TSTP Solution File: SWW637_2 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW637_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:25:43 EDT 2024
% Result : Theorem 11.91s 2.09s
% Output : CNFRefutation 11.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 89 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 1318 ( 10 equ)
% Maximal formula atoms : 36 ( 14 avg)
% Number of connectives : 508 ( 172 ~; 152 |; 144 &)
% ( 2 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 893 ( 893 fml; 0 var)
% Number arithmetic : 186 ( 119 atm; 0 fun; 0 num; 67 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 34 ( 29 usr; 15 prp; 0-4 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 229 ( 0 sgn 151 !; 43 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
tff(f35,axiom,
! [X0: ty,X12: uni,X11: uni] :
( distinct(X0,X12)
=> ( distinct(X0,X11)
=> ( ! [X1: uni] :
( sort(X0,X1)
=> ( mem(X0,X1,X12)
=> ~ mem(X0,X1,X11) ) )
=> distinct(X0,infix_plpl(X0,X12,X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct_append) ).
tff(f50,axiom,
! [X0: ty] :
( ! [X1: uni,X2: uni] : ( labels(X0,node(X0,X1,X2)) = infix_plpl(X0,labels(X0,X1),labels(X0,X2)) )
& ! [X1: uni] : ( cons(X0,X1,nil(X0)) = labels(X0,leaf(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',labels_def) ).
tff(f52,axiom,
! [X0: ty,X1: uni,X14: uni,X16: uni] :
( mem(X0,X1,labels(X0,node(X0,X14,X16)))
<=> ( mem(X0,X1,labels(X0,X16))
| mem(X0,X1,labels(X0,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',labels_Node) ).
tff(f54,axiom,
! [X0: ty,X17: ty,X12: uni,X18: uni,X11: uni,X19: uni] :
( same_shape(X17,X0,X12,X11)
=> ( same_shape(X17,X0,X18,X19)
=> same_shape(X17,X0,node(X0,X12,X18),node(X17,X11,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',same_shape_Node) ).
tff(f71,axiom,
! [X21: uni] : ( t2tb3(tb2t3(X21)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR3) ).
tff(f72,conjecture,
! [X16: $int,X1: tree_a1,X2: tree_a1,X18: $int,X22: tree_int] :
( ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,t2tb(X22)))
=> ( $lesseq(X3,X18)
& $less(X16,X3) ) )
& $lesseq(X16,X18)
& distinct(int,labels(int,t2tb(X22)))
& same_shape(int,a1,t2tb2(X2),t2tb(X22)) )
=> ! [X19: $int,X23: tree_int] :
( ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,t2tb(X23)))
=> ( $lesseq(X3,X19)
& $less(X18,X3) ) )
& $lesseq(X18,X19)
& distinct(int,labels(int,t2tb(X23)))
& same_shape(int,a1,t2tb2(X1),t2tb(X23)) )
=> ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,node(int,t2tb(X23),t2tb(X22))))
=> ( $lesseq(X3,X19)
& $less(X16,X3) ) )
& $lesseq(X16,X19)
& distinct(int,labels(int,node(int,t2tb(X23),t2tb(X22))))
& same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X23),t2tb(X22))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_relabel) ).
tff(f73,negated_conjecture,
~ ! [X16: $int,X1: tree_a1,X2: tree_a1,X18: $int,X22: tree_int] :
( ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,t2tb(X22)))
=> ( $lesseq(X3,X18)
& $less(X16,X3) ) )
& $lesseq(X16,X18)
& distinct(int,labels(int,t2tb(X22)))
& same_shape(int,a1,t2tb2(X2),t2tb(X22)) )
=> ! [X19: $int,X23: tree_int] :
( ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,t2tb(X23)))
=> ( $lesseq(X3,X19)
& $less(X18,X3) ) )
& $lesseq(X18,X19)
& distinct(int,labels(int,t2tb(X23)))
& same_shape(int,a1,t2tb2(X1),t2tb(X23)) )
=> ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,node(int,t2tb(X23),t2tb(X22))))
=> ( $lesseq(X3,X19)
& $less(X16,X3) ) )
& $lesseq(X16,X19)
& distinct(int,labels(int,node(int,t2tb(X23),t2tb(X22))))
& same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X23),t2tb(X22))) ) ) ),
inference(negated_conjecture,[],[f72]) ).
