))) => ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2))))),
  introduced(choice_axiom,[])).
fof(f118,plain,(
  ! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f116,f117])).
fof(f119,plain,(
  ! [X0,X1] : ((disjoint(X0,X1) | set_intersection2(X0,X1) != empty_set) & (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)))),
  inference(nnf_transformation,[],[f11])).
fof(f120,plain,(
  ! [X0,X1] : ((empty_set = set_difference(X0,X1) | ~subset(X0,X1)) & (subset(X0,X1) | empty_set != set_difference(X0,X1)))),
  inference(nnf_transformation,[],[f23])).
fof(f129,plain,(
  ! [X1,X0] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
  introduced(choice_axiom,[])).
fof(f130,plain,(
  ! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f82,f129])).
fof(f133,plain,(
  ? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
  introduced(choice_axiom,[])).
fof(f134,plain,(
  ~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f88,f133])).
fof(f137,plain,(
  ( ! [X0:$i,X1:$i] : (set_union2(X0,X1) = set_union2(X1,X0)) )),
  inference(cnf_transformation,[],[f3])).
fof(f138,plain,(
  ( ! [X0:$i,X1:$i] : (set_intersection2(X0,X1) = set_intersection2(X1,X0)) )),
  inference(cnf_transformation,[],[f4])).
fof(f141,plain,(
  ( ! [X0:$i,X1:$i] : (~subset(X1,X0) | X0 = X1 | ~subset(X0,X1)) )),
  inference(cnf_transformation,[],[f95])).
fof(f159,plain,(
  ( ! [X4:$i,X2:$i,X0:$i,X1:$i] : (in(X4,X0) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
  inference(cnf_transformation,[],[f118])).
fof(f160,plain,(
  ( ! [X4:$i,X2:$i,X0:$i,X1:$i] : (~in(X4,X1) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
  inference(cnf_transformation,[],[f118])).
fof(f165,plain,(
  ( ! [X0:$i,X1:$i] : (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f119])).
fof(f171,plain,(
  ( ! [X0:$i] : (set_union2(X0,X0) = X0) )),
  inference(cnf_transformation,[],[f58])).
fof(f174,plain,(
  ( ! [X0:$i,X1:$i] : (empty_set != set_difference(X0,X1) | subset(X0,X1)) )),
  inference(cnf_transformation,[],[f120])).
fof(f175,plain,(
  ( ! [X0:$i,X1:$i] : (~subset(X0,X1) | empty_set = set_difference(X0,X1)) )),
  inference(cnf_transformation,[],[f120])).
fof(f179,plain,(
  ( ! [X0:$i,X1:$i] : (~disjoint(X0,X1) | disjoint(X1,X0)) )),
  inference(cnf_transformation,[],[f72])).
fof(f180,plain,(
  ( ! [X0:$i,X1:$i] : (~subset(X0,X1) | set_union2(X0,X1) = X1) )),
  inference(cnf_transformation,[],[f73])).
fof(f192,plain,(
  ( ! [X0:$i,X1:$i] : (subset(set_difference(X0,X1),X0)) )),
  inference(cnf_transformation,[],[f39])).
fof(f195,plain,(
  ( ! [X0:$i,X1:$i] : (set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))) )),
  inference(cnf_transformation,[],[f41])).
fof(f196,plain,(
  ( ! [X0:$i] : (set_difference(X0,empty_set) = X0) )),
  inference(cnf_transformation,[],[f42])).
fof(f197,plain,(
  ( ! [X0:$i,X1:$i] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f130])).
fof(f198,plain,(
  ( ! [X0:$i,X1:$i] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
  inference(cnf_transformation,[],[f130])).
fof(f201,plain,(
  ( ! [X0:$i,X1:$i] : (set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)) )),
  inference(cnf_transformation,[],[f45])).
fof(f203,plain,(
  ( ! [X0:$i,X1:$i] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
  inference(cnf_transformation,[],[f47])).
fof(f208,plain,(
  subset(sK10,sK11)),
  inference(cnf_transformation,[],[f134])).
fof(f209,plain,(
  disjoint(sK11,sK12)),
  inference(cnf_transformation,[],[f134])).
fof(f210,plain,(
  ~disjoint(sK10,sK12)),
  inference(cnf_transformation,[],[f134])).
fof(f213,plain,(
  ( ! [X0:$i,X1:$i] : (subset(X0,set_union2(X0,X1))) )),
  inference(cnf_transformation,[],[f55])).
fof(f216,plain,(
  ( ! [X0:$i,X1:$i] : (set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0))) )),
