%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC311+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:15 PM UTC 2026
% Result : Theorem 6.96s 8.53s
% Output : CNFRefutation 6.96s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f214ERROR: Could not build tree for root c_23073ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X0
& app(cons(X8,nil),X9) = X1
& ssList(X9) )
& ssItem(X8) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& ? [X7] :
( neq(nil,X3)
& hd(X3) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X3) = X5
& ssList(X6) )
& ssList(X5) )
& X2 != X4
& ssList(X4) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X0
& app(cons(X8,nil),X9) = X1
& ssList(X9) )
& ssItem(X8) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& ? [X7] :
( neq(nil,X3)
& hd(X3) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X3) = X5
& ssList(X6) )
& ssList(X5) )
& X2 != X4
& ssList(X4) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X8] :
( ! [X9] :
( app(X9,cons(X8,nil)) != X0
| app(cons(X8,nil),X9) != X1
| ~ ssList(X9) )
| ~ ssItem(X8) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X3)
| ! [X7] :
( ~ neq(nil,X3)
| hd(X3) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X3) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X2 = X4
| ~ ssList(X4) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X8] :
( ! [X9] :
( app(X9,cons(X8,nil)) != X0
| app(cons(X8,nil),X9) != X1
| ~ ssList(X9) )
| ~ ssItem(X8) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X3)
| ! [X7] :
( ~ neq(nil,X3)
| hd(X3) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X3) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X2 = X4
| ~ ssList(X4) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f122]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f129]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f133]) ).
fof(f136,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f137,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ! [X8] :
( ! [X9] :
( app(X9,cons(X8,nil)) != sK0
| app(cons(X8,nil),X9) != sK1
| ~ ssList(X9) )
| ~ ssItem(X8) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(sK3,nil)
| ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK3)
| ! [X7] :
( ~ neq(nil,sK3)
| hd(sK3) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK3) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK2 = X4
| ~ ssList(X4) ) )
& ( nil != sK3
| nil = sK2 )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f143,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f145,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK8(X0)
& ssItem(sK8(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f127]) ).
fof(f146,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK9(X0)
& ssList(sK9(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f134]) ).
fof(f148,plain,
ssList(sK1),
inference(cnf_transformation,[],[f138]) ).
fof(f151,plain,
! [X8,X9] :
( app(X9,cons(X8,nil)) != sK0
| app(cons(X8,nil),X9) != sK1
| ~ ssList(X9)
| ~ ssItem(X8)
| nil != sK0 ),
inference(cnf_transformation,[],[f138]) ).
fof(f152,plain,
( neq(sK1,nil)
| nil != sK0 ),
inference(cnf_transformation,[],[f138]) ).
fof(f153,plain,
! [X8,X9] :
( app(X9,cons(X8,nil)) != sK0
| app(cons(X8,nil),X9) != sK1
| ~ ssList(X9)
| ~ ssItem(X8)
| nil = sK1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f154,plain,
( neq(sK1,nil)
| nil = sK1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f156,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f138]) ).
fof(f157,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f138]) ).
fof(f158,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f138]) ).
fof(f162,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f171,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f180,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f182,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f185,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f123]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK8(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f190,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK8(X0)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK9(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f195,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK9(X0)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f198,plain,
( neq(sK3,nil)
| nil = sK3 ),
inference(definition_unfolding,[],[f154,f158,f158]) ).
fof(f199,plain,
! [X8,X9] :
( app(X9,cons(X8,nil)) != sK2
| app(cons(X8,nil),X9) != sK3
| ~ ssList(X9)
| ~ ssItem(X8)
| nil = sK3 ),
inference(definition_unfolding,[],[f153,f158,f158,f157]) ).
fof(f200,plain,
( neq(sK3,nil)
| nil != sK2 ),
inference(definition_unfolding,[],[f152,f157,f158]) ).
fof(f201,plain,
! [X8,X9] :
( app(X9,cons(X8,nil)) != sK2
| app(cons(X8,nil),X9) != sK3
| ~ ssList(X9)
| ~ ssItem(X8)
| nil != sK2 ),
inference(definition_unfolding,[],[f151,f157,f158,f157]) ).
fof(f202,plain,
ssList(sK3),
inference(definition_unfolding,[],[f148,f158]) ).
tcf(c_49,negated_conjecture,
( ( nil = sK2 )
| ( nil != sK3 ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_50,negated_conjecture,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ neq(sK3,nil)
| ~ neq(nil,sK3)
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ~ ssList(cons(hd(sK3),nil))
| ~ ssList(app(tl(sK3),cons(hd(sK3),nil))) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_51,negated_conjecture,
( neq(sK3,nil)
| ( nil = sK3 ) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( ( nil = sK3 )
| ~ ssItem(X0)
| ~ ssList(X1)
| ( app(X1,cons(X0,nil)) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_53,negated_conjecture,
( neq(sK3,nil)
| ( nil != sK2 ) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( nil != sK2 )
| ( app(X1,cons(X0,nil)) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_57,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_82,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_85,plain,
ssList(nil),
inference(cnf_transformation,[],[f185]) ).
