TSTP Solution File: SWC313+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC313+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 : Thu Aug 31 20:42:28 EDT 2023
% Result : Theorem 13.82s 2.70s
% Output : CNFRefutation 13.82s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f595)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X0
& app(cons(X6,nil),X7) = X1
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X0
& app(cons(X6,nil),X7) = X1
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X0
& app(cons(X4,nil),X5) = X1
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X3
& nil != X2 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) != X2
& ssList(X7) )
& ssItem(X6) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f128,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f127]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f135,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f187,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f188,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f189,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f190,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f194,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f249,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f247,f248]) ).
fof(f331,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f336,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f337,plain,
! [X0] :
( ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f188,f336]) ).
fof(f338,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f190,f338]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != X3
| nil = X2 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = X2
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != X3
| nil = sK55 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = sK55
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != X3
| nil = sK55 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) = sK55
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != sK56
| nil = sK55 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != sK56
| app(X7,cons(X6,nil)) = sK55
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ( ( ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != sK56
| nil = sK55 )
& ! [X6] :
( ! [X7] :
( app(cons(X6,nil),X7) != sK56
| app(X7,cons(X6,nil)) = sK55
| ~ ssList(X7) )
| ~ ssItem(X6) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f223,f347,f346,f345,f344]) ).
fof(f361,plain,
! [X0,X1] :
( ssList(sK11(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f362,plain,
! [X0,X1] :
( app(X1,sK11(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f363,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f440,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f441,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f449,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f453,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f455,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f495,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f496,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f521,plain,
! [X0] :
( ssItem(sK51(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f522,plain,
! [X0] :
( hd(X0) = sK51(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f523,plain,
! [X0] :
( ssList(sK52(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f524,plain,
! [X0] :
( tl(X0) = sK52(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f526,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f549,plain,
ssList(sK54),
inference(cnf_transformation,[],[f348]) ).
fof(f552,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f348]) ).
fof(f553,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f348]) ).
fof(f554,plain,
! [X6,X7] :
( app(cons(X6,nil),X7) != sK56
| app(X7,cons(X6,nil)) = sK55
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f348]) ).
fof(f555,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f348]) ).
fof(f556,plain,
( neq(sK54,nil)
| nil = sK54 ),
inference(cnf_transformation,[],[f348]) ).
fof(f557,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f348]) ).
fof(f558,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5)
| ~ ssItem(X4)
| nil = sK54 ),
inference(cnf_transformation,[],[f348]) ).
fof(f559,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK53
| app(cons(X4,nil),X5) != sK54
| ~ ssList(X5)
| ~ ssItem(X4)
| nil != sK53 ),
inference(cnf_transformation,[],[f348]) ).
fof(f560,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK55
| app(cons(X4,nil),X5) != sK56
| ~ ssList(X5)
| ~ ssItem(X4)
| nil != sK55 ),
inference(definition_unfolding,[],[f559,f553,f552,f553]) ).
fof(f561,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK55
| app(cons(X4,nil),X5) != sK56
| ~ ssList(X5)
| ~ ssItem(X4)
| nil = sK56 ),
inference(definition_unfolding,[],[f558,f553,f552,f552]) ).
fof(f562,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f557,f552,f553]) ).
fof(f563,plain,
( neq(sK56,nil)
| nil = sK56 ),
inference(definition_unfolding,[],[f556,f552,f552]) ).
fof(f564,plain,
ssList(sK56),
inference(definition_unfolding,[],[f549,f552]) ).
fof(f569,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f363]) ).
fof(f585,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f496]) ).
cnf(c_61,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_62,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f362]) ).
cnf(c_63,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f361]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f595]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f440]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f441]) ).
cnf(c_149,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f449]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f453]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f455]) ).
cnf(c_177,plain,
( ~ frontsegP(X0,X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(cons(X2,X0),cons(X2,X1)) ),
inference(cnf_transformation,[],[f597]) ).
cnf(c_195,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(cnf_transformation,[],[f585]) ).
