%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET504-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:47:20 PM UTC 2026
% Result : Unsatisfiable 10.01s 2.31s
% Output : CNFRefutation 10.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 71 ( 25 unt; 5 def)
% Number of atoms : 167 ( 44 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 47 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 95 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f30,axiom,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
member(ordered_pair(x,universal_class),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_universal_class_not_set_1) ).
fof(f127,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f127]) ).
fof(f143,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f185,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(universal_class,universal_class))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f122,f127]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(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_169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
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_186,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != null_class ) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_214,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_215,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_255,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(universal_class,universal_class))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f185]) ).
tcf(c_2973,definition,
iPr_def_10 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2974,definition,
iPr_def_11 = unordered_pair(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2975,definition,
iPr_def_12 = unordered_pair(x,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2976,definition,
iPr_def_13 = unordered_pair(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2977,definition,
iPr_def_14 = cross_product(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2978,negated_conjecture,
member(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_255,c_2977,c_2974,c_2975,c_2973,c_2976]) ).
tcf(c_3890,plain,
( member(universal_class,iPr_def_11)
| ~ member(universal_class,universal_class) ),
inference(superposition,[status(thm)],[c_2974,c_170]) ).
tcf(c_3926,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_163,c_180]) ).
tcf(c_4510,plain,
! [X0: $i] :
( ( X0 = universal_class )
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2974,c_169]) ).
tcf(c_4607,plain,
( ( null_class = iPr_def_11 )
| ( regular(iPr_def_11) = universal_class ) ),
inference(superposition,[status(thm)],[c_214,c_4510]) ).
tcf(c_4760,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(unordered_pair(iPr_def_10,unordered_pair(x,unordered_pair(X0,X0))),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_2973,c_174]) ).
tcf(c_4813,plain,
( ( null_class = iPr_def_11 )
| ( intersection(iPr_def_11,universal_class) = null_class ) ),
inference(superposition,[status(thm)],[c_4607,c_215]) ).
tcf(c_4814,plain,
( member(universal_class,iPr_def_11)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4607,c_214]) ).
tcf(c_4823,plain,
! [X0: $i] :
( member(universal_class,X0)
| ( null_class = iPr_def_11 )
| ~ subclass(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4814,c_162]) ).
tcf(c_6199,plain,
! [X0: $i] :
( member(X0,null_class)
| ( null_class = iPr_def_11 )
| ~ member(X0,iPr_def_11)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_4813,c_182]) ).
tcf(c_6214,plain,
( member(universal_class,null_class)
| ( null_class = iPr_def_11 )
| ~ member(universal_class,iPr_def_11)
| ~ member(universal_class,universal_class) ),
inference(instantiation,[status(thm)],[c_6199]) ).
tcf(c_7826,plain,
( member(universal_class,universal_class)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_165,c_4823]) ).
tcf(c_8198,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_3926,c_164]) ).
tcf(c_8406,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_215,c_8198]) ).
tcf(c_8412,plain,
( subclass(null_class,iPr_def_11)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4813,c_8198]) ).
tcf(c_8469,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_8406,c_168]) ).
tcf(c_8532,plain,
( ( null_class = iPr_def_11 )
| ~ subclass(iPr_def_11,null_class) ),
inference(superposition,[status(thm)],[c_8412,c_168]) ).
tcf(c_8555,plain,
! [X0: $i] : intersection(null_class,X0) = null_class,
inference(superposition,[status(thm)],[c_8198,c_8469]) ).
tcf(c_8589,plain,
! [X0: $i] : ~ member(X0,domain_of(null_class)),
inference(superposition,[status(thm)],[c_8555,c_186]) ).
tcf(c_8706,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm)],[c_214,c_8589]) ).
tcf(c_8715,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(demodulation,[status(thm)],[c_8589,c_8706]) ).
tcf(c_8716,plain,
~ member(universal_class,null_class),
inference(instantiation,[status(thm)],[c_8715]) ).
tcf(c_8787,plain,
null_class = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_8532,c_4814,c_6214,c_7826,c_8716]) ).
tcf(c_8793,plain,
! [X0: $i] : ~ member(X0,iPr_def_11),
inference(demodulation,[status(thm)],[c_8715,c_8787]) ).
tcf(c_8893,plain,
~ member(universal_class,universal_class),
inference(backward_subsumption_resolution,[status(thm)],[c_3890,c_8793]) ).
tcf(c_9818,plain,
! [X0: $i,X1: $i] :
( member(universal_class,X1)
| ~ member(unordered_pair(iPr_def_10,unordered_pair(x,iPr_def_11)),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_2974,c_4760]) ).
tcf(c_9822,plain,
! [X0: $i,X1: $i] :
( member(universal_class,X1)
| ~ member(iPr_def_13,cross_product(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_9818,c_2975,c_2976]) ).
tcf(c_9900,plain,
( member(universal_class,universal_class)
| ~ member(iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_2977,c_9822]) ).
tcf(c_9901,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9900,c_8893,c_2978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET504-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 11:13:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 10.01/2.31 % SZS status Started for theBenchmark.p
% 10.01/2.31 % SZS status Unsatisfiable for theBenchmark.p
% 10.01/2.31
% 10.01/2.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.01/2.31
% 10.01/2.31 % ------ iProver source info
% 10.01/2.31
% 10.01/2.31 % git: date: 2026-07-19 20:42:38 +0200
% 10.01/2.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.01/2.31 % git: non_committed_changes: false
% 10.01/2.31
% 10.01/2.31 % ------ Parsing...% successful
% 10.01/2.31
% 10.01/2.31
% 10.01/2.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.01/2.31
% 10.01/2.31 % ------ 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 %
% 10.01/2.31
% 10.01/2.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.01/2.31
% 10.01/2.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.01/2.31 % ------ Proving...
% 10.01/2.31 % ------ Problem Properties
% 10.01/2.31
% 10.01/2.31 %
% 10.01/2.31 % clauses 87
% 10.01/2.31 % conjectures 1
% 10.01/2.31 % EPR 13
% 10.01/2.31 % Horn 79
% 10.01/2.31 % unary 26
% 10.01/2.31 % binary 40
% 10.01/2.31 % lits 175
% 10.01/2.31 % lits eq 30
% 10.01/2.31 % fd_pure 0
% 10.01/2.31 % fd_pseudo 0
% 10.01/2.31 % fd_cond 3
% 10.01/2.31 % fd_pseudo_cond 7
% 10.01/2.31 % AC symbols 0
% 10.01/2.31
% 10.01/2.31 % ------ Schedule dynamic 5 is on
% 10.01/2.31
% 10.01/2.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.01/2.31
% 10.01/2.31
% 10.01/2.31 % ------
% 10.01/2.31 % Current options:
% 10.01/2.31 % ------
% 10.01/2.31
% 10.01/2.31
% 10.01/2.31 %
% 10.01/2.31
% 10.01/2.31 % ------ Proving...
% 10.01/2.31 %
% 10.01/2.31
% 10.01/2.31 % SZS status Unsatisfiable for theBenchmark.p
% 10.01/2.31
% 10.01/2.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.01/2.31
% 10.01/2.31
%------------------------------------------------------------------------------