TSTP Solution File: SWC416+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC416+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 20:43:15 EDT 2023
% Result : Theorem 7.66s 1.67s
% Output : CNFRefutation 7.66s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f611)
% Comments :
%------------------------------------------------------------------------------
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(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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X7] :
( ssItem(X7)
=> app(cons(X7,nil),X2) != X3 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X1)
& hd(X1) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& app(X5,X0) = X4
& ssList(X5) )
& X1 = X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X7] :
( ssItem(X7)
=> app(cons(X7,nil),X2) != X3 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X1)
& hd(X1) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& app(X5,X0) = X4
& ssList(X5) )
& X1 = X4
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X4] :
( ssItem(X4)
=> app(cons(X4,nil),X2) != X3 )
| ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X1)
& hd(X1) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X6,X0) = X5
& ssList(X6) )
& X1 = X5
& ssList(X5) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
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(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(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,X0) != X5
| ~ ssList(X6) )
| X1 != X5
| ~ ssList(X5) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,X0) != X5
| ~ ssList(X6) )
| X1 != X5
| ~ ssList(X5) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,X0) != X5
| ~ ssList(X6) )
| X1 != X5
| ~ ssList(X5) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| X1 != X5
| ~ ssList(X5) )
& neq(X1,nil) ) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| X1 != X5
| ~ ssList(X5) )
& neq(X1,nil) ) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| sK54 != X5
| ~ ssList(X5) )
& neq(sK54,nil) ) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| sK54 != X5
| ~ ssList(X5) )
& neq(sK54,nil) ) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ? [X4] :
( app(cons(X4,nil),sK55) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| sK54 != X5
| ~ ssList(X5) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK54,nil) )
| ( ? [X4] :
( app(cons(X4,nil),sK55) = X3
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| sK54 != X5
| ~ ssList(X5) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ? [X4] :
( app(cons(X4,nil),sK55) = sK56
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| sK54 != X5
| ~ ssList(X5) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X4] :
( app(cons(X4,nil),sK55) = sK56
& ssItem(X4) )
=> ( sK56 = app(cons(sK57,nil),sK55)
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( sK56 = app(cons(sK57,nil),sK55)
& ssItem(sK57)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X6,sK53) != X5
| ~ ssList(X6) )
| sK54 != X5
| ~ ssList(X5) )
& 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])],[f223,f348,f347,f346,f345,f344]) ).
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(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(f454,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f530,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
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(f556,plain,
! [X6,X7,X5] :
( neq(sK54,nil)
| ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| app(X6,sK53) != X5
| ~ ssList(X6)
| sK54 != X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f349]) ).
fof(f560,plain,
! [X6,X7,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| app(X6,sK53) != X5
| ~ ssList(X6)
| sK54 != X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f349]) ).
fof(f561,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f562,plain,
( ~ neq(sK56,nil)
| sK56 = app(cons(sK57,nil),sK55) ),
inference(cnf_transformation,[],[f349]) ).
fof(f563,plain,
! [X6,X7,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| app(X6,sK55) != X5
| ~ ssList(X6)
| sK56 != X5
| ~ ssList(X5) ),
inference(definition_unfolding,[],[f560,f553,f553,f554,f553]) ).
fof(f567,plain,
! [X6,X7,X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| app(X6,sK55) != X5
| ~ ssList(X6)
| sK56 != X5
| ~ ssList(X5) ),
inference(definition_unfolding,[],[f556,f553,f553,f553,f554,f553]) ).
fof(f569,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
fof(f570,plain,
ssList(sK55),
inference(definition_unfolding,[],[f549,f554]) ).
fof(f598,plain,
! [X6,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| cons(hd(sK56),nil) != X6
| ~ ssItem(hd(sK56))
| app(X6,sK55) != X5
| ~ ssList(X6)
| sK56 != X5
| ~ ssList(X5) ),
inference(equality_resolution,[],[f563]) ).
fof(f599,plain,
! [X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| app(cons(hd(sK56),nil),sK55) != X5
| ~ ssList(cons(hd(sK56),nil))
| sK56 != X5
| ~ ssList(X5) ),
inference(equality_resolution,[],[f598]) ).
