TSTP Solution File: SWC015+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC015+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 20:40:19 EDT 2023
% Result : Theorem 62.62s 9.23s
% Output : CNFRefutation 62.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f605)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X1
& cons(X6,nil) = X0
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& app(X2,X5) = X4
& tl(X3) = X5
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X1
& cons(X6,nil) = X0
& ssList(X7) )
& ssItem(X6) )
| ? [X4] :
( ? [X5] :
( neq(nil,X3)
& app(X2,X5) = X4
& tl(X3) = X5
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X1
& cons(X4,nil) = X0
& ssList(X5) )
& ssItem(X4) )
| ? [X6] :
( ? [X7] :
( neq(nil,X3)
& app(X2,X7) = X6
& tl(X3) = X7
& ssList(X7) )
& X3 != X6
& ssList(X6) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
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(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f131,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f130]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
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(f195,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(X2,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(X2,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
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] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(X2,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X1
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(X2,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(X1,nil) ) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X1
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(X2,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(X1,nil) ) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(X2,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(X2,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(sK55,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,X3)
| app(sK55,X7) != X6
| tl(X3) != X7
| ~ ssList(X7) )
| X3 = X6
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,sK56)
| app(sK55,X7) != X6
| tl(sK56) != X7
| ~ ssList(X7) )
| sK56 = X6
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ~ neq(nil,sK56)
| app(sK55,X7) != X6
| tl(sK56) != X7
| ~ ssList(X7) )
| sK56 = X6
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& 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(f439,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f317]) ).
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(f451,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f453,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
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(f527,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f529,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f548,plain,
ssList(sK53),
inference(cnf_transformation,[],[f348]) ).
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(f556,plain,
! [X4,X5] :
( neq(sK54,nil)
| app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f348]) ).
fof(f558,plain,
! [X6,X7] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| app(sK55,X7) != X6
| tl(sK56) != X7
| ~ ssList(X7)
| sK56 = X6
| ~ ssList(X6) ),
inference(cnf_transformation,[],[f348]) ).
fof(f559,plain,
! [X4,X5] :
( ~ neq(sK56,nil)
| app(cons(X4,nil),X5) != sK54
| cons(X4,nil) != sK53
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f348]) ).
fof(f560,plain,
! [X4,X5] :
( ~ neq(sK56,nil)
| app(cons(X4,nil),X5) != sK56
| cons(X4,nil) != sK55
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f559,f552,f553]) ).
fof(f562,plain,
! [X4,X5] :
( neq(sK56,nil)
| app(cons(X4,nil),X5) != sK56
| cons(X4,nil) != sK55
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f556,f552,f552,f553]) ).
fof(f565,plain,
ssList(sK56),
inference(definition_unfolding,[],[f549,f552]) ).
fof(f566,plain,
ssList(sK55),
inference(definition_unfolding,[],[f548,f553]) ).
fof(f594,plain,
! [X7] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| tl(sK56) != X7
| ~ ssList(X7)
| app(sK55,X7) = sK56
| ~ ssList(app(sK55,X7)) ),
inference(equality_resolution,[],[f558]) ).
fof(f595,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(tl(sK56))
| sK56 = app(sK55,tl(sK56))
| ~ ssList(app(sK55,tl(sK56))) ),
inference(equality_resolution,[],[f594]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f439]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f600]) ).
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_151,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f451]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f453]) ).
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_225,plain,
( app(X0,X1) != app(X2,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X2 ),
inference(cnf_transformation,[],[f527]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f529]) ).
cnf(c_246,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| cons(X0,nil) != sK55
| ~ neq(sK56,nil)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f560]) ).
cnf(c_247,negated_conjecture,
( ~ ssList(app(sK55,tl(sK56)))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil)
| ~ ssList(tl(sK56))
| app(sK55,tl(sK56)) = sK56 ),
inference(cnf_transformation,[],[f595]) ).
cnf(c_248,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| cons(X0,nil) != sK55
| ~ ssItem(X0)
| ~ ssList(X1)
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_250,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f605]) ).
cnf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f565]) ).
cnf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f566]) ).
cnf(c_382,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_248,c_250]) ).
cnf(c_384,plain,
( ~ neq(nil,sK56)
| ~ ssList(app(sK55,tl(sK56)))
| ~ ssList(tl(sK56))
| app(sK55,tl(sK56)) = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_247,c_250,c_247]) ).