tff(f76,plain,
~ ! [X16: $int,X1: tree_a1,X2: tree_a1,X18: $int,X22: tree_int] :
( ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,t2tb(X22)))
=> ( ~ $less(X18,X3)
& $less(X16,X3) ) )
& ~ $less(X18,X16)
& distinct(int,labels(int,t2tb(X22)))
& same_shape(int,a1,t2tb2(X2),t2tb(X22)) )
=> ! [X19: $int,X23: tree_int] :
( ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,t2tb(X23)))
=> ( ~ $less(X19,X3)
& $less(X18,X3) ) )
& ~ $less(X19,X18)
& distinct(int,labels(int,t2tb(X23)))
& same_shape(int,a1,t2tb2(X1),t2tb(X23)) )
=> ( ! [X3: $int] :
( mem(int,t2tb3(X3),labels(int,node(int,t2tb(X23),t2tb(X22))))
=> ( ~ $less(X19,X3)
& $less(X16,X3) ) )
& ~ $less(X19,X16)
& distinct(int,labels(int,node(int,t2tb(X23),t2tb(X22))))
& same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X23),t2tb(X22))) ) ) ),
inference(theory_normalization,[],[f73]) ).
tff(f83,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_146,[]) ).
tff(f117,plain,
! [X0: ty,X1: uni,X2: uni] :
( distinct(X0,X1)
=> ( distinct(X0,X2)
=> ( ! [X3: uni] :
( sort(X0,X3)
=> ( mem(X0,X3,X1)
=> ~ mem(X0,X3,X2) ) )
=> distinct(X0,infix_plpl(X0,X1,X2)) ) ) ),
inference(rectify,[],[f35]) ).
tff(f126,plain,
! [X0: ty] :
( ! [X1: uni,X2: uni] : ( labels(X0,node(X0,X1,X2)) = infix_plpl(X0,labels(X0,X1),labels(X0,X2)) )
& ! [X3: uni] : ( cons(X0,X3,nil(X0)) = labels(X0,leaf(X0,X3)) ) ),
inference(rectify,[],[f50]) ).
tff(f128,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( mem(X0,X1,labels(X0,node(X0,X2,X3)))
<=> ( mem(X0,X1,labels(X0,X3))
| mem(X0,X1,labels(X0,X2)) ) ),
inference(rectify,[],[f52]) ).
tff(f130,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
( same_shape(X1,X0,X2,X4)
=> ( same_shape(X1,X0,X3,X5)
=> same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5)) ) ),
inference(rectify,[],[f54]) ).
tff(f145,plain,
! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 ),
inference(rectify,[],[f71]) ).
tff(f146,plain,
~ ! [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
( ( ! [X5: $int] :
( mem(int,t2tb3(X5),labels(int,t2tb(X4)))
=> ( ~ $less(X3,X5)
& $less(X0,X5) ) )
& ~ $less(X3,X0)
& distinct(int,labels(int,t2tb(X4)))
& same_shape(int,a1,t2tb2(X2),t2tb(X4)) )
=> ! [X6: $int,X7: tree_int] :
( ( ! [X8: $int] :
( mem(int,t2tb3(X8),labels(int,t2tb(X7)))
=> ( ~ $less(X6,X8)
& $less(X3,X8) ) )
& ~ $less(X6,X3)
& distinct(int,labels(int,t2tb(X7)))
& same_shape(int,a1,t2tb2(X1),t2tb(X7)) )
=> ( ! [X9: $int] :
( mem(int,t2tb3(X9),labels(int,node(int,t2tb(X7),t2tb(X4))))
=> ( ~ $less(X6,X9)
& $less(X0,X9) ) )
& ~ $less(X6,X0)
& distinct(int,labels(int,node(int,t2tb(X7),t2tb(X4))))
& same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X7),t2tb(X4))) ) ) ),
inference(rectify,[],[f76]) ).
