TSTP Solution File: SWC022+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC022+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 03:10:54 EDT 2024
% Result : Theorem 7.87s 1.65s
% Output : CNFRefutation 7.87s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f600)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
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(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) )
& ( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& hd(X3) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& 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) )
& ( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& hd(X3) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& 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] :
( neq(nil,X3)
& hd(X3) = X5
& cons(X5,nil) = X4
& ssItem(X5) )
& X2 != X4
& ssList(X4) )
| ? [X6] :
( frontsegP(X0,X6)
& frontsegP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) ) )
| 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(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(f121,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
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(f154,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
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(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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(X0,X6)
| ~ frontsegP(X1,X6)
| ~ neq(X6,nil)
| ~ 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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(X0,X6)
| ~ frontsegP(X1,X6)
| ~ neq(X6,nil)
| ~ ssList(X6) )
& neq(X1,nil) ) )
& 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(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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(X0,X6)
| ~ frontsegP(X1,X6)
| ~ neq(X6,nil)
| ~ 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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(X1,X6)
| ~ neq(X6,nil)
| ~ 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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(X1,X6)
| ~ neq(X6,nil)
| ~ 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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(sK54,X6)
| ~ neq(X6,nil)
| ~ 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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| X2 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(sK54,X6)
| ~ neq(X6,nil)
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| sK55 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(sK54,X6)
| ~ neq(X6,nil)
| ~ 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] :
( ~ neq(nil,X3)
| hd(X3) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| sK55 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(sK54,X6)
| ~ neq(X6,nil)
| ~ ssList(X6) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ! [X4] :
( ! [X5] :
( ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| sK55 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(sK54,X6)
| ~ neq(X6,nil)
| ~ 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] :
( ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5) )
| sK55 = X4
| ~ ssList(X4) )
& ! [X6] :
( ~ frontsegP(sK53,X6)
| ~ frontsegP(sK54,X6)
| ~ neq(X6,nil)
| ~ 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(f363,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
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(f442,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f121]) ).
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(f475,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
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(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)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f348]) ).
fof(f558,plain,
! [X6] :
( ~ neq(sK56,nil)
| ~ frontsegP(sK53,X6)
| ~ frontsegP(sK54,X6)
| ~ neq(X6,nil)
| ~ ssList(X6) ),
inference(cnf_transformation,[],[f348]) ).
fof(f559,plain,
! [X4,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f348]) ).
fof(f560,plain,
! [X6] :
( ~ neq(sK56,nil)
| ~ frontsegP(sK55,X6)
| ~ frontsegP(sK56,X6)
| ~ neq(X6,nil)
| ~ ssList(X6) ),
inference(definition_unfolding,[],[f558,f553,f552]) ).
fof(f562,plain,
! [X4,X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK55 = X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f556,f552]) ).
fof(f565,plain,
ssList(sK56),
inference(definition_unfolding,[],[f549,f552]) ).
fof(f566,plain,
ssList(sK55),
inference(definition_unfolding,[],[f548,f553]) ).
fof(f570,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f363]) ).
fof(f594,plain,
! [X4] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| cons(hd(sK56),nil) != X4
| ~ ssItem(hd(sK56))
| sK55 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f559]) ).
fof(f595,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f594]) ).
fof(f596,plain,
! [X4] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| cons(hd(sK56),nil) != X4
| ~ ssItem(hd(sK56))
| sK55 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f562]) ).
fof(f597,plain,
( neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f596]) ).
cnf(c_61,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f570]) ).
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_142,plain,
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f442]) ).
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_175,plain,
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(cnf_transformation,[],[f475]) ).
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_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f529]) ).
cnf(c_246,negated_conjecture,
( ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK56))
| cons(hd(sK56),nil) = sK55 ),
inference(cnf_transformation,[],[f595]) ).
cnf(c_247,negated_conjecture,
( ~ neq(X0,nil)
| ~ frontsegP(sK56,X0)
| ~ frontsegP(sK55,X0)
| ~ neq(sK56,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f560]) ).
cnf(c_248,negated_conjecture,
( ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| cons(hd(sK56),nil) = sK55
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f597]) ).
