TSTP Solution File: SWC314+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC314+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 : Fri May 3 03:11:58 EDT 2024
% Result : Theorem 20.27s 3.64s
% Output : CNFRefutation 20.27s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f613)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
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(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil = X0
| nil != X1 )
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( app(X9,cons(X8,nil)) = X0
| app(cons(X8,nil),X9) != X1
| ~ ssList(X9) ) ) )
| ( neq(X3,nil)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& ? [X7] :
( neq(nil,X3)
& hd(X3) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X3) = X5
& ssList(X6) )
& ssList(X5) )
& X2 != X4
& ssList(X4) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil = X0
| nil != X1 )
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( app(X9,cons(X8,nil)) = X0
| app(cons(X8,nil),X9) != X1
| ~ ssList(X9) ) ) )
| ( neq(X3,nil)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& ? [X7] :
( neq(nil,X3)
& hd(X3) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X3) = X5
& ssList(X6) )
& ssList(X5) )
& X2 != X4
& ssList(X4) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil = X0
| nil != X1 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) = X0
| app(cons(X4,nil),X5) != X1
| ~ ssList(X5) ) ) )
| ( neq(X3,nil)
& ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X3)
& ? [X9] :
( neq(nil,X3)
& hd(X3) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X3) = X7
& ssList(X8) )
& ssList(X7) )
& X2 != X6
& ssList(X6) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
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(f126,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
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(f129,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
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(f132,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != X0
& nil = X1 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != X0
& app(cons(X4,nil),X5) = X1
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X2 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f330,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f339,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f340,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f339]) ).
fof(f343,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != X0
& nil = X1 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != X0
& app(cons(X4,nil),X5) = X1
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X2 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != sK53
& nil = X1 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = X1
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X2 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != sK53
& nil = X1 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = X1
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X2 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil != sK53
& nil = sK54 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = sK54
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X2 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil != sK53
& nil = sK54 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = sK54
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X2 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil != sK53
& nil = sK54 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = sK54
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK55 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = sK55 )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ( ( nil != sK53
& nil = sK54 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = sK54
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK55 = X6
| ~ ssList(X6) ) )
& ( nil != X3
| nil = sK55 )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( nil != sK53
& nil = sK54 )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = sK54
& ssList(X5) )
& ssItem(X4) ) )
& ( ~ neq(sK56,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK56)
| ! [X9] :
( ~ neq(nil,sK56)
| hd(sK56) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK56) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK55 = X6
| ~ ssList(X6) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) != sK53
& app(cons(X4,nil),X5) = sK54
& ssList(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( sK53 != app(X5,cons(sK57,nil))
& sK54 = app(cons(sK57,nil),X5)
& ssList(X5) )
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X5] :
( sK53 != app(X5,cons(sK57,nil))
& sK54 = app(cons(sK57,nil),X5)
& ssList(X5) )
=> ( sK53 != app(sK58,cons(sK57,nil))
& sK54 = app(cons(sK57,nil),sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( ( nil != sK53
& nil = sK54 )
| ( sK53 != app(sK58,cons(sK57,nil))
& sK54 = app(cons(sK57,nil),sK58)
& ssList(sK58)
& ssItem(sK57) ) )
& ( ~ neq(sK56,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK56)
| ! [X9] :
( ~ neq(nil,sK56)
| hd(sK56) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK56) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK55 = X6
| ~ ssList(X6) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f222,f348,f347,f346,f345,f344,f343]) ).
fof(f351,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f440,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f441,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f442,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f449,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f450,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f451,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f452,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f453,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f454,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f496,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f497,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f530,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f533,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f550,plain,
ssList(sK54),
inference(cnf_transformation,[],[f349]) ).
fof(f553,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f349]) ).
fof(f554,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f349]) ).
fof(f555,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
( nil = sK54
| ssItem(sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
( nil = sK54
| ssList(sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
( nil = sK54
| sK54 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f560,plain,
( nil = sK54
| sK53 != app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f561,plain,
( nil != sK53
| ssItem(sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f562,plain,
( nil != sK53
| ssList(sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f563,plain,
( nil != sK53
| sK54 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f564,plain,
( nil != sK53
| sK53 != app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f565,plain,
( nil != sK55
| sK55 != app(sK58,cons(sK57,nil)) ),
inference(definition_unfolding,[],[f564,f554,f554]) ).
fof(f566,plain,
( nil != sK55
| sK56 = app(cons(sK57,nil),sK58) ),
inference(definition_unfolding,[],[f563,f554,f553]) ).
fof(f567,plain,
( nil != sK55
| ssList(sK58) ),
inference(definition_unfolding,[],[f562,f554]) ).
fof(f568,plain,
( nil != sK55
| ssItem(sK57) ),
inference(definition_unfolding,[],[f561,f554]) ).
fof(f569,plain,
( nil = sK56
| sK55 != app(sK58,cons(sK57,nil)) ),
inference(definition_unfolding,[],[f560,f553,f554]) ).
