%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM139-1 : 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 : n020.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 02:23:24 PM UTC 2026
% Result : Unsatisfiable 4.38s 1.52s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 24 ( 19 unt; 0 def)
% Number of atoms : 29 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
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(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).
fof(f56,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',power_class_definition) ).
fof(f176,negated_conjecture,
~ member(not_subclass_element(intersection(power_class(x),z),x),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complete_induction3_1) ).
fof(f177,negated_conjecture,
~ subclass(intersection(power_class(x),z),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complete_induction3_2) ).
fof(f179,plain,
! [X0,X1] : image(X0,X1) = domain_of(inverse(intersection(cross_product(X1,universal_class),X0))),
inference(definition_unfolding,[],[f43,f40,f29]) ).
fof(f180,plain,
! [X0] : power_class(X0) = complement(domain_of(inverse(intersection(cross_product(complement(X0),universal_class),element_relation)))),
inference(definition_unfolding,[],[f56,f179]) ).
fof(f182,plain,
~ member(not_subclass_element(intersection(complement(domain_of(inverse(intersection(cross_product(complement(x),universal_class),element_relation)))),z),x),z),
inference(definition_unfolding,[],[f176,f180]) ).
fof(f183,plain,
~ subclass(intersection(complement(domain_of(inverse(intersection(cross_product(complement(x),universal_class),element_relation)))),z),x),
inference(definition_unfolding,[],[f177,f180]) ).
fof(f184,plain,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = intersection(cross_product(X1,X2),X0),
inference(definition_unfolding,[],[f28,f29]) ).
tcf(c_209,negated_conjecture,
~ member(not_subclass_element(intersection(complement(domain_of(inverse(intersection(cross_product(complement(x),universal_class),element_relation)))),z),x),z),
inference(cnf_transformation,[],[f182]) ).
tcf(c_210,negated_conjecture,
~ subclass(intersection(complement(domain_of(inverse(intersection(cross_product(complement(x),universal_class),element_relation)))),z),x),
inference(cnf_transformation,[],[f183]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f184]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_584,plain,
~ subclass(intersection(complement(domain_of(inverse(intersection(element_relation,cross_product(complement(x),universal_class))))),z),x),
inference(demodulation,[status(thm)],[c_210,c_214]) ).
tcf(c_618,plain,
~ member(not_subclass_element(intersection(complement(domain_of(inverse(intersection(element_relation,cross_product(complement(x),universal_class))))),z),x),z),
inference(demodulation,[status(thm)],[c_209,c_214]) ).
tcf(c_1378,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_212,c_216]) ).
tcf(c_1506,plain,
subclass(intersection(complement(domain_of(inverse(intersection(element_relation,cross_product(complement(x),universal_class))))),z),x),
inference(superposition,[status(thm)],[c_1378,c_618]) ).
tcf(c_1507,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1506,c_584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM139-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 03:01:49 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.50 Running first-order theorem proving
% 0.24/0.50 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
% 0.24/0.52
% 0.24/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.52
% 0.24/0.52 % Detected problem language: tptp
% 0.24/0.54 % Proving...
% 4.38/1.52 % SZS status Started for theBenchmark.p
% 4.38/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 4.38/1.52
% 4.38/1.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.38/1.52
% 4.38/1.52 % ------ iProver source info
% 4.38/1.52
% 4.38/1.52 % git: date: 2026-07-19 20:42:38 +0200
% 4.38/1.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.38/1.52 % git: non_committed_changes: false
% 4.38/1.52
% 4.38/1.52 % ------ Parsing...% successful
% 4.38/1.52
% 4.38/1.52
% 4.38/1.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.38/1.52
% 4.38/1.52 % ------ Preprocessing... sup_sim: 7 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: 2 0s sf_e pe_s pe_e %
% 4.38/1.52
% 4.38/1.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.38/1.52
% 4.38/1.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.38/1.52 % ------ Proving...
% 4.38/1.52 % ------ Problem Properties
% 4.38/1.52
% 4.38/1.52 %
% 4.38/1.52 % clauses 29
% 4.38/1.52 % conjectures 0
% 4.38/1.52 % EPR 4
% 4.38/1.52 % Horn 26
% 4.38/1.52 % unary 7
% 4.38/1.52 % binary 13
% 4.38/1.52 % lits 61
% 4.38/1.52 % lits eq 4
% 4.38/1.52 % fd_pure 0
% 4.38/1.52 % fd_pseudo 0
% 4.38/1.52 % fd_cond 0
% 4.38/1.52 % fd_pseudo_cond 1
% 4.38/1.52 % AC symbols 0
% 4.38/1.52
% 4.38/1.52 % ------ Schedule dynamic 5 is on
% 4.38/1.52
% 4.38/1.52 % ------ no conjectures: strip conj schedule
% 4.38/1.52
% 4.38/1.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.38/1.52
% 4.38/1.52
% 4.38/1.52 % ------
% 4.38/1.52 % Current options:
% 4.38/1.52 % ------
% 4.38/1.52
% 4.38/1.52
% 4.38/1.52 %
% 4.38/1.52
% 4.38/1.52 % ------ Proving...
% 4.38/1.52 %
% 4.38/1.52
% 4.38/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 4.38/1.52
% 4.38/1.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.38/1.52
% 4.38/1.52
%------------------------------------------------------------------------------