TSTP Solution File: SWC376+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC376+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 20:42:57 EDT 2023
% Result : Theorem 165.85s 22.83s
% Output : CNFRefutation 165.85s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f603)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( ( memberP(X0,X4)
& memberP(X1,X4) )
| ( ~ memberP(X0,X4)
& ~ memberP(X1,X4) ) ) )
| 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)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( ( memberP(X0,X4)
& memberP(X1,X4) )
| ( ~ memberP(X0,X4)
& ~ memberP(X1,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] :
( ? [X6] :
( neq(nil,X2)
& ? [X7] :
( neq(nil,X2)
& hd(X2) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X2) = X5
& ssList(X6) )
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X8] :
( ssItem(X8)
=> ( ( memberP(X0,X8)
& memberP(X1,X8) )
| ( ~ memberP(X0,X8)
& ~ memberP(X1,X8) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
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(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f149,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
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] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ( ~ memberP(X0,X8)
| ~ memberP(X1,X8) )
& ( memberP(X0,X8)
| memberP(X1,X8) )
& ssItem(X8) )
& 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] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ( ~ memberP(X0,X8)
| ~ memberP(X1,X8) )
& ( memberP(X0,X8)
| memberP(X1,X8) )
& ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f237,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK8(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK8(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f240,plain,
! [X0,X1] :
( ? [X5] :
( app(sK8(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f238,f240,f239]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f323,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f147]) ).
fof(f324,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f323]) ).
fof(f325,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f326,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f325]) ).
fof(f331,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ( ~ memberP(X0,X8)
| ~ memberP(X1,X8) )
& ( memberP(X0,X8)
| memberP(X1,X8) )
& ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(X1,X8) )
& ( memberP(sK53,X8)
| memberP(X1,X8) )
& ssItem(X8) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(X1,X8) )
& ( memberP(sK53,X8)
| memberP(X1,X8) )
& ssItem(X8) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(sK54,X8) )
& ( memberP(sK53,X8)
| memberP(sK54,X8) )
& ssItem(X8) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(sK54,X8) )
& ( memberP(sK53,X8)
| memberP(sK54,X8) )
& ssItem(X8) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = sK55 )
& ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(sK54,X8) )
& ( memberP(sK53,X8)
| memberP(sK54,X8) )
& ssItem(X8) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = sK55 )
& ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(sK54,X8) )
& ( memberP(sK53,X8)
| memberP(sK54,X8) )
& ssItem(X8) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK56 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( nil != sK56
| nil = sK55 )
& ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(sK54,X8) )
& ( memberP(sK53,X8)
| memberP(sK54,X8) )
& ssItem(X8) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X8] :
( ( ~ memberP(sK53,X8)
| ~ memberP(sK54,X8) )
& ( memberP(sK53,X8)
| memberP(sK54,X8) )
& ssItem(X8) )
=> ( ( ~ memberP(sK53,sK57)
| ~ memberP(sK54,sK57) )
& ( memberP(sK53,sK57)
| memberP(sK54,sK57) )
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK56 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( nil != sK56
| nil = sK55 )
& ( ~ memberP(sK53,sK57)
| ~ memberP(sK54,sK57) )
& ( memberP(sK53,sK57)
| memberP(sK54,sK57) )
& ssItem(sK57)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f223,f348,f347,f346,f345,f344]) ).
fof(f351,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f358,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f440,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f317]) ).
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(f454,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f466,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f467,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f469,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f471,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f472,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f496,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f497,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f527,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f549,plain,
ssList(sK53),
inference(cnf_transformation,[],[f349]) ).
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,
ssItem(sK57),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
( memberP(sK53,sK57)
| memberP(sK54,sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
( ~ memberP(sK53,sK57)
| ~ memberP(sK54,sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f349]) ).
fof(f561,plain,
( ~ memberP(sK55,sK57)
| ~ memberP(sK56,sK57) ),
inference(definition_unfolding,[],[f557,f554,f553]) ).
fof(f562,plain,
( memberP(sK55,sK57)
| memberP(sK56,sK57) ),
inference(definition_unfolding,[],[f556,f554,f553]) ).
fof(f563,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
fof(f564,plain,
ssList(sK55),
inference(definition_unfolding,[],[f549,f554]) ).
fof(f566,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f358]) ).
fof(f584,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_50,plain,
( ~ neq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f596]) ).
cnf(c_54,plain,
( ~ ssList(app(X0,cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f598]) ).