fof(f600,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| sK56 != app(cons(hd(sK56),nil),sK55)
| ~ ssList(app(cons(hd(sK56),nil),sK55)) ),
inference(equality_resolution,[],[f599]) ).
fof(f601,plain,
! [X6,X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| cons(hd(sK56),nil) != X6
| ~ ssItem(hd(sK56))
| app(X6,sK55) != X5
| ~ ssList(X6)
| sK56 != X5
| ~ ssList(X5) ),
inference(equality_resolution,[],[f567]) ).
fof(f602,plain,
! [X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| app(cons(hd(sK56),nil),sK55) != X5
| ~ ssList(cons(hd(sK56),nil))
| sK56 != X5
| ~ ssList(X5) ),
inference(equality_resolution,[],[f601]) ).
fof(f603,plain,
( neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| sK56 != app(cons(hd(sK56),nil),sK55)
| ~ ssList(app(cons(hd(sK56),nil),sK55)) ),
inference(equality_resolution,[],[f602]) ).
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,[],[f606]) ).
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_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_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f530]) ).
cnf(c_246,negated_conjecture,
( ~ neq(sK56,nil)
| app(cons(sK57,nil),sK55) = sK56 ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_247,negated_conjecture,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f561]) ).
cnf(c_248,negated_conjecture,
( app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK56)) ),
inference(cnf_transformation,[],[f600]) ).
cnf(c_251,negated_conjecture,
( app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f603]) ).
cnf(c_252,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f611]) ).
cnf(c_255,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f569]) ).
cnf(c_256,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f570]) ).
cnf(c_365,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_247,c_252,c_247]) ).
cnf(c_381,negated_conjecture,
app(cons(sK57,nil),sK55) = sK56,
inference(global_subsumption_just,[status(thm)],[c_246,c_252,c_246]) ).
cnf(c_389,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_251,c_252]) ).
cnf(c_391,plain,
( ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssItem(hd(sK56)) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_252,c_248]) ).
cnf(c_392,negated_conjecture,
( app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56)) ),
inference(renaming,[status(thm)],[c_391]) ).
cnf(c_1956,plain,
( app(cons(hd(sK56),nil),sK55) != sK56
| X0 != nil
| X1 != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_392]) ).
cnf(c_1957,plain,
( app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ~ ssList(sK56)
| nil = sK56 ),
inference(unflattening,[status(thm)],[c_1956]) ).
cnf(c_1958,plain,
( app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| nil = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_1957,c_255,c_141,c_1957]) ).
cnf(c_1979,plain,
( X0 != nil
| X0 != sK56
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_389]) ).
cnf(c_1980,plain,
( nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_1979]) ).
cnf(c_1981,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_1980,c_141,c_1980]) ).
cnf(c_1986,plain,
( app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1958,c_1981]) ).
cnf(c_3548,plain,
( app(cons(hd(sK56),nil),sK55) != sK56
| ~ ssList(app(cons(hd(sK56),nil),sK55))
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56)) ),
inference(subtyping,[status(esa)],[c_1986]) ).
cnf(c_3549,plain,
nil != sK56,
inference(subtyping,[status(esa)],[c_1981]) ).
cnf(c_3558,negated_conjecture,
app(cons(sK57,nil),sK55) = sK56,
inference(subtyping,[status(esa)],[c_381]) ).
cnf(c_3563,negated_conjecture,
ssItem(sK57),
inference(subtyping,[status(esa)],[c_365]) ).
cnf(c_3564,negated_conjecture,
ssList(sK55),
inference(subtyping,[status(esa)],[c_256]) ).
cnf(c_3581,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_3644,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ssList(app(X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_153]) ).
cnf(c_3647,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| hd(cons(X0_14,X0_13)) = X0_14 ),
inference(subtyping,[status(esa)],[c_150]) ).
cnf(c_3648,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssItem(hd(X0_13)) ),
inference(subtyping,[status(esa)],[c_149]) ).
cnf(c_3657,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ssList(cons(X0_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_3737,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_6943,plain,
( nil != X0_13
| sK56 != X0_13 ),
inference(resolution,[status(thm)],[c_3737,c_3549]) ).
