%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET347-6 : 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 : n010.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 02:47:08 PM UTC 2026
% Result : Unsatisfiable 9.52s 12.31s
% Output : CNFRefutation 9.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 85 ( 41 unt; 3 def)
% Number of atoms : 177 ( 54 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 101 ( 53 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 119 ( 0 sgn 119 !; 0 ?; 68 :)
% 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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
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(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f30,axiom,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).
fof(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',sum_class_definition) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f122,negated_conjecture,
sum_class(null_class) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum_class_of_null_class_1) ).
fof(f123,plain,
null_class != sum_class(null_class),
inference(reorient_equations,[],[f122]) ).
fof(f124,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f54,f28]) ).
fof(f128,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(f138,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,f128]) ).
fof(f140,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f128]) ).
fof(f143,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f144,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(f186,plain,
null_class != domain_of(intersection(element_relation,cross_product(universal_class,null_class))),
inference(definition_unfolding,[],[f123,f124]) ).
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_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,[],[f138]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f143]) ).
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,[],[f144]) ).
tcf(c_214,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_255,negated_conjecture,
domain_of(intersection(element_relation,cross_product(universal_class,null_class))) != null_class,
inference(cnf_transformation,[],[f186]) ).
tcf(c_2974,definition,
iPr_def_10 = cross_product(universal_class,null_class),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2975,definition,
iPr_def_11 = intersection(element_relation,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2976,definition,
iPr_def_12 = domain_of(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2977,negated_conjecture,
iPr_def_12 != null_class,
inference(demodulation,[status(thm)],[c_255,c_2974,c_2975,c_2976]) ).
tcf(c_3848,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = intersection(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2974,c_185]) ).
tcf(c_3850,plain,
intersection(iPr_def_10,element_relation) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2975,c_3848]) ).
tcf(c_3873,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_3989,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_163,c_183]) ).
tcf(c_3990,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_214,c_183]) ).
tcf(c_3995,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_3990]) ).
tcf(c_4075,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_165,c_162]) ).
tcf(c_4200,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_163,c_4075]) ).
tcf(c_4528,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_4200,c_3989]) ).
tcf(c_4562,plain,
! [X0: $i] :
( ( complement(universal_class) = X0 )
| ~ subclass(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_4528,c_168]) ).
tcf(c_4563,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_4528,c_162]) ).
tcf(c_4576,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(superposition,[status(thm)],[c_214,c_4563]) ).
tcf(c_4579,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_4576]) ).
tcf(c_4586,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_4576,c_3995,c_4579]) ).
tcf(c_4588,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(demodulation,[status(thm)],[c_4562,c_4586]) ).
tcf(c_4589,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(demodulation,[status(thm)],[c_4563,c_4586]) ).
tcf(c_4590,plain,
! [X0: $i] : subclass(null_class,X0),
inference(demodulation,[status(thm)],[c_4528,c_4586]) ).
tcf(c_4600,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_4586,c_183]) ).
tcf(c_4607,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_4589,c_4075,c_4589,c_4600]) ).
tcf(c_4742,plain,
! [X0: $i,X1: $i] :
( member(X1,null_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2974,c_174]) ).
tcf(c_4743,plain,
! [X0: $i,X1: $i] : ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4742,c_4607]) ).
tcf(c_5042,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_3873,c_164]) ).
tcf(c_5163,plain,
! [X0: $i] : subclass(intersection(X0,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_3848,c_5042]) ).
tcf(c_5169,plain,
! [X0: $i] : intersection(null_class,X0) = null_class,
inference(superposition,[status(thm)],[c_5042,c_4588]) ).
tcf(c_5197,plain,
! [X0: $i] :
( ( intersection(X0,iPr_def_10) = iPr_def_10 )
| ~ subclass(iPr_def_10,intersection(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5163,c_168]) ).
tcf(c_5217,plain,
! [X0: $i] : ~ member(X0,domain_of(null_class)),
inference(superposition,[status(thm)],[c_5169,c_186]) ).
tcf(c_5224,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm)],[c_214,c_5217]) ).