tff(f160,plain,
! [X0: ty,X1: uni,X2: uni] :
( distinct(X0,infix_plpl(X0,X1,X2))
| ? [X3: uni] :
( mem(X0,X3,X2)
& mem(X0,X3,X1)
& sort(X0,X3) )
| ~ distinct(X0,X2)
| ~ distinct(X0,X1) ),
inference(ennf_transformation,[],[f117]) ).
tff(f161,plain,
! [X0: ty,X1: uni,X2: uni] :
( distinct(X0,infix_plpl(X0,X1,X2))
| ? [X3: uni] :
( mem(X0,X3,X2)
& mem(X0,X3,X1)
& sort(X0,X3) )
| ~ distinct(X0,X2)
| ~ distinct(X0,X1) ),
inference(flattening,[],[f160]) ).
tff(f167,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
( same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5))
| ~ same_shape(X1,X0,X3,X5)
| ~ same_shape(X1,X0,X2,X4) ),
inference(ennf_transformation,[],[f130]) ).
tff(f168,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
( same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5))
| ~ same_shape(X1,X0,X3,X5)
| ~ same_shape(X1,X0,X2,X4) ),
inference(flattening,[],[f167]) ).
tff(f173,plain,
? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
( ? [X6: $int,X7: tree_int] :
( ( ? [X9: $int] :
( ( $less(X6,X9)
| ~ $less(X0,X9) )
& mem(int,t2tb3(X9),labels(int,node(int,t2tb(X7),t2tb(X4)))) )
| $less(X6,X0)
| ~ distinct(int,labels(int,node(int,t2tb(X7),t2tb(X4))))
| ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X7),t2tb(X4))) )
& ! [X8: $int] :
( ( ~ $less(X6,X8)
& $less(X3,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(X7))) )
& ~ $less(X6,X3)
& distinct(int,labels(int,t2tb(X7)))
& same_shape(int,a1,t2tb2(X1),t2tb(X7)) )
& ! [X5: $int] :
( ( ~ $less(X3,X5)
& $less(X0,X5) )
| ~ mem(int,t2tb3(X5),labels(int,t2tb(X4))) )
& ~ $less(X3,X0)
& distinct(int,labels(int,t2tb(X4)))
& same_shape(int,a1,t2tb2(X2),t2tb(X4)) ),
inference(ennf_transformation,[],[f146]) ).
tff(f174,plain,
? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
( ? [X6: $int,X7: tree_int] :
( ( ? [X9: $int] :
( ( $less(X6,X9)
| ~ $less(X0,X9) )
& mem(int,t2tb3(X9),labels(int,node(int,t2tb(X7),t2tb(X4)))) )
| $less(X6,X0)
| ~ distinct(int,labels(int,node(int,t2tb(X7),t2tb(X4))))
| ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X7),t2tb(X4))) )
& ! [X8: $int] :
( ( ~ $less(X6,X8)
& $less(X3,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(X7))) )
& ~ $less(X6,X3)
& distinct(int,labels(int,t2tb(X7)))
& same_shape(int,a1,t2tb2(X1),t2tb(X7)) )
& ! [X5: $int] :
( ( ~ $less(X3,X5)
& $less(X0,X5) )
| ~ mem(int,t2tb3(X5),labels(int,t2tb(X4))) )
& ~ $less(X3,X0)
& distinct(int,labels(int,t2tb(X4)))
& same_shape(int,a1,t2tb2(X2),t2tb(X4)) ),
inference(flattening,[],[f173]) ).
tff(f193,plain,
! [X0: ty,X1: uni,X2: uni] :
( ? [X3: uni] :
( mem(X0,X3,X2)
& mem(X0,X3,X1)
& sort(X0,X3) )
=> ( mem(X0,sK7(X0,X1,X2),X2)
& mem(X0,sK7(X0,X1,X2),X1)
& sort(X0,sK7(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f194,plain,
! [X0: ty,X1: uni,X2: uni] :
( distinct(X0,infix_plpl(X0,X1,X2))
| ( mem(X0,sK7(X0,X1,X2),X2)
& mem(X0,sK7(X0,X1,X2),X1)
& sort(X0,sK7(X0,X1,X2)) )
| ~ distinct(X0,X2)
| ~ distinct(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f161,f193]) ).