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_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
cnf(c_166,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f467]) ).
cnf(c_167,plain,
( ~ memberP(app(X0,X1),X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,X2)
| memberP(X1,X2) ),
inference(cnf_transformation,[],[f466]) ).
cnf(c_168,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| memberP(cons(X2,X0),X1) ),
inference(cnf_transformation,[],[f471]) ).
cnf(c_169,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| memberP(cons(X0,X1),X0) ),
inference(cnf_transformation,[],[f599]) ).
cnf(c_170,plain,
( ~ memberP(cons(X0,X1),X2)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2) ),
inference(cnf_transformation,[],[f469]) ).
cnf(c_171,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f472]) ).
cnf(c_195,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(cnf_transformation,[],[f584]) ).
cnf(c_196,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f496]) ).
cnf(c_224,plain,
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| X0 = nil ),
inference(cnf_transformation,[],[f527]) ).
cnf(c_246,negated_conjecture,
( ~ ssList(app(tl(sK55),cons(hd(sK55),nil)))
| ~ ssList(cons(hd(sK55),nil))
| ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(cnf_transformation,[],[f603]) ).
cnf(c_247,negated_conjecture,
( ~ neq(sK56,nil)
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_248,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_249,negated_conjecture,
( ~ memberP(sK55,sK57)
| ~ memberP(sK56,sK57) ),
inference(cnf_transformation,[],[f561]) ).
cnf(c_250,negated_conjecture,
( memberP(sK55,sK57)
| memberP(sK56,sK57) ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_251,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f555]) ).
cnf(c_254,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f563]) ).
cnf(c_255,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f564]) ).
cnf(c_285,plain,
( ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_139]) ).
cnf(c_305,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| nil = nil ),
inference(instantiation,[status(thm)],[c_196]) ).
cnf(c_1294,plain,
( ~ ssList(cons(hd(sK55),nil))
| ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(backward_subsumption_resolution,[status(thm)],[c_246,c_153]) ).
cnf(c_7290,plain,
X0 = X0,
theory(equality) ).
cnf(c_7292,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_7293,plain,
( X0 != X1
| X2 != X3
| ~ neq(X1,X3)
| neq(X0,X2) ),
theory(equality) ).
cnf(c_7297,plain,
( X0 != X1
| X2 != X3
| ~ memberP(X1,X3)
| memberP(X0,X2) ),
theory(equality) ).
cnf(c_7298,plain,
( X0 != X1
| ~ ssList(X1)
| ssList(X0) ),
theory(equality) ).
cnf(c_11144,plain,
( ~ ssItem(nil)
| ~ ssItem(sK56)
| nil = sK56
| neq(sK55,nil) ),
inference(superposition,[status(thm)],[c_49,c_247]) ).
cnf(c_11147,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| nil = sK56
| neq(sK55,nil) ),
inference(superposition,[status(thm)],[c_138,c_247]) ).
cnf(c_11148,plain,
( nil = sK56
| neq(sK55,nil) ),
inference(global_subsumption_just,[status(thm)],[c_11144,c_254,c_141,c_11147]) ).
cnf(c_11166,plain,
( ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssList(nil)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(superposition,[status(thm)],[c_140,c_1294]) ).
cnf(c_11167,plain,
( ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(sK56,nil)
| ~ neq(nil,sK55)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_11166,c_141,c_11166]) ).
cnf(c_11168,plain,
( ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(renaming,[status(thm)],[c_11167]) ).
cnf(c_11187,plain,
( ~ neq(nil,sK55)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssList(nil)
| ~ ssList(sK56)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_138,c_11168]) ).
cnf(c_11190,plain,
( ~ ssList(X0)
| hd(cons(sK57,X0)) = sK57 ),
inference(superposition,[status(thm)],[c_251,c_150]) ).
cnf(c_11191,plain,
( ~ ssList(nil)
| hd(cons(sK57,nil)) = sK57 ),
inference(instantiation,[status(thm)],[c_11190]) ).
