%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET222-6 : 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 : n016.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 02:46:58 PM UTC 2026
% Result : Unsatisfiable 127.11s 29.28s
% Output : CNFRefutation 127.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 82 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 31 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 8 ( 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 : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 111 ( 0 sgn 111 !; 0 ?; 57 :)
% 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(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(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(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
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(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(f122,negated_conjecture,
~ subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property4_1) ).
fof(f127,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(f136,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,f127]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f127]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f127]) ).
fof(f139,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,f127]) ).
fof(f142,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_173,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,[],[f136]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_176,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,[],[f139]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f142]) ).
tcf(c_255,negated_conjecture,
~ subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_59039,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_163,c_180]) ).
tcf(c_59042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ member(X0,intersection(cross_product(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_185,c_180]) ).
tcf(c_59048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,cross_product(X2,X3))) ),
inference(superposition,[status(thm)],[c_185,c_181]) ).
tcf(c_59184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),X2) ),
inference(superposition,[status(thm)],[c_163,c_59042]) ).
tcf(c_59199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_163,c_59048]) ).
tcf(c_59512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) = not_subclass_element(intersection(cross_product(X0,X1),X2),X3) ) ),
inference(superposition,[status(thm)],[c_59039,c_176]) ).
tcf(c_65801,plain,
unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)))),unordered_pair(first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),unordered_pair(second(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),second(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)))))) = not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),
inference(superposition,[status(thm)],[c_59512,c_255]) ).
tcf(c_65847,plain,
! [X0: $i,X1: $i] :
( member(second(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),X1)
| ~ member(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_65801,c_174]) ).
tcf(c_65848,plain,
! [X0: $i,X1: $i] :
( member(first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),X0)
| ~ member(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_65801,c_173]) ).
tcf(c_65860,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),cross_product(X0,X1))
| ~ member(second(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),X1)
| ~ member(first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),X0) ),
inference(superposition,[status(thm)],[c_65801,c_175]) ).
tcf(c_66354,plain,
( subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))
| member(second(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),z) ),
inference(superposition,[status(thm)],[c_59184,c_65847]) ).
tcf(c_66360,plain,
member(second(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),z),
inference(forward_subsumption_resolution,[status(thm)],[c_66354,c_255]) ).
tcf(c_66530,plain,
( subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))
| member(first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),w) ),
inference(superposition,[status(thm)],[c_59199,c_65848]) ).
tcf(c_66533,plain,
member(first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),w),
inference(forward_subsumption_resolution,[status(thm)],[c_66530,c_255]) ).
tcf(c_66737,plain,
( subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))
| ~ member(second(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),z)
| ~ member(first(not_subclass_element(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),w) ),
inference(superposition,[status(thm)],[c_65860,c_164]) ).
tcf(c_66745,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_66737,c_255,c_66360,c_66533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET222-6 : 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 : n016.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 10:22:57 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.50 Running first-order theorem proving
% 0.18/0.50 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
% 0.26/0.51
% 0.26/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.51
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.53 % Proving...
% 127.11/29.28 % SZS status Started for theBenchmark.p
% 127.11/29.28 % SZS status Unsatisfiable for theBenchmark.p
% 127.11/29.28
% 127.11/29.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 127.11/29.28
% 127.11/29.28 % ------ iProver source info
% 127.11/29.28
% 127.11/29.28 % git: date: 2026-07-19 20:42:38 +0200
% 127.11/29.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 127.11/29.28 % git: non_committed_changes: false
% 127.11/29.28
% 127.11/29.28 % ------ Parsing...% successful
% 127.11/29.28
% 127.11/29.28
% 127.11/29.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 127.11/29.28
% 127.11/29.28 % ------ 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 %
% 127.11/29.28
% 127.11/29.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 127.11/29.28
% 127.11/29.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 127.11/29.28 % ------ Proving...
% 127.11/29.28 % ------ Problem Properties
% 127.11/29.28
% 127.11/29.28 %
% 127.11/29.28 % clauses 82
% 127.11/29.28 % conjectures 1
% 127.11/29.28 % EPR 12
% 127.11/29.28 % Horn 74
% 127.11/29.28 % unary 21
% 127.11/29.28 % binary 40
% 127.11/29.28 % lits 170
% 127.11/29.28 % lits eq 25
% 127.11/29.28 % fd_pure 0
% 127.11/29.28 % fd_pseudo 0
% 127.11/29.28 % fd_cond 3
% 127.11/29.28 % fd_pseudo_cond 7
% 127.11/29.28 % AC symbols 0
% 127.11/29.28
% 127.11/29.28 % ------ Input Options Time Limit: Unbounded
% 127.11/29.28
% 127.11/29.28
% 127.11/29.28 % ------
% 127.11/29.28 % Current options:
% 127.11/29.28 % ------
% 127.11/29.28
% 127.11/29.28
% 127.11/29.28 %
% 127.11/29.28
% 127.11/29.28 % ------ Proving...
% 127.11/29.28 %
% 127.11/29.28
% 127.11/29.28 % SZS status Unsatisfiable for theBenchmark.p
% 127.11/29.28
% 127.11/29.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 127.11/29.28
% 127.11/29.28
%------------------------------------------------------------------------------