cnf(c_385,negated_conjecture,
( ~ ssList(app(sK55,tl(sK56)))
| ~ neq(nil,sK56)
| ~ ssList(tl(sK56))
| app(sK55,tl(sK56)) = sK56 ),
inference(renaming,[status(thm)],[c_384]) ).
cnf(c_386,plain,
( cons(X0,nil) != sK55
| app(cons(X0,nil),X1) != sK56
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_246,c_250,c_246]) ).
cnf(c_387,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| cons(X0,nil) != sK55
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(renaming,[status(thm)],[c_386]) ).
cnf(c_3238,plain,
( X0 != nil
| X1 != sK56
| ~ ssList(app(sK55,tl(sK56)))
| ~ ssList(tl(sK56))
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK55,tl(sK56)) = sK56
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_385]) ).
cnf(c_3239,plain,
( ~ ssList(app(sK55,tl(sK56)))
| ~ ssList(tl(sK56))
| ~ ssList(nil)
| ~ ssList(sK56)
| app(sK55,tl(sK56)) = sK56
| nil = sK56 ),
inference(unflattening,[status(thm)],[c_3238]) ).
cnf(c_3240,plain,
( ~ ssList(app(sK55,tl(sK56)))
| ~ ssList(tl(sK56))
| app(sK55,tl(sK56)) = sK56
| nil = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_3239,c_253,c_141,c_3239]) ).
cnf(c_3258,plain,
( X0 != nil
| X0 != sK56
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_382]) ).
cnf(c_3259,plain,
( nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3258]) ).
cnf(c_3260,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3259,c_141,c_3259]) ).
cnf(c_3265,plain,
( ~ ssList(app(sK55,tl(sK56)))
| ~ ssList(tl(sK56))
| app(sK55,tl(sK56)) = sK56 ),
inference(backward_subsumption_resolution,[status(thm)],[c_3240,c_3260]) ).
cnf(c_8878,plain,
( ~ ssList(app(sK55,tl(sK56)))
| ~ ssList(tl(sK56))
| app(sK55,tl(sK56)) = sK56 ),
inference(subtyping,[status(esa)],[c_3265]) ).
cnf(c_8879,plain,
nil != sK56,
inference(subtyping,[status(esa)],[c_3260]) ).
cnf(c_8886,negated_conjecture,
( app(cons(X0_14,nil),X0_13) != sK56
| cons(X0_14,nil) != sK55
| ~ ssItem(X0_14)
| ~ ssList(X0_13) ),
inference(subtyping,[status(esa)],[c_387]) ).
cnf(c_8893,negated_conjecture,
ssList(sK55),
inference(subtyping,[status(esa)],[c_254]) ).
cnf(c_8894,negated_conjecture,
ssList(sK56),
inference(subtyping,[status(esa)],[c_253]) ).
cnf(c_8910,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| app(cons(X0_14,nil),X0_13) = cons(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_227]) ).
cnf(c_8912,plain,
( app(X0_13,X1_13) != app(X2_13,X1_13)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| X0_13 = X2_13 ),
inference(subtyping,[status(esa)],[c_225]) ).
cnf(c_8913,plain,
( ~ ssList(X0_13)
| cons(hd(X0_13),tl(X0_13)) = X0_13
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_224]) ).
cnf(c_8915,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssList(sK52(X0_13)) ),
inference(subtyping,[status(esa)],[c_222]) ).
cnf(c_8916,plain,
( ~ ssList(X0_13)
| tl(X0_13) = sK52(X0_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_221]) ).
cnf(c_8917,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssItem(sK51(X0_13)) ),
inference(subtyping,[status(esa)],[c_220]) ).
cnf(c_8918,plain,
( ~ ssList(X0_13)
| hd(X0_13) = sK51(X0_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_219]) ).
cnf(c_8973,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ssList(app(X1_13,X0_13)) ),
inference(subtyping,[status(esa)],[c_153]) ).
cnf(c_8975,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssList(tl(X0_13)) ),
inference(subtyping,[status(esa)],[c_151]) ).
cnf(c_8977,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssItem(hd(X0_13)) ),
inference(subtyping,[status(esa)],[c_149]) ).
cnf(c_8986,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ssList(cons(X0_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_9064,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_9066,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_9093,plain,
nil = nil,
inference(instantiation,[status(thm)],[c_9064]) ).
cnf(c_11996,plain,
( nil != X0_13
| sK56 != X0_13
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_9066]) ).
cnf(c_11997,plain,
( nil != nil
| sK56 != nil
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_11996]) ).