  inference(definition_unfolding,[],[f138,f203,f203])).
fof(f224,plain,(
  ( ! [X0:$i,X1:$i] : (~disjoint(X0,X1) | empty_set = set_difference(X0,set_difference(X0,X1))) )),
  inference(definition_unfolding,[],[f165,f203])).
fof(f243,plain,(
  ( ! [X4:$i,X0:$i,X1:$i] : (~in(X4,set_difference(X0,X1)) | ~in(X4,X1)) )),
  inference(equality_resolution,[],[f160])).
fof(f244,plain,(
  ( ! [X4:$i,X0:$i,X1:$i] : (~in(X4,set_difference(X0,X1)) | in(X4,X0)) )),
  inference(equality_resolution,[],[f159])).
fof(f273,plain,(
  disjoint(sK12,sK11)),
  inference(resolution,[],[f179,f209])).
fof(f286,plain,(
  ( ! [X6:$i,X7:$i] : (subset(X6,set_union2(X7,X6))) )),
  inference(superposition,[],[f213,f137])).
fof(f324,plain,(
  ( ! [X4:$i,X3:$i] : (empty_set = set_difference(X3,set_union2(X4,X3))) )),
  inference(resolution,[],[f175,f286])).
fof(f340,plain,(
  set_union2(sK10,sK11) = sK11),
  inference(resolution,[],[f180,f208])).
fof(f399,plain,(
  ( ! [X10:$i,X8:$i,X9:$i] : (~in(sK8(X8,set_difference(X9,X10)),X10) | disjoint(X8,set_difference(X9,X10))) )),
  inference(resolution,[],[f243,f198])).
fof(f405,plain,(
  ( ! [X4:$i,X2:$i,X3:$i] : (in(sK8(set_difference(X2,X3),X4),X2) | disjoint(set_difference(X2,X3),X4)) )),
  inference(resolution,[],[f244,f197])).
fof(f468,plain,(
  ( ! [X4:$i,X5:$i] : (set_union2(X5,set_union2(X4,X5)) = set_union2(X5,set_difference(X4,X5))) )),
  inference(superposition,[],[f195,f201])).
fof(f477,plain,(
  ( ! [X4:$i,X5:$i] : (set_union2(X5,X4) = set_union2(X5,set_union2(X4,X5))) )),
  inference(forward_demodulation,[],[f468,f195])).
fof(f616,plain,(
  empty_set = set_difference(sK12,set_difference(sK12,sK11))),
  inference(resolution,[],[f224,f273])).
fof(f730,plain,(
  ( ! [X6:$i,X7:$i] : (set_difference(X7,set_difference(X7,set_union2(X6,X7))) = set_difference(set_union2(X6,X7),set_difference(X6,X7))) )),
  inference(superposition,[],[f216,f201])).
fof(f776,plain,(
  ( ! [X6:$i,X7:$i] : (set_difference(X7,empty_set) = set_difference(set_union2(X6,X7),set_difference(X6,X7))) )),
  inference(forward_demodulation,[],[f730,f324])).
fof(f777,plain,(
  ( ! [X6:$i,X7:$i] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = X7) )),
  inference(forward_demodulation,[],[f776,f196])).
fof(f1528,plain,(
  empty_set != empty_set | subset(sK12,set_difference(sK12,sK11))),
  inference(superposition,[],[f174,f616])).
fof(f1552,plain,(
  subset(sK12,set_difference(sK12,sK11))),
  inference(trivial_inequality_removal,[],[f1528])).
fof(f1598,plain,(
  set_difference(sK12,sK11) = sK12 | ~subset(set_difference(sK12,sK11),sK12)),
  inference(resolution,[],[f1552,f141])).
fof(f1606,plain,(
  set_difference(sK12,sK11) = sK12),
  inference(subsumption_resolution,[],[f1598,f192])).
fof(f2126,plain,(
  set_union2(sK11,sK10) = set_union2(sK11,sK11)),
  inference(superposition,[],[f477,f340])).
fof(f2160,plain,(
  set_union2(sK11,sK10) = sK11),
  inference(forward_demodulation,[],[f2126,f171])).
fof(f2214,plain,(
  set_difference(sK11,set_difference(sK11,sK10)) = sK10),
  inference(superposition,[],[f777,f2160])).
fof(f4333,plain,(
  ( ! [X4:$i,X2:$i,X3:$i] : (disjoint(set_difference(X2,X3),set_difference(X4,X2)) | disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
  inference(resolution,[],[f405,f399])).
fof(f4367,plain,(
  ( ! [X4:$i,X2:$i,X3:$i] : (disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
  inference(duplicate_literal_removal,[],[f4333])).
fof(f4414,plain,(
  ( ! [X40:$i] : (disjoint(sK10,set_difference(X40,sK11))) )),
  inference(superposition,[],[f4367,f2214])).
fof(f4549,plain,(
  disjoint(sK10,sK12)),
  inference(superposition,[],[f4414,f1606])).
fof(f4551,plain,(
  $false),
  inference(subsumption_resolution,[],[f4549,f210])).