cnf(c_11222,plain,
( ~ neq(sK57,sK57)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_11223,plain,
( ~ ssList(X0)
| ~ ssItem(sK57)
| ssList(cons(sK57,X0)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_11224,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| ssList(cons(sK57,nil)) ),
inference(instantiation,[status(thm)],[c_11223]) ).
cnf(c_11225,plain,
( cons(sK57,X0) != nil
| ~ ssList(X0)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_148]) ).
cnf(c_11226,plain,
( cons(sK57,nil) != nil
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_11225]) ).
cnf(c_11235,plain,
( cons(hd(sK55),tl(sK55)) = sK55
| nil = sK55 ),
inference(superposition,[status(thm)],[c_255,c_224]) ).
cnf(c_11251,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| nil = sK55
| memberP(sK55,hd(sK55)) ),
inference(superposition,[status(thm)],[c_11235,c_169]) ).
cnf(c_11253,plain,
( ~ memberP(tl(sK55),X0)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssItem(X0)
| nil = sK55
| memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_11235,c_168]) ).
cnf(c_11257,plain,
( ~ ssItem(X0)
| ~ ssItem(sK57)
| X0 = sK57
| neq(X0,sK57) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_11259,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| nil = sK56
| neq(nil,sK56) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_11266,plain,
( nil != X0
| sK56 != X0
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_7292]) ).
cnf(c_11267,plain,
( nil != nil
| sK56 != nil
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_11266]) ).
cnf(c_11280,plain,
( X0 != sK55
| X1 != nil
| ~ neq(sK55,nil)
| neq(X0,X1) ),
inference(instantiation,[status(thm)],[c_7293]) ).
cnf(c_11281,plain,
( nil != nil
| nil != sK55
| ~ neq(sK55,nil)
| neq(nil,nil) ),
inference(instantiation,[status(thm)],[c_11280]) ).
cnf(c_11282,plain,
( X0 != sK55
| X1 != sK57
| ~ memberP(sK55,sK57)
| memberP(X0,X1) ),
inference(instantiation,[status(thm)],[c_7297]) ).
cnf(c_11308,plain,
( ~ ssList(cons(sK57,X0))
| cons(sK57,X0) = nil
| ssItem(hd(cons(sK57,X0))) ),
inference(instantiation,[status(thm)],[c_149]) ).
cnf(c_11309,plain,
( ~ ssList(cons(sK57,nil))
| cons(sK57,nil) = nil
| ssItem(hd(cons(sK57,nil))) ),
inference(instantiation,[status(thm)],[c_11308]) ).
cnf(c_11390,plain,
( ~ ssItem(sK57)
| sK57 = sK57
| neq(sK57,sK57) ),
inference(instantiation,[status(thm)],[c_11257]) ).
cnf(c_11392,plain,
( X0 != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(X0,sK57) ),
inference(instantiation,[status(thm)],[c_11282]) ).
cnf(c_11394,plain,
( nil != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(nil,sK57) ),
inference(instantiation,[status(thm)],[c_11392]) ).
cnf(c_11415,plain,
( X0 != sK56
| X1 != sK57
| ~ memberP(sK56,sK57)
| memberP(X0,X1) ),
inference(instantiation,[status(thm)],[c_7297]) ).
cnf(c_11526,plain,
( hd(cons(sK57,X0)) != sK57
| X1 != sK56
| ~ memberP(sK56,sK57)
| memberP(X1,hd(cons(sK57,X0))) ),
inference(instantiation,[status(thm)],[c_11415]) ).
cnf(c_11527,plain,
( hd(cons(sK57,nil)) != sK57
| nil != sK56
| ~ memberP(sK56,sK57)
| memberP(nil,hd(cons(sK57,nil))) ),
inference(instantiation,[status(thm)],[c_11526]) ).
cnf(c_11530,plain,
( X0 != sK56
| sK57 != sK57
| ~ memberP(sK56,sK57)
| memberP(X0,sK57) ),
inference(instantiation,[status(thm)],[c_11415]) ).
cnf(c_11657,plain,
( ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_1294,c_254,c_141,c_195,c_247,c_285,c_248,c_305,c_11187,c_11281]) ).