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_377,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
cnf(c_382,plain,
( ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_247,c_250,c_247]) ).
cnf(c_383,negated_conjecture,
( ~ neq(X0,nil)
| ~ frontsegP(sK56,X0)
| ~ frontsegP(sK55,X0)
| ~ ssList(X0) ),
inference(renaming,[status(thm)],[c_382]) ).
cnf(c_384,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_248,c_250]) ).
cnf(c_386,plain,
( ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| cons(hd(sK56),nil) = sK55 ),
inference(global_subsumption_just,[status(thm)],[c_246,c_250,c_246]) ).
cnf(c_387,negated_conjecture,
( ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| cons(hd(sK56),nil) = sK55 ),
inference(renaming,[status(thm)],[c_386]) ).
cnf(c_3237,plain,
( X0 != nil
| X1 != sK56
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(X0)
| ~ ssList(X1)
| cons(hd(sK56),nil) = sK55
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_387]) ).
cnf(c_3238,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ~ ssList(sK56)
| cons(hd(sK56),nil) = sK55
| nil = sK56 ),
inference(unflattening,[status(thm)],[c_3237]) ).
cnf(c_3239,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| cons(hd(sK56),nil) = sK55
| nil = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_3238,c_253,c_141,c_3238]) ).
cnf(c_3257,plain,
( X0 != X1
| X2 != nil
| ~ frontsegP(sK56,X1)
| ~ frontsegP(sK55,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X2 ),
inference(resolution_lifted,[status(thm)],[c_138,c_383]) ).
cnf(c_3258,plain,
( ~ frontsegP(sK56,X0)
| ~ frontsegP(sK55,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| X0 = nil ),
inference(unflattening,[status(thm)],[c_3257]) ).
cnf(c_3260,plain,
( ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0)
| X0 = nil ),
inference(global_subsumption_just,[status(thm)],[c_3258,c_141,c_3258]) ).
cnf(c_3261,plain,
( ~ frontsegP(sK56,X0)
| ~ frontsegP(sK55,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(renaming,[status(thm)],[c_3260]) ).
cnf(c_3279,plain,
( X0 != nil
| X0 != sK56
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_384]) ).
cnf(c_3280,plain,
( nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3279]) ).
cnf(c_3281,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3280,c_141,c_3280]) ).
cnf(c_3286,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| cons(hd(sK56),nil) = sK55 ),
inference(backward_subsumption_resolution,[status(thm)],[c_3239,c_3281]) ).
cnf(c_8923,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
cnf(c_8924,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
cnf(c_11835,plain,
( ~ frontsegP(sK56,sK55)
| ~ ssList(sK55)
| nil = sK55 ),
inference(superposition,[status(thm)],[c_175,c_3261]) ).
cnf(c_11838,plain,
( ~ frontsegP(sK56,sK55)
| nil = sK55 ),
inference(forward_subsumption_resolution,[status(thm)],[c_11835,c_8923]) ).
cnf(c_12266,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| cons(hd(sK56),nil) = sK55 ),
inference(superposition,[status(thm)],[c_140,c_3286]) ).
cnf(c_12267,plain,
( ~ ssItem(hd(sK56))
| cons(hd(sK56),nil) = sK55 ),
inference(forward_subsumption_resolution,[status(thm)],[c_12266,c_141]) ).
cnf(c_12369,plain,
( ~ ssList(sK56)
| cons(hd(sK56),nil) = sK55
| nil = sK56 ),
inference(superposition,[status(thm)],[c_149,c_12267]) ).
cnf(c_12370,plain,
cons(hd(sK56),nil) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_12369,c_3281,c_8924]) ).
cnf(c_13316,plain,
( nil != sK55
| ~ ssItem(hd(sK56))
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_12370,c_142]) ).
cnf(c_13317,plain,
( nil != sK55
| ~ ssItem(hd(sK56)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13316,c_141]) ).
cnf(c_14318,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_8924,c_219]) ).
cnf(c_14322,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14318,c_3281]) ).
