%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET165-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 02:46:48 PM UTC 2026
% Result : Unsatisfiable 24.16s 4.29s
% Output : CNFRefutation 24.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 67 ( 27 unt; 7 def)
% Number of atoms : 210 ( 23 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 100 ( 47 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f122,negated_conjecture,
union(x,union(x,y)) != union(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_idempotency_of_union_1) ).
fof(f123,plain,
union(x,y) != union(x,union(x,y)),
inference(reorient_equations,[],[f122]) ).
fof(f186,plain,
complement(intersection(complement(x),complement(y))) != complement(intersection(complement(x),complement(complement(intersection(complement(x),complement(y)))))),
inference(definition_unfolding,[],[f123,f26,f26,f26]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_165,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_255,negated_conjecture,
complement(intersection(complement(x),complement(complement(intersection(complement(x),complement(y)))))) != complement(intersection(complement(x),complement(y))),
inference(cnf_transformation,[],[f186]) ).
tcf(c_2974,definition,
iPr_def_10 = complement(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2975,definition,
iPr_def_11 = complement(y),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2976,definition,
iPr_def_12 = intersection(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2977,definition,
iPr_def_13 = complement(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2978,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2979,definition,
iPr_def_15 = intersection(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2980,definition,
iPr_def_16 = complement(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2981,negated_conjecture,
iPr_def_16 != iPr_def_13,
inference(demodulation,[status(thm)],[c_255,c_2975,c_2976,c_2977,c_2978,c_2974,c_2979,c_2980]) ).
tcf(c_3893,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2976,c_180]) ).
tcf(c_3968,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| ~ member(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_2979,c_181]) ).
tcf(c_3997,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_13)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2977,c_183]) ).
tcf(c_3998,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2978,c_183]) ).
tcf(c_4048,plain,
! [X0: $i] :
( subclass(iPr_def_15,X0)
| member(not_subclass_element(iPr_def_15,X0),iPr_def_14) ),
inference(superposition,[status(thm)],[c_163,c_3968]) ).
tcf(c_4110,plain,
! [X0: $i] :
( subclass(iPr_def_12,X0)
| ~ member(not_subclass_element(iPr_def_12,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_163,c_3997]) ).
tcf(c_4121,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| ~ member(not_subclass_element(iPr_def_14,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_163,c_3998]) ).
tcf(c_4181,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_165,c_162]) ).
tcf(c_4233,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| member(X0,iPr_def_12)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2977,c_184]) ).
tcf(c_4234,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,iPr_def_13)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2978,c_184]) ).
tcf(c_4335,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_163,c_4181]) ).
tcf(c_4370,plain,
subclass(iPr_def_15,iPr_def_14),
inference(superposition,[status(thm)],[c_4048,c_164]) ).
tcf(c_4389,plain,
( ( iPr_def_14 = iPr_def_15 )
| ~ subclass(iPr_def_14,iPr_def_15) ),
inference(superposition,[status(thm)],[c_4370,c_168]) ).
tcf(c_4487,plain,
! [X0: $i] :
( member(X0,iPr_def_15)
| ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2979,c_182]) ).
tcf(c_5263,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_13)
| member(not_subclass_element(X0,X1),iPr_def_12) ),
inference(superposition,[status(thm)],[c_4335,c_4233]) ).
tcf(c_5330,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_14)
| member(not_subclass_element(X0,X1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_4335,c_4234]) ).
tcf(c_29276,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| member(not_subclass_element(iPr_def_14,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_5263,c_4121]) ).
tcf(c_30369,plain,
subclass(iPr_def_14,iPr_def_12),
inference(superposition,[status(thm)],[c_29276,c_164]) ).
tcf(c_30375,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| member(not_subclass_element(iPr_def_14,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_29276,c_3893]) ).
tcf(c_30389,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ subclass(iPr_def_12,iPr_def_14) ),
inference(superposition,[status(thm)],[c_30369,c_168]) ).