Sample solution for `NLP042+1`

# SZS output start Saturation.
tff(u283,axiom,
    (![X1, X0] : ((~woman(X0,X1) | human_person(X0,X1))))).

tff(u282,axiom,
    (![X1, X0] : ((~woman(X0,X1) | female(X0,X1))))).

tff(u281,negated_conjecture,
    woman(sK0,sK1)).

tff(u280,negated_conjecture,
    ~female(sK0,sK4)).

tff(u279,negated_conjecture,
    ~female(sK0,sK2)).

tff(u278,negated_conjecture,
    ~female(sK0,sK3)).

tff(u277,negated_conjecture,
    female(sK0,sK1)).

tff(u276,axiom,
    (![X1, X0] : ((~human_person(X0,X1) | organism(X0,X1))))).

tff(u275,axiom,
    (![X1, X0] : ((~human_person(X0,X1) | human(X0,X1))))).

tff(u274,axiom,
    (![X1, X0] : ((~human_person(X0,X1) | animate(X0,X1))))).

tff(u273,negated_conjecture,
    human_person(sK0,sK1)).

tff(u272,negated_conjecture,
    ~animate(sK0,sK3)).

tff(u271,negated_conjecture,
    animate(sK0,sK1)).

tff(u270,negated_conjecture,
    ~human(sK0,sK2)).

tff(u269,negated_conjecture,
    human(sK0,sK1)).

tff(u268,axiom,
    (![X1, X0] : ((~organism(X0,X1) | entity(X0,X1))))).

tff(u267,axiom,
    (![X1, X0] : ((~organism(X0,X1) | living(X0,X1))))).

tff(u266,negated_conjecture,
    organism(sK0,sK1)).

tff(u265,negated_conjecture,
    ~living(sK0,sK3)).

tff(u264,negated_conjecture,
    living(sK0,sK1)).

tff(u263,axiom,
    (![X1, X0] : ((~entity(X0,X1) | specific(X0,X1))))).

tff(u262,axiom,
    (![X1, X0] : ((~entity(X0,X1) | existent(X0,X1))))).

tff(u261,negated_conjecture,
    entity(sK0,sK1)).

tff(u260,negated_conjecture,
    entity(sK0,sK3)).

tff(u259,axiom,
    (![X1, X0] : ((~mia_forename(X0,X1) | forename(X0,X1))))).

tff(u258,negated_conjecture,
    mia_forename(sK0,sK2)).

tff(u257,axiom,
    (![X1, X0] : ((~forename(X0,X1) | relname(X0,X1))))).

tff(u256,negated_conjecture,
    forename(sK0,sK2)).

tff(u255,axiom,
    (![X1, X0] : ((~abstraction(X0,X1) | nonhuman(X0,X1))))).

