%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET468-6 : 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 : n019.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 02:47:17 PM UTC 2026
% Result : Unsatisfiable 25.12s 4.49s
% Output : CNFRefutation 25.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 69 ( 23 unt; 1 def)
% Number of atoms : 131 ( 49 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 45 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 107 ( 0 sgn 107 !; 0 ?; 61 :)
% 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(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
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(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/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/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,
x = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sets_with_one_member2_1) ).
fof(f123,plain,
null_class = x,
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
~ subclass(cross_product(x,x),identity_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sets_with_one_member2_2) ).
fof(f129,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(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f14,f129]) ).
fof(f141,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,f129]) ).
fof(f145,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| x != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) ),
inference(definition_unfolding,[],[f30,f28,f12,f123]) ).
fof(f165,plain,
! [X0] :
( member(regular(X0),X0)
| x = X0 ),
inference(definition_unfolding,[],[f68,f123]) ).
fof(f166,plain,
! [X0] :
( intersection(X0,regular(X0)) = x
| x = X0 ),
inference(definition_unfolding,[],[f70,f123,f123]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_166,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_177,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,[],[f141]) ).
tcf(c_181,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,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_187,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != x ) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_215,negated_conjecture,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = x ) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_216,negated_conjecture,
! [X0: $i] :
( ( X0 = x )
| ( intersection(X0,regular(X0)) = x ) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_256,negated_conjecture,
~ subclass(cross_product(x,x),identity_relation),
inference(cnf_transformation,[],[f124]) ).
tcf(c_2975,definition,
iPr_def_10 = cross_product(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2977,negated_conjecture,
~ subclass(iPr_def_10,identity_relation),
inference(demodulation,[status(thm)],[c_256,c_2975]) ).
tcf(c_2979,negated_conjecture,
! [X0: $i] :
( ( X0 = x )
| ( intersection(X0,regular(X0)) = x ) ),
inference(demodulation,[status(thm)],[c_216]) ).
tcf(c_2980,negated_conjecture,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = x ) ),
inference(demodulation,[status(thm)],[c_215]) ).
tcf(c_2982,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != x ) ),
inference(demodulation,[status(thm)],[c_187]) ).
tcf(c_3904,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = x ) ),
inference(superposition,[status(thm)],[c_2980,c_181]) ).
tcf(c_4050,plain,
! [X0: $i,X1: $i] :
( member(X0,regular(X1))
| ( X1 = x )
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2979,c_182]) ).
tcf(c_4080,plain,
! [X0: $i] :
( ( complement(X0) = x )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_2980,c_184]) ).
tcf(c_4357,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_166,c_163]) ).
tcf(c_4589,plain,
! [X0: $i] :
( member(regular(X0),universal_class)
| ( X0 = x ) ),
inference(superposition,[status(thm)],[c_2980,c_4357]) ).
tcf(c_4599,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ( X1 = x )
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_4050,c_4357]) ).
tcf(c_4662,plain,
complement(universal_class) = x,
inference(superposition,[status(thm)],[c_4589,c_4080]) ).
tcf(c_4688,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_4662,c_184]) ).
tcf(c_4697,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,x)
| ( X1 = x ) ),
inference(global_subsumption_just,[status(thm)],[c_4599,c_4599,c_4688]) ).
tcf(c_4698,plain,
! [X0: $i,X1: $i] :
( ( X1 = x )
| ~ member(X0,x) ),
inference(renaming,[status(thm)],[c_4697]) ).
tcf(c_4707,plain,
! [X0: $i,X1: $i] :
( ( X1 = x )
| ( intersection(x,X0) = x ) ),
inference(superposition,[status(thm)],[c_3904,c_4698]) ).
tcf(c_4915,plain,
! [X0: $i] :
( ( intersection(x,X0) = x )
| ( x != x ) ),
inference(equality_factoring,[status(thm)],[c_4707]) ).
tcf(c_4954,plain,
! [X0: $i] : intersection(x,X0) = x,
inference(equality_resolution_simp,[status(thm)],[c_4915]) ).
