TSTP Solution File: SWW629_2 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW629_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 : Mon Jun 24 18:17:51 EDT 2024
% Result : Theorem 23.46s 3.67s
% Output : CNFRefutation 23.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
tff(f45,axiom,
! [X0: ty,X14: uni,X13: uni,X15: uni] :
( permut(X0,X14,X13)
=> ( permut(X0,X13,X15)
=> permut(X0,X14,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permut_trans) ).
tff(f50,axiom,
! [X0: ty,X14: uni,X13: uni,X16: uni,X17: uni] :
( permut(X0,X14,X16)
=> ( permut(X0,X13,X17)
=> permut(X0,infix_plpl(X0,X14,X13),infix_plpl(X0,X16,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permut_append) ).
tff(f74,conjecture,
! [X18: list_elt] :
( $less(1,length2(elt,t2tb(X18)))
=> ! [X21: list_elt] :
( ( tb2t(nil(elt)) = X21 )
=> ! [X22: list_elt] :
( ( tb2t(nil(elt)) = X22 )
=> ! [X23: list_elt,X24: list_elt,X25: list_elt] :
( ( ( ( ( length2(elt,t2tb(X24)) = $sum(length2(elt,t2tb(X23)),1) )
& ( 0 = length2(elt,t2tb(X25)) ) )
| ( length2(elt,t2tb(X24)) = length2(elt,t2tb(X23)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X25)),t2tb(X18)) )
=> ! [X26: bool1] :
( ( ( true1 = X26 )
<=> ( tb2t(nil(elt)) = X25 ) )
=> ( ( true1 = X26 )
=> ( ( tb2t(nil(elt)) = X25 )
=> ( permut(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X18))
=> ! [X27: list_elt] :
( ( permut(elt,t2tb(X27),t2tb(X24))
& sorted1(X27) )
=> ! [X28: list_elt] :
( ( permut(elt,t2tb(X28),t2tb(X23))
& sorted1(X28) )
=> ( ( sorted1(X28)
& sorted1(X27)
& ( tb2t(nil(elt)) = X25 ) )
=> ! [X29: list_elt] :
( ( permut(elt,t2tb(X29),infix_plpl(elt,t2tb(X27),t2tb(X28)))
& sorted1(X29) )
=> ( permut(elt,t2tb(X29),t2tb(X18))
& sorted1(X29) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_mergesort) ).
tff(f75,negated_conjecture,
~ ! [X18: list_elt] :
( $less(1,length2(elt,t2tb(X18)))
=> ! [X21: list_elt] :
( ( tb2t(nil(elt)) = X21 )
=> ! [X22: list_elt] :
( ( tb2t(nil(elt)) = X22 )
=> ! [X23: list_elt,X24: list_elt,X25: list_elt] :
( ( ( ( ( length2(elt,t2tb(X24)) = $sum(length2(elt,t2tb(X23)),1) )
& ( 0 = length2(elt,t2tb(X25)) ) )
| ( length2(elt,t2tb(X24)) = length2(elt,t2tb(X23)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X25)),t2tb(X18)) )
=> ! [X26: bool1] :
( ( ( true1 = X26 )
<=> ( tb2t(nil(elt)) = X25 ) )
=> ( ( true1 = X26 )
=> ( ( tb2t(nil(elt)) = X25 )
=> ( permut(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X18))
=> ! [X27: list_elt] :
( ( permut(elt,t2tb(X27),t2tb(X24))
& sorted1(X27) )
=> ! [X28: list_elt] :
( ( permut(elt,t2tb(X28),t2tb(X23))
& sorted1(X28) )
=> ( ( sorted1(X28)
& sorted1(X27)
& ( tb2t(nil(elt)) = X25 ) )
=> ! [X29: list_elt] :
( ( permut(elt,t2tb(X29),infix_plpl(elt,t2tb(X27),t2tb(X28)))
& sorted1(X29) )
=> ( permut(elt,t2tb(X29),t2tb(X18))
& sorted1(X29) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f74]) ).
tff(f127,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( permut(X0,X1,X2)
=> ( permut(X0,X2,X3)
=> permut(X0,X1,X3) ) ),
inference(rectify,[],[f45]) ).
tff(f132,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
( permut(X0,X1,X3)
=> ( permut(X0,X2,X4)
=> permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4)) ) ),
inference(rectify,[],[f50]) ).
