%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC011+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 : n020.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 03:07:30 PM UTC 2026
% Result : Theorem 4.54s 1.51s
% Output : CNFRefutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 49 ( 10 unt; 1 def)
% Number of atoms : 247 ( 84 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 320 ( 122 ~; 110 |; 74 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 172 ( 0 sgn 139 !; 33 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(X8,X9) != X2
| app(app(X8,cons(X7,nil)),X9) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X5,X6) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(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)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(X8,X9) != X2
| app(app(X8,cons(X7,nil)),X9) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X5,X6) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| 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)
& neq(X1,nil) )
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& 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)
& neq(X1,nil) )
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f125,plain,
( ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ssList(sK7)
& ( ( ~ neq(sK7,nil)
& neq(sK5,nil) )
| sP0(sK5,sK4,sK7,sK6) )
& sK4 = sK6
& sK5 = sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f121]) ).
fof(f143,plain,
( ~ neq(sK7,nil)
| sP0(sK5,sK4,sK7,sK6) ),
inference(cnf_transformation,[],[f125]) ).
fof(f144,plain,
( neq(sK5,nil)
| sP0(sK5,sK4,sK7,sK6) ),
inference(cnf_transformation,[],[f125]) ).
fof(f145,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f125]) ).
fof(f146,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f125]) ).
fof(f174,plain,
( neq(sK7,nil)
| sP0(sK7,sK6,sK7,sK6) ),
inference(definition_unfolding,[],[f144,f146,f145,f146]) ).
fof(f175,plain,
( ~ neq(sK7,nil)
| sP0(sK7,sK6,sK7,sK6) ),
inference(definition_unfolding,[],[f143,f146,f145]) ).
tcf(c_56,negated_conjecture,
( neq(sK7,nil)
| sP0(sK7,sK6,sK7,sK6) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_57,negated_conjecture,
( sP0(sK7,sK6,sK7,sK6)
| ~ neq(sK7,nil) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_113,negated_conjecture,
sP0(sK7,sK6,sK7,sK6),
inference(global_subsumption_just,[status(thm)],[c_56,c_56,c_57]) ).
tcf(c_115,negated_conjecture,
sP0(sK7,sK6,sK7,sK6),
inference(global_subsumption_just,[status(thm)],[c_57,c_113]) ).
fof(f120,definition,
! [X1,X0,X3,X2] :
( ~ sP0(X1,X0,X3,X2)
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f121,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP0(X1,X0,X3,X2) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f120]) ).
fof(f122,plain,
! [X1,X0,X3,X2] :
( ~ sP0(X1,X0,X3,X2)
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& app(X8,X9) = X2
& app(app(X8,cons(X7,nil)),X9) = X3 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X5,X6) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& app(X8,X9) = X3
& app(app(X8,cons(X7,nil)),X9) = X2 ) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ssItem(sK1(X2,X3))
& ssList(sK2(X2,X3))
& ssList(sK3(X2,X3))
& app(sK2(X2,X3),sK3(X2,X3)) = X3
& app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X7,sK1(X2,X3)),skolemize(X8,sK2(X2,X3)),skolemize(X9,sK3(X2,X3))],[f123]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK2(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK3(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(sK2(X2,X3),sK3(X2,X3)) = X3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2 ),
inference(cnf_transformation,[],[f124]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(X0,X1,X2,X3)
| app(X5,X6) != X1
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f124]) ).
fof(f178,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ sP0(app(app(X5,cons(X4,nil)),X6),X1,X2,X3)
| app(X5,X6) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f137]) ).
fof(f179,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP0(app(app(X5,cons(X4,nil)),X6),app(X5,X6),X2,X3)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f178]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ sP0(app(app(X0,cons(X1,nil)),X2),app(X0,X2),X3,X4) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK2(X2,X3),sK3(X2,X3)) = X3 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK3(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK2(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X2,X3))
| ( X3 != sK6 )
| ( X2 != sK7 )
| ( X1 != sK6 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_115]) ).
tcf(c_519,plain,
ssItem(sK1(sK7,sK6)),
inference(unflattening,[status(thm)],[c_518]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK2(X2,X3))
| ( X3 != sK6 )
| ( X2 != sK7 )
| ( X1 != sK6 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_115]) ).
tcf(c_524,plain,
ssList(sK2(sK7,sK6)),
inference(unflattening,[status(thm)],[c_523]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK3(X2,X3))
| ( X3 != sK6 )
| ( X2 != sK7 )
| ( X1 != sK6 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_115]) ).