tcf(c_5370,plain,
! [X0: $i] : ~ member(X0,domain_of(x)),
inference(superposition,[status(thm)],[c_4954,c_2982]) ).
tcf(c_5377,plain,
! [X0: $i] : subclass(domain_of(x),X0),
inference(superposition,[status(thm)],[c_164,c_5370]) ).
tcf(c_5379,plain,
domain_of(x) = x,
inference(superposition,[status(thm)],[c_2980,c_5370]) ).
tcf(c_5387,plain,
! [X0: $i] : ~ member(X0,x),
inference(demodulation,[status(thm)],[c_5370,c_5379]) ).
tcf(c_5393,plain,
! [X0: $i] : subclass(x,X0),
inference(light_normalisation,[status(thm)],[c_5377,c_5379]) ).
tcf(c_5866,plain,
! [X0: $i,X1: $i] :
( member(X0,x)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2975,c_174]) ).
tcf(c_5867,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_5866,c_5387]) ).
tcf(c_7889,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = x )
| ( 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_2980,c_177]) ).
tcf(c_19983,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = x )
| ~ member(regular(cross_product(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7889,c_5867]) ).
tcf(c_22758,plain,
( ( cross_product(x,x) = x )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2975,c_19983]) ).
tcf(c_22759,plain,
( ( x = iPr_def_10 )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_22758,c_2975]) ).
tcf(c_22766,plain,
x = iPr_def_10,
inference(superposition,[status(thm)],[c_2980,c_22759]) ).
tcf(c_22891,plain,
! [X0: $i] : subclass(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_5393,c_22766]) ).
tcf(c_22976,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2977,c_22891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET468-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 11:02:09 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.53
% 0.24/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.53
% 0.24/0.53 % Detected problem language: tptp
% 0.24/0.55 % Proving...
% 25.12/4.49 % SZS status Started for theBenchmark.p
% 25.12/4.49 % SZS status Unsatisfiable for theBenchmark.p
% 25.12/4.49
% 25.12/4.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.12/4.49
% 25.12/4.49 % ------ iProver source info
% 25.12/4.49
% 25.12/4.49 % git: date: 2026-07-19 20:42:38 +0200
% 25.12/4.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.12/4.49 % git: non_committed_changes: false
% 25.12/4.49
% 25.12/4.49 % ------ Parsing...% successful
% 25.12/4.49
% 25.12/4.49
% 25.12/4.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.12/4.49
% 25.12/4.49 % ------ 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 %
% 25.12/4.49
% 25.12/4.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 25.12/4.49
% 25.12/4.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.12/4.49 % ------ Proving...
% 25.12/4.49 % ------ Problem Properties
% 25.12/4.49
% 25.12/4.49 %
% 25.12/4.49 % clauses 83
% 25.12/4.49 % conjectures 6
% 25.12/4.49 % EPR 13
% 25.12/4.49 % Horn 75
% 25.12/4.49 % unary 22
% 25.12/4.49 % binary 40
% 25.12/4.49 % lits 171
% 25.12/4.49 % lits eq 26
% 25.12/4.49 % fd_pure 0
% 25.12/4.49 % fd_pseudo 0
% 25.12/4.49 % fd_cond 3
% 25.12/4.49 % fd_pseudo_cond 7
% 25.12/4.49 % AC symbols 0
% 25.12/4.49
% 25.12/4.49 % ------ Schedule dynamic 5 is on
% 25.12/4.49
% 25.12/4.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 25.12/4.49
% 25.12/4.49
% 25.12/4.49 % ------
% 25.12/4.49 % Current options:
% 25.12/4.49 % ------
% 25.12/4.49
% 25.12/4.49
% 25.12/4.49 %
% 25.12/4.49
% 25.12/4.49 % ------ Proving...
% 25.12/4.49 %
% 25.12/4.49
% 25.12/4.49 % SZS status Unsatisfiable for theBenchmark.p
% 25.12/4.49
% 25.12/4.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.12/4.49
% 25.12/4.49
%------------------------------------------------------------------------------