cnf(c_196,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f495]) ).
cnf(c_219,plain,
( ~ ssList(X0)
| hd(X0) = sK51(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f522]) ).
cnf(c_220,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f521]) ).
cnf(c_221,plain,
( ~ ssList(X0)
| tl(X0) = sK52(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f524]) ).
cnf(c_222,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f523]) ).
cnf(c_224,plain,
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| X0 = nil ),
inference(cnf_transformation,[],[f526]) ).
cnf(c_246,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| app(X1,cons(X0,nil)) != sK55
| nil != sK55
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f560]) ).
cnf(c_247,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| app(X1,cons(X0,nil)) != sK55
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = sK56 ),
inference(cnf_transformation,[],[f561]) ).
cnf(c_248,negated_conjecture,
( nil != sK55
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_249,negated_conjecture,
( nil = sK56
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f563]) ).
cnf(c_250,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_251,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| ~ ssItem(X0)
| ~ ssList(X1)
| app(X1,cons(X0,nil)) = sK55 ),
inference(cnf_transformation,[],[f554]) ).
cnf(c_254,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f564]) ).
cnf(c_305,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| nil = nil ),
inference(instantiation,[status(thm)],[c_196]) ).
cnf(c_371,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_249,c_248,c_250]) ).
cnf(c_373,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_248,c_371]) ).
cnf(c_384,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
cnf(c_387,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| app(cons(X0,nil),X1) != sK56 ),
inference(global_subsumption_just,[status(thm)],[c_251,c_250,c_251,c_247,c_246]) ).
cnf(c_388,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(renaming,[status(thm)],[c_387]) ).
cnf(c_392,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_246,c_388]) ).
cnf(c_3231,plain,
( X0 != nil
| X0 != sK56
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_373]) ).
cnf(c_3232,plain,
( nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3231]) ).
cnf(c_3233,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3232,c_141,c_3232]) ).
cnf(c_8832,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_13465,plain,
( nil != X0
| sK56 != X0
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_8832]) ).
cnf(c_13466,plain,
( nil != nil
| sK56 != nil
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_13465]) ).
cnf(c_14147,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_254,c_219]) ).
cnf(c_14151,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14147,c_3233]) ).
cnf(c_14312,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_254,c_221]) ).
cnf(c_14316,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14312,c_3233]) ).
cnf(c_14470,plain,
( ~ ssList(sK56)
| sK56 = nil
| ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_149]) ).
cnf(c_14561,plain,
( ~ ssList(sK56)
| nil = sK56
| ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_14151,c_220]) ).
cnf(c_14562,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14561,c_3233,c_254]) ).
cnf(c_14579,plain,
( ~ ssList(sK56)
| nil = sK56
| ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_14316,c_222]) ).
cnf(c_14580,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14579,c_3233,c_254]) ).
cnf(c_14592,plain,
app(nil,tl(sK56)) = tl(sK56),
inference(superposition,[status(thm)],[c_14580,c_155]) ).
cnf(c_15207,plain,
( ~ ssList(tl(sK56))
| ~ ssList(nil)
| frontsegP(tl(sK56),nil) ),
inference(superposition,[status(thm)],[c_14592,c_384]) ).
cnf(c_15210,plain,
frontsegP(tl(sK56),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_15207,c_141,c_14580]) ).
cnf(c_16102,plain,
( cons(hd(sK56),tl(sK56)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_254,c_224]) ).
cnf(c_16109,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_16102,c_3233]) ).
cnf(c_20414,plain,
( ~ frontsegP(tl(sK56),X0)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| ~ ssList(X0)
| frontsegP(sK56,cons(hd(sK56),X0)) ),
inference(superposition,[status(thm)],[c_16109,c_177]) ).
cnf(c_20439,plain,
( ~ frontsegP(tl(sK56),X0)
| ~ ssList(X0)
| frontsegP(sK56,cons(hd(sK56),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20414,c_14580,c_14562]) ).
