TSTP Solution File: SWC063+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC063+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:40:42 EDT 2023
% Result : Theorem 17.70s 3.08s
% Output : CNFRefutation 17.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 18
% Syntax : Number of formulae : 151 ( 36 unt; 0 def)
% Number of atoms : 657 ( 195 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 833 ( 327 ~; 303 |; 166 &)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 199 ( 0 sgn; 94 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2
| ~ ssList(X6) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(rectify,[],[f97]) ).
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(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(f135,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f173,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f202,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
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] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = sK55 )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = sK55 )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(sK56,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = sK56
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = sK56
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) )
=> ( ? [X6] :
( sK56 = app(X6,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),X6)
& ssList(X6) )
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X6] :
( sK56 = app(X6,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),X6)
& ssList(X6) )
=> ( sK56 = app(sK58,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(sK56,nil)
| ( sK56 = app(sK58,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),sK58)
& ssList(sK58)
& ssItem(sK57) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f222,f348,f347,f346,f345,f344,f343]) ).
fof(f371,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(f440,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f441,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f442,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f449,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f456,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f493,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f530,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f535,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
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,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
( ~ neq(sK56,nil)
| sK55 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
( ~ neq(sK56,nil)
| sK56 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f560,plain,
( neq(sK54,nil)
| nil = sK54 ),
inference(cnf_transformation,[],[f349]) ).
fof(f561,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f349]) ).
fof(f562,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK54 ),
inference(cnf_transformation,[],[f349]) ).
fof(f563,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK53 ),
inference(cnf_transformation,[],[f349]) ).
fof(f564,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK55 ),
inference(definition_unfolding,[],[f563,f554,f553,f554]) ).
fof(f565,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK56 ),
inference(definition_unfolding,[],[f562,f554,f553,f553]) ).
fof(f566,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f561,f553,f554]) ).
fof(f567,plain,
( neq(sK56,nil)
| nil = sK56 ),
inference(definition_unfolding,[],[f560,f553,f553]) ).
fof(f568,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
fof(f569,plain,
ssList(sK55),
inference(definition_unfolding,[],[f549,f554]) ).
fof(f575,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,[],[f371]) ).
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,[],[f575]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f442]) ).
cnf(c_148,plain,
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f449]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f456]) ).
cnf(c_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f493]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f530]) ).
cnf(c_232,plain,
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f535]) ).
cnf(c_246,negated_conjecture,
( nil != sK55
| ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f564]) ).
cnf(c_247,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| nil = sK56 ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_248,negated_conjecture,
( nil != sK55
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_249,negated_conjecture,
( nil = sK56
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f567]) ).
cnf(c_250,negated_conjecture,
( ~ neq(sK56,nil)
| app(sK58,cons(sK57,nil)) = sK56 ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_251,negated_conjecture,
( ~ neq(sK56,nil)
| app(cons(sK57,nil),sK58) = sK55 ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_252,negated_conjecture,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f557]) ).
cnf(c_253,negated_conjecture,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f556]) ).
cnf(c_254,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_257,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f568]) ).
cnf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f569]) ).
cnf(c_367,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_249,c_248,c_254]) ).
cnf(c_369,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_249,c_248,c_254]) ).
cnf(c_377,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_249,c_248,c_254]) ).
cnf(c_387,negated_conjecture,
app(cons(sK57,nil),sK58) = sK55,
inference(global_subsumption_just,[status(thm)],[c_251,c_249,c_248,c_254,c_251]) ).
cnf(c_389,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK56,
inference(global_subsumption_just,[status(thm)],[c_250,c_250,c_377]) ).
cnf(c_397,plain,
( ~ ssList(X0)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ neq(X0,nil) ),
inference(global_subsumption_just,[status(thm)],[c_247,c_254,c_247,c_246]) ).
cnf(c_398,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(renaming,[status(thm)],[c_397]) ).
cnf(c_399,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_246,c_398]) ).
cnf(c_2609,plain,
( X0 != X1
| X2 != nil
| ~ segmentP(sK55,X1)
| ~ segmentP(sK56,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X2 ),
inference(resolution_lifted,[status(thm)],[c_138,c_399]) ).