cnf(c_11834,plain,
( X0 != X1
| sK57 != X1
| sK57 = X0 ),
inference(instantiation,[status(thm)],[c_7292]) ).
cnf(c_11905,plain,
( ~ ssItem(nil)
| ~ ssItem(sK56)
| nil = sK55
| neq(nil,sK56) ),
inference(resolution,[status(thm)],[c_49,c_248]) ).
cnf(c_11932,plain,
( nil = sK55
| neq(nil,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_11905,c_254,c_141,c_248,c_11259]) ).
cnf(c_12235,plain,
( X0 != X1
| ~ ssList(X1)
| ~ ssList(X2)
| X2 = X0
| neq(X2,X1) ),
inference(resolution,[status(thm)],[c_7292,c_138]) ).
cnf(c_12246,plain,
( X0 != sK55
| nil = X0
| neq(nil,sK56) ),
inference(resolution,[status(thm)],[c_7292,c_11932]) ).
cnf(c_12247,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_7292,c_7290]) ).
cnf(c_12273,plain,
( ~ ssList(sK55)
| sK55 = nil
| ssList(tl(sK55)) ),
inference(instantiation,[status(thm)],[c_151]) ).
cnf(c_12274,plain,
( ~ ssList(sK55)
| sK55 = nil
| ssItem(hd(sK55)) ),
inference(instantiation,[status(thm)],[c_149]) ).
cnf(c_12279,plain,
sK55 = sK55,
inference(instantiation,[status(thm)],[c_7290]) ).
cnf(c_12280,plain,
( X0 != X1
| sK55 != X1
| sK55 = X0 ),
inference(instantiation,[status(thm)],[c_7292]) ).
cnf(c_12365,plain,
( cons(X0,X1) != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(cons(X0,X1),sK57) ),
inference(instantiation,[status(thm)],[c_11392]) ).
cnf(c_12366,plain,
( ~ memberP(cons(X0,X1),sK57)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(sK57)
| X0 = sK57
| memberP(X1,sK57) ),
inference(instantiation,[status(thm)],[c_170]) ).
cnf(c_12370,plain,
( ~ memberP(nil,sK57)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_171]) ).
cnf(c_12414,plain,
( ~ memberP(nil,hd(cons(sK57,X0)))
| ~ ssItem(hd(cons(sK57,X0))) ),
inference(instantiation,[status(thm)],[c_171]) ).
cnf(c_12415,plain,
( ~ memberP(nil,hd(cons(sK57,nil)))
| ~ ssItem(hd(cons(sK57,nil))) ),
inference(instantiation,[status(thm)],[c_12414]) ).
cnf(c_12509,plain,
neq(nil,sK56),
inference(global_subsumption_just,[status(thm)],[c_12246,c_254,c_251,c_141,c_250,c_11191,c_11222,c_11224,c_11226,c_11259,c_11309,c_11390,c_11394,c_11527,c_11932,c_12370,c_12415]) ).
cnf(c_12527,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| X1 = X0
| neq(X0,X1) ),
inference(resolution,[status(thm)],[c_12247,c_49]) ).
cnf(c_12583,plain,
( ~ ssList(X0)
| ~ ssList(sK55)
| X0 = sK55
| neq(X0,sK55) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_12584,plain,
( ~ ssList(nil)
| ~ ssList(sK55)
| nil = sK55
| neq(nil,sK55) ),
inference(instantiation,[status(thm)],[c_12583]) ).
cnf(c_12588,plain,
( X0 != X1
| sK55 != X1
| X0 = sK55 ),
inference(instantiation,[status(thm)],[c_7292]) ).
cnf(c_12589,plain,
( nil != nil
| sK55 != nil
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_12588]) ).
cnf(c_12613,plain,
( X0 != nil
| X1 != sK56
| ~ neq(nil,sK56)
| neq(X0,X1) ),
inference(instantiation,[status(thm)],[c_7293]) ).
cnf(c_12614,plain,
( nil != nil
| nil != sK56
| ~ neq(nil,sK56)
| neq(nil,nil) ),
inference(instantiation,[status(thm)],[c_12613]) ).
cnf(c_12623,plain,
( ~ ssList(X0)
| ~ ssList(sK56)
| sK56 = X0
| neq(sK56,X0) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_12624,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| sK56 = nil
| neq(sK56,nil) ),
inference(instantiation,[status(thm)],[c_12623]) ).