tcf(c_31537,plain,
subclass(iPr_def_14,iPr_def_10),
inference(superposition,[status(thm)],[c_30375,c_164]) ).
tcf(c_31555,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_31537,c_162]) ).
tcf(c_31618,plain,
! [X0: $i] :
( member(X0,iPr_def_15)
| ~ member(X0,iPr_def_14) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4487,c_31555]) ).
tcf(c_31938,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| member(not_subclass_element(iPr_def_14,X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_163,c_31618]) ).
tcf(c_32869,plain,
subclass(iPr_def_14,iPr_def_15),
inference(superposition,[status(thm)],[c_31938,c_164]) ).
tcf(c_32884,plain,
iPr_def_14 = iPr_def_15,
inference(backward_subsumption_resolution,[status(thm)],[c_4389,c_32869]) ).
tcf(c_32960,plain,
complement(iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_2980,c_32884]) ).
tcf(c_40449,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| member(not_subclass_element(X0,iPr_def_14),iPr_def_13) ),
inference(superposition,[status(thm)],[c_5330,c_164]) ).
tcf(c_40481,plain,
subclass(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_40449,c_4110]) ).
tcf(c_40489,plain,
iPr_def_12 = iPr_def_14,
inference(backward_subsumption_resolution,[status(thm)],[c_30389,c_40481]) ).
tcf(c_40538,plain,
complement(iPr_def_12) = iPr_def_16,
inference(demodulation,[status(thm)],[c_32960,c_40489]) ).
tcf(c_40586,plain,
iPr_def_13 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_40538,c_2977]) ).
tcf(c_40608,plain,
iPr_def_13 != iPr_def_13,
inference(demodulation,[status(thm)],[c_2981,c_40586]) ).
tcf(c_40609,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_40608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET165-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 10:08:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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...
% 24.16/4.29 % SZS status Started for theBenchmark.p
% 24.16/4.29 % SZS status Unsatisfiable for theBenchmark.p
% 24.16/4.29
% 24.16/4.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 24.16/4.29
% 24.16/4.29 % ------ iProver source info
% 24.16/4.29
% 24.16/4.29 % git: date: 2026-07-19 20:42:38 +0200
% 24.16/4.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 24.16/4.29 % git: non_committed_changes: false
% 24.16/4.29
% 24.16/4.29 % ------ Parsing...% successful
% 24.16/4.29
% 24.16/4.29
% 24.16/4.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 24.16/4.29
% 24.16/4.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 24.16/4.29
% 24.16/4.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 24.16/4.29
% 24.16/4.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.16/4.29 % ------ Proving...
% 24.16/4.29 % ------ Problem Properties
% 24.16/4.29
% 24.16/4.29 %
% 24.16/4.29 % clauses 89
% 24.16/4.29 % conjectures 1
% 24.16/4.29 % EPR 13
% 24.16/4.29 % Horn 81
% 24.16/4.29 % unary 28
% 24.16/4.29 % binary 40
% 24.16/4.29 % lits 177
% 24.16/4.29 % lits eq 33
% 24.16/4.29 % fd_pure 0
% 24.16/4.29 % fd_pseudo 0
% 24.16/4.29 % fd_cond 3
% 24.16/4.29 % fd_pseudo_cond 7
% 24.16/4.29 % AC symbols 0
% 24.16/4.29
% 24.16/4.29 % ------ Schedule dynamic 5 is on
% 24.16/4.29
% 24.16/4.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 24.16/4.29
% 24.16/4.29
% 24.16/4.29 % ------
% 24.16/4.29 % Current options:
% 24.16/4.29 % ------
% 24.16/4.29
% 24.16/4.29
% 24.16/4.29 %
% 24.16/4.29
% 24.16/4.29 % ------ Proving...
% 24.16/4.29 %
% 24.16/4.29
% 24.16/4.29 % SZS status Unsatisfiable for theBenchmark.p
% 24.16/4.29
% 24.16/4.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.16/4.29
% 24.16/4.29
%------------------------------------------------------------------------------