cnf(c_2610,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| X0 = nil ),
inference(unflattening,[status(thm)],[c_2609]) ).
cnf(c_2612,plain,
( ~ ssList(X0)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| X0 = nil ),
inference(global_subsumption_just,[status(thm)],[c_2610,c_141,c_2610]) ).
cnf(c_2613,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(renaming,[status(thm)],[c_2612]) ).
cnf(c_7660,plain,
( ~ segmentP(sK55,X0_13)
| ~ segmentP(sK56,X0_13)
| ~ ssList(X0_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_2613]) ).
cnf(c_7669,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK56,
inference(subtyping,[status(esa)],[c_389]) ).
cnf(c_7670,negated_conjecture,
app(cons(sK57,nil),sK58) = sK55,
inference(subtyping,[status(esa)],[c_387]) ).
cnf(c_7675,negated_conjecture,
ssList(sK58),
inference(subtyping,[status(esa)],[c_369]) ).
cnf(c_7676,negated_conjecture,
ssItem(sK57),
inference(subtyping,[status(esa)],[c_367]) ).
cnf(c_7677,negated_conjecture,
ssList(sK55),
inference(subtyping,[status(esa)],[c_258]) ).
cnf(c_7678,negated_conjecture,
ssList(sK56),
inference(subtyping,[status(esa)],[c_257]) ).
cnf(c_7690,plain,
( ~ ssList(X0_13)
| app(X0_13,nil) = X0_13 ),
inference(subtyping,[status(esa)],[c_232]) ).
cnf(c_7694,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| app(cons(X0_14,nil),X0_13) = cons(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_227]) ).
cnf(c_7720,plain,
( ~ ssList(X0_13)
| segmentP(X0_13,X0_13) ),
inference(subtyping,[status(esa)],[c_192]) ).
cnf(c_7755,plain,
( ~ ssList(X0_13)
| app(nil,X0_13) = X0_13 ),
inference(subtyping,[status(esa)],[c_155]) ).
cnf(c_7762,plain,
( cons(X0_14,X0_13) != nil
| ~ ssItem(X0_14)
| ~ ssList(X0_13) ),
inference(subtyping,[status(esa)],[c_148]) ).
cnf(c_7769,plain,
ssList(nil),
inference(subtyping,[status(esa)],[c_141]) ).
cnf(c_7770,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ssList(cons(X0_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_7832,plain,
( ~ ssList(app(app(X0_13,X1_13),X2_13))
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| segmentP(app(app(X0_13,X1_13),X2_13),X1_13) ),
inference(subtyping,[status(esa)],[c_67]) ).
cnf(c_19189,plain,
app(sK56,nil) = sK56,
inference(superposition,[status(thm)],[c_7678,c_7690]) ).
cnf(c_19190,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_7677,c_7690]) ).
cnf(c_19217,plain,
( ~ ssItem(X0_14)
| app(cons(X0_14,nil),sK58) = cons(X0_14,sK58) ),
inference(superposition,[status(thm)],[c_7675,c_7694]) ).
cnf(c_19350,plain,
app(nil,sK58) = sK58,
inference(superposition,[status(thm)],[c_7675,c_7755]) ).
cnf(c_19531,plain,
( ~ ssList(app(app(sK58,cons(sK57,nil)),X0_13))
| ~ ssList(cons(sK57,nil))
| ~ ssList(X0_13)
| ~ ssList(sK58)
| segmentP(app(sK56,X0_13),cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_7669,c_7832]) ).
cnf(c_19532,plain,
( ~ ssList(app(app(cons(sK57,nil),sK58),X0_13))
| ~ ssList(cons(sK57,nil))
| ~ ssList(X0_13)
| ~ ssList(sK58)
| segmentP(app(sK55,X0_13),sK58) ),
inference(superposition,[status(thm)],[c_7670,c_7832]) ).
cnf(c_19538,plain,
( ~ ssList(app(app(cons(sK57,nil),sK58),X0_13))
| ~ ssList(cons(sK57,nil))
| ~ ssList(X0_13)
| segmentP(app(sK55,X0_13),sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19532,c_7675]) ).
