%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM042-1 : 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 : n015.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 02:23:17 PM UTC 2026
% Result : Unsatisfiable 1.10s 1.73s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 49 ( 31 unt; 11 def)
% Number of atoms : 107 ( 23 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 44 ( 23 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?; 26 :)
% 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(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
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(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f122,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
fof(f124,axiom,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(restrict(X0,X1,X1),complement(identity_relation)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
fof(f176,negated_conjecture,
subclass(x,complement(identity_relation)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_1) ).
fof(f177,negated_conjecture,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_2) ).
fof(f191,plain,
! [X0] : symmetrization_of(X0) = complement(intersection(complement(X0),complement(domain_of(flip(cross_product(X0,universal_class)))))),
inference(definition_unfolding,[],[f122,f26,f39]) ).
fof(f201,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f245,plain,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(definition_unfolding,[],[f124,f28]) ).
fof(f268,plain,
~ irreflexive(x,domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))),
inference(definition_unfolding,[],[f177,f191]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f201]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_344,negated_conjecture,
subclass(x,complement(identity_relation)),
inference(cnf_transformation,[],[f176]) ).
tcf(c_345,negated_conjecture,
~ irreflexive(x,domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))),
inference(cnf_transformation,[],[f268]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] :
( ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| irreflexive(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_303]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(renaming,[status(thm)],[c_458]) ).
tcf(c_2114,plain,
! [X0: $i,X1: $i] :
( ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| ( X0 != x )
| ( domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_459,c_345]) ).
tcf(c_2115,plain,
~ subclass(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),
inference(unflattening,[status(thm)],[c_2114]) ).
tcf(c_4635,definition,
iPr_def_10 = complement(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4636,definition,
iPr_def_11 = cross_product(x,universal_class),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4637,definition,
iPr_def_12 = flip(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_4638,definition,
iPr_def_13 = domain_of(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_4639,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_4640,definition,
iPr_def_15 = intersection(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_4641,definition,
iPr_def_16 = complement(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_4642,definition,
iPr_def_17 = domain_of(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_4643,definition,
iPr_def_18 = cross_product(iPr_def_17,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_4644,definition,
iPr_def_19 = intersection(x,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_4645,definition,
iPr_def_20 = complement(identity_relation),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_4646,plain,
~ subclass(iPr_def_19,iPr_def_20),
inference(demodulation,[status(thm)],[c_2115,c_4645,c_4636,c_4637,c_4638,c_4639,c_4635,c_4640,c_4641,c_4642,c_4643,c_4644]) ).
tcf(c_4647,negated_conjecture,
subclass(x,iPr_def_20),
inference(demodulation,[status(thm)],[c_344]) ).
tcf(c_5866,plain,
! [X0: $i] : intersection(X0,iPr_def_18) = intersection(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_4643,c_232]) ).
tcf(c_5869,plain,
intersection(iPr_def_18,x) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4644,c_5866]) ).
tcf(c_6063,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_5869,c_228]) ).
tcf(c_6182,plain,
! [X0: $i] :
( subclass(iPr_def_19,X0)
| member(not_subclass_element(iPr_def_19,X0),x) ),
inference(superposition,[status(thm)],[c_210,c_6063]) ).
tcf(c_6321,plain,
! [X0: $i] :
( member(X0,iPr_def_20)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_4647,c_209]) ).
tcf(c_6819,plain,
! [X0: $i] :
( subclass(iPr_def_19,X0)
| member(not_subclass_element(iPr_def_19,X0),iPr_def_20) ),
inference(superposition,[status(thm)],[c_6182,c_6321]) ).
tcf(c_6854,plain,
subclass(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_6819,c_211]) ).
tcf(c_6857,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6854,c_4646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 02:48:11 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.10/1.73 % SZS status Started for theBenchmark.p
% 1.10/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.10/1.73
% 1.10/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.10/1.73
% 1.10/1.73 % ------ iProver source info
% 1.10/1.73
% 1.10/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 1.10/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.10/1.73 % git: non_committed_changes: false
% 1.10/1.73
% 1.10/1.73 % ------ Parsing...% successful
% 1.10/1.73
% 1.10/1.73
% 1.10/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.10/1.73
% 1.10/1.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 1.10/1.73
% 1.10/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.10/1.73
% 1.10/1.73 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.10/1.73 % ------ Proving...
% 1.10/1.73 % ------ Problem Properties
% 1.10/1.73
% 1.10/1.73 %
% 1.10/1.73 % clauses 127
% 1.10/1.73 % conjectures 1
% 1.10/1.73 % EPR 16
% 1.10/1.73 % Horn 115
% 1.10/1.73 % unary 38
% 1.10/1.73 % binary 58
% 1.10/1.73 % lits 261
% 1.10/1.73 % lits eq 50
% 1.10/1.73 % fd_pure 0
% 1.10/1.73 % fd_pseudo 0
% 1.10/1.73 % fd_cond 5
% 1.10/1.73 % fd_pseudo_cond 10
% 1.10/1.73 % AC symbols 0
% 1.10/1.73
% 1.10/1.73 % ------ Schedule dynamic 5 is on
% 1.10/1.73
% 1.10/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.10/1.73
% 1.10/1.73
% 1.10/1.73 % ------
% 1.10/1.73 % Current options:
% 1.10/1.73 % ------
% 1.10/1.73
% 1.10/1.73
% 1.10/1.73 %
% 1.10/1.73
% 1.10/1.73 % ------ Proving...
% 1.10/1.73 %
% 1.10/1.73
% 1.10/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.10/1.73
% 1.10/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.10/1.73
% 1.10/1.73
%------------------------------------------------------------------------------