%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC416+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 03:09:42 PM UTC 2026
% Result : Theorem 1.12s 16.78s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f558ERROR: Could not build tree for root c_8882ERROR: 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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
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)
=> ( ( ( 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/sandbox/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,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| nil != cons(X1,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f128,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [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(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [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(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ssItem(sK57)
& sK56 = app(cons(sK57,nil),sK55)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK54)
| hd(sK54) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6) )
| app(X5,sK53) != X4
| ~ ssList(X5) )
| sK54 != X4
| ~ ssList(X4) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != cons(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f398,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| sK56 = app(cons(sK57,nil),sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
! [X6,X4,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK54)
| hd(sK54) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| app(X5,sK53) != X4
| ~ ssList(X5)
| sK54 != X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
! [X6,X4,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| app(X5,sK55) != X4
| ~ ssList(X5)
| sK56 != X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f504,f509,f508,f509,f509]) ).
fof(f516,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f509]) ).
fof(f517,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f508]) ).
fof(f548,plain,
! [X6,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK56 != app(X5,sK55)
| ~ ssList(X5)
| ~ ssList(sK56) ),
inference(equality_resolution,[],[f513]) ).
fof(f549,plain,
! [X6] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| ~ ssItem(X6)
| sK56 != app(cons(X6,nil),sK55)
| ~ ssList(cons(X6,nil))
| ~ ssList(sK56) ),
inference(equality_resolution,[],[f548]) ).
fof(f550,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK56 != app(cons(hd(sK56),nil),sK55)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(sK56) ),
inference(equality_resolution,[],[f549]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f558]) ).
tcf(c_248,negated_conjecture,
( ~ ssList(sK56)
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(cons(hd(sK56),nil),sK55) != sK56 ) ),
inference(cnf_transformation,[],[f550]) ).
tcf(c_250,negated_conjecture,
( ( app(cons(sK57,nil),sK55) = sK56 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_252,negated_conjecture,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_255,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f516]) ).
tcf(c_256,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f517]) ).
tcf(c_319,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_252,c_246,c_252]) ).
tcf(c_368,negated_conjecture,
app(cons(sK57,nil),sK55) = sK56,
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_378,plain,
! [X0: $i] :
( ( hd(cons(sK57,X0)) = sK57 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_319,c_150]) ).
tcf(c_420,plain,
! [X0: $i] :
( ( app(cons(sK57,nil),X0) = cons(sK57,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_319,c_227]) ).
tcf(c_584,plain,
( ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(cons(hd(sK56),nil),sK55) != sK56 )
| ~ ssItem(hd(sK56)) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_255,c_246,c_248]) ).
tcf(c_585,negated_conjecture,
( ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(cons(hd(sK56),nil),sK55) != sK56 ) ),
inference(renaming,[status(thm)],[c_584]) ).
tcf(c_612,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_252,c_246,c_252]) ).
tcf(c_729,negated_conjecture,
app(cons(sK57,nil),sK55) = sK56,
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_740,plain,
hd(cons(sK57,sK55)) = sK57,
inference(superposition,[status(thm)],[c_256,c_378]) ).
tcf(c_750,plain,
! [X0: $i] :
( ( hd(cons(sK57,X0)) = sK57 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_612,c_150]) ).
tcf(c_806,plain,
! [X0: $i] :
( ( app(cons(sK57,nil),X0) = cons(sK57,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_612,c_227]) ).
tcf(c_824,plain,
app(cons(sK57,nil),sK55) = cons(sK57,sK55),
inference(superposition,[status(thm)],[c_256,c_420]) ).
tcf(c_1071,plain,
( ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(cons(hd(sK56),nil),sK55) != sK56 )
| ~ ssItem(hd(sK56)) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_585]) ).
tcf(c_1072,negated_conjecture,
( ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(cons(hd(sK56),nil),sK55) != sK56 ) ),
inference(renaming,[status(thm)],[c_1071]) ).
tcf(c_1415,plain,
hd(cons(sK57,sK55)) = sK57,
inference(superposition,[status(thm)],[c_256,c_750]) ).
tcf(c_1488,plain,
app(cons(sK57,nil),sK55) = cons(sK57,sK55),
inference(superposition,[status(thm)],[c_256,c_806]) ).
tcf(c_1787,plain,
cons(sK57,sK55) = sK56,
inference(light_normalisation,[status(thm)],[c_824,c_368]) ).