cnf(c_6960,plain,
( nil != nil
| ~ ssList(sK56)
| ssItem(hd(sK56)) ),
inference(resolution,[status(thm)],[c_6943,c_3648]) ).
cnf(c_6985,plain,
( ~ ssList(sK56)
| ssItem(hd(sK56)) ),
inference(equality_resolution_simp,[status(thm)],[c_6960]) ).
cnf(c_7342,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ssList(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_3657]) ).
cnf(c_8469,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ ssList(sK55)
| ssList(app(cons(hd(sK56),nil),sK55)) ),
inference(instantiation,[status(thm)],[c_3644]) ).
cnf(c_15243,plain,
app(cons(hd(sK56),nil),sK55) != sK56,
inference(global_subsumption_just,[status(thm)],[c_3548,c_256,c_255,c_141,c_3548,c_6985,c_7342,c_8469]) ).
cnf(c_15503,plain,
( ~ ssList(X0_13)
| hd(cons(sK57,X0_13)) = sK57 ),
inference(superposition,[status(thm)],[c_3563,c_3647]) ).
cnf(c_15626,plain,
hd(cons(sK57,sK55)) = sK57,
inference(superposition,[status(thm)],[c_3564,c_15503]) ).
cnf(c_16201,plain,
( ~ ssList(X0_13)
| app(cons(sK57,nil),X0_13) = cons(sK57,X0_13) ),
inference(superposition,[status(thm)],[c_3563,c_3581]) ).
cnf(c_16590,plain,
app(cons(sK57,nil),sK55) = cons(sK57,sK55),
inference(superposition,[status(thm)],[c_3564,c_16201]) ).
cnf(c_17244,plain,
cons(sK57,sK55) = sK56,
inference(superposition,[status(thm)],[c_3558,c_16590]) ).
cnf(c_17532,plain,
hd(sK56) = sK57,
inference(superposition,[status(thm)],[c_17244,c_15626]) ).
cnf(c_17559,plain,
app(cons(sK57,nil),sK55) != sK56,
inference(superposition,[status(thm)],[c_17532,c_15243]) ).
cnf(c_17561,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17559,c_3558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC416+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 19:16:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.66/1.67 % SZS status Started for theBenchmark.p
% 7.66/1.67 % SZS status Theorem for theBenchmark.p
% 7.66/1.67
% 7.66/1.67 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.66/1.67
% 7.66/1.67 ------ iProver source info
% 7.66/1.67
% 7.66/1.67 git: date: 2023-05-31 18:12:56 +0000
% 7.66/1.67 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.66/1.67 git: non_committed_changes: false
% 7.66/1.67 git: last_make_outside_of_git: false
% 7.66/1.67
% 7.66/1.67 ------ Parsing...
% 7.66/1.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.66/1.67
% 7.66/1.67 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e
% 7.66/1.67
% 7.66/1.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.66/1.67
% 7.66/1.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.66/1.67 ------ Proving...
% 7.66/1.67 ------ Problem Properties
% 7.66/1.67
% 7.66/1.67
% 7.66/1.67 clauses 186
% 7.66/1.67 conjectures 4
% 7.66/1.67 EPR 53
% 7.66/1.67 Horn 118
% 7.66/1.67 unary 21
% 7.66/1.67 binary 40
% 7.66/1.67 lits 627
% 7.66/1.67 lits eq 81
% 7.66/1.67 fd_pure 0
% 7.66/1.67 fd_pseudo 0
% 7.66/1.67 fd_cond 21
% 7.66/1.67 fd_pseudo_cond 14
% 7.66/1.67 AC symbols 0
% 7.66/1.67
% 7.66/1.67 ------ Input Options Time Limit: Unbounded
% 7.66/1.67
% 7.66/1.67
% 7.66/1.67 ------
% 7.66/1.67 Current options:
% 7.66/1.67 ------
% 7.66/1.67
% 7.66/1.67
% 7.66/1.67
% 7.66/1.67
% 7.66/1.67 ------ Proving...
% 7.66/1.67
% 7.66/1.67
% 7.66/1.67 % SZS status Theorem for theBenchmark.p
% 7.66/1.67
% 7.66/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.66/1.67
% 7.66/1.68
%------------------------------------------------------------------------------