%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM030-1 : 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 : n008.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 02:23:16 PM UTC 2026
% Result : Unsatisfiable 10.02s 2.26s
% Output : CNFRefutation 10.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 61 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 27 |; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?; 24 :)
% 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(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(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f122,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
fof(f176,negated_conjecture,
symmetrization_of(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_1) ).
fof(f177,plain,
x = symmetrization_of(x),
inference(reorient_equations,[],[f176]) ).
fof(f178,negated_conjecture,
~ subclass(inverse(x),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_2) ).
fof(f192,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(f269,plain,
x = complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))),
inference(definition_unfolding,[],[f177,f192]) ).
fof(f270,plain,
~ subclass(domain_of(flip(cross_product(x,universal_class))),x),
inference(definition_unfolding,[],[f178,f39]) ).
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_212,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_344,negated_conjecture,
complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))) = x,
inference(cnf_transformation,[],[f269]) ).
tcf(c_345,negated_conjecture,
~ subclass(domain_of(flip(cross_product(x,universal_class))),x),
inference(cnf_transformation,[],[f270]) ).
tcf(c_6455,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_212,c_209]) ).
tcf(c_6568,plain,
! [X0: $i] :
( member(X0,x)
| member(X0,intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_344,c_231]) ).
tcf(c_6765,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_210,c_6455]) ).
tcf(c_6875,plain,
! [X0: $i] :
( member(X0,x)
| member(X0,complement(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_6568,c_228]) ).
tcf(c_6909,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,universal_class)
| ~ member(X0,domain_of(flip(cross_product(x,universal_class)))) ),
inference(superposition,[status(thm)],[c_6875,c_230]) ).
tcf(c_6930,plain,
! [X0: $i] :
( subclass(domain_of(flip(cross_product(x,universal_class))),X0)
| member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),X0),x)
| ~ member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),X0),universal_class) ),
inference(superposition,[status(thm)],[c_210,c_6909]) ).
tcf(c_7142,plain,
! [X0: $i] :
( subclass(domain_of(flip(cross_product(x,universal_class))),X0)
| member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),X0),x) ),
inference(superposition,[status(thm)],[c_6765,c_6930]) ).
tcf(c_7144,plain,
subclass(domain_of(flip(cross_product(x,universal_class))),x),
inference(superposition,[status(thm)],[c_7142,c_211]) ).
tcf(c_7145,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7144,c_345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM030-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 02:43:24 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 10.02/2.26 % SZS status Started for theBenchmark.p
% 10.02/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 10.02/2.26
% 10.02/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.02/2.26
% 10.02/2.26 % ------ iProver source info
% 10.02/2.26
% 10.02/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 10.02/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.02/2.26 % git: non_committed_changes: false
% 10.02/2.26
% 10.02/2.26 % ------ Parsing...% successful
% 10.02/2.26
% 10.02/2.26
% 10.02/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.02/2.26
% 10.02/2.26 % ------ 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: 3 0s sf_e pe_s pe_e %
% 10.02/2.26
% 10.02/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.02/2.26
% 10.02/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.02/2.26 % ------ Proving...
% 10.02/2.26 % ------ Problem Properties
% 10.02/2.26
% 10.02/2.26 %
% 10.02/2.26 % clauses 116
% 10.02/2.26 % conjectures 2
% 10.02/2.26 % EPR 14
% 10.02/2.26 % Horn 104
% 10.02/2.26 % unary 27
% 10.02/2.26 % binary 58
% 10.02/2.26 % lits 250
% 10.02/2.26 % lits eq 40
% 10.02/2.26 % fd_pure 0
% 10.02/2.26 % fd_pseudo 0
% 10.02/2.26 % fd_cond 5
% 10.02/2.26 % fd_pseudo_cond 10
% 10.02/2.26 % AC symbols 0
% 10.02/2.26
% 10.02/2.26 % ------ Input Options Time Limit: Unbounded
% 10.02/2.26
% 10.02/2.26
% 10.02/2.26 % ------
% 10.02/2.26 % Current options:
% 10.02/2.26 % ------
% 10.02/2.26
% 10.02/2.26
% 10.02/2.26 %
% 10.02/2.26
% 10.02/2.26 % ------ Proving...
% 10.02/2.26 %
% 10.02/2.26
% 10.02/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 10.02/2.26
% 10.02/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.02/2.26
% 10.02/2.26
%------------------------------------------------------------------------------