TSTP Solution File: SWC083+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC083+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 03:11:09 EDT 2024
% Result : Theorem 10.21s 2.13s
% Output : CNFRefutation 10.21s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( app(X5,X7) != X3
| app(app(X5,X6),X7) != X2
| ~ ssList(X7) ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| 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] :
( ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( app(X5,X7) != X3
| app(app(X5,X6),X7) != X2
| ~ ssList(X7) ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( app(X4,X6) != X3
| app(app(X4,X5),X6) != X2
| ~ ssList(X6) ) ) )
| ? [X7] :
( segmentP(X0,X7)
& segmentP(X1,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(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(f104,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f135,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f155,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f173,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f202,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(X0,X7)
| ~ segmentP(X1,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f245,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(f246,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,[],[f245]) ).
fof(f247,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f248,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])],[f246,f247]) ).
fof(f253,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f254,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f253]) ).
fof(f255,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK13(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f256,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK13(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1))
& ssList(sK13(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f254,f256,f255]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f343,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(X0,X7)
| ~ segmentP(X1,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(X1,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(X1,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(X1,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(X1,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(sK54,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(sK54,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(sK54,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(sK54,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = sK55
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(sK54,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X3
& app(app(X4,X5),X6) = sK55
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(sK54,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = sK56
& app(app(X4,X5),X6) = sK55
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(sK54,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = sK56
& app(app(X4,X5),X6) = sK55
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ? [X6] :
( sK56 = app(sK57,X6)
& sK55 = app(app(sK57,X5),X6)
& ssList(X6) )
& ssList(X5) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X5] :
( ? [X6] :
( sK56 = app(sK57,X6)
& sK55 = app(app(sK57,X5),X6)
& ssList(X6) )
& ssList(X5) )
=> ( ? [X6] :
( sK56 = app(sK57,X6)
& sK55 = app(app(sK57,sK58),X6)
& ssList(X6) )
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ? [X6] :
( sK56 = app(sK57,X6)
& sK55 = app(app(sK57,sK58),X6)
& ssList(X6) )
=> ( sK56 = app(sK57,sK59)
& sK55 = app(app(sK57,sK58),sK59)
& ssList(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
( sK56 = app(sK57,sK59)
& sK55 = app(app(sK57,sK58),sK59)
& ssList(sK59)
& ssList(sK58)
& ssList(sK57)
& ! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(sK54,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) )
& 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,sK57,sK58,sK59])],[f222,f349,f348,f347,f346,f345,f344,f343]) ).
fof(f363,plain,
! [X0,X1] :
( ssList(sK11(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f364,plain,
! [X0,X1] :
( app(X1,sK11(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f365,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f372,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f257]) ).
fof(f441,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f443,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f455,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f457,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f478,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f494,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f536,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f550,plain,
ssList(sK53),
inference(cnf_transformation,[],[f350]) ).
fof(f551,plain,
ssList(sK54),
inference(cnf_transformation,[],[f350]) ).
fof(f554,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f350]) ).
fof(f555,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f350]) ).
fof(f556,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f350]) ).
fof(f557,plain,
! [X7] :
( ~ segmentP(sK53,X7)
| ~ segmentP(sK54,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) ),
inference(cnf_transformation,[],[f350]) ).
fof(f558,plain,
ssList(sK57),
inference(cnf_transformation,[],[f350]) ).
fof(f559,plain,
ssList(sK58),
inference(cnf_transformation,[],[f350]) ).
fof(f560,plain,
ssList(sK59),
inference(cnf_transformation,[],[f350]) ).
fof(f561,plain,
sK55 = app(app(sK57,sK58),sK59),
inference(cnf_transformation,[],[f350]) ).
fof(f562,plain,
sK56 = app(sK57,sK59),
inference(cnf_transformation,[],[f350]) ).
fof(f563,plain,
! [X7] :
( ~ segmentP(sK55,X7)
| ~ segmentP(sK56,X7)
| ~ neq(X7,nil)
| ~ ssList(X7) ),
inference(definition_unfolding,[],[f557,f555,f554]) ).
fof(f564,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f556,f554]) ).
fof(f565,plain,
ssList(sK56),
inference(definition_unfolding,[],[f551,f554]) ).
fof(f566,plain,
ssList(sK55),
inference(definition_unfolding,[],[f550,f555]) ).
fof(f570,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f365]) ).
fof(f572,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f372]) ).
cnf(c_61,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f570]) ).
cnf(c_62,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f364]) ).
cnf(c_63,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f363]) ).