cnf(c_19539,plain,
( ~ ssList(app(sK55,X0_13))
| ~ ssList(cons(sK57,nil))
| ~ ssList(X0_13)
| segmentP(app(sK55,X0_13),sK58) ),
inference(demodulation,[status(thm)],[c_19538,c_7670]) ).
cnf(c_19540,plain,
( ~ ssList(app(app(sK58,cons(sK57,nil)),X0_13))
| ~ ssList(cons(sK57,nil))
| ~ ssList(X0_13)
| segmentP(app(sK56,X0_13),cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19531,c_7675]) ).
cnf(c_19541,plain,
( ~ ssList(app(sK56,X0_13))
| ~ ssList(cons(sK57,nil))
| ~ ssList(X0_13)
| segmentP(app(sK56,X0_13),cons(sK57,nil)) ),
inference(demodulation,[status(thm)],[c_19540,c_7669]) ).
cnf(c_19767,plain,
app(cons(sK57,nil),sK58) = cons(sK57,sK58),
inference(superposition,[status(thm)],[c_7676,c_19217]) ).
cnf(c_19777,plain,
cons(sK57,sK58) = sK55,
inference(demodulation,[status(thm)],[c_19767,c_7670]) ).
cnf(c_20216,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(app(sK55,nil))
| ~ ssList(nil)
| segmentP(sK55,sK58) ),
inference(superposition,[status(thm)],[c_19190,c_19539]) ).
cnf(c_20221,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(app(sK55,nil))
| segmentP(sK55,sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20216,c_7769]) ).
cnf(c_20222,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(sK55)
| segmentP(sK55,sK58) ),
inference(demodulation,[status(thm)],[c_20221,c_19190]) ).
cnf(c_20223,plain,
( ~ ssList(cons(sK57,nil))
| segmentP(sK55,sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20222,c_7677]) ).
cnf(c_20320,plain,
( ~ ssList(app(app(nil,sK58),X0_13))
| ~ ssList(X0_13)
| ~ ssList(nil)
| ~ ssList(sK58)
| segmentP(app(sK58,X0_13),sK58) ),
inference(superposition,[status(thm)],[c_19350,c_7832]) ).
cnf(c_20337,plain,
( ~ ssList(app(app(nil,sK58),X0_13))
| ~ ssList(X0_13)
| segmentP(app(sK58,X0_13),sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20320,c_7675,c_7769]) ).
cnf(c_20338,plain,
( ~ ssList(app(sK58,X0_13))
| ~ ssList(X0_13)
| segmentP(app(sK58,X0_13),sK58) ),
inference(demodulation,[status(thm)],[c_20337,c_19350]) ).
cnf(c_20673,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(app(sK56,nil))
| ~ ssList(nil)
| segmentP(sK56,cons(sK57,nil)) ),
inference(superposition,[status(thm)],[c_19189,c_19541]) ).
cnf(c_20678,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(app(sK56,nil))
| segmentP(sK56,cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20673,c_7769]) ).
cnf(c_20679,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(sK56)
| segmentP(sK56,cons(sK57,nil)) ),
inference(demodulation,[status(thm)],[c_20678,c_19189]) ).
cnf(c_20680,plain,
( ~ ssList(cons(sK57,nil))
| segmentP(sK56,cons(sK57,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20679,c_7678]) ).
cnf(c_20748,plain,
( nil != sK55
| ~ ssItem(sK57)
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_19777,c_7762]) ).
cnf(c_20752,plain,
nil != sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_20748,c_7675,c_7676]) ).
cnf(c_23742,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| segmentP(sK55,sK58) ),
inference(superposition,[status(thm)],[c_7770,c_20223]) ).
cnf(c_23743,plain,
segmentP(sK55,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_23742,c_7769,c_7676]) ).
cnf(c_25414,plain,
( ~ ssList(app(sK58,cons(sK57,nil)))
| ~ ssList(cons(sK57,nil))
| segmentP(sK56,sK58) ),
inference(superposition,[status(thm)],[c_7669,c_20338]) ).
cnf(c_25457,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(sK56)
| segmentP(sK56,sK58) ),
inference(demodulation,[status(thm)],[c_25414,c_7669]) ).