tcf(c_87,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_89,plain,
! [X0: $i] :
( ssItem(sK8(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_90,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK8(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_92,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_94,plain,
! [X0: $i] :
( ssList(sK9(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_95,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK9(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_97,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_129,negated_conjecture,
neq(sK3,nil),
inference(global_subsumption_just,[status(thm)],[c_51,c_51,c_53,c_49]) ).
tcf(c_131,negated_conjecture,
neq(sK3,nil),
inference(global_subsumption_just,[status(thm)],[c_53,c_129]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) != sK3 )
| ( app(X1,cons(X0,nil)) != sK2 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_49,c_52,c_54]) ).
tcf(c_136,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( app(X1,cons(X0,nil)) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(renaming,[status(thm)],[c_135]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( app(cons(X0,nil),X1) != sK3 )
| ( app(X1,cons(X0,nil)) != sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_54,c_136]) ).
tcf(c_139,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( app(X1,cons(X0,nil)) != sK2 )
| ( app(cons(X0,nil),X1) != sK3 ) ),
inference(renaming,[status(thm)],[c_138]) ).
tcf(c_140,plain,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssList(app(tl(sK3),cons(hd(sK3),nil)))
| ~ ssList(cons(hd(sK3),nil))
| ~ ssList(tl(sK3))
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_51,c_53,c_49,c_50]) ).
tcf(c_141,negated_conjecture,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ neq(nil,sK3)
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ~ ssList(cons(hd(sK3),nil))
| ~ ssList(app(tl(sK3),cons(hd(sK3),nil))) ),
inference(renaming,[status(thm)],[c_140]) ).
tcf(c_202,plain,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ neq(nil,sK3)
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ~ ssList(cons(hd(sK3),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_141,c_80]) ).
tcf(c_691,plain,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ~ ssList(cons(hd(sK3),nil))
| ( nil != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_202,c_131]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ~ ssList(cons(hd(sK3),nil))
| ( X1 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_202,c_81]) ).
tcf(c_730,plain,
( ( nil = sK3 )
| ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssList(sK3)
| ~ ssList(nil)
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ~ ssList(cons(hd(sK3),nil)) ),
inference(unflattening,[status(thm)],[c_729]) ).
tcf(c_731,plain,
( ~ ssList(cons(hd(sK3),nil))
| ~ ssList(tl(sK3))
| ~ ssItem(hd(sK3))
| ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_730,c_57,c_85,c_691,c_730]) ).
tcf(c_732,plain,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ~ ssList(cons(hd(sK3),nil)) ),
inference(renaming,[status(thm)],[c_731]) ).
tcf(c_753,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_131,c_82]) ).
tcf(c_754,plain,
( ~ ssList(nil)
| ( nil != sK3 ) ),
inference(unflattening,[status(thm)],[c_753]) ).
tcf(c_755,plain,
nil != sK3,
inference(global_subsumption_just,[status(thm)],[c_754,c_85,c_754]) ).
tcf(c_1905,plain,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssList(nil)
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3)) ),
inference(superposition,[status(thm)],[c_71,c_732]) ).
tcf(c_1914,plain,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1905,c_85]) ).
tcf(c_1958,plain,
( ( nil = sK3 )
| ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssList(sK3)
| ~ ssList(tl(sK3)) ),
inference(superposition,[status(thm)],[c_92,c_1914]) ).
tcf(c_1959,plain,
( ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssList(tl(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1958,c_755,c_57]) ).
tcf(c_2019,plain,
( ( nil = sK3 )
| ( app(tl(sK3),cons(hd(sK3),nil)) = sK2 )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_97,c_1959]) ).
tcf(c_2029,plain,
app(tl(sK3),cons(hd(sK3),nil)) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_2019,c_755,c_57]) ).
tcf(c_2052,plain,
( ( nil = sK3 )
| ( hd(sK3) = sK8(sK3) ) ),
inference(superposition,[status(thm)],[c_57,c_90]) ).
tcf(c_2062,plain,
hd(sK3) = sK8(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2052,c_755]) ).
tcf(c_2084,plain,
( ssItem(hd(sK3))
| ( nil = sK3 )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2062,c_89]) ).
tcf(c_2085,plain,
ssItem(hd(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2084,c_755,c_57]) ).
