%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC325+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 03:09:19 PM UTC 2026
% Result : Theorem 0.83s 1.28s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f173ERROR: Could not build tree for root c_1492ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X3
| app(cons(X6,nil),X7) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,X4) = X0
& app(X4,X5) = X1
& ssList(X5) )
& ssList(X4) )
| 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)
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X3
| app(cons(X6,nil),X7) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,X4) = X0
& app(X4,X5) = X1
& ssList(X5) )
& ssList(X4) )
| 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)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& app(cons(X6,nil),X7) = X2 ) ) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(X5,X4) != X0
| app(X4,X5) != X1
| ~ ssList(X5) )
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& app(cons(X6,nil),X7) = X2 ) ) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(X5,X4) != X0
| app(X4,X5) != X1
| ~ ssList(X5) )
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ~ neq(sK3,nil)
| ( ssItem(sK4)
& ssList(sK5)
& sK3 = app(sK5,cons(sK4,nil))
& sK2 = app(cons(sK4,nil),sK5) ) )
& ( nil != sK3
| nil = sK2 )
& ! [X4] :
( ! [X5] :
( app(X5,X4) != sK0
| app(X4,X5) != sK1
| ~ ssList(X5) )
| ~ ssList(X4) )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X6,sK4),skolemize(X7,sK5)],[f99]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f128,plain,
ssList(sK1),
inference(cnf_transformation,[],[f120]) ).
fof(f131,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f120]) ).
fof(f132,plain,
( ~ neq(sK3,nil)
| ssList(sK5) ),
inference(cnf_transformation,[],[f120]) ).
fof(f133,plain,
( ~ neq(sK3,nil)
| sK3 = app(sK5,cons(sK4,nil)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f134,plain,
( ~ neq(sK3,nil)
| sK2 = app(cons(sK4,nil),sK5) ),
inference(cnf_transformation,[],[f120]) ).
fof(f135,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f136,plain,
! [X4,X5] :
( app(X5,X4) != sK0
| app(X4,X5) != sK1
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f120]) ).
fof(f137,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f138,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f120]) ).
fof(f151,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f159,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f162,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f165,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f166,plain,
! [X4,X5] :
( app(X5,X4) != sK2
| app(X4,X5) != sK3
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f136,f138,f137]) ).
fof(f167,plain,
ssList(sK3),
inference(definition_unfolding,[],[f128,f138]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(X1,X0) != sK2 )
| ( app(X0,X1) != sK3 ) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_50,negated_conjecture,
( ( sK2 = nil )
| ( sK3 != nil ) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_51,negated_conjecture,
( ( app(cons(sK4,nil),sK5) = sK2 )
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_52,negated_conjecture,
( ( app(sK5,cons(sK4,nil)) = sK3 )
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_53,negated_conjecture,
( ssList(sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_54,negated_conjecture,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_57,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f167]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_73,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_79,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_85,plain,
ssList(nil),
inference(cnf_transformation,[],[f165]) ).
tcf(c_88,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_104,plain,
app(nil,nil) = nil,
inference(global_subsumption_just,[status(thm)],[c_73,c_85,c_88]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i] :
( ssItem(sK4)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_81]) ).
tcf(c_509,plain,
( ssItem(sK4)
| ( sK3 = nil )
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(unflattening,[status(thm)],[c_508]) ).
tcf(c_510,plain,
( ssItem(sK4)
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_509,c_57,c_85,c_509]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i] :
( ssList(sK5)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_81]) ).
tcf(c_533,plain,
( ssList(sK5)
| ( sK3 = nil )
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(unflattening,[status(thm)],[c_532]) ).
tcf(c_534,plain,
( ssList(sK5)
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_533,c_57,c_85,c_533]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(sK5,cons(sK4,nil)) = sK3 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_81]) ).
tcf(c_557,plain,
( ( sK3 = nil )
| ( app(sK5,cons(sK4,nil)) = sK3 )
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(unflattening,[status(thm)],[c_556]) ).
