%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC198+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 : 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 03:08:50 PM UTC 2026
% Result : Theorem 10.34s 2.73s
% Output : CNFRefutation 10.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 293 ( 116 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 353 ( 133 ~; 134 |; 63 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 2 ( 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; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 82 !; 18 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax2) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X6,X7)
& memberP(X3,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X3,X6)
| cons(X6,nil) != X2 ) ) )
| ? [X4] :
( ! [X5] :
( ssItem(X5)
=> ( X4 = X5
| ~ memberP(X0,X5) ) )
& ssItem(X4) )
| 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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X6,X7)
& memberP(X3,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X3,X6)
| cons(X6,nil) != X2 ) ) )
| ? [X4] :
( ! [X5] :
( ssItem(X5)
=> ( X4 = X5
| ~ memberP(X0,X5) ) )
& ssItem(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)
& ( ( nil = X2
& nil = X3 )
| ? [X6] :
( ssItem(X6)
& ! [X7] :
( ~ leq(X6,X7)
| ~ memberP(X3,X7)
| X6 = X7
| ~ ssItem(X7) )
& memberP(X3,X6)
& cons(X6,nil) = X2 ) )
& ! [X4] :
( ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X0,X5) )
| ~ ssItem(X4) )
& 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 )
| ? [X6] :
( ssItem(X6)
& ! [X7] :
( ~ leq(X6,X7)
| ~ memberP(X3,X7)
| X6 = X7
| ~ ssItem(X7) )
& memberP(X3,X6)
& cons(X6,nil) = X2 ) )
& ! [X4] :
( ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X0,X5) )
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f109,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f110,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f137,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( nil = sK2
& nil = sK3 )
| ( ssItem(sK5)
& ! [X7] :
( ~ leq(sK5,X7)
| ~ memberP(sK3,X7)
| sK5 = X7
| ~ ssItem(X7) )
& memberP(sK3,sK5)
& sK2 = cons(sK5,nil) ) )
& ! [X4] :
( ( ssItem(sK4(X4))
& sK4(X4) != X4
& memberP(sK0,sK4(X4)) )
| ~ ssItem(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(X5,sK4(X4)),skolemize(X6,sK5)],[f99]) ).
fof(f138,plain,
( sK6 != sK7
& ssItem(sK7)
& ssItem(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f2]) ).
fof(f140,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f141,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f140]) ).
fof(f149,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f150,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f149]) ).
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,
! [X4] :
( ssItem(sK4(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f164,plain,
! [X4] :
( sK4(X4) != X4
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f165,plain,
! [X4] :
( memberP(sK0,sK4(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f166,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f137]) ).
fof(f170,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f138]) ).
fof(f181,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f182,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f141]) ).
fof(f202,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f150]) ).
fof(f208,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f130]) ).
fof(f213,plain,
! [X4] :
( memberP(sK2,sK4(X4))
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f165,f166]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( memberP(sK2,sK4(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ( sK4(X0) != X0 ) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( ssItem(sK4(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_52,negated_conjecture,
( ( nil = sK3 )
| ( cons(sK5,nil) = sK2 ) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_53,negated_conjecture,
( ( sK2 = nil )
| ( cons(sK5,nil) = sK2 ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_58,negated_conjecture,
( ssItem(sK5)
| ( nil = sK3 ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_59,negated_conjecture,
( ssItem(sK5)
| ( sK2 = nil ) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_64,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f170]) ).
tcf(c_77,plain,
ssList(nil),
inference(cnf_transformation,[],[f181]) ).
tcf(c_78,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_104,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_115,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_124,plain,
( ( nil = nil )
| ~ ssList(nil)
| ( app(nil,nil) != nil ) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_1644,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1646,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3029,plain,
( ssItem(sK4(sK6))
| ~ ssItem(sK6) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_3030,plain,
( memberP(sK2,sK4(sK6))
| ~ ssItem(sK6) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_3766,plain,
( ~ ssItem(sK4(sK6))
| ~ memberP(nil,sK4(sK6)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_4171,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sK2,sK4(sK6))
| ( X1 != sK4(sK6) )
| ( X0 != sK2 ) ),
inference(instantiation,[status(thm)],[c_1648]) ).
tcf(c_9813,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK2 )
| ( sK2 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1646]) ).
tcf(c_9814,plain,
( ( nil = sK2 )
| ( nil != nil )
| ( sK2 != nil ) ),
inference(instantiation,[status(thm)],[c_9813]) ).
