%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC098-1 : 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 : n015.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 03:07:53 PM UTC 2026
% Result : Unsatisfiable 2.63s 1.38s
% Output : CNFRefutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 70 ( 18 unt; 1 def)
% Number of atoms : 197 ( 76 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 235 ( 114 ~; 121 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0] :
( ~ memberP(sk2,X0)
| ssItem(sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( ~ memberP(sk2,X0)
| memberP(sk2,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ memberP(sk2,X0)
| leq(X0,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ memberP(sk2,X0)
| X0 != sk5(X0)
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
! [X0] :
( ~ memberP(sk2,X0)
| sk5(X0) != X0
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( nil = sk4
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f213,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f214,negated_conjecture,
( nil = sk4
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f215,plain,
( nil = sk4
| sk3 = cons(sk6,nil) ),
inference(reorient_equations,[],[f214]) ).
fof(f216,negated_conjecture,
( nil = sk4
| memberP(sk4,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
! [X0] :
( nil = sk4
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f218,negated_conjecture,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f219,plain,
( nil = sk3
| sk3 = cons(sk6,nil) ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
( nil = sk3
| memberP(sk4,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f221,negated_conjecture,
! [X0] :
( nil = sk3
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f224,plain,
! [X0] :
( ~ memberP(sk4,X0)
| ssItem(sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f206,f205,f204]) ).
fof(f225,plain,
! [X0] :
( ~ memberP(sk4,X0)
| memberP(sk4,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f207,f205,f204,f204]) ).
fof(f226,plain,
! [X0] :
( ~ memberP(sk4,X0)
| leq(X0,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f208,f205,f204]) ).
fof(f227,plain,
! [X0] :
( ~ memberP(sk4,X0)
| sk5(X0) != X0
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f210,f205,f204]) ).
fof(f228,plain,
( nil != sk3
| nil != sk4 ),
inference(definition_unfolding,[],[f211,f204,f205]) ).
tcf(c_442,negated_conjecture,
! [X0: $i] :
( ssItem(sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != sk3 ) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_443,negated_conjecture,
! [X0: $i] :
( memberP(sk4,sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != sk3 ) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_444,negated_conjecture,
! [X0: $i] :
( leq(X0,sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != sk3 ) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_445,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( sk5(X0) != X0 )
| ( cons(X0,nil) != sk3 ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_446,negated_conjecture,
( ( sk4 != nil )
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_447,negated_conjecture,
( ssItem(sk6)
| ( sk4 = nil ) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_448,negated_conjecture,
( ssItem(sk6)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_449,negated_conjecture,
( ( sk4 = nil )
| ( cons(sk6,nil) = sk3 ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_450,negated_conjecture,
( memberP(sk4,sk6)
| ( sk4 = nil ) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_451,negated_conjecture,
! [X0: $i] :
( ( sk4 = nil )
| ( X0 = sk6 )
| ~ ssItem(X0)
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_452,negated_conjecture,
( ( sk3 = nil )
| ( cons(sk6,nil) = sk3 ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_453,negated_conjecture,
( memberP(sk4,sk6)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_454,negated_conjecture,
! [X0: $i] :
( ( sk3 = nil )
| ( X0 = sk6 )
| ~ ssItem(X0)
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_568,negated_conjecture,
ssItem(sk6),
inference(global_subsumption_just,[status(thm)],[c_448,c_448,c_447,c_446]) ).
tcf(c_570,negated_conjecture,
ssItem(sk6),
inference(global_subsumption_just,[status(thm)],[c_447,c_568]) ).
tcf(c_578,negated_conjecture,
memberP(sk4,sk6),
inference(global_subsumption_just,[status(thm)],[c_453,c_453,c_450,c_446]) ).
tcf(c_580,negated_conjecture,
memberP(sk4,sk6),
inference(global_subsumption_just,[status(thm)],[c_450,c_578]) ).