tff(f196,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( ( mem(X0,X1,labels(X0,node(X0,X2,X3)))
| ( ~ mem(X0,X1,labels(X0,X3))
& ~ mem(X0,X1,labels(X0,X2)) ) )
& ( mem(X0,X1,labels(X0,X3))
| mem(X0,X1,labels(X0,X2))
| ~ mem(X0,X1,labels(X0,node(X0,X2,X3))) ) ),
inference(nnf_transformation,[],[f128]) ).
tff(f197,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( ( mem(X0,X1,labels(X0,node(X0,X2,X3)))
| ( ~ mem(X0,X1,labels(X0,X3))
& ~ mem(X0,X1,labels(X0,X2)) ) )
& ( mem(X0,X1,labels(X0,X3))
| mem(X0,X1,labels(X0,X2))
| ~ mem(X0,X1,labels(X0,node(X0,X2,X3))) ) ),
inference(flattening,[],[f196]) ).
tff(f205,plain,
? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
( ? [X5: $int,X6: tree_int] :
( ( ? [X7: $int] :
( ( $less(X5,X7)
| ~ $less(X0,X7) )
& mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(X4)))) )
| $less(X5,X0)
| ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(X4))))
| ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X6),t2tb(X4))) )
& ! [X8: $int] :
( ( ~ $less(X5,X8)
& $less(X3,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
& ~ $less(X5,X3)
& distinct(int,labels(int,t2tb(X6)))
& same_shape(int,a1,t2tb2(X1),t2tb(X6)) )
& ! [X9: $int] :
( ( ~ $less(X3,X9)
& $less(X0,X9) )
| ~ mem(int,t2tb3(X9),labels(int,t2tb(X4))) )
& ~ $less(X3,X0)
& distinct(int,labels(int,t2tb(X4)))
& same_shape(int,a1,t2tb2(X2),t2tb(X4)) ),
inference(rectify,[],[f174]) ).
tff(f206,plain,
( ? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
( ? [X5: $int,X6: tree_int] :
( ( ? [X7: $int] :
( ( $less(X5,X7)
| ~ $less(X0,X7) )
& mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(X4)))) )
| $less(X5,X0)
| ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(X4))))
| ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X6),t2tb(X4))) )
& ! [X8: $int] :
( ( ~ $less(X5,X8)
& $less(X3,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
& ~ $less(X5,X3)
& distinct(int,labels(int,t2tb(X6)))
& same_shape(int,a1,t2tb2(X1),t2tb(X6)) )
& ! [X9: $int] :
( ( ~ $less(X3,X9)
& $less(X0,X9) )
| ~ mem(int,t2tb3(X9),labels(int,t2tb(X4))) )
& ~ $less(X3,X0)
& distinct(int,labels(int,t2tb(X4)))
& same_shape(int,a1,t2tb2(X2),t2tb(X4)) )
=> ( ? [X6: tree_int,X5: $int] :
( ( ? [X7: $int] :
( ( $less(X5,X7)
| ~ $less(sK14,X7) )
& mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(sK18)))) )
| $less(X5,sK14)
| ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(sK18))))
| ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(X6),t2tb(sK18))) )
& ! [X8: $int] :
( ( ~ $less(X5,X8)
& $less(sK17,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
& ~ $less(X5,sK17)
& distinct(int,labels(int,t2tb(X6)))
& same_shape(int,a1,t2tb2(sK15),t2tb(X6)) )
& ! [X9: $int] :
( ( ~ $less(sK17,X9)
& $less(sK14,X9) )
| ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) )
& ~ $less(sK17,sK14)
& distinct(int,labels(int,t2tb(sK18)))
& same_shape(int,a1,t2tb2(sK16),t2tb(sK18)) ) ),
introduced(choice_axiom,[]) ).