cnf(c_14498,plain,
( ~ ssList(sK56)
| nil = sK56
| ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_14322,c_220]) ).
cnf(c_14499,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14498,c_3281,c_8924]) ).
cnf(c_14500,plain,
nil != sK55,
inference(backward_subsumption_resolution,[status(thm)],[c_13317,c_14499]) ).
cnf(c_14506,plain,
~ frontsegP(sK56,sK55),
inference(backward_subsumption_resolution,[status(thm)],[c_11838,c_14500]) ).
cnf(c_14732,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_8924,c_221]) ).
cnf(c_14736,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14732,c_3281]) ).
cnf(c_15065,plain,
( ~ ssList(sK56)
| nil = sK56
| ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_14736,c_222]) ).
cnf(c_15066,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_15065,c_3281,c_8924]) ).
cnf(c_16411,plain,
( cons(hd(sK56),tl(sK56)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_8924,c_224]) ).
cnf(c_16416,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_16411,c_3281]) ).
cnf(c_16676,plain,
( ~ ssList(X0)
| app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) ),
inference(superposition,[status(thm)],[c_14499,c_227]) ).
cnf(c_16681,plain,
( ~ ssList(X0)
| cons(hd(sK56),X0) = app(sK55,X0) ),
inference(light_normalisation,[status(thm)],[c_16676,c_12370]) ).
cnf(c_17193,plain,
cons(hd(sK56),tl(sK56)) = app(sK55,tl(sK56)),
inference(superposition,[status(thm)],[c_15066,c_16681]) ).
cnf(c_17196,plain,
app(sK55,tl(sK56)) = sK56,
inference(light_normalisation,[status(thm)],[c_17193,c_16416]) ).
cnf(c_17900,plain,
( ~ ssList(tl(sK56))
| ~ ssList(sK55)
| frontsegP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_17196,c_377]) ).
cnf(c_17901,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_17900,c_14506,c_8923,c_15066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC022+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 23:19:50 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 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
% 7.87/1.65 % SZS status Started for theBenchmark.p
% 7.87/1.65 % SZS status Theorem for theBenchmark.p
% 7.87/1.65
% 7.87/1.65 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.87/1.65
% 7.87/1.65 ------ iProver source info
% 7.87/1.65
% 7.87/1.65 git: date: 2024-05-02 19:28:25 +0000
% 7.87/1.65 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.87/1.65 git: non_committed_changes: false
% 7.87/1.65
% 7.87/1.65 ------ Parsing...
% 7.87/1.65 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.87/1.65
% 7.87/1.65 ------ 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
% 7.87/1.65
% 7.87/1.65 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.87/1.65
% 7.87/1.65 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.87/1.65 ------ Proving...
% 7.87/1.65 ------ Problem Properties
% 7.87/1.65
% 7.87/1.65
% 7.87/1.65 clauses 186
% 7.87/1.65 conjectures 2
% 7.87/1.65 EPR 54
% 7.87/1.65 Horn 118
% 7.87/1.65 unary 19
% 7.87/1.65 binary 41
% 7.87/1.65 lits 630
% 7.87/1.65 lits eq 81
% 7.87/1.65 fd_pure 0
% 7.87/1.65 fd_pseudo 0
% 7.87/1.65 fd_cond 22
% 7.87/1.65 fd_pseudo_cond 14
% 7.87/1.65 AC symbols 0
% 7.87/1.65
% 7.87/1.65 ------ Schedule dynamic 5 is on
% 7.87/1.65
% 7.87/1.65 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.87/1.65
% 7.87/1.65
% 7.87/1.65 ------
% 7.87/1.65 Current options:
% 7.87/1.65 ------
% 7.87/1.65
% 7.87/1.65
% 7.87/1.65
% 7.87/1.65
% 7.87/1.65 ------ Proving...
% 7.87/1.65
% 7.87/1.65
% 7.87/1.65 % SZS status Theorem for theBenchmark.p
% 7.87/1.65
% 7.87/1.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.87/1.65
% 7.87/1.66
%------------------------------------------------------------------------------