tcf(c_584,negated_conjecture,
cons(sk6,nil) = sk3,
inference(global_subsumption_just,[status(thm)],[c_452,c_452,c_449,c_446]) ).
tcf(c_586,negated_conjecture,
cons(sk6,nil) = sk3,
inference(global_subsumption_just,[status(thm)],[c_449,c_584]) ).
tcf(c_592,plain,
! [X0: $i] :
( ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| ~ ssItem(X0)
| ( X0 = sk6 ) ),
inference(global_subsumption_just,[status(thm)],[c_454,c_446,c_454,c_451]) ).
tcf(c_593,negated_conjecture,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssItem(X0)
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0) ),
inference(renaming,[status(thm)],[c_592]) ).
tcf(c_595,plain,
! [X0: $i] :
( ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| ~ ssItem(X0)
| ( X0 = sk6 ) ),
inference(global_subsumption_just,[status(thm)],[c_451,c_593]) ).
tcf(c_596,negated_conjecture,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssItem(X0)
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0) ),
inference(renaming,[status(thm)],[c_595]) ).
tcf(c_6641,definition,
iPr_def_12 = cons(sk6,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6642,negated_conjecture,
! [X0: $i] :
( ( X0 = sk6 )
| ~ ssItem(X0)
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0) ),
inference(demodulation,[status(thm)],[c_596]) ).
tcf(c_6643,negated_conjecture,
iPr_def_12 = sk3,
inference(demodulation,[status(thm)],[c_586,c_6641]) ).
tcf(c_6644,negated_conjecture,
memberP(sk4,sk6),
inference(demodulation,[status(thm)],[c_580]) ).
tcf(c_6645,negated_conjecture,
ssItem(sk6),
inference(demodulation,[status(thm)],[c_570]) ).
tcf(c_6647,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( sk5(X0) != X0 )
| ( cons(X0,nil) != sk3 ) ),
inference(demodulation,[status(thm)],[c_445]) ).
tcf(c_6648,negated_conjecture,
! [X0: $i] :
( leq(X0,sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != sk3 ) ),
inference(demodulation,[status(thm)],[c_444]) ).
tcf(c_6649,negated_conjecture,
! [X0: $i] :
( memberP(sk4,sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != sk3 ) ),
inference(demodulation,[status(thm)],[c_443]) ).
tcf(c_6650,negated_conjecture,
! [X0: $i] :
( ssItem(sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != sk3 ) ),
inference(demodulation,[status(thm)],[c_442]) ).
tcf(c_9246,plain,
! [X0: $i] :
( ssItem(sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6650,c_6643]) ).
tcf(c_9259,plain,
! [X0: $i] :
( leq(X0,sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6648,c_6643]) ).
tcf(c_9272,plain,
! [X0: $i] :
( memberP(sk4,sk5(X0))
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( cons(X0,nil) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6649,c_6643]) ).
tcf(c_9285,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ( sk5(X0) != X0 )
| ( cons(X0,nil) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_6647,c_6643]) ).
tcf(c_9302,plain,
( ~ ssItem(sk6)
| ~ memberP(sk4,sk6)
| ( sk5(sk6) != sk6 ) ),
inference(superposition,[status(thm)],[c_6641,c_9285]) ).
tcf(c_9303,plain,
( memberP(sk4,sk5(sk6))
| ~ ssItem(sk6)
| ~ memberP(sk4,sk6) ),
inference(superposition,[status(thm)],[c_6641,c_9272]) ).
tcf(c_9304,plain,
( leq(sk6,sk5(sk6))
| ~ ssItem(sk6)
| ~ memberP(sk4,sk6) ),
inference(superposition,[status(thm)],[c_6641,c_9259]) ).
tcf(c_9305,plain,
( ssItem(sk5(sk6))
| ~ ssItem(sk6)
| ~ memberP(sk4,sk6) ),
inference(superposition,[status(thm)],[c_6641,c_9246]) ).
