%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET287-6 : 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 02:47:04 PM UTC 2026
% Result : Unsatisfiable 1.03s 6.29s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 76 ( 36 unt; 3 def)
% Number of atoms : 163 ( 33 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 90 ( 48 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?; 48 :)
% 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(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(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(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(f48,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
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(f108,axiom,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-1.ax',definition_of_domain_relation2) ).
fof(f109,axiom,
! [X0] :
( member(ordered_pair(X0,domain_of(X0)),domain_relation)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-1.ax',definition_of_domain_relation3) ).
fof(f122,negated_conjecture,
subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_property8_1) ).
fof(f123,negated_conjecture,
domain_of(intersection(complement(y),x)) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_property8_2) ).
fof(f124,plain,
null_class != domain_of(intersection(complement(y),x)),
inference(reorient_equations,[],[f123]) ).
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(f144,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f145,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(f180,plain,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
inference(definition_unfolding,[],[f108,f129]) ).
fof(f181,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f109,f129]) ).
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_165,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_166,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
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_186,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f144]) ).
tcf(c_187,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,[],[f145]) ).
tcf(c_198,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_201,plain,
inductive(omega),
inference(cnf_transformation,[],[f51]) ).
tcf(c_215,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] :
( ( domain_of(X0) = X1 )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_246,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_256,negated_conjecture,
subclass(x,y),
inference(cnf_transformation,[],[f122]) ).
tcf(c_257,negated_conjecture,
domain_of(intersection(complement(y),x)) != null_class,
inference(cnf_transformation,[],[f124]) ).
tcf(c_392,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(prop_impl_just,[status(thm)],[c_198]) ).
tcf(c_1492,plain,
! [X0: $i] :
( member(null_class,X0)
| ( X0 != omega ) ),
inference(resolution_lifted,[status(thm)],[c_392,c_201]) ).
tcf(c_1493,plain,
member(null_class,omega),
inference(unflattening,[status(thm)],[c_1492]) ).
tcf(c_2981,definition,
iPr_def_10 = complement(y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2982,definition,
iPr_def_11 = intersection(iPr_def_10,x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2983,definition,
iPr_def_12 = domain_of(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2984,negated_conjecture,
iPr_def_12 != null_class,
inference(demodulation,[status(thm)],[c_257,c_2981,c_2982,c_2983]) ).
tcf(c_2985,negated_conjecture,
subclass(x,y),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_3883,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2982,c_181]) ).
tcf(c_3919,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2982,c_182]) ).
tcf(c_3931,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| member(not_subclass_element(iPr_def_11,X0),x) ),
inference(superposition,[status(thm)],[c_164,c_3919]) ).
tcf(c_3953,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_2981,c_184]) ).
tcf(c_4005,plain,
! [X0: $i] :
( member(X0,y)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2985,c_163]) ).
tcf(c_4010,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_166,c_163]) ).
tcf(c_4088,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| member(not_subclass_element(iPr_def_11,X0),y) ),
inference(superposition,[status(thm)],[c_3931,c_4005]) ).
tcf(c_4110,plain,
member(null_class,universal_class),
inference(superposition,[status(thm)],[c_1493,c_4010]) ).
tcf(c_4143,plain,
subclass(iPr_def_11,y),
inference(superposition,[status(thm)],[c_4088,c_165]) ).
tcf(c_4153,plain,
! [X0: $i] :
( member(X0,y)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4143,c_163]) ).
tcf(c_4286,plain,
! [X0: $i] : ~ member(X0,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_4153,c_3883,c_3953,c_4153]) ).
tcf(c_4290,plain,
null_class = iPr_def_11,
inference(superposition,[status(thm)],[c_215,c_4286]) ).
tcf(c_4291,plain,
member(iPr_def_11,universal_class),
inference(demodulation,[status(thm)],[c_4110,c_4290]) ).
tcf(c_4295,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_215,c_4290]) ).
tcf(c_4297,plain,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_2984,c_4290]) ).
tcf(c_4339,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X1)
| ( intersection(X0,X1) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4295,c_182]) ).
tcf(c_4670,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_187,c_4290]) ).
tcf(c_4879,plain,
( member(unordered_pair(unordered_pair(iPr_def_11,iPr_def_11),unordered_pair(iPr_def_11,unordered_pair(iPr_def_12,iPr_def_12))),domain_relation)
| ~ member(iPr_def_11,universal_class) ),
inference(superposition,[status(thm)],[c_2983,c_246]) ).
tcf(c_4883,plain,
member(unordered_pair(unordered_pair(iPr_def_11,iPr_def_11),unordered_pair(iPr_def_11,unordered_pair(iPr_def_12,iPr_def_12))),domain_relation),
inference(forward_subsumption_resolution,[status(thm)],[c_4879,c_4291]) ).
tcf(c_4911,plain,
domain_of(iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_4883,c_245]) ).
tcf(c_4931,plain,
! [X0: $i] : intersection(X0,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_4339,c_4286]) ).
tcf(c_5180,plain,
! [X0: $i,X1: $i] : intersection(iPr_def_11,cross_product(X0,X1)) = iPr_def_11,
inference(superposition,[status(thm)],[c_4931,c_186]) ).
tcf(c_5192,plain,
! [X0: $i] : ~ member(X0,domain_of(iPr_def_11)),
inference(superposition,[status(thm)],[c_5180,c_4670]) ).
tcf(c_5194,plain,
! [X0: $i] : ~ member(X0,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_5192,c_4911]) ).
tcf(c_5526,plain,
iPr_def_11 = iPr_def_12,
inference(superposition,[status(thm)],[c_4295,c_5194]) ).
tcf(c_5529,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5526,c_4297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET287-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 10:32:01 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.42 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 1.03/6.29 % SZS status Started for theBenchmark.p
% 1.03/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.03/6.29
% 1.03/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.03/6.29
% 1.03/6.29 % ------ iProver source info
% 1.03/6.29
% 1.03/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.03/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.03/6.29 % git: non_committed_changes: false
% 1.03/6.29
% 1.03/6.29 % ------ Parsing...% successful
% 1.03/6.29
% 1.03/6.29
% 1.03/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.03/6.29
% 1.03/6.29 % ------ 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 %
% 1.03/6.29
% 1.03/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.03/6.29
% 1.03/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.03/6.29 % ------ Proving...
% 1.03/6.29 % ------ Problem Properties
% 1.03/6.29
% 1.03/6.29 %
% 1.03/6.29 % clauses 86
% 1.03/6.29 % conjectures 2
% 1.03/6.29 % EPR 14
% 1.03/6.29 % Horn 78
% 1.03/6.29 % unary 25
% 1.03/6.29 % binary 40
% 1.03/6.29 % lits 174
% 1.03/6.29 % lits eq 29
% 1.03/6.29 % fd_pure 0
% 1.03/6.29 % fd_pseudo 0
% 1.03/6.29 % fd_cond 3
% 1.03/6.29 % fd_pseudo_cond 7
% 1.03/6.29 % AC symbols 0
% 1.03/6.29
% 1.03/6.29 % ------ Schedule dynamic 5 is on
% 1.03/6.29
% 1.03/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.03/6.29
% 1.03/6.29
% 1.03/6.29 % ------
% 1.03/6.29 % Current options:
% 1.03/6.29 % ------
% 1.03/6.29
% 1.03/6.29
% 1.03/6.29 %
% 1.03/6.29
% 1.03/6.29 % ------ Proving...
% 1.03/6.29 %
% 1.03/6.29
% 1.03/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.03/6.29
% 1.03/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.03/6.29
% 1.03/6.29
%------------------------------------------------------------------------------