tff(f207,plain,
( ? [X6: tree_int,X5: $int] :
( ( ? [X7: $int] :
( ( $less(X5,X7)
| ~ $less(sK14,X7) )
& mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(sK18)))) )
| $less(X5,sK14)
| ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(sK18))))
| ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(X6),t2tb(sK18))) )
& ! [X8: $int] :
( ( ~ $less(X5,X8)
& $less(sK17,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
& ~ $less(X5,sK17)
& distinct(int,labels(int,t2tb(X6)))
& same_shape(int,a1,t2tb2(sK15),t2tb(X6)) )
=> ( ( ? [X7: $int] :
( ( $less(sK19,X7)
| ~ $less(sK14,X7) )
& mem(int,t2tb3(X7),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) )
| $less(sK19,sK14)
| ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) )
& ! [X8: $int] :
( ( ~ $less(sK19,X8)
& $less(sK17,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) )
& ~ $less(sK19,sK17)
& distinct(int,labels(int,t2tb(sK20)))
& same_shape(int,a1,t2tb2(sK15),t2tb(sK20)) ) ),
introduced(choice_axiom,[]) ).
tff(f208,plain,
( ? [X7: $int] :
( ( $less(sK19,X7)
| ~ $less(sK14,X7) )
& mem(int,t2tb3(X7),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) )
=> ( ( $less(sK19,sK21)
| ~ $less(sK14,sK21) )
& mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) ) ),
introduced(choice_axiom,[]) ).
tff(f209,plain,
( ( ( ( $less(sK19,sK21)
| ~ $less(sK14,sK21) )
& mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) )
| $less(sK19,sK14)
| ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) )
& ! [X8: $int] :
( ( ~ $less(sK19,X8)
& $less(sK17,X8) )
| ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) )
& ~ $less(sK19,sK17)
& distinct(int,labels(int,t2tb(sK20)))
& same_shape(int,a1,t2tb2(sK15),t2tb(sK20))
& ! [X9: $int] :
( ( ~ $less(sK17,X9)
& $less(sK14,X9) )
| ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) )
& ~ $less(sK17,sK14)
& distinct(int,labels(int,t2tb(sK18)))
& same_shape(int,a1,t2tb2(sK16),t2tb(sK18)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21])],[f205,f208,f207,f206]) ).
tff(f261,plain,
! [X2: uni,X0: ty,X1: uni] :
( distinct(X0,infix_plpl(X0,X1,X2))
| mem(X0,sK7(X0,X1,X2),X1)
| ~ distinct(X0,X2)
| ~ distinct(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
tff(f262,plain,
! [X2: uni,X0: ty,X1: uni] :
( distinct(X0,infix_plpl(X0,X1,X2))
| mem(X0,sK7(X0,X1,X2),X2)
| ~ distinct(X0,X2)
| ~ distinct(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
tff(f278,plain,
! [X2: uni,X0: ty,X1: uni] : ( labels(X0,node(X0,X1,X2)) = infix_plpl(X0,labels(X0,X1),labels(X0,X2)) ),
inference(cnf_transformation,[],[f126]) ).
tff(f281,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( mem(X0,X1,labels(X0,X3))
| mem(X0,X1,labels(X0,X2))
| ~ mem(X0,X1,labels(X0,node(X0,X2,X3))) ),
inference(cnf_transformation,[],[f197]) ).
tff(f285,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni,X5: uni] :
( same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5))
| ~ same_shape(X1,X0,X3,X5)
| ~ same_shape(X1,X0,X2,X4) ),
inference(cnf_transformation,[],[f168]) ).
tff(f313,plain,
! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 ),
inference(cnf_transformation,[],[f145]) ).
tff(f314,plain,
same_shape(int,a1,t2tb2(sK16),t2tb(sK18)),
inference(cnf_transformation,[],[f209]) ).
tff(f315,plain,
distinct(int,labels(int,t2tb(sK18))),
inference(cnf_transformation,[],[f209]) ).
tff(f316,plain,
~ $less(sK17,sK14),
inference(cnf_transformation,[],[f209]) ).
tff(f317,plain,
! [X9: $int] :
( $less(sK14,X9)
| ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) ),
inference(cnf_transformation,[],[f209]) ).
tff(f318,plain,
! [X9: $int] :
( ~ $less(sK17,X9)
| ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) ),
inference(cnf_transformation,[],[f209]) ).
tff(f319,plain,
same_shape(int,a1,t2tb2(sK15),t2tb(sK20)),
inference(cnf_transformation,[],[f209]) ).