cnf(c_13076,plain,
( X0 != X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X3)
| neq(X3,X2)
| memberP(X0,X3) ),
inference(resolution,[status(thm)],[c_7297,c_49]) ).
cnf(c_13087,plain,
( X0 != X1
| ~ memberP(X1,X2)
| memberP(X0,X2) ),
inference(resolution,[status(thm)],[c_7297,c_7290]) ).
cnf(c_13116,plain,
( X0 != sK57
| sK57 != sK57
| sK57 = X0 ),
inference(instantiation,[status(thm)],[c_11834]) ).
cnf(c_13552,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(X0)
| ssList(cons(hd(sK55),X0)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_13554,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(nil)
| ssList(cons(hd(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_13552]) ).
cnf(c_14290,plain,
( X0 != sK55
| sK55 != sK55
| sK55 = X0 ),
inference(instantiation,[status(thm)],[c_12280]) ).
cnf(c_14462,plain,
( ~ memberP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X2)
| neq(X2,X0)
| memberP(X2,X1) ),
inference(resolution,[status(thm)],[c_13087,c_138]) ).
cnf(c_14721,plain,
( ~ neq(sK56,sK56)
| ~ ssList(sK56) ),
inference(instantiation,[status(thm)],[c_139]) ).
cnf(c_14839,plain,
( hd(sK55) != sK57
| sK57 != sK57
| sK57 = hd(sK55) ),
inference(instantiation,[status(thm)],[c_13116]) ).
cnf(c_14981,plain,
( ~ ssList(X0)
| ~ ssList(sK56)
| X0 = sK56
| neq(X0,sK56) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_15491,plain,
( ~ ssItem(nil)
| ~ ssItem(sK56)
| nil = sK55
| neq(sK56,nil) ),
inference(resolution,[status(thm)],[c_12527,c_248]) ).
cnf(c_15686,plain,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_15491,c_254,c_141,c_195,c_285,c_305,c_11267,c_12509,c_12614,c_12624]) ).
cnf(c_15693,plain,
( ~ neq(nil,sK55)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(backward_subsumption_resolution,[status(thm)],[c_11657,c_15686]) ).
cnf(c_15699,plain,
( cons(hd(sK55),tl(sK55)) != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(cons(hd(sK55),tl(sK55)),sK57) ),
inference(instantiation,[status(thm)],[c_12365]) ).
cnf(c_15740,plain,
app(tl(sK55),cons(hd(sK55),nil)) = sK56,
inference(global_subsumption_just,[status(thm)],[c_15693,c_255,c_254,c_141,c_195,c_285,c_305,c_11148,c_11187,c_11281,c_12274,c_12273,c_12509,c_12584,c_12589,c_12614]) ).
cnf(c_15747,plain,
( ~ ssList(sK56)
| ssList(app(tl(sK55),cons(hd(sK55),nil))) ),
inference(resolution,[status(thm)],[c_15740,c_7298]) ).
cnf(c_15748,plain,
sK56 = app(tl(sK55),cons(hd(sK55),nil)),
inference(resolution,[status(thm)],[c_15740,c_12247]) ).
cnf(c_15753,plain,
( ~ memberP(sK56,X0)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),X0) ),
inference(resolution,[status(thm)],[c_15740,c_13087]) ).
cnf(c_16079,plain,
( ~ memberP(cons(hd(sK55),X0),sK57)
| ~ ssItem(hd(sK55))
| ~ ssList(X0)
| ~ ssItem(sK57)
| hd(sK55) = sK57
| memberP(X0,sK57) ),
inference(instantiation,[status(thm)],[c_12366]) ).
cnf(c_18212,plain,
( cons(hd(sK55),tl(sK55)) != sK55
| sK55 != sK55
| sK55 = cons(hd(sK55),tl(sK55)) ),
inference(instantiation,[status(thm)],[c_14290]) ).
cnf(c_24061,plain,
( ~ ssList(X0)
| ~ ssList(sK56)
| X0 = app(tl(sK55),cons(hd(sK55),nil))
| neq(X0,sK56) ),
inference(resolution,[status(thm)],[c_12235,c_15740]) ).