tff(u254,axiom,
    (![X1, X0] : ((~abstraction(X0,X1) | general(X0,X1))))).

tff(u253,axiom,
    (![X1, X0] : ((~abstraction(X0,X1) | unisex(X0,X1))))).

tff(u252,negated_conjecture,
    abstraction(sK0,sK2)).

tff(u251,axiom,
    (![X1, X0] : ((~unisex(X0,X1) | ~female(X0,X1))))).

tff(u250,negated_conjecture,
    unisex(sK0,sK2)).

tff(u249,negated_conjecture,
    unisex(sK0,sK4)).

tff(u248,negated_conjecture,
    unisex(sK0,sK3)).

tff(u247,negated_conjecture,
    ~general(sK0,sK4)).

tff(u246,negated_conjecture,
    ~general(sK0,sK1)).

tff(u245,negated_conjecture,
    ~general(sK0,sK3)).

tff(u244,negated_conjecture,
    general(sK0,sK2)).

tff(u243,axiom,
    (![X1, X0] : ((~nonhuman(X0,X1) | ~human(X0,X1))))).

tff(u242,negated_conjecture,
    nonhuman(sK0,sK2)).

tff(u241,axiom,
    (![X1, X0] : ((~relation(X0,X1) | abstraction(X0,X1))))).

tff(u240,negated_conjecture,
    relation(sK0,sK2)).

tff(u239,axiom,
    (![X1, X0] : ((~relname(X0,X1) | relation(X0,X1))))).

tff(u238,negated_conjecture,
    relname(sK0,sK2)).

tff(u237,axiom,
    (![X1, X0] : ((~object(X0,X1) | entity(X0,X1))))).

tff(u236,axiom,
    (![X1, X0] : ((~object(X0,X1) | nonliving(X0,X1))))).

tff(u235,axiom,
    (![X1, X0] : ((~object(X0,X1) | unisex(X0,X1))))).

tff(u234,negated_conjecture,
    object(sK0,sK3)).

tff(u233,axiom,
    (![X1, X0] : ((~nonliving(X0,X1) | ~living(X0,X1))))).

tff(u232,axiom,
    (![X1, X0] : ((~nonliving(X0,X1) | ~animate(X0,X1))))).

tff(u231,negated_conjecture,
    nonliving(sK0,sK3)).

tff(u230,negated_conjecture,
    ~existent(sK0,sK4)).

tff(u229,negated_conjecture,
    existent(sK0,sK1)).

tff(u228,negated_conjecture,
    existent(sK0,sK3)).

tff(u227,axiom,
    (![X1, X0] : ((~specific(X0,X1) | ~general(X0,X1))))).

tff(u226,negated_conjecture,
    specific(sK0,sK1)).

tff(u225,negated_conjecture,
    specific(sK0,sK4)).

tff(u224,negated_conjecture,
    specific(sK0,sK3)).

tff(u223,axiom,
    (![X1, X0] : ((~substance_matter(X0,X1) | object(X0,X1))))).

tff(u222,negated_conjecture,
    substance_matter(sK0,sK3)).

tff(u221,axiom,
    (![X1, X0] : ((~food(X0,X1) | substance_matter(X0,X1))))).

tff(u220,negated_conjecture,
    food(sK0,sK3)).

tff(u219,axiom,
    (![X1, X0] : ((~beverage(X0,X1) | food(X0,X1))))).

tff(u218,negated_conjecture,
    beverage(sK0,sK3)).

tff(u217,axiom,
    (![X1, X0] : ((~shake_beverage(X0,X1) | beverage(X0,X1))))).

tff(u216,negated_conjecture,
    shake_beverage(sK0,sK3)).

tff(u215,axiom,
    (![X1, X0] : ((~order(X0,X1) | act(X0,X1))))).

tff(u214,axiom,
    (![X1, X0] : ((~order(X0,X1) | event(X0,X1))))).

tff(u213,negated_conjecture,
    order(sK0,sK4)).

tff(u212,axiom,
    (![X1, X0] : ((~event(X0,X1) | eventuality(X0,X1))))).