tcf(c_558,plain,
( ( sK3 = nil )
| ( app(sK5,cons(sK4,nil)) = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_557,c_57,c_85,c_557]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(cons(sK4,nil),sK5) = sK2 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_81]) ).
tcf(c_581,plain,
( ( sK3 = nil )
| ( app(cons(sK4,nil),sK5) = sK2 )
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(unflattening,[status(thm)],[c_580]) ).
tcf(c_582,plain,
( ( sK3 = nil )
| ( app(cons(sK4,nil),sK5) = sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_581,c_57,c_85,c_581]) ).
tcf(c_1392,plain,
( ( sK3 = nil )
| ~ ssList(sK5)
| ~ ssList(cons(sK4,nil))
| ( app(cons(sK4,nil),sK5) != sK2 ) ),
inference(superposition,[status(thm)],[c_558,c_49]) ).
tcf(c_1407,plain,
( ~ ssList(nil)
| ( sK3 != nil )
| ( app(nil,nil) != sK2 ) ),
inference(superposition,[status(thm)],[c_104,c_49]) ).
tcf(c_1408,plain,
( ~ ssList(nil)
| ( sK2 != nil )
| ( sK3 != nil ) ),
inference(light_normalisation,[status(thm)],[c_1407,c_104]) ).
tcf(c_1432,plain,
( ( sK3 = nil )
| ~ ssList(cons(sK4,nil)) ),
inference(global_subsumption_just,[status(thm)],[c_1392,c_85,c_50,c_534,c_582,c_1392,c_1408]) ).
tcf(c_1434,plain,
~ ssList(cons(sK4,nil)),
inference(global_subsumption_just,[status(thm)],[c_1432,c_85,c_50,c_534,c_582,c_1392,c_1408]) ).
tcf(c_1445,plain,
sK3 != nil,
inference(global_subsumption_just,[status(thm)],[c_1408,c_85,c_50,c_1408]) ).
tcf(c_1450,plain,
ssItem(sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_510,c_1445]) ).
tcf(c_1491,plain,
( ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_71,c_1434]) ).
tcf(c_1492,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1491,c_1450,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC325+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 17:38:03 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 0.83/1.28 % SZS status Started for theBenchmark.p
% 0.83/1.28 % SZS status Theorem for theBenchmark.p
% 0.83/1.28
% 0.83/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.83/1.28
% 0.83/1.28 % ------ iProver source info
% 0.83/1.28
% 0.83/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.83/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.83/1.28 % git: non_committed_changes: false
% 0.83/1.28
% 0.83/1.28 % ------ Parsing...
% 0.83/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.83/1.28
% 0.83/1.28 % ------ 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 %
% 0.83/1.28
% 0.83/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.83/1.28
% 0.83/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.83/1.28 % ------ Proving...
% 0.83/1.28 % ------ Problem Properties
% 0.83/1.28
% 0.83/1.28 %
% 0.83/1.28 % clauses 31
% 0.83/1.28 % conjectures 4
% 0.83/1.28 % EPR 9
% 0.83/1.28 % Horn 24
% 0.83/1.28 % unary 7
% 0.83/1.28 % binary 7
% 0.83/1.28 % lits 87
% 0.83/1.28 % lits eq 35
% 0.83/1.28 % fd_pure 0
% 0.83/1.28 % fd_pseudo 0
% 0.83/1.28 % fd_cond 4
% 0.83/1.28 % fd_pseudo_cond 4
% 0.83/1.28 % AC symbols 0
% 0.83/1.28
% 0.83/1.28 % ------ Schedule dynamic 5 is on
% 0.83/1.28
% 0.83/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.83/1.28
% 0.83/1.28
% 0.83/1.28 % ------
% 0.83/1.28 % Current options:
% 0.83/1.28 % ------
% 0.83/1.28
% 0.83/1.28
% 0.83/1.28 %
% 0.83/1.28
% 0.83/1.28 % ------ Proving...
% 0.83/1.28 %
% 0.83/1.28
% 0.83/1.28 % SZS status Theorem for theBenchmark.p
% 0.83/1.28
% 0.83/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.83/1.29
% 0.83/1.29
%------------------------------------------------------------------------------