cnf(c_67,plain,
( ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f572]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f443]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f455]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f457]) ).
cnf(c_176,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f478]) ).
cnf(c_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f494]) ).
cnf(c_232,plain,
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f536]) ).
cnf(c_246,negated_conjecture,
app(sK57,sK59) = sK56,
inference(cnf_transformation,[],[f562]) ).
cnf(c_247,negated_conjecture,
app(app(sK57,sK58),sK59) = sK55,
inference(cnf_transformation,[],[f561]) ).
cnf(c_248,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f560]) ).
cnf(c_249,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f559]) ).
cnf(c_250,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f558]) ).
cnf(c_251,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f563]) ).
cnf(c_252,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f564]) ).
cnf(c_255,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f565]) ).
cnf(c_256,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f566]) ).
cnf(c_378,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
cnf(c_3224,plain,
( X0 != X1
| X2 != nil
| ~ segmentP(sK56,X1)
| ~ segmentP(sK55,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X2 ),
inference(resolution_lifted,[status(thm)],[c_138,c_251]) ).
cnf(c_3225,plain,
( ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| X0 = nil ),
inference(unflattening,[status(thm)],[c_3224]) ).
cnf(c_3227,plain,
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| X0 = nil ),
inference(global_subsumption_just,[status(thm)],[c_3225,c_141,c_3225]) ).
cnf(c_3228,plain,
( ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(renaming,[status(thm)],[c_3227]) ).
cnf(c_3255,plain,
( X0 != sK56
| nil != nil
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_251,c_252]) ).
cnf(c_3256,plain,
( ~ segmentP(sK56,sK56)
| ~ segmentP(sK55,sK56)
| ~ ssList(sK56) ),
inference(unflattening,[status(thm)],[c_3255]) ).
cnf(c_3257,plain,
( ~ segmentP(sK55,sK56)
| ~ segmentP(sK56,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_3256,c_255,c_3256]) ).
cnf(c_3258,plain,
( ~ segmentP(sK56,sK56)
| ~ segmentP(sK55,sK56) ),
inference(renaming,[status(thm)],[c_3257]) ).
cnf(c_8883,plain,
app(sK57,sK58) = sP0_iProver_def,
definition ).
cnf(c_8884,plain,
app(sP0_iProver_def,sK59) = sP1_iProver_def,
definition ).
cnf(c_8885,plain,
app(sK57,sK59) = sP2_iProver_def,
definition ).
cnf(c_8886,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_256]) ).
cnf(c_8887,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_255]) ).
cnf(c_8888,negated_conjecture,
ssList(sK57),
inference(demodulation,[status(thm)],[c_250]) ).
cnf(c_8889,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_249]) ).
cnf(c_8890,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_248]) ).
cnf(c_8891,negated_conjecture,
sP1_iProver_def = sK55,
inference(demodulation,[status(thm)],[c_247,c_8883,c_8884]) ).
cnf(c_8892,negated_conjecture,
sP2_iProver_def = sK56,
inference(demodulation,[status(thm)],[c_246,c_8885]) ).
cnf(c_11732,plain,
ssList(sP1_iProver_def),
inference(light_normalisation,[status(thm)],[c_8886,c_8891]) ).
cnf(c_11733,plain,
ssList(sP2_iProver_def),
inference(light_normalisation,[status(thm)],[c_8887,c_8892]) ).
cnf(c_11735,plain,
( ~ segmentP(sP1_iProver_def,sP2_iProver_def)
| ~ segmentP(sP2_iProver_def,sP2_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_3258,c_8891,c_8892]) ).
cnf(c_11738,plain,
( ~ segmentP(sP1_iProver_def,X0)
| ~ segmentP(sP2_iProver_def,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(light_normalisation,[status(thm)],[c_3228,c_8891,c_8892]) ).
cnf(c_11831,plain,
( ~ segmentP(sP1_iProver_def,sP2_iProver_def)
| ~ ssList(sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_192,c_11735]) ).
cnf(c_11833,plain,
~ segmentP(sP1_iProver_def,sP2_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_11831,c_11733]) ).
cnf(c_12061,plain,
app(nil,sK59) = sK59,
inference(superposition,[status(thm)],[c_8890,c_155]) ).
cnf(c_12063,plain,
app(nil,sK57) = sK57,
inference(superposition,[status(thm)],[c_8888,c_155]) ).
cnf(c_12151,plain,
app(sP1_iProver_def,nil) = sP1_iProver_def,
inference(superposition,[status(thm)],[c_11732,c_232]) ).