cnf(c_20491,plain,
( ~ frontsegP(tl(sK56),nil)
| ~ ssList(nil)
| frontsegP(sK56,cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_20439]) ).
cnf(c_22485,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(X0)
| ssList(cons(hd(sK56),X0)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_22500,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ssList(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_22485]) ).
cnf(c_29687,plain,
( app(cons(X0,nil),sK11(sK56,cons(X0,nil))) != sK56
| ~ ssList(sK11(sK56,cons(X0,nil)))
| ~ ssItem(X0) ),
inference(instantiation,[status(thm)],[c_392]) ).
cnf(c_29688,plain,
( ~ frontsegP(sK56,cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssList(sK56)
| app(cons(X0,nil),sK11(sK56,cons(X0,nil))) = sK56 ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_35050,plain,
( ~ frontsegP(sK56,cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssList(sK56)
| ssList(sK11(sK56,cons(X0,nil))) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_61938,plain,
( ~ frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(sK56)
| ssList(sK11(sK56,cons(hd(sK56),nil))) ),
inference(instantiation,[status(thm)],[c_35050]) ).
cnf(c_68623,plain,
( app(cons(hd(sK56),nil),sK11(sK56,cons(hd(sK56),nil))) != sK56
| ~ ssList(sK11(sK56,cons(hd(sK56),nil)))
| ~ ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_29687]) ).
cnf(c_69639,plain,
( ~ frontsegP(sK56,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(sK56)
| app(cons(hd(sK56),nil),sK11(sK56,cons(hd(sK56),nil))) = sK56 ),
inference(instantiation,[status(thm)],[c_29688]) ).
cnf(c_69640,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_69639,c_68623,c_61938,c_22500,c_20491,c_15210,c_14470,c_13466,c_3232,c_305,c_195,c_141,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC313+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 16:04:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.82/2.70 % SZS status Started for theBenchmark.p
% 13.82/2.70 % SZS status Theorem for theBenchmark.p
% 13.82/2.70
% 13.82/2.70 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 13.82/2.70
% 13.82/2.70 ------ iProver source info
% 13.82/2.70
% 13.82/2.70 git: date: 2023-05-31 18:12:56 +0000
% 13.82/2.70 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 13.82/2.70 git: non_committed_changes: false
% 13.82/2.70 git: last_make_outside_of_git: false
% 13.82/2.70
% 13.82/2.70 ------ Parsing...
% 13.82/2.70 ------ Clausification by vclausify_rel & Parsing by iProver...
% 13.82/2.70
% 13.82/2.70 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e
% 13.82/2.70
% 13.82/2.70 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 13.82/2.70
% 13.82/2.70 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 13.82/2.70 ------ Proving...
% 13.82/2.70 ------ Problem Properties
% 13.82/2.70
% 13.82/2.70
% 13.82/2.70 clauses 184
% 13.82/2.70 conjectures 3
% 13.82/2.70 EPR 52
% 13.82/2.70 Horn 116
% 13.82/2.70 unary 19
% 13.82/2.70 binary 40
% 13.82/2.70 lits 624
% 13.82/2.70 lits eq 80
% 13.82/2.70 fd_pure 0
% 13.82/2.70 fd_pseudo 0
% 13.82/2.70 fd_cond 21
% 13.82/2.70 fd_pseudo_cond 14
% 13.82/2.70 AC symbols 0
% 13.82/2.70
% 13.82/2.70 ------ Schedule dynamic 5 is on
% 13.82/2.70
% 13.82/2.70 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 13.82/2.70
% 13.82/2.70
% 13.82/2.70 ------
% 13.82/2.70 Current options:
% 13.82/2.70 ------
% 13.82/2.70
% 13.82/2.70
% 13.82/2.70
% 13.82/2.70
% 13.82/2.70 ------ Proving...
% 13.82/2.70
% 13.82/2.70
% 13.82/2.70 % SZS status Theorem for theBenchmark.p
% 13.82/2.70
% 13.82/2.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.82/2.70
% 13.82/2.70
%------------------------------------------------------------------------------