cnf(c_12054,plain,
( app(cons(X0_14,nil),X0_13) != app(sK55,X0_13)
| ~ ssList(cons(X0_14,nil))
| ~ ssList(X0_13)
| ~ ssList(sK55)
| cons(X0_14,nil) = sK55 ),
inference(instantiation,[status(thm)],[c_8912]) ).
cnf(c_12431,plain,
( app(cons(X0_14,nil),X0_13) != X1_13
| app(sK55,X0_13) != X1_13
| app(cons(X0_14,nil),X0_13) = app(sK55,X0_13) ),
inference(instantiation,[status(thm)],[c_9066]) ).
cnf(c_12473,plain,
( ~ ssList(tl(sK56))
| ~ ssList(sK55)
| app(sK55,tl(sK56)) = sK56 ),
inference(superposition,[status(thm)],[c_8973,c_8878]) ).
cnf(c_12476,plain,
( ~ ssList(tl(sK56))
| app(sK55,tl(sK56)) = sK56 ),
inference(forward_subsumption_resolution,[status(thm)],[c_12473,c_8893]) ).
cnf(c_12492,plain,
( ~ ssList(sK56)
| app(sK55,tl(sK56)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_8975,c_12476]) ).
cnf(c_12495,plain,
app(sK55,tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_12492,c_8879,c_8894]) ).
cnf(c_12509,plain,
( ~ ssList(sK56)
| cons(hd(sK56),tl(sK56)) = sK56
| sK56 = nil ),
inference(instantiation,[status(thm)],[c_8913]) ).
cnf(c_12515,plain,
( ~ ssList(sK56)
| sK56 = nil
| ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_8977]) ).
cnf(c_12516,plain,
( ~ ssList(sK56)
| sK56 = nil
| ssList(tl(sK56)) ),
inference(instantiation,[status(thm)],[c_8975]) ).
cnf(c_13158,plain,
( cons(X0_14,X0_13) != X1_13
| X2_13 != X1_13
| X2_13 = cons(X0_14,X0_13) ),
inference(instantiation,[status(thm)],[c_9066]) ).
cnf(c_14055,plain,
app(sK55,tl(sK56)) = sK56,
inference(global_subsumption_just,[status(thm)],[c_8878,c_12495]) ).
cnf(c_14710,plain,
( X0_13 != X1_13
| X1_13 = X0_13 ),
inference(resolution,[status(thm)],[c_9066,c_9064]) ).
cnf(c_15597,plain,
( app(cons(X0_14,nil),X0_13) != cons(X0_14,X0_13)
| app(sK55,X0_13) != cons(X0_14,X0_13)
| app(cons(X0_14,nil),X0_13) = app(sK55,X0_13) ),
inference(instantiation,[status(thm)],[c_12431]) ).
cnf(c_15609,plain,
( app(cons(X0_14,nil),X0_13) != X1_13
| X2_13 != X1_13
| app(cons(X0_14,nil),X0_13) = X2_13 ),
inference(instantiation,[status(thm)],[c_9066]) ).
cnf(c_17807,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_8894,c_8916]) ).
cnf(c_17834,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_17807,c_8879]) ).
cnf(c_17853,plain,
( ~ ssList(sK56)
| nil = sK56
| ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_17834,c_8915]) ).
cnf(c_17854,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_17853,c_8879,c_8894]) ).
cnf(c_17874,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_8894,c_8918]) ).
cnf(c_17902,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_17874,c_8879]) ).
cnf(c_17926,plain,
( ~ ssList(sK56)
| nil = sK56
| ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_17902,c_8917]) ).
cnf(c_17927,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_17926,c_8879,c_8894]) ).
cnf(c_18529,plain,
( ~ ssList(X0_13)
| app(cons(hd(sK56),nil),X0_13) = cons(hd(sK56),X0_13) ),
inference(superposition,[status(thm)],[c_17927,c_8910]) ).
cnf(c_18587,plain,
app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
inference(superposition,[status(thm)],[c_17854,c_18529]) ).
cnf(c_19535,plain,
( cons(hd(sK56),tl(sK56)) != sK56
| X0_13 != sK56
| X0_13 = cons(hd(sK56),tl(sK56)) ),
inference(instantiation,[status(thm)],[c_13158]) ).
cnf(c_20030,plain,
sK56 = app(sK55,tl(sK56)),
inference(resolution,[status(thm)],[c_14710,c_14055]) ).
cnf(c_32347,plain,
( cons(hd(sK56),tl(sK56)) != sK56
| app(sK55,tl(sK56)) != sK56
| app(sK55,tl(sK56)) = cons(hd(sK56),tl(sK56)) ),
inference(instantiation,[status(thm)],[c_19535]) ).
