%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC220+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 : n002.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 03:08:55 PM UTC 2026
% Result : Theorem 4.00s 1.30s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 53 ( 14 unt; 0 def)
% Number of atoms : 284 ( 62 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 382 ( 151 ~; 149 |; 66 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn 77 !; 24 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X11] :
( leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ~ leq(X11,X8)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X2 ) ) ) )
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X7,X4)
| ~ leq(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/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X11] :
( leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ~ leq(X11,X8)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X2 ) ) ) )
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X7,X4)
| ~ leq(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)
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X11] :
( ~ leq(X8,X11)
| ~ memberP(X10,X11)
| ~ memberP(X9,X11)
| leq(X11,X8)
| ~ ssItem(X11) )
& app(app(X9,cons(X8,nil)),X10) = X2 ) ) )
| nil = X2 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X7,X4)
& leq(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)
& ( ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ! [X11] :
( ~ leq(X8,X11)
| ~ memberP(X10,X11)
| ~ memberP(X9,X11)
| leq(X11,X8)
| ~ ssItem(X11) )
& app(app(X9,cons(X8,nil)),X10) = X2 ) ) )
| nil = X2 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X7,X4)
& leq(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(f137,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ssItem(sK5)
& ssList(sK6)
& ssList(sK7)
& ! [X11] :
( ~ leq(sK5,X11)
| ~ memberP(sK7,X11)
| ~ memberP(sK6,X11)
| leq(X11,sK5)
| ~ ssItem(X11) )
& sK2 = app(app(sK6,cons(sK5,nil)),sK7) )
| nil = sK2 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ssItem(sK4(X4,X5,X6))
& ~ leq(sK4(X4,X5,X6),X4)
& leq(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,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4(X4,X5,X6)),skolemize(X8,sK5),skolemize(X9,sK6),skolemize(X10,sK7)],[f99]) ).
fof(f155,plain,
( ssItem(sK5)
| nil = sK2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f156,plain,
( ssList(sK6)
| nil = sK2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f157,plain,
( ssList(sK7)
| nil = sK2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f158,plain,
! [X11] :
( ~ leq(sK5,X11)
| ~ memberP(sK7,X11)
| ~ memberP(sK6,X11)
| leq(X11,sK5)
| ~ ssItem(X11)
| nil = sK2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f159,plain,
( sK2 = app(app(sK6,cons(sK5,nil)),sK7)
| nil = sK2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f160,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(f161,plain,
! [X6,X4,X5] :
( ~ leq(sK4(X4,X5,X6),X4)
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f162,plain,
! [X6,X4,X5] :
( leq(X4,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f163,plain,
! [X6,X4,X5] :
( memberP(X6,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f137]) ).
fof(f164,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(f165,plain,
nil != sK0,
inference(cnf_transformation,[],[f137]) ).
fof(f166,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f137]) ).
fof(f213,plain,
nil != sK2,
inference(definition_unfolding,[],[f165,f166]) ).
fof(f214,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,[],[f164,f166]) ).
fof(f215,plain,
! [X6,X4,X5] :
( memberP(X6,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f163,f166]) ).
fof(f216,plain,
! [X6,X4,X5] :
( leq(X4,sK4(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f162,f166]) ).
fof(f217,plain,
! [X6,X4,X5] :
( ~ leq(sK4(X4,X5,X6),X4)
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f161,f166]) ).
fof(f218,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,[],[f160,f166]) ).
tcf(c_49,negated_conjecture,
nil != sK2,
inference(cnf_transformation,[],[f213]) ).
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,[],[f214]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X2,sK4(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( leq(X1,sK4(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ leq(sK4(X1,X0,X2),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,[],[f218]) ).
tcf(c_55,negated_conjecture,
( ( nil = sK2 )
| ( app(app(sK6,cons(sK5,nil)),sK7) = sK2 ) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( leq(X0,sK5)
| ( nil = sK2 )
| ~ ssItem(X0)
| ~ leq(sK5,X0)
| ~ memberP(sK7,X0)
| ~ memberP(sK6,X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_57,negated_conjecture,
( ssList(sK7)
| ( nil = sK2 ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_58,negated_conjecture,
( ssList(sK6)
| ( nil = sK2 ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_59,negated_conjecture,
( ssItem(sK5)
| ( nil = sK2 ) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_136,negated_conjecture,
ssItem(sK5),
inference(global_subsumption_just,[status(thm)],[c_59,c_49,c_59]) ).
tcf(c_138,negated_conjecture,
ssList(sK6),
inference(global_subsumption_just,[status(thm)],[c_58,c_49,c_58]) ).
tcf(c_140,negated_conjecture,
ssList(sK7),
inference(global_subsumption_just,[status(thm)],[c_57,c_49,c_57]) ).
tcf(c_144,negated_conjecture,
app(app(sK6,cons(sK5,nil)),sK7) = sK2,
inference(global_subsumption_just,[status(thm)],[c_55,c_49,c_55]) ).