tcf(c_529,plain,
ssList(sK3(sK7,sK6)),
inference(unflattening,[status(thm)],[c_528]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK2(X2,X3),sK3(X2,X3)) = X3 )
| ( X3 != sK6 )
| ( X2 != sK7 )
| ( X1 != sK6 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_115]) ).
tcf(c_534,plain,
app(sK2(sK7,sK6),sK3(sK7,sK6)) = sK6,
inference(unflattening,[status(thm)],[c_533]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2 )
| ( X3 != sK6 )
| ( X2 != sK7 )
| ( X1 != sK6 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_115]) ).
tcf(c_539,plain,
app(app(sK2(sK7,sK6),cons(sK1(sK7,sK6),nil)),sK3(sK7,sK6)) = sK7,
inference(unflattening,[status(thm)],[c_538]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( X4 != sK6 )
| ( X3 != sK7 )
| ( app(X0,X2) != sK6 )
| ( app(app(X0,cons(X1,nil)),X2) != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_115]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(X0,X2) != sK6 )
| ( app(app(X0,cons(X1,nil)),X2) != sK7 ) ),
inference(unflattening,[status(thm)],[c_548]) ).
tcf(c_1379,plain,
( ~ ssList(sK3(sK7,sK6))
| ~ ssList(sK2(sK7,sK6))
| ~ ssItem(sK1(sK7,sK6))
| ( app(sK2(sK7,sK6),sK3(sK7,sK6)) != sK6 ) ),
inference(superposition,[status(thm)],[c_539,c_549]) ).
tcf(c_1380,plain,
( ~ ssList(sK3(sK7,sK6))
| ~ ssList(sK2(sK7,sK6))
| ~ ssItem(sK1(sK7,sK6)) ),
inference(ground_joinability,[status(thm)],[c_1379,c_534]) ).
tcf(c_1381,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1380,c_529,c_524,c_519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC011+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.57 % Computer : n020.cluster.edu
% 0.08/0.57 % Model : x86_64 x86_64
% 0.08/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.57 % Memory : 8046.5625MB
% 0.08/0.57 % OS : Linux 6.8.0-71-generic
% 0.08/0.57 % CPULimit : 300
% 0.08/0.57 % WCLimit : 300
% 0.08/0.57 % DateTime : Thu Sep 24 15:55:05 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.60 Running first-order theorem proving
% 0.08/0.60 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
% 0.08/0.62
% 0.08/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.62
% 0.08/0.62 % Detected problem language: tptp
% 0.13/0.63 % Proving...
% 4.54/1.51 % SZS status Started for theBenchmark.p
% 4.54/1.51 % SZS status Theorem for theBenchmark.p
% 4.54/1.51
% 4.54/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.54/1.51
% 4.54/1.51 % ------ iProver source info
% 4.54/1.51
% 4.54/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 4.54/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.54/1.51 % git: non_committed_changes: false
% 4.54/1.51
% 4.54/1.51 % ------ Parsing...
% 4.54/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.54/1.51
% 4.54/1.51 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.54/1.51
% 4.54/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.54/1.51
% 4.54/1.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.54/1.51 % ------ Proving...
% 4.54/1.51 % ------ Problem Properties
% 4.54/1.51
% 4.54/1.51 %
% 4.54/1.51 % clauses 32
% 4.54/1.51 % conjectures 2
% 4.54/1.51 % EPR 7
% 4.54/1.51 % Horn 29
% 4.54/1.51 % unary 13
% 4.54/1.51 % binary 2
% 4.54/1.51 % lits 84
% 4.54/1.51 % lits eq 30
% 4.54/1.51 % fd_pure 0
% 4.54/1.51 % fd_pseudo 0
% 4.54/1.51 % fd_cond 4
% 4.54/1.51 % fd_pseudo_cond 4
% 4.54/1.51 % AC symbols 0
% 4.54/1.51
% 4.54/1.51 % ------ Schedule dynamic 5 is on
% 4.54/1.51
% 4.54/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.54/1.51
% 4.54/1.51
% 4.54/1.51 % ------
% 4.54/1.51 % Current options:
% 4.54/1.51 % ------
% 4.54/1.51
% 4.54/1.51
% 4.54/1.51 %
% 4.54/1.51
% 4.54/1.51 % ------ Proving...
% 4.54/1.51 %
% 4.54/1.51
% 4.54/1.51 % SZS status Theorem for theBenchmark.p
% 4.54/1.51
% 4.54/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.54/1.51
% 4.54/1.51
%------------------------------------------------------------------------------