tcf(c_2219,plain,
( ( nil = sK3 )
| ( tl(sK3) = sK9(sK3) ) ),
inference(superposition,[status(thm)],[c_57,c_95]) ).
tcf(c_2229,plain,
tl(sK3) = sK9(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2219,c_755]) ).
tcf(c_2366,plain,
( ( nil = sK3 )
| ( cons(hd(sK3),tl(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_57,c_87]) ).
tcf(c_2376,plain,
cons(hd(sK3),tl(sK3)) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_2366,c_755]) ).
tcf(c_2406,plain,
( ssList(tl(sK3))
| ( nil = sK3 )
| ~ ssList(sK3) ),
inference(superposition,[status(thm)],[c_2229,c_94]) ).
tcf(c_2407,plain,
ssList(tl(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2406,c_755,c_57]) ).
tcf(c_2611,plain,
! [X0: $i] :
( ( app(cons(X0,nil),tl(sK3)) = cons(X0,tl(sK3)) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_2407,c_62]) ).
tcf(c_22962,plain,
app(cons(hd(sK3),nil),tl(sK3)) = cons(hd(sK3),tl(sK3)),
inference(superposition,[status(thm)],[c_2085,c_2611]) ).
tcf(c_22971,plain,
app(cons(hd(sK3),nil),tl(sK3)) = sK3,
inference(light_normalisation,[status(thm)],[c_22962,c_2376]) ).
tcf(c_23059,plain,
( ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3))
| ( app(tl(sK3),cons(hd(sK3),nil)) != sK2 ) ),
inference(superposition,[status(thm)],[c_22971,c_139]) ).
tcf(c_23072,plain,
( ~ ssItem(hd(sK3))
| ~ ssList(tl(sK3)) ),
inference(ground_joinability,[status(thm)],[c_23059,c_2029]) ).
tcf(c_23073,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23072,c_2085,c_2407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC311+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.59 % Computer : n006.cluster.edu
% 0.12/5.59 % Model : x86_64 x86_64
% 0.12/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.59 % Memory : 8046.5625MB
% 0.12/5.59 % OS : Linux 6.8.0-71-generic
% 0.12/5.59 % CPULimit : 300
% 0.12/5.59 % WCLimit : 300
% 0.12/5.59 % DateTime : Thu Sep 24 17:33:34 UTC 2026
% 0.12/5.60 % CPUTime :
% 0.12/5.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.64 Running first-order theorem proving
% 0.15/5.64 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.65
% 0.15/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.65
% 0.15/5.65 % Detected problem language: tptp
% 0.15/5.66 % Proving...
% 6.96/8.53 % SZS status Started for theBenchmark.p
% 6.96/8.53 % SZS status Theorem for theBenchmark.p
% 6.96/8.53
% 6.96/8.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.96/8.53
% 6.96/8.53 % ------ iProver source info
% 6.96/8.53
% 6.96/8.53 % git: date: 2026-07-19 20:42:38 +0200
% 6.96/8.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.96/8.53 % git: non_committed_changes: false
% 6.96/8.53
% 6.96/8.53 % ------ Parsing...
% 6.96/8.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.96/8.53
% 6.96/8.53 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 6.96/8.53
% 6.96/8.53 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.96/8.53
% 6.96/8.53 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.96/8.53 % ------ Proving...
% 6.96/8.53 % ------ Problem Properties
% 6.96/8.53
% 6.96/8.53 %
% 6.96/8.53 % clauses 40
% 6.96/8.53 % conjectures 3
% 6.96/8.53 % EPR 7
% 6.96/8.53 % Horn 27
% 6.96/8.53 % unary 8
% 6.96/8.53 % binary 2
% 6.96/8.53 % lits 124
% 6.96/8.53 % lits eq 50
% 6.96/8.53 % fd_pure 0
% 6.96/8.53 % fd_pseudo 0
% 6.96/8.53 % fd_cond 12
% 6.96/8.53 % fd_pseudo_cond 5
% 6.96/8.53 % AC symbols 0
% 6.96/8.53
% 6.96/8.53 % ------ Schedule dynamic 5 is on
% 6.96/8.53
% 6.96/8.53 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.96/8.53
% 6.96/8.53
% 6.96/8.53 % ------
% 6.96/8.53 % Current options:
% 6.96/8.53 % ------
% 6.96/8.53
% 6.96/8.53
% 6.96/8.53 %
% 6.96/8.53
% 6.96/8.53 % ------ Proving...
% 6.96/8.53 %
% 6.96/8.53
% 6.96/8.53 % SZS status Theorem for theBenchmark.p
% 6.96/8.53
% 6.96/8.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.96/8.54
% 6.96/8.54
%------------------------------------------------------------------------------