cnf(c_25458,plain,
( ~ ssList(cons(sK57,nil))
| segmentP(sK56,sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25457,c_7678]) ).
cnf(c_31586,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| segmentP(sK56,sK58) ),
inference(superposition,[status(thm)],[c_7770,c_25458]) ).
cnf(c_31587,plain,
segmentP(sK56,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_31586,c_7769,c_7676]) ).
cnf(c_31588,plain,
( ~ segmentP(sK55,sK58)
| ~ ssList(sK58)
| nil = sK58 ),
inference(superposition,[status(thm)],[c_31587,c_7660]) ).
cnf(c_31638,plain,
nil = sK58,
inference(forward_subsumption_resolution,[status(thm)],[c_31588,c_7675,c_23743]) ).
cnf(c_31756,plain,
( ~ ssList(cons(sK57,nil))
| segmentP(sK56,cons(sK57,sK58)) ),
inference(superposition,[status(thm)],[c_31638,c_20680]) ).
cnf(c_31814,plain,
( ~ ssList(sK55)
| segmentP(sK56,sK55) ),
inference(demodulation,[status(thm)],[c_31756,c_19777,c_31638]) ).
cnf(c_31815,plain,
segmentP(sK56,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_31814,c_7677]) ).
cnf(c_34553,plain,
( ~ segmentP(sK55,sK55)
| ~ ssList(sK55)
| nil = sK55 ),
inference(superposition,[status(thm)],[c_31815,c_7660]) ).
cnf(c_34607,plain,
~ segmentP(sK55,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_34553,c_20752,c_7677]) ).
cnf(c_35368,plain,
~ ssList(sK55),
inference(superposition,[status(thm)],[c_7720,c_34607]) ).
cnf(c_35369,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_35368,c_7677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWC063+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.11 % Command : run_iprover %s %d THM
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.30 % CPULimit : 300
% 0.15/0.30 % WCLimit : 300
% 0.15/0.30 % DateTime : Mon Aug 28 16:45:31 EDT 2023
% 0.15/0.30 % CPUTime :
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.70/3.08 % SZS status Started for theBenchmark.p
% 17.70/3.08 % SZS status Theorem for theBenchmark.p
% 17.70/3.08
% 17.70/3.08 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.70/3.08
% 17.70/3.08 ------ iProver source info
% 17.70/3.08
% 17.70/3.08 git: date: 2023-05-31 18:12:56 +0000
% 17.70/3.08 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.70/3.08 git: non_committed_changes: false
% 17.70/3.08 git: last_make_outside_of_git: false
% 17.70/3.08
% 17.70/3.08 ------ Parsing...
% 17.70/3.08 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.70/3.08
% 17.70/3.08 ------ 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
% 17.70/3.08
% 17.70/3.08 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.70/3.08
% 17.70/3.08 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.70/3.08 ------ Proving...
% 17.70/3.08 ------ Problem Properties
% 17.70/3.08
% 17.70/3.08
% 17.70/3.08 clauses 189
% 17.70/3.08 conjectures 6
% 17.70/3.08 EPR 56
% 17.70/3.08 Horn 121
% 17.70/3.08 unary 23
% 17.70/3.08 binary 41
% 17.70/3.08 lits 631
% 17.70/3.08 lits eq 82
% 17.70/3.08 fd_pure 0
% 17.70/3.08 fd_pseudo 0
% 17.70/3.08 fd_cond 22
% 17.70/3.08 fd_pseudo_cond 14
% 17.70/3.08 AC symbols 0
% 17.70/3.08
% 17.70/3.08 ------ Input Options Time Limit: Unbounded
% 17.70/3.08
% 17.70/3.08
% 17.70/3.08 ------
% 17.70/3.08 Current options:
% 17.70/3.08 ------
% 17.70/3.08
% 17.70/3.08
% 17.70/3.08
% 17.70/3.08
% 17.70/3.08 ------ Proving...
% 17.70/3.08
% 17.70/3.08
% 17.70/3.08 % SZS status Theorem for theBenchmark.p
% 17.70/3.08
% 17.70/3.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.70/3.08
% 17.70/3.09
%------------------------------------------------------------------------------