cnf(c_24439,plain,
( ~ ssList(X0)
| X0 = app(tl(sK55),cons(hd(sK55),nil))
| neq(X0,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_24061,c_254,c_24061]) ).
cnf(c_24462,plain,
( ~ memberP(app(tl(sK55),cons(hd(sK55),nil)),X0)
| ~ ssList(X1)
| memberP(X1,X0)
| neq(X1,sK56) ),
inference(resolution,[status(thm)],[c_24439,c_13087]) ).
cnf(c_25941,plain,
( ~ memberP(sK56,X0)
| ~ ssList(X1)
| memberP(X1,X0)
| neq(X1,sK56) ),
inference(resolution,[status(thm)],[c_24462,c_15753]) ).
cnf(c_26073,plain,
( ~ ssList(X0)
| neq(X0,sK56)
| memberP(X0,sK57)
| memberP(sK55,sK57) ),
inference(resolution,[status(thm)],[c_25941,c_250]) ).
cnf(c_37694,plain,
( ~ memberP(cons(hd(sK55),tl(sK55)),sK57)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssItem(sK57)
| hd(sK55) = sK57
| memberP(tl(sK55),sK57) ),
inference(instantiation,[status(thm)],[c_16079]) ).
cnf(c_41199,plain,
( ~ memberP(sK56,X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),X1)
| neq(X1,X0) ),
inference(resolution,[status(thm)],[c_13076,c_15740]) ).
cnf(c_43253,plain,
( ~ ssItem(X0)
| ~ ssItem(sK57)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),X0)
| neq(X0,sK57)
| memberP(sK55,sK57) ),
inference(resolution,[status(thm)],[c_41199,c_250]) ).
cnf(c_43302,plain,
( ~ ssItem(X0)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),X0)
| neq(X0,sK57)
| memberP(sK55,sK57) ),
inference(global_subsumption_just,[status(thm)],[c_43253,c_251,c_43253]) ).
cnf(c_43354,plain,
( ~ ssList(cons(hd(sK55),nil))
| ~ ssList(tl(sK55))
| ~ ssItem(X0)
| memberP(cons(hd(sK55),nil),X0)
| memberP(tl(sK55),X0)
| neq(X0,sK57)
| memberP(sK55,sK57) ),
inference(resolution,[status(thm)],[c_43302,c_167]) ).
cnf(c_46567,plain,
( ~ ssItem(X0)
| memberP(cons(hd(sK55),nil),X0)
| memberP(tl(sK55),X0)
| neq(X0,sK57)
| memberP(sK55,sK57) ),
inference(global_subsumption_just,[status(thm)],[c_43354,c_255,c_141,c_195,c_285,c_305,c_11148,c_11281,c_12274,c_12273,c_12509,c_12589,c_12614,c_13554,c_43354]) ).
cnf(c_46590,plain,
( ~ ssItem(hd(sK55))
| ~ ssItem(X0)
| ~ ssList(nil)
| hd(sK55) = X0
| memberP(tl(sK55),X0)
| neq(X0,sK57)
| memberP(nil,X0)
| memberP(sK55,sK57) ),
inference(resolution,[status(thm)],[c_46567,c_170]) ).
cnf(c_66002,plain,
( neq(X0,sK57)
| memberP(tl(sK55),X0)
| hd(sK55) = X0
| ~ ssItem(X0)
| memberP(sK55,sK57) ),
inference(global_subsumption_just,[status(thm)],[c_46590,c_255,c_141,c_195,c_171,c_285,c_305,c_11148,c_11281,c_12274,c_12509,c_12589,c_12614,c_46590]) ).
cnf(c_66003,plain,
( ~ ssItem(X0)
| hd(sK55) = X0
| memberP(tl(sK55),X0)
| neq(X0,sK57)
| memberP(sK55,sK57) ),
inference(renaming,[status(thm)],[c_66002]) ).
cnf(c_66529,plain,
( ~ ssItem(X0)
| X0 = hd(sK55)
| memberP(tl(sK55),X0)
| neq(X0,sK57)
| memberP(sK55,sK57) ),
inference(resolution,[status(thm)],[c_66003,c_12247]) ).