tcf(c_146,plain,
! [X0: $i] :
( leq(X0,sK5)
| ~ memberP(sK6,X0)
| ~ memberP(sK7,X0)
| ~ leq(sK5,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_49,c_56]) ).
tcf(c_147,negated_conjecture,
! [X0: $i] :
( leq(X0,sK5)
| ~ ssItem(X0)
| ~ leq(sK5,X0)
| ~ memberP(sK7,X0)
| ~ memberP(sK6,X0) ),
inference(renaming,[status(thm)],[c_146]) ).
tcf(c_2626,plain,
( ssItem(sK4(sK5,sK6,sK7))
| ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5) ),
inference(superposition,[status(thm)],[c_144,c_54]) ).
tcf(c_2627,plain,
ssItem(sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_2626,c_140,c_138,c_136]) ).
tcf(c_2638,plain,
( memberP(sK6,sK4(sK5,sK6,sK7))
| ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5) ),
inference(superposition,[status(thm)],[c_144,c_50]) ).
tcf(c_2639,plain,
memberP(sK6,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_2638,c_140,c_138,c_136]) ).
tcf(c_2650,plain,
( memberP(sK7,sK4(sK5,sK6,sK7))
| ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5) ),
inference(superposition,[status(thm)],[c_144,c_51]) ).
tcf(c_2651,plain,
memberP(sK7,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_2650,c_140,c_138,c_136]) ).
tcf(c_2662,plain,
( leq(sK5,sK4(sK5,sK6,sK7))
| ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5) ),
inference(superposition,[status(thm)],[c_144,c_52]) ).
tcf(c_2663,plain,
leq(sK5,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[status(thm)],[c_2662,c_140,c_138,c_136]) ).
tcf(c_2674,plain,
( ~ ssList(sK7)
| ~ ssList(sK6)
| ~ ssItem(sK5)
| ~ leq(sK4(sK5,sK6,sK7),sK5) ),
inference(superposition,[status(thm)],[c_144,c_53]) ).
tcf(c_2675,plain,
~ leq(sK4(sK5,sK6,sK7),sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_2674,c_140,c_138,c_136]) ).
tcf(c_2720,plain,
( leq(sK4(sK5,sK6,sK7),sK5)
| ~ ssItem(sK4(sK5,sK6,sK7))
| ~ leq(sK5,sK4(sK5,sK6,sK7))
| ~ memberP(sK7,sK4(sK5,sK6,sK7)) ),
inference(superposition,[status(thm)],[c_2639,c_147]) ).
tcf(c_2721,plain,
( leq(sK4(sK5,sK6,sK7),sK5)
| ~ leq(sK5,sK4(sK5,sK6,sK7))
| ~ memberP(sK7,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2720,c_2627]) ).
tcf(c_2725,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2721,c_2675,c_2663,c_2651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 17:05:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 4.00/1.30 % SZS status Started for theBenchmark.p
% 4.00/1.30 % SZS status Theorem for theBenchmark.p
% 4.00/1.30
% 4.00/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.00/1.30
% 4.00/1.30 % ------ iProver source info
% 4.00/1.30
% 4.00/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.00/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.00/1.30 % git: non_committed_changes: false
% 4.00/1.30
% 4.00/1.30 % ------ Parsing...
% 4.00/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.00/1.30
% 4.00/1.30 % ------ 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 %
% 4.00/1.30
% 4.00/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.00/1.30
% 4.00/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.00/1.30 % ------ Proving...
% 4.00/1.30 % ------ Problem Properties
% 4.00/1.30
% 4.00/1.30 %
% 4.00/1.30 % clauses 56
% 4.00/1.30 % conjectures 13
% 4.00/1.30 % EPR 21
% 4.00/1.30 % Horn 50
% 4.00/1.30 % unary 12
% 4.00/1.30 % binary 5
% 4.00/1.30 % lits 197
% 4.00/1.30 % lits eq 36
% 4.00/1.30 % fd_pure 0
% 4.00/1.30 % fd_pseudo 0
% 4.00/1.30 % fd_cond 4
% 4.00/1.30 % fd_pseudo_cond 7
% 4.00/1.30 % AC symbols 0
% 4.00/1.30
% 4.00/1.30 % ------ Schedule dynamic 5 is on
% 4.00/1.30
% 4.00/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.00/1.30
% 4.00/1.30
% 4.00/1.30 % ------
% 4.00/1.30 % Current options:
% 4.00/1.30 % ------
% 4.00/1.30
% 4.00/1.30
% 4.00/1.30 %
% 4.00/1.30
% 4.00/1.30 % ------ Proving...
% 4.00/1.30 %
% 4.00/1.30
% 4.00/1.30 % SZS status Theorem for theBenchmark.p
% 4.00/1.30
% 4.00/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.00/1.30
% 4.00/1.30
%------------------------------------------------------------------------------