tcf(c_21343,plain,
! [X0: $i] :
( memberP(X0,sK4(sK6))
| ~ memberP(sK2,sK4(sK6))
| ( X0 != sK2 )
| ( sK4(sK6) != sK4(sK6) ) ),
inference(instantiation,[status(thm)],[c_4171]) ).
tcf(c_21344,plain,
sK4(sK6) = sK4(sK6),
inference(instantiation,[status(thm)],[c_1644]) ).
tcf(c_21345,plain,
( memberP(nil,sK4(sK6))
| ~ memberP(sK2,sK4(sK6))
| ( nil != sK2 )
| ( sK4(sK6) != sK4(sK6) ) ),
inference(instantiation,[status(thm)],[c_21343]) ).
tcf(c_25553,negated_conjecture,
ssItem(sK5),
inference(global_subsumption_just,[status(thm)],[c_58,c_77,c_64,c_59,c_115,c_124,c_3030,c_3029,c_3766,c_9814,c_21345,c_21344]) ).
tcf(c_25593,negated_conjecture,
cons(sK5,nil) = sK2,
inference(global_subsumption_just,[status(thm)],[c_52,c_77,c_64,c_115,c_53,c_124,c_3030,c_3029,c_3766,c_9814,c_21345,c_21344]) ).
tcf(c_27504,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK5 )
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_25593,c_81]) ).
tcf(c_27508,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK5 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27504,c_77,c_25553]) ).
tcf(c_29279,plain,
! [X0: $i] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0)
| ( X0 = sK5 ) ),
inference(global_subsumption_just,[status(thm)],[c_27508,c_78,c_27508]) ).
tcf(c_29280,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(renaming,[status(thm)],[c_29279]) ).
tcf(c_29288,plain,
! [X0: $i] :
( ( sK4(X0) = sK5 )
| ~ ssItem(X0)
| ~ ssItem(sK4(X0)) ),
inference(superposition,[status(thm)],[c_49,c_29280]) ).
tcf(c_29294,plain,
! [X0: $i] :
( ( sK4(X0) = sK5 )
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_29288,c_51,c_29288]) ).
tcf(c_29302,plain,
sK4(sK5) = sK5,
inference(superposition,[status(thm)],[c_25553,c_29294]) ).
tcf(c_29312,plain,
~ ssItem(sK5),
inference(superposition,[status(thm)],[c_29302,c_50]) ).
tcf(c_29315,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29312,c_25553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC198+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % 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 16:55:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 10.34/2.73 % SZS status Started for theBenchmark.p
% 10.34/2.73 % SZS status Theorem for theBenchmark.p
% 10.34/2.73
% 10.34/2.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.34/2.73
% 10.34/2.73 % ------ iProver source info
% 10.34/2.73
% 10.34/2.73 % git: date: 2026-07-19 20:42:38 +0200
% 10.34/2.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.34/2.73 % git: non_committed_changes: false
% 10.34/2.73
% 10.34/2.73 % ------ Parsing...
% 10.34/2.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.34/2.73
% 10.34/2.73 % ------ 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 %
% 10.34/2.73
% 10.34/2.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.34/2.73
% 10.34/2.73 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.34/2.73 % ------ Proving...
% 10.34/2.73 % ------ Problem Properties
% 10.34/2.73
% 10.34/2.73 %
% 10.34/2.73 % clauses 56
% 10.34/2.73 % conjectures 13
% 10.34/2.73 % EPR 22
% 10.34/2.73 % Horn 42
% 10.34/2.73 % unary 7
% 10.34/2.73 % binary 14
% 10.34/2.73 % lits 190
% 10.34/2.73 % lits eq 42
% 10.34/2.73 % fd_pure 0
% 10.34/2.73 % fd_pseudo 0
% 10.34/2.73 % fd_cond 6
% 10.34/2.73 % fd_pseudo_cond 7
% 10.34/2.73 % AC symbols 0
% 10.34/2.73
% 10.34/2.73 % ------ Schedule dynamic 5 is on
% 10.34/2.73
% 10.34/2.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.34/2.73
% 10.34/2.73
% 10.34/2.73 % ------
% 10.34/2.73 % Current options:
% 10.34/2.73 % ------
% 10.34/2.73
% 10.34/2.73
% 10.34/2.73 %
% 10.34/2.73
% 10.34/2.73 % ------ Proving...
% 10.34/2.73 %
% 10.34/2.73
% 10.34/2.73 % SZS status Theorem for theBenchmark.p
% 10.34/2.73
% 10.34/2.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.34/2.73
% 10.34/2.73
%------------------------------------------------------------------------------