tff(u211,negated_conjecture,
    event(sK0,sK4)).

tff(u210,axiom,
    (![X1, X0] : ((~eventuality(X0,X1) | specific(X0,X1))))).

tff(u209,axiom,
    (![X1, X0] : ((~eventuality(X0,X1) | nonexistent(X0,X1))))).

tff(u208,axiom,
    (![X1, X0] : ((~eventuality(X0,X1) | unisex(X0,X1))))).

tff(u207,negated_conjecture,
    eventuality(sK0,sK4)).

tff(u206,axiom,
    (![X1, X0] : ((~nonexistent(X0,X1) | ~existent(X0,X1))))).

tff(u205,negated_conjecture,
    nonexistent(sK0,sK4)).

tff(u204,axiom,
    (![X1, X0] : ((~act(X0,X1) | event(X0,X1))))).

tff(u203,negated_conjecture,
    act(sK0,sK4)).

tff(u202,axiom,
    (![X1, X3, X0, X2] : ((~of(X0,X3,X1) | (X2 = X3) | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1))))).

tff(u201,negated_conjecture,
    (![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0))))).

tff(u200,negated_conjecture,
    of(sK0,sK2,sK1)).

tff(u199,negated_conjecture,
    nonreflexive(sK0,sK4)).

tff(u198,negated_conjecture,
    ~agent(sK0,sK4,sK3)).

tff(u197,negated_conjecture,
    agent(sK0,sK4,sK1)).

tff(u196,axiom,
    (![X1, X3, X0] : ((~patient(X0,X1,X3) | ~agent(X0,X1,X3) | ~nonreflexive(X0,X1))))).

tff(u195,negated_conjecture,
    patient(sK0,sK4,sK3)).

# SZS output end Saturation.

Sample solution for `SWV017+1`

tff(declare$i,type,$i:$tType).
tff(declare_$i1,type,at:$i).
tff(declare_$i2,type,an_a_nonce:$i).
tff(finite_domain,axiom,
      ! [X:$i] : (
         X = at | X = an_a_nonce
      ) ).

tff(distinct_domain,axiom,
         at != an_a_nonce
).

tff(declare_t,type,t:$i).
tff(t_definition,axiom,t = at).
tff(declare_a,type,a:$i).
tff(a_definition,axiom,a = at).
tff(declare_b,type,b:$i).
tff(b_definition,axiom,b = at).
tff(declare_bt,type,bt:$i).
tff(bt_definition,axiom,bt = an_a_nonce).
tff(declare_an_intruder_nonce,type,an_intruder_nonce:$i).
tff(an_intruder_nonce_definition,axiom,an_intruder_nonce = an_a_nonce).
tff(declare_key,type,key: $i * $i > $i).
tff(function_key,axiom,
           key(at,at) = at
         & key(at,an_a_nonce) = at
         & key(an_a_nonce,at) = at
         & key(an_a_nonce,an_a_nonce) = an_a_nonce

).

tff(declare_pair,type,pair: $i * $i > $i).
tff(function_pair,axiom,
           pair(at,at) = at
         & pair(at,an_a_nonce) = an_a_nonce
         & pair(an_a_nonce,at) = at
         & pair(an_a_nonce,an_a_nonce) = at

).

tff(declare_sent,type,sent: $i * $i * $i > $i).
tff(function_sent,axiom,
           sent(at,at,at) = at
         & sent(at,at,an_a_nonce) = at
         & sent(at,an_a_nonce,at) = at
         & sent(at,an_a_nonce,an_a_nonce) = an_a_nonce
         & sent(an_a_nonce,at,at) = at
         & sent(an_a_nonce,at,an_a_nonce) = at
         & sent(an_a_nonce,an_a_nonce,at) = at
         & sent(an_a_nonce,an_a_nonce,an_a_nonce) = at

).

