%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC239+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 : n005.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 03:08:58 PM UTC 2026
% Result : Theorem 3.11s 1.19s
% Output : CNFRefutation 3.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 18 unt; 0 def)
% Number of atoms : 249 ( 81 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 305 ( 115 ~; 111 |; 64 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 66 !; 20 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
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(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X8,X9)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| 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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X8,X9)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| 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)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ leq(X8,X9)
| ~ memberP(X3,X9)
| X8 = X9
| ~ ssItem(X9) )
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ leq(X8,X9)
| ~ memberP(X3,X9)
| X8 = X9
| ~ ssItem(X9) )
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f109,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f118,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f137,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( nil = sK2
& nil = sK3 )
| ( ssItem(sK5)
& ! [X9] :
( ~ leq(sK5,X9)
| ~ memberP(sK3,X9)
| sK5 = X9
| ~ ssItem(X9) )
& memberP(sK3,sK5)
& sK2 = cons(sK5,nil) ) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ssItem(sK4(X4,X5,X6))
& ~ leq(X4,sK4(X4,X5,X6))
& lt(X4,sK4(X4,X5,X6))
& memberP(X6,sK4(X4,X5,X6))
& memberP(X5,sK4(X4,X5,X6)) )
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK0
& 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(X7,sK4(X4,X5,X6)),skolemize(X8,sK5)],[f99]) ).
fof(f151,plain,
ssList(sK0),
inference(cnf_transformation,[],[f137]) ).
fof(f155,plain,
( nil = sK2
| ssItem(sK5) ),
inference(cnf_transformation,[],[f137]) ).
fof(f156,plain,
( nil = sK3
| ssItem(sK5) ),
inference(cnf_transformation,[],[f137]) ).
fof(f161,plain,
( nil = sK2
| sK2 = cons(sK5,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f162,plain,
( nil = sK3
| sK2 = cons(sK5,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f163,plain,
! [X6,X4,X5] :
( ssItem(sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f167,plain,
! [X6,X4,X5] :
( memberP(X5,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f168,plain,
nil != sK0,
inference(cnf_transformation,[],[f137]) ).
fof(f169,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f137]) ).
fof(f184,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f109]) ).
fof(f191,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f193,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f194,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f216,plain,
nil != sK2,
inference(definition_unfolding,[],[f168,f169]) ).
fof(f217,plain,
! [X6,X4,X5] :
( memberP(X5,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f167,f169]) ).
fof(f221,plain,
! [X6,X4,X5] :
( ssItem(sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f163,f169]) ).
fof(f223,plain,
ssList(sK2),
inference(definition_unfolding,[],[f151,f169]) ).
tcf(c_49,negated_conjecture,
nil != sK2,
inference(cnf_transformation,[],[f216]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X0,sK4(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sK4(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_55,negated_conjecture,
( ( nil = sK3 )
| ( cons(sK5,nil) = sK2 ) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_56,negated_conjecture,
( ( nil = sK2 )
| ( cons(sK5,nil) = sK2 ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_61,negated_conjecture,
( ssItem(sK5)
| ( nil = sK3 ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_62,negated_conjecture,
( ssItem(sK5)
| ( nil = sK2 ) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_66,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f223]) ).
tcf(c_80,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_87,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_89,plain,
ssList(nil),
inference(cnf_transformation,[],[f193]) ).
tcf(c_90,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_142,negated_conjecture,
ssItem(sK5),
inference(global_subsumption_just,[status(thm)],[c_61,c_49,c_62]) ).
tcf(c_152,negated_conjecture,
cons(sK5,nil) = sK2,
inference(global_subsumption_just,[status(thm)],[c_55,c_49,c_56]) ).
tcf(c_2609,plain,
! [X0: $i,X1: $i] :
( ssItem(sK4(sK5,X0,X1))
| ~ ssItem(sK5)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK2),X1) != sK2 ) ),
inference(superposition,[status(thm)],[c_152,c_54]) ).
tcf(c_2610,plain,
! [X0: $i,X1: $i] :
( ssItem(sK4(sK5,X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK2),X1) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2609,c_142]) ).
tcf(c_2634,plain,
app(sK2,nil) = sK2,
inference(superposition,[status(thm)],[c_66,c_80]) ).