tff(f320,plain,
distinct(int,labels(int,t2tb(sK20))),
inference(cnf_transformation,[],[f209]) ).
tff(f321,plain,
~ $less(sK19,sK17),
inference(cnf_transformation,[],[f209]) ).
tff(f322,plain,
! [X8: $int] :
( $less(sK17,X8)
| ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) ),
inference(cnf_transformation,[],[f209]) ).
tff(f323,plain,
! [X8: $int] :
( ~ $less(sK19,X8)
| ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) ),
inference(cnf_transformation,[],[f209]) ).
tff(f324,plain,
( mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| $less(sK19,sK14)
| ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) ),
inference(cnf_transformation,[],[f209]) ).
tff(f325,plain,
( $less(sK19,sK21)
| ~ $less(sK14,sK21)
| $less(sK19,sK14)
| ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_60,plain,
( ~ $less_int(X0_3,X1_3)
| ~ $less_int(X1_3,X2_3)
| $less_int(X0_3,X2_3) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_117,plain,
( ~ distinct(X0_14,X0_13)
| ~ distinct(X0_14,X1_13)
| mem(X0_14,sK7(X0_14,X1_13,X0_13),X0_13)
| distinct(X0_14,infix_plpl(X0_14,X1_13,X0_13)) ),
inference(cnf_transformation,[],[f262]) ).
cnf(c_118,plain,
( ~ distinct(X0_14,X0_13)
| ~ distinct(X0_14,X1_13)
| mem(X0_14,sK7(X0_14,X1_13,X0_13),X1_13)
| distinct(X0_14,infix_plpl(X0_14,X1_13,X0_13)) ),
inference(cnf_transformation,[],[f261]) ).
cnf(c_134,plain,
infix_plpl(X0_14,labels(X0_14,X0_13),labels(X0_14,X1_13)) = labels(X0_14,node(X0_14,X0_13,X1_13)),
inference(cnf_transformation,[],[f278]) ).
cnf(c_140,plain,
( ~ mem(X0_14,X0_13,labels(X0_14,node(X0_14,X1_13,X2_13)))
| mem(X0_14,X0_13,labels(X0_14,X1_13))
| mem(X0_14,X0_13,labels(X0_14,X2_13)) ),
inference(cnf_transformation,[],[f281]) ).
cnf(c_142,plain,
( ~ same_shape(X0_14,X1_14,X0_13,X1_13)
| ~ same_shape(X0_14,X1_14,X2_13,X3_13)
| same_shape(X0_14,X1_14,node(X1_14,X0_13,X2_13),node(X0_14,X1_13,X3_13)) ),
inference(cnf_transformation,[],[f285]) ).
cnf(c_170,plain,
t2tb3(tb2t3(X0_13)) = X0_13,
inference(cnf_transformation,[],[f313]) ).
cnf(c_171,negated_conjecture,
( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
| ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| ~ $less_int(sK14,sK21)
| $less_int(sK19,sK14)
| $less_int(sK19,sK21) ),
inference(cnf_transformation,[],[f325]) ).
cnf(c_172,negated_conjecture,
( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
| ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| $less_int(sK19,sK14) ),
inference(cnf_transformation,[],[f324]) ).
cnf(c_173,negated_conjecture,
( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK20)))
| ~ $less_int(sK19,X0_3) ),
inference(cnf_transformation,[],[f323]) ).
cnf(c_174,negated_conjecture,
( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK20)))
| $less_int(sK17,X0_3) ),
inference(cnf_transformation,[],[f322]) ).
cnf(c_175,negated_conjecture,
~ $less_int(sK19,sK17),
inference(cnf_transformation,[],[f321]) ).
cnf(c_176,negated_conjecture,
distinct(int,labels(int,t2tb(sK20))),
inference(cnf_transformation,[],[f320]) ).
cnf(c_177,negated_conjecture,
same_shape(int,a1,t2tb2(sK15),t2tb(sK20)),
inference(cnf_transformation,[],[f319]) ).
cnf(c_178,negated_conjecture,
( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK18)))
| ~ $less_int(sK17,X0_3) ),
inference(cnf_transformation,[],[f318]) ).
cnf(c_179,negated_conjecture,
( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK18)))
| $less_int(sK14,X0_3) ),
inference(cnf_transformation,[],[f317]) ).