cnf(c_12276,plain,
( ~ ssList(sK57)
| ~ ssList(sK58)
| ssList(sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_8883,c_153]) ).
cnf(c_12290,plain,
ssList(sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_12276,c_8889,c_8888]) ).
cnf(c_13179,plain,
( ~ ssList(sK57)
| ~ ssList(sK58)
| frontsegP(sP0_iProver_def,sK57) ),
inference(superposition,[status(thm)],[c_8883,c_378]) ).
cnf(c_13218,plain,
frontsegP(sP0_iProver_def,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_13179,c_8889,c_8888]) ).
cnf(c_18537,plain,
( ~ frontsegP(sP0_iProver_def,X0)
| ~ ssList(X0)
| ~ ssList(sK59)
| ~ ssList(sP0_iProver_def)
| frontsegP(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_8884,c_176]) ).
cnf(c_18614,plain,
( ~ frontsegP(sP0_iProver_def,X0)
| ~ ssList(X0)
| frontsegP(sP1_iProver_def,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18537,c_12290,c_8890]) ).
cnf(c_21760,plain,
( ~ ssList(sK57)
| frontsegP(sP1_iProver_def,sK57) ),
inference(superposition,[status(thm)],[c_13218,c_18614]) ).
cnf(c_21763,plain,
frontsegP(sP1_iProver_def,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_21760,c_8888]) ).
cnf(c_21766,plain,
( ~ ssList(sK57)
| ~ ssList(sP1_iProver_def)
| app(sK57,sK11(sP1_iProver_def,sK57)) = sP1_iProver_def ),
inference(superposition,[status(thm)],[c_21763,c_62]) ).
cnf(c_21767,plain,
app(sK57,sK11(sP1_iProver_def,sK57)) = sP1_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_21766,c_11732,c_8888]) ).
cnf(c_27951,plain,
( ~ ssList(app(app(sP0_iProver_def,sK59),X0))
| ~ ssList(X0)
| ~ ssList(sK59)
| ~ ssList(sP0_iProver_def)
| segmentP(app(sP1_iProver_def,X0),sK59) ),
inference(superposition,[status(thm)],[c_8884,c_67]) ).
cnf(c_27954,plain,
( ~ ssList(app(app(nil,sK57),X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK57)
| segmentP(app(sK57,X0),sK57) ),
inference(superposition,[status(thm)],[c_12063,c_67]) ).
cnf(c_28080,plain,
( ~ ssList(app(sK57,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK57)
| segmentP(app(sK57,X0),sK57) ),
inference(light_normalisation,[status(thm)],[c_27954,c_12063]) ).
cnf(c_28081,plain,
( ~ ssList(app(sK57,X0))
| ~ ssList(X0)
| segmentP(app(sK57,X0),sK57) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28080,c_8888,c_141]) ).
cnf(c_28095,plain,
( ~ ssList(app(sP1_iProver_def,X0))
| ~ ssList(X0)
| ~ ssList(sK59)
| ~ ssList(sP0_iProver_def)
| segmentP(app(sP1_iProver_def,X0),sK59) ),
inference(light_normalisation,[status(thm)],[c_27951,c_8884]) ).
cnf(c_28096,plain,
( ~ ssList(app(sP1_iProver_def,X0))
| ~ ssList(X0)
| segmentP(app(sP1_iProver_def,X0),sK59) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28095,c_12290,c_8890]) ).
cnf(c_29987,plain,
( ~ ssList(app(sK57,sK59))
| ~ ssList(sK59)
| segmentP(sP2_iProver_def,sK57) ),
inference(superposition,[status(thm)],[c_8885,c_28081]) ).
cnf(c_29993,plain,
( ~ ssList(app(sK57,sK11(sP1_iProver_def,sK57)))
| ~ ssList(sK11(sP1_iProver_def,sK57))
| segmentP(sP1_iProver_def,sK57) ),
inference(superposition,[status(thm)],[c_21767,c_28081]) ).
cnf(c_30001,plain,
( ~ ssList(sK59)
| ~ ssList(sP2_iProver_def)
| segmentP(sP2_iProver_def,sK57) ),
inference(light_normalisation,[status(thm)],[c_29987,c_8885]) ).
cnf(c_30002,plain,
segmentP(sP2_iProver_def,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_30001,c_11733,c_8890]) ).