tcf(c_2646,plain,
! [X0: $i,X1: $i] :
( memberP(X0,sK4(sK5,X0,X1))
| ~ ssItem(sK5)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK2),X1) != sK2 ) ),
inference(superposition,[status(thm)],[c_152,c_50]) ).
tcf(c_2647,plain,
! [X0: $i,X1: $i] :
( memberP(X0,sK4(sK5,X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK2),X1) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2646,c_142]) ).
tcf(c_2732,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_66,c_87]) ).
tcf(c_2771,plain,
! [X0: $i] :
( memberP(nil,sK4(sK5,nil,X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ( app(sK2,X0) != sK2 ) ),
inference(superposition,[status(thm)],[c_2732,c_2647]) ).
tcf(c_2772,plain,
! [X0: $i] :
( ssItem(sK4(sK5,nil,X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ( app(sK2,X0) != sK2 ) ),
inference(superposition,[status(thm)],[c_2732,c_2610]) ).
tcf(c_2773,plain,
! [X0: $i] :
( ssItem(sK4(sK5,nil,X0))
| ~ ssList(X0)
| ( app(sK2,X0) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2772,c_89]) ).
tcf(c_2777,plain,
! [X0: $i] :
( memberP(nil,sK4(sK5,nil,X0))
| ~ ssList(X0)
| ( app(sK2,X0) != sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2771,c_89]) ).
tcf(c_2850,plain,
( ssItem(sK4(sK5,nil,nil))
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_2634,c_2773]) ).
tcf(c_2851,plain,
ssItem(sK4(sK5,nil,nil)),
inference(forward_subsumption_resolution,[status(thm)],[c_2850,c_89]) ).
tcf(c_2858,plain,
( memberP(nil,sK4(sK5,nil,nil))
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_2634,c_2777]) ).
tcf(c_2859,plain,
memberP(nil,sK4(sK5,nil,nil)),
inference(forward_subsumption_resolution,[status(thm)],[c_2858,c_89]) ).
tcf(c_2860,plain,
~ ssItem(sK4(sK5,nil,nil)),
inference(superposition,[status(thm)],[c_2859,c_90]) ).
tcf(c_2861,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2860,c_2851]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC239+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 17:09:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.11/1.19 % SZS status Started for theBenchmark.p
% 3.11/1.19 % SZS status Theorem for theBenchmark.p
% 3.11/1.19
% 3.11/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.11/1.19
% 3.11/1.19 % ------ iProver source info
% 3.11/1.19
% 3.11/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.11/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.11/1.19 % git: non_committed_changes: false
% 3.11/1.19
% 3.11/1.19 % ------ Parsing...
% 3.11/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.11/1.19
% 3.11/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.11/1.19
% 3.11/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.11/1.19
% 3.11/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.11/1.19 % ------ Proving...
% 3.11/1.19 % ------ Problem Properties
% 3.11/1.19
% 3.11/1.19 %
% 3.11/1.19 % clauses 55
% 3.11/1.19 % conjectures 12
% 3.11/1.19 % EPR 20
% 3.11/1.19 % Horn 49
% 3.11/1.19 % unary 11
% 3.11/1.19 % binary 5
% 3.11/1.19 % lits 195
% 3.11/1.19 % lits eq 37
% 3.11/1.19 % fd_pure 0
% 3.11/1.19 % fd_pseudo 0
% 3.11/1.19 % fd_cond 5
% 3.11/1.19 % fd_pseudo_cond 7
% 3.11/1.19 % AC symbols 0
% 3.11/1.19
% 3.11/1.19 % ------ Schedule dynamic 5 is on
% 3.11/1.19
% 3.11/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.11/1.19
% 3.11/1.19
% 3.11/1.19 % ------
% 3.11/1.19 % Current options:
% 3.11/1.19 % ------
% 3.11/1.19
% 3.11/1.19
% 3.11/1.19 %
% 3.11/1.19
% 3.11/1.19 % ------ Proving...
% 3.11/1.19 %
% 3.11/1.19
% 3.11/1.19 % SZS status Theorem for theBenchmark.p
% 3.11/1.19
% 3.11/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.11/1.19
%------------------------------------------------------------------------------