tff(f153,plain,
~ ! [X0: list_elt] :
( $less(1,length2(elt,t2tb(X0)))
=> ! [X1: list_elt] :
( ( tb2t(nil(elt)) = X1 )
=> ! [X2: list_elt] :
( ( tb2t(nil(elt)) = X2 )
=> ! [X3: list_elt,X4: list_elt,X5: list_elt] :
( ( ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
=> ! [X6: bool1] :
( ( ( true1 = X6 )
<=> ( tb2t(nil(elt)) = X5 ) )
=> ( ( true1 = X6 )
=> ( ( tb2t(nil(elt)) = X5 )
=> ( permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
=> ! [X7: list_elt] :
( ( permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
=> ! [X8: list_elt] :
( ( permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
=> ( ( sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 ) )
=> ! [X9: list_elt] :
( ( permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
=> ( permut(elt,t2tb(X9),t2tb(X0))
& sorted1(X9) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f75]) ).
tff(f166,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( permut(X0,X1,X3)
| ~ permut(X0,X2,X3)
| ~ permut(X0,X1,X2) ),
inference(ennf_transformation,[],[f127]) ).
tff(f167,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( permut(X0,X1,X3)
| ~ permut(X0,X2,X3)
| ~ permut(X0,X1,X2) ),
inference(flattening,[],[f166]) ).
tff(f169,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
| ~ permut(X0,X2,X4)
| ~ permut(X0,X1,X3) ),
inference(ennf_transformation,[],[f132]) ).
tff(f170,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
| ~ permut(X0,X2,X4)
| ~ permut(X0,X1,X3) ),
inference(flattening,[],[f169]) ).
tff(f184,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
<=> ( tb2t(nil(elt)) = X5 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(ennf_transformation,[],[f153]) ).
tff(f185,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
<=> ( tb2t(nil(elt)) = X5 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(flattening,[],[f184]) ).
tff(f210,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(nnf_transformation,[],[f185]) ).
tff(f211,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(flattening,[],[f210]) ).
tff(f212,plain,
( ? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) )
=> ( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(sK10))) ) ),
introduced(choice_axiom,[]) ).
tff(f213,plain,
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
=> ( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = sK11 ) ) ),
introduced(choice_axiom,[]) ).
tff(f214,plain,
( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
=> ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = sK12 ) ) ),
introduced(choice_axiom,[]) ).
tff(f215,plain,
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
=> ( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(sK14)) = $sum(length2(elt,t2tb(sK13)),1) )
& ( 0 = length2(elt,t2tb(sK15)) ) )
| ( length2(elt,t2tb(sK14)) = length2(elt,t2tb(sK13)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK15)),t2tb(sK10)) ) ),
introduced(choice_axiom,[]) ).
tff(f216,plain,
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != X6 ) ) )
=> ( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = sK16 )
& ( ( true1 = sK16 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != sK16 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f217,plain,
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
=> ( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(sK17),t2tb(sK14))
& sorted1(sK17) ) ),
introduced(choice_axiom,[]) ).
tff(f218,plain,
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
=> ( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(X9) )
& sorted1(sK18)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(sK18),t2tb(sK13))
& sorted1(sK18) ) ),
introduced(choice_axiom,[]) ).
tff(f219,plain,
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(X9) )
=> ( ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) )
& permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(sK19) ) ),
introduced(choice_axiom,[]) ).
tff(f220,plain,
( ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) )
& permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(sK19)
& sorted1(sK18)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(sK18),t2tb(sK13))
& sorted1(sK18)
& permut(elt,t2tb(sK17),t2tb(sK14))
& sorted1(sK17)
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = sK16 )
& ( ( true1 = sK16 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != sK16 ) )
& ( ( ( length2(elt,t2tb(sK14)) = $sum(length2(elt,t2tb(sK13)),1) )
& ( 0 = length2(elt,t2tb(sK15)) ) )
| ( length2(elt,t2tb(sK14)) = length2(elt,t2tb(sK13)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK15)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK12 )
& ( tb2t(nil(elt)) = sK11 )
& $less(1,length2(elt,t2tb(sK10))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19])],[f211,f219,f218,f217,f216,f215,f214,f213,f212]) ).
tff(f282,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( permut(X0,X1,X3)
| ~ permut(X0,X2,X3)
| ~ permut(X0,X1,X2) ),
inference(cnf_transformation,[],[f167]) ).