cnf(c_69365,plain,
( ~ memberP(X0,sK57)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK57)
| memberP(app(X0,X1),sK57) ),
inference(instantiation,[status(thm)],[c_166]) ).
cnf(c_69931,plain,
( ~ ssList(app(X0,cons(hd(sK55),X1)))
| ~ ssItem(hd(sK55))
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(app(X0,cons(hd(sK55),X1)),hd(sK55)) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_79299,plain,
( ~ memberP(tl(sK55),sK57)
| ~ ssList(tl(sK55))
| ~ ssList(X0)
| ~ ssItem(sK57)
| memberP(app(tl(sK55),X0),sK57) ),
inference(instantiation,[status(thm)],[c_69365]) ).
cnf(c_100582,plain,
( cons(X0,X1) != X2
| X3 != X4
| ~ memberP(X2,X4)
| memberP(cons(X0,X1),X3) ),
inference(instantiation,[status(thm)],[c_7297]) ).
cnf(c_100584,plain,
( sK56 != X0
| sK57 != X1
| ~ memberP(X0,X1)
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_7297]) ).
cnf(c_102998,plain,
( sK56 != app(tl(sK55),cons(hd(sK55),nil))
| sK57 != X0
| ~ memberP(app(tl(sK55),cons(hd(sK55),nil)),X0)
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_100584]) ).
cnf(c_105492,plain,
( cons(hd(sK55),tl(sK55)) != sK55
| X0 != X1
| ~ memberP(sK55,X1)
| memberP(cons(hd(sK55),tl(sK55)),X0) ),
inference(instantiation,[status(thm)],[c_100582]) ).
cnf(c_106020,plain,
( ~ ssList(app(tl(sK55),cons(hd(sK55),nil)))
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssList(nil)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),hd(sK55)) ),
inference(instantiation,[status(thm)],[c_69931]) ).
cnf(c_114544,plain,
( sK56 != app(tl(sK55),cons(hd(sK55),nil))
| sK57 != sK57
| ~ memberP(app(tl(sK55),cons(hd(sK55),nil)),sK57)
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_102998]) ).
cnf(c_114545,plain,
( ~ ssList(cons(hd(sK55),nil))
| ~ memberP(tl(sK55),sK57)
| ~ ssList(tl(sK55))
| ~ ssItem(sK57)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),sK57) ),
inference(instantiation,[status(thm)],[c_79299]) ).
cnf(c_118960,plain,
( cons(hd(sK55),tl(sK55)) != sK55
| X0 != hd(sK55)
| ~ memberP(sK55,hd(sK55))
| memberP(cons(hd(sK55),tl(sK55)),X0) ),
inference(instantiation,[status(thm)],[c_105492]) ).
cnf(c_134022,plain,
( sK56 != app(tl(sK55),cons(hd(sK55),nil))
| sK57 != hd(sK55)
| ~ memberP(app(tl(sK55),cons(hd(sK55),nil)),hd(sK55))
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_102998]) ).
cnf(c_146220,plain,
( ~ ssList(X0)
| ~ ssList(sK56)
| neq(X0,sK56)
| memberP(X0,sK57)
| memberP(sK55,sK57) ),
inference(resolution,[status(thm)],[c_14462,c_250]) ).
cnf(c_148867,plain,
( memberP(X0,sK57)
| neq(X0,sK56)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_146220,c_255,c_254,c_251,c_141,c_250,c_195,c_285,c_305,c_11147,c_11191,c_11222,c_11224,c_11226,c_11235,c_11259,c_11281,c_11309,c_11390,c_11394,c_11527,c_11530,c_11932,c_12274,c_12273,c_12370,c_12415,c_12589,c_12614,c_13554,c_14839,c_14981,c_15699,c_15748,c_15747,c_26073,c_37694,c_106020,c_114544,c_114545,c_134022]) ).
cnf(c_148868,plain,
( ~ ssList(X0)
| neq(X0,sK56)
| memberP(X0,sK57) ),
inference(renaming,[status(thm)],[c_148867]) ).
cnf(c_148890,plain,
( ~ memberP(sK55,sK57)
| ~ ssList(sK56)
| neq(sK56,sK56) ),
inference(resolution,[status(thm)],[c_148868,c_249]) ).