cnf(c_32611,plain,
( app(cons(hd(sK56),nil),tl(sK56)) != cons(hd(sK56),tl(sK56))
| app(sK55,tl(sK56)) != cons(hd(sK56),tl(sK56))
| app(cons(hd(sK56),nil),tl(sK56)) = app(sK55,tl(sK56)) ),
inference(instantiation,[status(thm)],[c_15597]) ).
cnf(c_40479,plain,
( app(cons(hd(sK56),nil),tl(sK56)) != app(sK55,tl(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(sK55)
| cons(hd(sK56),nil) = sK55 ),
inference(instantiation,[status(thm)],[c_12054]) ).
cnf(c_40486,plain,
( app(cons(hd(sK56),nil),tl(sK56)) != app(sK55,tl(sK56))
| X0_13 != app(sK55,tl(sK56))
| app(cons(hd(sK56),nil),tl(sK56)) = X0_13 ),
inference(instantiation,[status(thm)],[c_15609]) ).
cnf(c_52694,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ssList(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_8986]) ).
cnf(c_56615,plain,
( app(cons(hd(sK56),nil),tl(sK56)) != app(sK55,tl(sK56))
| sK56 != app(sK55,tl(sK56))
| app(cons(hd(sK56),nil),tl(sK56)) = sK56 ),
inference(instantiation,[status(thm)],[c_40486]) ).
cnf(c_61897,plain,
( app(cons(hd(sK56),nil),X0_13) != sK56
| cons(hd(sK56),nil) != sK55
| ~ ssItem(hd(sK56))
| ~ ssList(X0_13) ),
inference(instantiation,[status(thm)],[c_8886]) ).
cnf(c_71852,plain,
( app(cons(hd(sK56),nil),tl(sK56)) != sK56
| cons(hd(sK56),nil) != sK55
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56)) ),
inference(instantiation,[status(thm)],[c_61897]) ).
cnf(c_71853,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_71852,c_56615,c_52694,c_40479,c_32611,c_32347,c_20030,c_18587,c_12509,c_12515,c_12516,c_12495,c_11997,c_8879,c_9093,c_141,c_253,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWC015+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.11 % Command : run_iprover %s %d THM
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Aug 28 14:41:18 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.18/0.43 Running first-order theorem proving
% 0.18/0.43 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 62.62/9.23 % SZS status Started for theBenchmark.p
% 62.62/9.23 % SZS status Theorem for theBenchmark.p
% 62.62/9.23
% 62.62/9.23 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 62.62/9.23
% 62.62/9.23 ------ iProver source info
% 62.62/9.23
% 62.62/9.23 git: date: 2023-05-31 18:12:56 +0000
% 62.62/9.23 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 62.62/9.23 git: non_committed_changes: false
% 62.62/9.23 git: last_make_outside_of_git: false
% 62.62/9.23
% 62.62/9.23 ------ Parsing...
% 62.62/9.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 62.62/9.23
% 62.62/9.23 ------ 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
% 62.62/9.23
% 62.62/9.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 62.62/9.23
% 62.62/9.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 62.62/9.23 ------ Proving...
% 62.62/9.23 ------ Problem Properties
% 62.62/9.23
% 62.62/9.23
% 62.62/9.23 clauses 185
% 62.62/9.23 conjectures 3
% 62.62/9.23 EPR 52
% 62.62/9.23 Horn 117
% 62.62/9.23 unary 19
% 62.62/9.23 binary 40
% 62.62/9.23 lits 628
% 62.62/9.23 lits eq 82
% 62.62/9.23 fd_pure 0
% 62.62/9.23 fd_pseudo 0
% 62.62/9.23 fd_cond 21
% 62.62/9.23 fd_pseudo_cond 14
% 62.62/9.23 AC symbols 0
% 62.62/9.23
% 62.62/9.23 ------ Input Options Time Limit: Unbounded
% 62.62/9.23
% 62.62/9.23
% 62.62/9.23 ------
% 62.62/9.23 Current options:
% 62.62/9.23 ------
% 62.62/9.23
% 62.62/9.23
% 62.62/9.23
% 62.62/9.23
% 62.62/9.23 ------ Proving...
% 62.62/9.23
% 62.62/9.23
% 62.62/9.23 % SZS status Theorem for theBenchmark.p
% 62.62/9.23
% 62.62/9.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.62/9.23
% 62.62/9.23
%------------------------------------------------------------------------------