tcf(c_9306,plain,
ssItem(sk5(sk6)),
inference(forward_subsumption_resolution,[status(thm)],[c_9305,c_6645,c_6644]) ).
tcf(c_9307,plain,
leq(sk6,sk5(sk6)),
inference(forward_subsumption_resolution,[status(thm)],[c_9304,c_6645,c_6644]) ).
tcf(c_9308,plain,
memberP(sk4,sk5(sk6)),
inference(forward_subsumption_resolution,[status(thm)],[c_9303,c_6645,c_6644]) ).
tcf(c_9309,plain,
sk5(sk6) != sk6,
inference(forward_subsumption_resolution,[status(thm)],[c_9302,c_6645,c_6644]) ).
tcf(c_9310,plain,
( ( sk5(sk6) = sk6 )
| ~ ssItem(sk5(sk6))
| ~ leq(sk6,sk5(sk6)) ),
inference(superposition,[status(thm)],[c_9308,c_6642]) ).
tcf(c_9311,plain,
sk5(sk6) = sk6,
inference(forward_subsumption_resolution,[status(thm)],[c_9310,c_9306,c_9307]) ).
tcf(c_9315,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9311,c_9309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.56 % Computer : n015.cluster.edu
% 0.02/0.56 % Model : x86_64 x86_64
% 0.02/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.56 % Memory : 8046.5625MB
% 0.02/0.56 % OS : Linux 6.8.0-71-generic
% 0.02/0.56 % CPULimit : 300
% 0.02/0.56 % WCLimit : 300
% 0.02/0.56 % DateTime : Thu Sep 24 16:25:41 UTC 2026
% 0.02/0.56 % CPUTime :
% 0.02/0.56 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.60 Running first-order theorem proving
% 0.02/0.60 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
% 0.02/0.62
% 0.02/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.62
% 0.02/0.62 % Detected problem language: tptp
% 0.02/0.63 % Proving...
% 2.63/1.38 % SZS status Started for theBenchmark.p
% 2.63/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 2.63/1.38
% 2.63/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.63/1.38
% 2.63/1.38 % ------ iProver source info
% 2.63/1.38
% 2.63/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 2.63/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.63/1.38 % git: non_committed_changes: false
% 2.63/1.38
% 2.63/1.38 % ------ Parsing...% successful
% 2.63/1.38
% 2.63/1.38
% 2.63/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.63/1.38
% 2.63/1.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.63/1.38
% 2.63/1.38 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.63/1.38
% 2.63/1.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.63/1.38 % ------ Proving...
% 2.63/1.38 % ------ Problem Properties
% 2.63/1.38
% 2.63/1.38 %
% 2.63/1.38 % clauses 189
% 2.63/1.38 % conjectures 11
% 2.63/1.38 % EPR 59
% 2.63/1.38 % Horn 161
% 2.63/1.38 % unary 64
% 2.63/1.38 % binary 22
% 2.63/1.38 % lits 569
% 2.63/1.39 % lits eq 79
% 2.63/1.39 % fd_pure 0
% 2.63/1.39 % fd_pseudo 0
% 2.63/1.39 % fd_cond 16
% 2.63/1.39 % fd_pseudo_cond 14
% 2.63/1.39 % AC symbols 0
% 2.63/1.39
% 2.63/1.39 % ------ Schedule dynamic 5 is on
% 2.63/1.39
% 2.63/1.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.63/1.39
% 2.63/1.39
% 2.63/1.39 % ------
% 2.63/1.39 % Current options:
% 2.63/1.39 % ------
% 2.63/1.39
% 2.63/1.39
% 2.63/1.39 %
% 2.63/1.39
% 2.63/1.39 % ------ Proving...
% 2.63/1.39 %
% 2.63/1.39
% 2.63/1.39 % SZS status Unsatisfiable for theBenchmark.p
% 2.63/1.39
% 2.63/1.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.63/1.39
% 2.63/1.39
%------------------------------------------------------------------------------