tcf(c_1795,plain,
( ~ ssList(sK55)
| ~ ssItem(sK57)
| ( nil != sK56 ) ),
inference(superposition,[status(thm)],[c_1787,c_148]) ).
tcf(c_1797,plain,
hd(sK56) = sK57,
inference(superposition,[status(thm)],[c_1787,c_740]) ).
tcf(c_1800,plain,
( ~ ssItem(sK57)
| ~ neq(nil,sK56)
| ~ ssList(cons(sK57,nil))
| ( app(cons(sK57,nil),sK55) != sK56 ) ),
inference(demodulation,[status(thm)],[c_585,c_1797]) ).
tcf(c_3164,plain,
cons(sK57,sK55) = sK56,
inference(light_normalisation,[status(thm)],[c_1488,c_729]) ).
tcf(c_3174,plain,
hd(sK56) = sK57,
inference(superposition,[status(thm)],[c_3164,c_1415]) ).
tcf(c_3177,plain,
( ~ ssItem(sK57)
| ~ neq(nil,sK56)
| ~ ssList(cons(sK57,nil))
| ( app(cons(sK57,nil),sK55) != sK56 ) ),
inference(demodulation,[status(thm)],[c_1072,c_3174]) ).
tcf(c_4463,plain,
( ~ ssList(cons(sK57,nil))
| ~ neq(nil,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_1800,c_246,c_252,c_250,c_1800]) ).
tcf(c_4464,plain,
( ~ neq(nil,sK56)
| ~ ssList(cons(sK57,nil)) ),
inference(renaming,[status(thm)],[c_4463]) ).
tcf(c_4469,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ~ neq(nil,sK56) ),
inference(superposition,[status(thm)],[c_140,c_4464]) ).
tcf(c_8878,plain,
~ neq(nil,sK56),
inference(global_subsumption_just,[status(thm)],[c_3177,c_141,c_246,c_252,c_4469]) ).
tcf(c_8881,plain,
( ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_8878]) ).
tcf(c_8882,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8881,c_1795,c_252,c_246,c_141,c_255,c_256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC416+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/15.38 % Computer : n006.cluster.edu
% 0.10/15.38 % Model : x86_64 x86_64
% 0.10/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.38 % Memory : 8046.5625MB
% 0.10/15.38 % OS : Linux 6.8.0-71-generic
% 0.10/15.38 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Thu Sep 24 18:08:14 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/15.43 Running first-order theorem proving
% 0.15/15.43 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
% 0.15/15.44
% 0.15/15.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.44
% 0.15/15.44 % Detected problem language: tptp
% 0.15/15.45 % Proving...
% 1.12/16.78 % SZS status Started for theBenchmark.p
% 1.12/16.78 % SZS status Theorem for theBenchmark.p
% 1.12/16.78
% 1.12/16.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.12/16.78
% 1.12/16.78 % ------ iProver source info
% 1.12/16.78
% 1.12/16.78 % git: date: 2026-07-19 20:42:38 +0200
% 1.12/16.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.12/16.78 % git: non_committed_changes: false
% 1.12/16.78
% 1.12/16.78 % ------ Parsing...
% 1.12/16.78 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.12/16.78 % ------ Proving...
% 1.12/16.78 % ------ Problem Properties
% 1.12/16.78
% 1.12/16.78 %
% 1.12/16.78 % clauses 208
% 1.12/16.78 % conjectures 11
% 1.12/16.78 % EPR 71
% 1.12/16.78 % Horn 135
% 1.12/16.78 % unary 17
% 1.12/16.78 % binary 57
% 1.12/16.78 % lits 695
% 1.12/16.78 % lits eq 85
% 1.12/16.78 % fd_pure 0
% 1.12/16.78 % fd_pseudo 0
% 1.12/16.78 % fd_cond 21
% 1.12/16.78 % fd_pseudo_cond 17
% 1.12/16.78 % AC symbols 0
% 1.12/16.78
% 1.12/16.78 % ------ Input Options Time Limit: Unbounded
% 1.12/16.78
% 1.12/16.78
% 1.12/16.78 % ------
% 1.12/16.78 % Current options:
% 1.12/16.78 % ------
% 1.12/16.78
% 1.12/16.78
% 1.12/16.78 %
% 1.12/16.78
% 1.12/16.78 % ------ Proving...
% 1.12/16.78 %
% 1.12/16.78
% 1.12/16.78 % SZS status Theorem for theBenchmark.p
% 1.12/16.78
% 1.12/16.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.12/16.78
% 1.12/16.78
%------------------------------------------------------------------------------