cnf(c_30003,plain,
( ~ ssList(sK11(sP1_iProver_def,sK57))
| ~ ssList(sP1_iProver_def)
| segmentP(sP1_iProver_def,sK57) ),
inference(light_normalisation,[status(thm)],[c_29993,c_21767]) ).
cnf(c_30004,plain,
( ~ ssList(sK11(sP1_iProver_def,sK57))
| segmentP(sP1_iProver_def,sK57) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30003,c_11732]) ).
cnf(c_30042,plain,
( ~ segmentP(sP1_iProver_def,sK57)
| ~ ssList(sK57)
| nil = sK57 ),
inference(superposition,[status(thm)],[c_30002,c_11738]) ).
cnf(c_30043,plain,
( ~ segmentP(sP1_iProver_def,sK57)
| nil = sK57 ),
inference(forward_subsumption_resolution,[status(thm)],[c_30042,c_8888]) ).
cnf(c_31021,plain,
( ~ frontsegP(sP1_iProver_def,sK57)
| ~ ssList(sK57)
| ~ ssList(sP1_iProver_def)
| segmentP(sP1_iProver_def,sK57) ),
inference(superposition,[status(thm)],[c_63,c_30004]) ).
cnf(c_31022,plain,
segmentP(sP1_iProver_def,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_31021,c_11732,c_8888,c_21763]) ).
cnf(c_31039,plain,
nil = sK57,
inference(global_subsumption_just,[status(thm)],[c_30043,c_30043,c_31022]) ).
cnf(c_31101,plain,
app(nil,sK59) = sP2_iProver_def,
inference(demodulation,[status(thm)],[c_8885,c_31039]) ).
cnf(c_31105,plain,
sK59 = sP2_iProver_def,
inference(light_normalisation,[status(thm)],[c_31101,c_12061]) ).
cnf(c_31733,plain,
( ~ ssList(app(sP1_iProver_def,X0))
| ~ ssList(X0)
| segmentP(app(sP1_iProver_def,X0),sP2_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_28096,c_31105]) ).
cnf(c_31740,plain,
( ~ ssList(app(sP1_iProver_def,nil))
| ~ ssList(nil)
| segmentP(sP1_iProver_def,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_12151,c_31733]) ).
cnf(c_31745,plain,
( ~ ssList(nil)
| ~ ssList(sP1_iProver_def)
| segmentP(sP1_iProver_def,sP2_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_31740,c_12151]) ).
cnf(c_31746,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_31745,c_11833,c_11732,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC083+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu May 2 23:29:01 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 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
% 10.21/2.13 % SZS status Started for theBenchmark.p
% 10.21/2.13 % SZS status Theorem for theBenchmark.p
% 10.21/2.13
% 10.21/2.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.21/2.13
% 10.21/2.13 ------ iProver source info
% 10.21/2.13
% 10.21/2.13 git: date: 2024-05-02 19:28:25 +0000
% 10.21/2.13 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 10.21/2.13 git: non_committed_changes: false
% 10.21/2.13
% 10.21/2.13 ------ Parsing...
% 10.21/2.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.21/2.13
% 10.21/2.13 ------ 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
% 10.21/2.13
% 10.21/2.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.21/2.13
% 10.21/2.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.21/2.13 ------ Proving...
% 10.21/2.13 ------ Problem Properties
% 10.21/2.13
% 10.21/2.13
% 10.21/2.13 clauses 193
% 10.21/2.13 conjectures 7
% 10.21/2.13 EPR 59
% 10.21/2.13 Horn 125
% 10.21/2.13 unary 27
% 10.21/2.13 binary 41
% 10.21/2.13 lits 635
% 10.21/2.13 lits eq 85
% 10.21/2.13 fd_pure 0
% 10.21/2.13 fd_pseudo 0
% 10.21/2.13 fd_cond 22
% 10.21/2.13 fd_pseudo_cond 14
% 10.21/2.13 AC symbols 0
% 10.21/2.13
% 10.21/2.13 ------ Schedule dynamic 5 is on
% 10.21/2.13
% 10.21/2.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.21/2.13
% 10.21/2.13
% 10.21/2.13 ------
% 10.21/2.13 Current options:
% 10.21/2.13 ------
% 10.21/2.13
% 10.21/2.13
% 10.21/2.13
% 10.21/2.13
% 10.21/2.13 ------ Proving...
% 10.21/2.13
% 10.21/2.13
% 10.21/2.13 % SZS status Theorem for theBenchmark.p
% 10.21/2.13
% 10.21/2.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.21/2.13
% 10.21/2.13
%------------------------------------------------------------------------------