tff(f287,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni,X4: uni] :
( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
| ~ permut(X0,X2,X4)
| ~ permut(X0,X1,X3) ),
inference(cnf_transformation,[],[f170]) ).
tff(f331,plain,
permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10)),
inference(cnf_transformation,[],[f220]) ).
tff(f333,plain,
permut(elt,t2tb(sK17),t2tb(sK14)),
inference(cnf_transformation,[],[f220]) ).
tff(f335,plain,
permut(elt,t2tb(sK18),t2tb(sK13)),
inference(cnf_transformation,[],[f220]) ).
tff(f339,plain,
sorted1(sK19),
inference(cnf_transformation,[],[f220]) ).
tff(f340,plain,
permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18))),
inference(cnf_transformation,[],[f220]) ).
tff(f341,plain,
( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) ),
inference(cnf_transformation,[],[f220]) ).
cnf(c_128,plain,
( ~ permut(X0_14,X0_13,X1_13)
| ~ permut(X0_14,X2_13,X0_13)
| permut(X0_14,X2_13,X1_13) ),
inference(cnf_transformation,[],[f282]) ).
cnf(c_133,plain,
( ~ permut(X0_14,X0_13,X1_13)
| ~ permut(X0_14,X2_13,X3_13)
| permut(X0_14,infix_plpl(X0_14,X2_13,X0_13),infix_plpl(X0_14,X3_13,X1_13)) ),
inference(cnf_transformation,[],[f287]) ).
cnf(c_166,negated_conjecture,
( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) ),
inference(cnf_transformation,[],[f341]) ).
cnf(c_167,negated_conjecture,
permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18))),
inference(cnf_transformation,[],[f340]) ).
cnf(c_168,negated_conjecture,
sorted1(sK19),
inference(cnf_transformation,[],[f339]) ).
cnf(c_172,negated_conjecture,
permut(elt,t2tb(sK18),t2tb(sK13)),
inference(cnf_transformation,[],[f335]) ).
cnf(c_174,negated_conjecture,
permut(elt,t2tb(sK17),t2tb(sK14)),
inference(cnf_transformation,[],[f333]) ).
cnf(c_176,negated_conjecture,
permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10)),
inference(cnf_transformation,[],[f331]) ).
cnf(c_284,negated_conjecture,
~ permut(elt,t2tb(sK19),t2tb(sK10)),
inference(global_subsumption_just,[status(thm)],[c_166,c_168,c_166]) ).
cnf(c_2450,plain,
t2tb(sK19) = sP0_iProver_def,
definition ).
cnf(c_2451,plain,
t2tb(sK10) = sP1_iProver_def,
definition ).
cnf(c_2455,plain,
t2tb(sK14) = sP5_iProver_def,
definition ).
cnf(c_2456,plain,
t2tb(sK13) = sP6_iProver_def,
definition ).
cnf(c_2457,plain,
infix_plpl(elt,sP5_iProver_def,sP6_iProver_def) = sP7_iProver_def,
definition ).
cnf(c_2458,plain,
t2tb(sK17) = sP8_iProver_def,
definition ).
cnf(c_2459,plain,
t2tb(sK18) = sP9_iProver_def,
definition ).
cnf(c_2460,plain,
infix_plpl(elt,sP8_iProver_def,sP9_iProver_def) = sP10_iProver_def,
definition ).
cnf(c_2462,negated_conjecture,
~ permut(elt,sP0_iProver_def,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_284,c_2451,c_2450]) ).
cnf(c_2466,negated_conjecture,
permut(elt,sP7_iProver_def,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_176,c_2456,c_2455,c_2457]) ).
cnf(c_2467,negated_conjecture,
permut(elt,sP8_iProver_def,sP5_iProver_def),
inference(demodulation,[status(thm)],[c_174,c_2458]) ).
cnf(c_2468,negated_conjecture,
permut(elt,sP9_iProver_def,sP6_iProver_def),
inference(demodulation,[status(thm)],[c_172,c_2459]) ).
cnf(c_2473,negated_conjecture,
permut(elt,sP0_iProver_def,sP10_iProver_def),
inference(demodulation,[status(thm)],[c_167,c_2460]) ).