tff(declare_quadruple,type,quadruple: $i * $i * $i * $i > $i).
tff(function_quadruple,axiom,
           quadruple(at,at,at,at) = at
         & quadruple(at,at,at,an_a_nonce) = at
         & quadruple(at,at,an_a_nonce,at) = at
         & quadruple(at,at,an_a_nonce,an_a_nonce) = at
         & quadruple(at,an_a_nonce,at,at) = at
         & quadruple(at,an_a_nonce,at,an_a_nonce) = at
         & quadruple(at,an_a_nonce,an_a_nonce,at) = at
         & quadruple(at,an_a_nonce,an_a_nonce,an_a_nonce) = at
         & quadruple(an_a_nonce,at,at,at) = at
         & quadruple(an_a_nonce,at,at,an_a_nonce) = an_a_nonce
         & quadruple(an_a_nonce,at,an_a_nonce,at) = an_a_nonce
         & quadruple(an_a_nonce,at,an_a_nonce,an_a_nonce) = an_a_nonce
         & quadruple(an_a_nonce,an_a_nonce,at,at) = an_a_nonce
         & quadruple(an_a_nonce,an_a_nonce,at,an_a_nonce) = at
         & quadruple(an_a_nonce,an_a_nonce,an_a_nonce,at) = an_a_nonce
         & quadruple(an_a_nonce,an_a_nonce,an_a_nonce,an_a_nonce) = an_a_nonce

).

tff(declare_encrypt,type,encrypt: $i * $i > $i).
tff(function_encrypt,axiom,
           encrypt(at,at) = an_a_nonce
         & encrypt(at,an_a_nonce) = an_a_nonce
         & encrypt(an_a_nonce,at) = at
         & encrypt(an_a_nonce,an_a_nonce) = at

).

tff(declare_triple,type,triple: $i * $i * $i > $i).
tff(function_triple,axiom,
           triple(at,at,at) = at
         & triple(at,at,an_a_nonce) = an_a_nonce
         & triple(at,an_a_nonce,at) = at
         & triple(at,an_a_nonce,an_a_nonce) = at
         & triple(an_a_nonce,at,at) = at
         & triple(an_a_nonce,at,an_a_nonce) = an_a_nonce
         & triple(an_a_nonce,an_a_nonce,at) = at
         & triple(an_a_nonce,an_a_nonce,an_a_nonce) = an_a_nonce

).

tff(declare_generate_b_nonce,type,generate_b_nonce: $i > $i).
tff(function_generate_b_nonce,axiom,
           generate_b_nonce(at) = an_a_nonce
         & generate_b_nonce(an_a_nonce) = an_a_nonce

).

tff(declare_generate_expiration_time,type,generate_expiration_time: $i > $i).
tff(function_generate_expiration_time,axiom,
           generate_expiration_time(at) = an_a_nonce
         & generate_expiration_time(an_a_nonce) = an_a_nonce

).

tff(declare_generate_key,type,generate_key: $i > $i).
tff(function_generate_key,axiom,
           generate_key(at) = at
         & generate_key(an_a_nonce) = at

).

tff(declare_generate_intruder_nonce,type,generate_intruder_nonce: $i > $i).
tff(function_generate_intruder_nonce,axiom,
           generate_intruder_nonce(at) = at
         & generate_intruder_nonce(an_a_nonce) = an_a_nonce

).

tff(declare_a_holds,type,a_holds: $i > $o ).
fof(predicate_a_holds,axiom,
           a_holds(at)
         & a_holds(an_a_nonce)

).

tff(declare_party_of_protocol,type,party_of_protocol: $i > $o ).
fof(predicate_party_of_protocol,axiom,
           party_of_protocol(at)
         & party_of_protocol(an_a_nonce)

).

tff(declare_message,type,message: $i > $o ).
fof(predicate_message,axiom,
           message(at)
         & message(an_a_nonce)

).

tff(declare_a_stored,type,a_stored: $i > $o ).
fof(predicate_a_stored,axiom,
           ~a_stored(at)
         & a_stored(an_a_nonce)

).

tff(declare_b_holds,type,b_holds: $i > $o ).
fof(predicate_b_holds,axiom,
           b_holds(at)
         & b_holds(an_a_nonce)

).

tff(declare_fresh_to_b,type,fresh_to_b: $i > $o ).
fof(predicate_fresh_to_b,axiom,
           fresh_to_b(at)
         & fresh_to_b(an_a_nonce)