cnf(c_148902,plain,
~ memberP(sK55,sK57),
inference(global_subsumption_just,[status(thm)],[c_148890,c_254,c_14721,c_148890]) ).
cnf(c_150394,plain,
( ~ ssItem(X0)
| X0 = hd(sK55)
| memberP(tl(sK55),X0)
| neq(X0,sK57) ),
inference(backward_subsumption_resolution,[status(thm)],[c_66529,c_148902]) ).
cnf(c_171589,plain,
( sK55 != X0
| sK57 != X1
| ~ memberP(X0,X1)
| memberP(sK55,sK57) ),
inference(instantiation,[status(thm)],[c_7297]) ).
cnf(c_177562,plain,
( sK55 != sK55
| sK57 != X0
| ~ memberP(sK55,X0)
| memberP(sK55,sK57) ),
inference(instantiation,[status(thm)],[c_171589]) ).
cnf(c_178631,plain,
( sK55 != cons(hd(sK55),tl(sK55))
| sK57 != X0
| ~ memberP(cons(hd(sK55),tl(sK55)),X0)
| memberP(sK55,sK57) ),
inference(instantiation,[status(thm)],[c_171589]) ).
cnf(c_255522,plain,
( ~ ssItem(X0)
| neq(X0,sK57) ),
inference(global_subsumption_just,[status(thm)],[c_150394,c_255,c_254,c_251,c_141,c_195,c_285,c_305,c_11148,c_11222,c_11235,c_11251,c_11253,c_11257,c_11281,c_11390,c_12274,c_12273,c_12279,c_12509,c_12589,c_12614,c_13116,c_14721,c_18212,c_66529,c_118960,c_148890,c_177562,c_178631]) ).
cnf(c_255532,plain,
~ ssItem(sK57),
inference(resolution,[status(thm)],[c_255522,c_50]) ).
cnf(c_255534,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_255532,c_251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC376+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 17:16:55 EDT 2023
% 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 --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 165.85/22.83 % SZS status Started for theBenchmark.p
% 165.85/22.83 % SZS status Theorem for theBenchmark.p
% 165.85/22.83
% 165.85/22.83 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 165.85/22.83
% 165.85/22.83 ------ iProver source info
% 165.85/22.83
% 165.85/22.83 git: date: 2023-05-31 18:12:56 +0000
% 165.85/22.83 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 165.85/22.83 git: non_committed_changes: false
% 165.85/22.83 git: last_make_outside_of_git: false
% 165.85/22.83
% 165.85/22.83 ------ Parsing...
% 165.85/22.83 ------ Clausification by vclausify_rel & Parsing by iProver...
% 165.85/22.83
% 165.85/22.83 ------ 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
% 165.85/22.83
% 165.85/22.83 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 165.85/22.83
% 165.85/22.83 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 165.85/22.83 ------ Proving...
% 165.85/22.83 ------ Problem Properties
% 165.85/22.83
% 165.85/22.83
% 165.85/22.83 clauses 192
% 165.85/22.83 conjectures 7
% 165.85/22.83 EPR 60
% 165.85/22.83 Horn 121
% 165.85/22.83 unary 19
% 165.85/22.83 binary 46
% 165.85/22.83 lits 647
% 165.85/22.83 lits eq 83
% 165.85/22.83 fd_pure 0
% 165.85/22.83 fd_pseudo 0
% 165.85/22.83 fd_cond 21
% 165.85/22.83 fd_pseudo_cond 16
% 165.85/22.83 AC symbols 0
% 165.85/22.83
% 165.85/22.83 ------ Input Options Time Limit: Unbounded
% 165.85/22.83
% 165.85/22.83
% 165.85/22.83 ------
% 165.85/22.83 Current options:
% 165.85/22.83 ------
% 165.85/22.83
% 165.85/22.83
% 165.85/22.83
% 165.85/22.83
% 165.85/22.83 ------ Proving...
% 165.85/22.83
% 165.85/22.83
% 165.85/22.83 ------ Proving...
% 165.85/22.83
% 165.85/22.83
% 165.85/22.83 % SZS status Theorem for theBenchmark.p
% 165.85/22.83
% 165.85/22.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 165.85/22.83
% 165.85/22.83
%------------------------------------------------------------------------------