cnf(c_4738,plain,
( ~ permut(elt,X0_13,sP1_iProver_def)
| ~ permut(elt,sP0_iProver_def,X0_13)
| permut(elt,sP0_iProver_def,sP1_iProver_def) ),
inference(instantiation,[status(thm)],[c_128]) ).
cnf(c_5320,plain,
( ~ permut(elt,sP8_iProver_def,X0_13)
| ~ permut(elt,sP9_iProver_def,X1_13)
| permut(elt,sP10_iProver_def,infix_plpl(elt,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_2460,c_133]) ).
cnf(c_6610,plain,
( ~ permut(elt,X0_13,X1_13)
| ~ permut(elt,sP0_iProver_def,X0_13)
| permut(elt,sP0_iProver_def,X1_13) ),
inference(instantiation,[status(thm)],[c_128]) ).
cnf(c_10998,plain,
( ~ permut(elt,sP8_iProver_def,sP5_iProver_def)
| ~ permut(elt,sP9_iProver_def,sP6_iProver_def)
| permut(elt,sP10_iProver_def,sP7_iProver_def) ),
inference(superposition,[status(thm)],[c_2457,c_5320]) ).
cnf(c_39255,plain,
( ~ permut(elt,sP0_iProver_def,sP7_iProver_def)
| ~ permut(elt,sP7_iProver_def,sP1_iProver_def)
| permut(elt,sP0_iProver_def,sP1_iProver_def) ),
inference(instantiation,[status(thm)],[c_4738]) ).
cnf(c_40872,plain,
( ~ permut(elt,sP10_iProver_def,X0_13)
| ~ permut(elt,sP0_iProver_def,sP10_iProver_def)
| permut(elt,sP0_iProver_def,X0_13) ),
inference(instantiation,[status(thm)],[c_6610]) ).
cnf(c_41410,plain,
( ~ permut(elt,sP0_iProver_def,sP10_iProver_def)
| ~ permut(elt,sP10_iProver_def,sP7_iProver_def)
| permut(elt,sP0_iProver_def,sP7_iProver_def) ),
inference(instantiation,[status(thm)],[c_40872]) ).
cnf(c_41411,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_41410,c_39255,c_10998,c_2473,c_2468,c_2467,c_2466,c_2462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW629_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 08:26:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.47 Running TFA theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.46/3.67 % SZS status Started for theBenchmark.p
% 23.46/3.67 % SZS status Theorem for theBenchmark.p
% 23.46/3.67
% 23.46/3.67 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 23.46/3.67
% 23.46/3.67 ------ iProver source info
% 23.46/3.67
% 23.46/3.67 git: date: 2024-06-12 09:56:46 +0000
% 23.46/3.67 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 23.46/3.67 git: non_committed_changes: false
% 23.46/3.67
% 23.46/3.67 ------ Parsing...
% 23.46/3.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 23.46/3.67
% 23.46/3.67 ------ Preprocessing... sup_sim: 8 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
% 23.46/3.67
% 23.46/3.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 23.46/3.67
% 23.46/3.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 23.46/3.67 ------ Proving...
% 23.46/3.67 ------ Problem Properties
% 23.46/3.67
% 23.46/3.67
% 23.46/3.67 clauses 137
% 23.46/3.67 conjectures 69
% 23.46/3.67 EPR 26
% 23.46/3.67 Horn 119
% 23.46/3.67 unary 79
% 23.46/3.67 binary 35
% 23.46/3.67 lits 229
% 23.46/3.67 lits eq 81
% 23.46/3.67 fd_pure 1
% 23.46/3.67 fd_pseudo 0
% 23.46/3.67 fd_cond 0
% 23.46/3.67 fd_pseudo_cond 5
% 23.46/3.67 AC symbols 2
% 23.46/3.67
% 23.46/3.67 ------ Input Options Time Limit: Unbounded
% 23.46/3.67
% 23.46/3.67
% 23.46/3.67 ------
% 23.46/3.67 Current options:
% 23.46/3.67 ------
% 23.46/3.67
% 23.46/3.67
% 23.46/3.67
% 23.46/3.67
% 23.46/3.67 ------ Proving...
% 23.46/3.67
% 23.46/3.67
% 23.46/3.67 % SZS status Theorem for theBenchmark.p
% 23.46/3.67
% 23.46/3.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 23.46/3.67
% 23.46/3.69
%------------------------------------------------------------------------------