cnf(c_180,negated_conjecture,
~ $less_int(sK17,sK14),
inference(cnf_transformation,[],[f316]) ).
cnf(c_181,negated_conjecture,
distinct(int,labels(int,t2tb(sK18))),
inference(cnf_transformation,[],[f315]) ).
cnf(c_182,negated_conjecture,
same_shape(int,a1,t2tb2(sK16),t2tb(sK18)),
inference(cnf_transformation,[],[f314]) ).
cnf(c_969,plain,
( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
| ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| ~ $less_int(sK14,sK21)
| $less_int(sK19,sK21) ),
inference(backward_subsumption_resolution,[status(thm)],[c_171,c_60]) ).
cnf(c_6378,plain,
( ~ mem(int,X0_13,labels(int,t2tb(sK18)))
| ~ $less_int(sK17,tb2t3(X0_13)) ),
inference(superposition,[status(thm)],[c_170,c_178]) ).
cnf(c_6382,plain,
( ~ mem(int,X0_13,labels(int,t2tb(sK20)))
| $less_int(sK17,tb2t3(X0_13)) ),
inference(superposition,[status(thm)],[c_170,c_174]) ).
cnf(c_8394,plain,
( ~ same_shape(int,a1,t2tb2(sK16),t2tb(sK18))
| ~ same_shape(int,a1,X0_13,X1_13)
| same_shape(int,a1,node(a1,X0_13,t2tb2(sK16)),node(int,X1_13,t2tb(sK18))) ),
inference(instantiation,[status(thm)],[c_142]) ).
cnf(c_12227,plain,
( ~ same_shape(int,a1,t2tb2(sK15),t2tb(sK20))
| ~ same_shape(int,a1,t2tb2(sK16),t2tb(sK18))
| same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) ),
inference(instantiation,[status(thm)],[c_8394]) ).
cnf(c_13275,plain,
( ~ $less_int(sK17,tb2t3(sK7(int,X0_13,labels(int,t2tb(sK18)))))
| ~ distinct(int,labels(int,t2tb(sK18)))
| ~ distinct(int,X0_13)
| distinct(int,infix_plpl(int,X0_13,labels(int,t2tb(sK18)))) ),
inference(superposition,[status(thm)],[c_117,c_6378]) ).
cnf(c_13292,plain,
( ~ $less_int(sK17,tb2t3(sK7(int,X0_13,labels(int,t2tb(sK18)))))
| ~ distinct(int,X0_13)
| distinct(int,infix_plpl(int,X0_13,labels(int,t2tb(sK18)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13275,c_181]) ).
cnf(c_13354,plain,
( ~ distinct(int,labels(int,t2tb(sK20)))
| ~ distinct(int,X0_13)
| $less_int(sK17,tb2t3(sK7(int,labels(int,t2tb(sK20)),X0_13)))
| distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),X0_13)) ),
inference(superposition,[status(thm)],[c_118,c_6382]) ).
cnf(c_13356,plain,
( ~ distinct(int,X0_13)
| $less_int(sK17,tb2t3(sK7(int,labels(int,t2tb(sK20)),X0_13)))
| distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13354,c_176]) ).
cnf(c_13747,plain,
( ~ distinct(int,labels(int,t2tb(sK18)))
| ~ distinct(int,labels(int,t2tb(sK20)))
| distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),labels(int,t2tb(sK18)))) ),
inference(superposition,[status(thm)],[c_13356,c_13292]) ).
cnf(c_13748,plain,
distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),labels(int,t2tb(sK18)))),
inference(forward_subsumption_resolution,[status(thm)],[c_13747,c_176,c_181]) ).
cnf(c_13861,plain,
distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18)))),
inference(demodulation,[status(thm)],[c_13748,c_134]) ).
cnf(c_13862,plain,
( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
| ~ $less_int(sK14,sK21)
| $less_int(sK19,sK21) ),
inference(backward_subsumption_resolution,[status(thm)],[c_969,c_13861]) ).
cnf(c_13863,plain,
( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
| mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| $less_int(sK19,sK14) ),
inference(backward_subsumption_resolution,[status(thm)],[c_172,c_13861]) ).