).

tff(declare_b_stored,type,b_stored: $i > $o ).
fof(predicate_b_stored,axiom,
           b_stored(at)
         & b_stored(an_a_nonce)

).

tff(declare_a_key,type,a_key: $i > $o ).
fof(predicate_a_key,axiom,
           a_key(at)
         & ~a_key(an_a_nonce)

).

tff(declare_t_holds,type,t_holds: $i > $o ).
fof(predicate_t_holds,axiom,
           t_holds(at)
         & ~t_holds(an_a_nonce)

).

tff(declare_a_nonce,type,a_nonce: $i > $o ).
fof(predicate_a_nonce,axiom,
           ~a_nonce(at)
         & a_nonce(an_a_nonce)

).

tff(declare_intruder_message,type,intruder_message: $i > $o ).
fof(predicate_intruder_message,axiom,
           intruder_message(at)
         & intruder_message(an_a_nonce)

).

tff(declare_intruder_holds,type,intruder_holds: $i > $o ).
fof(predicate_intruder_holds,axiom,
           intruder_holds(at)
         & intruder_holds(an_a_nonce)

).

tff(declare_fresh_intruder_nonce,type,fresh_intruder_nonce: $i > $o ).
fof(predicate_fresh_intruder_nonce,axiom,
           ~fresh_intruder_nonce(at)
         & fresh_intruder_nonce(an_a_nonce)

).

VampireZ3 1.0

Giles Reger
University of Manchester, United Kingdom

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

Entrants' Sample Solutions

Beagle 0.9.47

Sample solution for DAT013=1

CVC4 1.5.1

Sample solution for DAT013=1

Sample solution for SEU140+2

Sample solution for NLP042+1

Sample solution for SWV017+1

E 2.0

Sample solution for SEU140+2

Sample solution for NLP042+1

Sample solution for SWV017+1

Geo-III 2016C

Sample proof for SEU140+2

Sample proof for PUZ001+1

Sample proof for NLP042+1

Sample proof for SWV017+1

iProver 2.5

Sample proof for SEU140+2

Sample model for NLP042+1

Sample model for SWV017+1

leanCoP 2.2

Sample solution for SEU140+2

LEO-II 1.7.0

Sample solution for SET014^4

Leo-III 1.0 and Leo+III 1.0

Sample solution for SET014^4

Princess 160606

Sample solution for DAT013=1

Prover9 2009-11A

Sample solution for SEU140+2

Satallax 2.8

Sample solution for SET014^4

Satallax 3.0

Sample solution for SET014^4

Sample solution for SYO553^1

Vampire 4.0

Sample solution for SEU140+2

Sample solution for NLP042+1

Sample solution for SWV017+1

Vampire 4.1

Sample solution for DAT013=1

Sample solution for SEU140+2

Sample solution for NLP042+1

Sample solution for SWV017+1

VampireZ3 1.0

Sample solution for DAT013=1

Sample solution for `DAT013=1`

Sample solution for `DAT013=1`

Sample solution for `SEU140+2`

Sample solution for `NLP042+1`

Sample solution for `SWV017+1`

Sample solution for `SEU140+2`

Sample solution for `NLP042+1`

Sample solution for `SWV017+1`

Sample proof for `SEU140+2`

Sample proof for `PUZ001+1`

Sample proof for `NLP042+1`

Sample proof for `SWV017+1`

Sample proof for `SEU140+2`

Sample model for `NLP042+1`

Sample model for `SWV017+1`

Sample solution for `SEU140+2`

Sample solution for `SET014^4`

Sample solution for `SET014^4`

Sample solution for `DAT013=1`

Sample solution for `SEU140+2`

Sample solution for `SET014^4`

Sample solution for `SET014^4`

Sample solution for `SYO553^1`

Sample solution for `SEU140+2`

Sample solution for `NLP042+1`

Sample solution for `SWV017+1`

Sample solution for `DAT013=1`

Sample solution for `SEU140+2`

Sample solution for `NLP042+1`

Sample solution for `SWV017+1`

Sample solution for `DAT013=1`