fof(f570,plain,
( nil = sK56
| sK56 = app(cons(sK57,nil),sK58) ),
inference(definition_unfolding,[],[f559,f553,f553]) ).
fof(f571,plain,
( nil = sK56
| ssList(sK58) ),
inference(definition_unfolding,[],[f558,f553]) ).
fof(f572,plain,
( nil = sK56
| ssItem(sK57) ),
inference(definition_unfolding,[],[f557,f553]) ).
fof(f573,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
fof(f594,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f497]) ).
cnf(c_49,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f351]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f442]) ).
cnf(c_148,plain,
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f449]) ).
cnf(c_149,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f450]) ).
cnf(c_150,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f451]) ).
cnf(c_151,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f452]) ).
cnf(c_152,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f453]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
cnf(c_195,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(cnf_transformation,[],[f594]) ).
cnf(c_196,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f496]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f530]) ).
cnf(c_230,plain,
( app(X0,X1) != nil
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = nil ),
inference(cnf_transformation,[],[f533]) ).
cnf(c_246,negated_conjecture,
( app(sK58,cons(sK57,nil)) != sK55
| nil != sK55 ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_247,negated_conjecture,
( nil != sK55
| app(cons(sK57,nil),sK58) = sK56 ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_248,negated_conjecture,
( nil != sK55
| ssList(sK58) ),
inference(cnf_transformation,[],[f567]) ).
cnf(c_249,negated_conjecture,
( nil != sK55
| ssItem(sK57) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_250,negated_conjecture,
( app(sK58,cons(sK57,nil)) != sK55
| nil = sK56 ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_251,negated_conjecture,
( app(cons(sK57,nil),sK58) = sK56
| nil = sK56 ),
inference(cnf_transformation,[],[f570]) ).
cnf(c_252,negated_conjecture,
( nil = sK56
| ssList(sK58) ),
inference(cnf_transformation,[],[f571]) ).
cnf(c_253,negated_conjecture,
( nil = sK56
| ssItem(sK57) ),
inference(cnf_transformation,[],[f572]) ).
cnf(c_254,negated_conjecture,
( ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
inference(cnf_transformation,[],[f613]) ).
cnf(c_255,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_258,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f573]) ).
cnf(c_309,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| nil = nil ),
inference(instantiation,[status(thm)],[c_196]) ).
cnf(c_366,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_249,c_255]) ).
cnf(c_368,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_248,c_255]) ).
cnf(c_376,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_249,c_366]) ).
cnf(c_378,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_248,c_368]) ).
cnf(c_386,negated_conjecture,
app(cons(sK57,nil),sK58) = sK56,
inference(global_subsumption_just,[status(thm)],[c_251,c_255,c_251,c_247]) ).
cnf(c_388,negated_conjecture,
app(sK58,cons(sK57,nil)) != sK55,
inference(global_subsumption_just,[status(thm)],[c_250,c_255,c_250,c_246]) ).
cnf(c_390,negated_conjecture,
app(cons(sK57,nil),sK58) = sK56,
inference(global_subsumption_just,[status(thm)],[c_247,c_386]) ).
cnf(c_832,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
inference(backward_subsumption_resolution,[status(thm)],[c_254,c_153]) ).
cnf(c_6388,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_9290,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| nil = sK56
| neq(nil,sK56) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_9301,plain,
( nil != X0
| sK56 != X0
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_6388]) ).
cnf(c_9302,plain,
( nil != nil
| sK56 != nil
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_9301]) ).
cnf(c_9339,plain,
( cons(sK57,X0) != nil
| ~ ssList(X0)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_148]) ).
cnf(c_9343,plain,
( cons(sK57,nil) != nil
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_9339]) ).
cnf(c_9422,plain,
( ~ ssList(X0)
| ~ ssList(sK56)
| sK56 = X0
| neq(sK56,X0) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_9423,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| sK56 = nil
| neq(sK56,nil) ),
inference(instantiation,[status(thm)],[c_9422]) ).
cnf(c_10293,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| ssList(cons(sK57,nil)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_11135,plain,
( ~ ssList(sK56)
| sK56 = nil
| ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_149]) ).
cnf(c_11136,plain,
( ~ ssList(sK56)
| sK56 = nil
| ssList(tl(sK56)) ),
inference(instantiation,[status(thm)],[c_151]) ).
cnf(c_11702,plain,
( ~ neq(nil,sK56)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| ~ ssList(nil)
| app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
inference(superposition,[status(thm)],[c_140,c_832]) ).
cnf(c_11792,plain,
( ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
inference(global_subsumption_just,[status(thm)],[c_11702,c_141,c_11702]) ).
cnf(c_11793,plain,
( ~ neq(nil,sK56)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
inference(renaming,[status(thm)],[c_11792]) ).
