%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET234-6 : 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 : n019.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 02:46:59 PM UTC 2026
% Result : Unsatisfiable 4.01s 6.31s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 23 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
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(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f122,negated_conjecture,
member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property9_1) ).
fof(f123,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property9_2) ).
tcf(c_163,negated_conjecture,
member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),z),
inference(cnf_transformation,[],[f122]) ).
tcf(c_164,negated_conjecture,
~ subclass(cross_product(x,y),z),
inference(cnf_transformation,[],[f123]) ).
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,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ordered_pair(first(X0),second(X0)) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(cross_product(X0,X1),X2)
| ( ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_166,c_170]) ).
tcf(c_826,plain,
( subclass(cross_product(x,y),z)
| ~ member(not_subclass_element(cross_product(x,y),z),z) ),
inference(instantiation,[status(thm)],[c_165]) ).
tcf(c_2629,plain,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) = not_subclass_element(cross_product(x,y),z),
inference(superposition,[status(thm)],[c_633,c_164]) ).
tcf(c_2695,plain,
member(not_subclass_element(cross_product(x,y),z),z),
inference(demodulation,[status(thm)],[c_163,c_2629]) ).
tcf(c_2763,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2695,c_826,c_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET234-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n019.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Thu Sep 24 10:19:56 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.45
% 0.15/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.45
% 0.15/5.45 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 4.01/6.31 % SZS status Started for theBenchmark.p
% 4.01/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.01/6.31
% 4.01/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.01/6.31
% 4.01/6.31 % ------ iProver source info
% 4.01/6.31
% 4.01/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.01/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.01/6.31 % git: non_committed_changes: false
% 4.01/6.31
% 4.01/6.31 % ------ Parsing...% successful
% 4.01/6.31
% 4.01/6.31
% 4.01/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.01/6.31
% 4.01/6.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.01/6.31
% 4.01/6.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.01/6.31
% 4.01/6.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.01/6.31 % ------ Proving...
% 4.01/6.31 % ------ Problem Properties
% 4.01/6.31
% 4.01/6.31 %
% 4.01/6.31 % clauses 12
% 4.01/6.31 % conjectures 2
% 4.01/6.31 % EPR 4
% 4.01/6.31 % Horn 11
% 4.01/6.31 % unary 4
% 4.01/6.31 % binary 5
% 4.01/6.31 % lits 23
% 4.01/6.31 % lits eq 2
% 4.01/6.31 % fd_pure 0
% 4.01/6.31 % fd_pseudo 0
% 4.01/6.31 % fd_cond 0
% 4.01/6.31 % fd_pseudo_cond 1
% 4.01/6.31 % AC symbols 0
% 4.01/6.31
% 4.01/6.31 % ------ Schedule dynamic 5 is on
% 4.01/6.31
% 4.01/6.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.01/6.31
% 4.01/6.31
% 4.01/6.31 % ------
% 4.01/6.31 % Current options:
% 4.01/6.31 % ------
% 4.01/6.31
% 4.01/6.31
% 4.01/6.31 %
% 4.01/6.31
% 4.01/6.31 % ------ Proving...
% 4.01/6.31 %
% 4.01/6.31
% 4.01/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.01/6.31
% 4.01/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.01/6.31
% 4.01/6.31
%------------------------------------------------------------------------------