tcf(c_5356,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = null_class )
| ( unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))) = regular(cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_214,c_176]) ).
tcf(c_8557,plain,
! [X0: $i] :
( ( intersection(X0,iPr_def_10) = iPr_def_10 )
| ~ subclass(iPr_def_10,intersection(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_3848,c_5197]) ).
tcf(c_9034,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = null_class )
| ~ member(regular(cross_product(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5356,c_4743]) ).
tcf(c_15693,plain,
( ( cross_product(universal_class,null_class) = null_class )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2974,c_9034]) ).
tcf(c_15694,plain,
( ( null_class = iPr_def_10 )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_15693,c_2974]) ).
tcf(c_15701,plain,
null_class = iPr_def_10,
inference(superposition,[status(thm)],[c_214,c_15694]) ).
tcf(c_15766,plain,
domain_of(iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5224,c_15701]) ).
tcf(c_15775,plain,
! [X0: $i] : subclass(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_4590,c_15701]) ).
tcf(c_15790,plain,
iPr_def_10 != iPr_def_12,
inference(demodulation,[status(thm)],[c_2977,c_15701]) ).
tcf(c_15812,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_8557,c_15775]) ).
tcf(c_15839,plain,
! [X0: $i] : intersection(iPr_def_10,X0) = iPr_def_10,
inference(demodulation,[status(thm)],[c_3848,c_15812]) ).
tcf(c_15840,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_3850,c_15839]) ).
tcf(c_15865,plain,
domain_of(iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2976,c_15840]) ).
tcf(c_16115,plain,
iPr_def_10 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_15865,c_15766]) ).
tcf(c_16116,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16115,c_15790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET347-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.39 % Computer : n010.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Thu Sep 24 10:40:16 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.45 % Detected problem language: tptp
% 0.15/10.46 % Proving...
% 9.52/12.31 % SZS status Started for theBenchmark.p
% 9.52/12.31 % SZS status Unsatisfiable for theBenchmark.p
% 9.52/12.31
% 9.52/12.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.52/12.31
% 9.52/12.31 % ------ iProver source info
% 9.52/12.31
% 9.52/12.31 % git: date: 2026-07-19 20:42:38 +0200
% 9.52/12.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.52/12.31 % git: non_committed_changes: false
% 9.52/12.31
% 9.52/12.31 % ------ Parsing...% successful
% 9.52/12.31
% 9.52/12.31
% 9.52/12.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.52/12.31
% 9.52/12.31 % ------ 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 %
% 9.52/12.31
% 9.52/12.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.52/12.31
% 9.52/12.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.52/12.31 % ------ Proving...
% 9.52/12.31 % ------ Problem Properties
% 9.52/12.31
% 9.52/12.31 %
% 9.52/12.31 % clauses 85
% 9.52/12.31 % conjectures 1
% 9.52/12.31 % EPR 13
% 9.52/12.31 % Horn 77
% 9.52/12.31 % unary 24
% 9.52/12.31 % binary 40
% 9.52/12.31 % lits 173
% 9.52/12.31 % lits eq 29
% 9.52/12.31 % fd_pure 0
% 9.52/12.31 % fd_pseudo 0
% 9.52/12.31 % fd_cond 3
% 9.52/12.31 % fd_pseudo_cond 7
% 9.52/12.31 % AC symbols 0
% 9.52/12.31
% 9.52/12.31 % ------ Schedule dynamic 5 is on
% 9.52/12.31
% 9.52/12.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.52/12.31
% 9.52/12.31
% 9.52/12.31 % ------
% 9.52/12.31 % Current options:
% 9.52/12.31 % ------
% 9.52/12.31
% 9.52/12.31
% 9.52/12.31 %
% 9.52/12.31
% 9.52/12.31 % ------ Proving...
% 9.52/12.31 %
% 9.52/12.31
% 9.52/12.31 % SZS status Unsatisfiable for theBenchmark.p
% 9.52/12.31
% 9.52/12.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.52/12.31
% 9.52/12.31
%------------------------------------------------------------------------------