cnf(c_12280,plain,
( ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| ~ ssItem(nil)
| ~ ssItem(sK56)
| app(tl(sK56),cons(hd(sK56),nil)) = sK55
| nil = sK56 ),
inference(superposition,[status(thm)],[c_49,c_11793]) ).
cnf(c_12329,plain,
( app(tl(sK56),cons(hd(sK56),nil)) = sK55
| nil = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_12280,c_258,c_141,c_195,c_309,c_9290,c_9302,c_9423,c_11136,c_11135,c_11702]) ).
cnf(c_22045,plain,
( nil != sK56
| ~ ssList(cons(sK57,nil))
| ~ ssList(sK58)
| cons(sK57,nil) = nil ),
inference(superposition,[status(thm)],[c_390,c_230]) ).
cnf(c_36267,plain,
app(tl(sK56),cons(hd(sK56),nil)) = sK55,
inference(global_subsumption_just,[status(thm)],[c_832,c_141,c_253,c_252,c_249,c_248,c_255,c_9343,c_10293,c_12329,c_22045]) ).
cnf(c_36449,plain,
( ~ ssList(X0)
| hd(cons(sK57,X0)) = sK57 ),
inference(superposition,[status(thm)],[c_376,c_150]) ).
cnf(c_36595,plain,
hd(cons(sK57,sK58)) = sK57,
inference(superposition,[status(thm)],[c_378,c_36449]) ).
cnf(c_36621,plain,
( ~ ssList(X0)
| tl(cons(sK57,X0)) = X0 ),
inference(superposition,[status(thm)],[c_376,c_152]) ).
cnf(c_36743,plain,
tl(cons(sK57,sK58)) = sK58,
inference(superposition,[status(thm)],[c_378,c_36621]) ).
cnf(c_36927,plain,
( ~ ssList(X0)
| app(cons(sK57,nil),X0) = cons(sK57,X0) ),
inference(superposition,[status(thm)],[c_376,c_227]) ).
cnf(c_37028,plain,
app(cons(sK57,nil),sK58) = cons(sK57,sK58),
inference(superposition,[status(thm)],[c_378,c_36927]) ).
cnf(c_37038,plain,
cons(sK57,sK58) = sK56,
inference(superposition,[status(thm)],[c_37028,c_390]) ).
cnf(c_37045,plain,
tl(sK56) = sK58,
inference(superposition,[status(thm)],[c_37038,c_36743]) ).
cnf(c_37046,plain,
hd(sK56) = sK57,
inference(superposition,[status(thm)],[c_37038,c_36595]) ).
cnf(c_37104,plain,
app(sK58,cons(hd(sK56),nil)) = sK55,
inference(superposition,[status(thm)],[c_37045,c_36267]) ).
cnf(c_37128,plain,
app(sK58,cons(sK57,nil)) = sK55,
inference(superposition,[status(thm)],[c_37046,c_37104]) ).
cnf(c_37134,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_37128,c_388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC314+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n013.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 23:24:04 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.27/3.64 % SZS status Started for theBenchmark.p
% 20.27/3.64 % SZS status Theorem for theBenchmark.p
% 20.27/3.64
% 20.27/3.64 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.27/3.64
% 20.27/3.64 ------ iProver source info
% 20.27/3.64
% 20.27/3.64 git: date: 2024-05-02 19:28:25 +0000
% 20.27/3.64 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.27/3.64 git: non_committed_changes: false
% 20.27/3.64
% 20.27/3.64 ------ Parsing...
% 20.27/3.64 ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.27/3.64
% 20.27/3.64 ------ 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: 4 0s sf_e pe_s pe_e
% 20.27/3.64
% 20.27/3.64 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 20.27/3.64
% 20.27/3.64 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.27/3.64 ------ Proving...
% 20.27/3.64 ------ Problem Properties
% 20.27/3.64
% 20.27/3.64
% 20.27/3.64 clauses 192
% 20.27/3.64 conjectures 7
% 20.27/3.64 EPR 58
% 20.27/3.64 Horn 122
% 20.27/3.64 unary 22
% 20.27/3.64 binary 43
% 20.27/3.64 lits 644
% 20.27/3.64 lits eq 85
% 20.27/3.64 fd_pure 0
% 20.27/3.64 fd_pseudo 0
% 20.27/3.64 fd_cond 21
% 20.27/3.64 fd_pseudo_cond 16
% 20.27/3.64 AC symbols 0
% 20.27/3.64
% 20.27/3.64 ------ Input Options Time Limit: Unbounded
% 20.27/3.64
% 20.27/3.64
% 20.27/3.64 ------
% 20.27/3.64 Current options:
% 20.27/3.64 ------
% 20.27/3.64
% 20.27/3.64
% 20.27/3.64
% 20.27/3.64
% 20.27/3.64 ------ Proving...
% 20.27/3.64
% 20.27/3.64
% 20.27/3.64 % SZS status Theorem for theBenchmark.p
% 20.27/3.64
% 20.27/3.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.27/3.64
% 20.27/3.65
%------------------------------------------------------------------------------