cnf(c_14341,plain,
( mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
| $less_int(sK19,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_13863,c_182,c_177,c_12227,c_13863]) ).
cnf(c_14350,plain,
( ~ $less_int(sK14,sK21)
| $less_int(sK19,sK21) ),
inference(global_subsumption_just,[status(thm)],[c_13862,c_182,c_177,c_12227,c_13862]) ).
cnf(c_14644,plain,
( mem(int,t2tb3(sK21),labels(int,t2tb(sK18)))
| mem(int,t2tb3(sK21),labels(int,t2tb(sK20)))
| $less_int(sK19,sK14) ),
inference(superposition,[status(thm)],[c_14341,c_140]) ).
cnf(c_14885,plain,
( ~ $less_int(sK19,sK21)
| mem(int,t2tb3(sK21),labels(int,t2tb(sK18)))
| $less_int(sK19,sK14) ),
inference(superposition,[status(thm)],[c_14644,c_173]) ).
cnf(c_14886,plain,
( mem(int,t2tb3(sK21),labels(int,t2tb(sK18)))
| $less_int(sK17,sK21)
| $less_int(sK19,sK14) ),
inference(superposition,[status(thm)],[c_14644,c_174]) ).
cnf(c_14912,plain,
( $less_int(sK14,sK21)
| $less_int(sK17,sK21)
| $less_int(sK19,sK14) ),
inference(superposition,[status(thm)],[c_14886,c_179]) ).
cnf(c_15022,plain,
( ~ $less_int(sK17,sK21)
| ~ $less_int(sK19,sK21)
| $less_int(sK19,sK14) ),
inference(superposition,[status(thm)],[c_14885,c_178]) ).
cnf(c_20435,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_15022,c_14912,c_14350,c_180,c_175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWW637_2 : TPTP v8.1.2. Released v6.1.0.
% 0.05/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n004.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu May 2 22:13:33 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.16/0.42 Running TFA theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.91/2.09 % SZS status Started for theBenchmark.p
% 11.91/2.09 % SZS status Theorem for theBenchmark.p
% 11.91/2.09
% 11.91/2.09 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 11.91/2.09
% 11.91/2.09 ------ iProver source info
% 11.91/2.09
% 11.91/2.09 git: date: 2024-05-02 19:28:25 +0000
% 11.91/2.09 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 11.91/2.09 git: non_committed_changes: false
% 11.91/2.09
% 11.91/2.09 ------ Parsing...
% 11.91/2.09 ------ Clausification by vclausify_rel & Parsing by iProver...
% 11.91/2.09
% 11.91/2.09 ------ Preprocessing... sup_sim: 3 sf_s rm: 4 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 11.91/2.09
% 11.91/2.09 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 11.91/2.09
% 11.91/2.09 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.91/2.09 ------ Proving...
% 11.91/2.09 ------ Problem Properties
% 11.91/2.09
% 11.91/2.09
% 11.91/2.09 clauses 132
% 11.91/2.09 conjectures 11
% 11.91/2.09 EPR 8
% 11.91/2.09 Horn 111
% 11.91/2.09 unary 67
% 11.91/2.09 binary 43
% 11.91/2.09 lits 230
% 11.91/2.09 lits eq 67
% 11.91/2.09 fd_pure 1
% 11.91/2.09 fd_pseudo 0
% 11.91/2.09 fd_cond 0
% 11.91/2.09 fd_pseudo_cond 6
% 11.91/2.09 AC symbols 2
% 11.91/2.09
% 11.91/2.09 ------ Input Options Time Limit: Unbounded
% 11.91/2.09
% 11.91/2.09
% 11.91/2.09 ------
% 11.91/2.09 Current options:
% 11.91/2.09 ------
% 11.91/2.09
% 11.91/2.09
% 11.91/2.09
% 11.91/2.09
% 11.91/2.09 ------ Proving...
% 11.91/2.09
% 11.91/2.09
% 11.91/2.09 % SZS status Theorem for theBenchmark.p
% 11.91/2.09
% 11.91/2.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.91/2.10
% 11.91/2.10
%------------------------------------------------------------------------------