%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET233-6 : 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 : n001.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 7.14s 6.88s
% Output : CNFRefutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 47 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 51 ( 26 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 32 ( 0 sgn 32 !; 0 ?; 23 :)
% 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(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property8_1) ).
fof(f123,negated_conjecture,
~ member(second(not_subclass_element(cross_product(x,y),z)),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property8_2) ).
tcf(c_163,negated_conjecture,
~ subclass(cross_product(x,y),z),
inference(cnf_transformation,[],[f122]) ).
tcf(c_164,negated_conjecture,
~ member(second(not_subclass_element(cross_product(x,y),z)),y),
inference(cnf_transformation,[],[f123]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_175,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_727,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1321,plain,
( subclass(cross_product(x,y),z)
| member(not_subclass_element(cross_product(x,y),z),cross_product(x,y)) ),
inference(instantiation,[status(thm)],[c_174]) ).
tcf(c_1362,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) )
| ~ member(not_subclass_element(cross_product(x,y),z),cross_product(x,y)) ),
inference(instantiation,[status(thm)],[c_175]) ).
tcf(c_1363,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(not_subclass_element(cross_product(x,y),z),cross_product(x,y))
| ( X1 != cross_product(x,y) )
| ( X0 != not_subclass_element(cross_product(x,y),z) ) ),
inference(instantiation,[status(thm)],[c_734]) ).
tcf(c_1829,plain,
cross_product(x,y) = cross_product(x,y),
inference(instantiation,[status(thm)],[c_727]) ).
tcf(c_1833,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,cross_product(X0,X1))
| ~ member(not_subclass_element(cross_product(x,y),z),cross_product(x,y))
| ( X2 != not_subclass_element(cross_product(x,y),z) )
| ( cross_product(X0,X1) != cross_product(x,y) ) ),
inference(instantiation,[status(thm)],[c_1363]) ).
tcf(c_2230,plain,
! [X0: $i,X1: $i] :
( member(X1,y)
| ~ member(ordered_pair(X0,X1),cross_product(x,y)) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_2828,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),cross_product(X0,X1))
| ~ member(not_subclass_element(cross_product(x,y),z),cross_product(x,y))
| ( cross_product(X0,X1) != cross_product(x,y) )
| ( 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(instantiation,[status(thm)],[c_1833]) ).
tcf(c_4156,plain,
( member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),cross_product(x,y))
| ~ member(not_subclass_element(cross_product(x,y),z),cross_product(x,y))
| ( cross_product(x,y) != cross_product(x,y) )
| ( 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(instantiation,[status(thm)],[c_2828]) ).
tcf(c_9737,plain,
( member(second(not_subclass_element(cross_product(x,y),z)),y)
| ~ member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),cross_product(x,y)) ),
inference(instantiation,[status(thm)],[c_2230]) ).
tcf(c_9739,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9737,c_4156,c_1829,c_1362,c_1321,c_164,c_163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET233-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.41 % Computer : n001.cluster.edu
% 0.16/5.41 % Model : x86_64 x86_64
% 0.16/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.41 % Memory : 8046.5625MB
% 0.16/5.41 % OS : Linux 6.8.0-71-generic
% 0.16/5.41 % CPULimit : 300
% 0.16/5.41 % WCLimit : 300
% 0.16/5.41 % DateTime : Thu Sep 24 10:25:44 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.47 Running first-order theorem proving
% 0.16/5.48 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
% 0.16/5.49
% 0.16/5.49 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.49
% 0.16/5.49 % Detected problem language: tptp
% 0.19/5.50 % Proving...
% 7.14/6.88 % SZS status Started for theBenchmark.p
% 7.14/6.88 % SZS status Unsatisfiable for theBenchmark.p
% 7.14/6.88
% 7.14/6.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.14/6.88
% 7.14/6.88 % ------ iProver source info
% 7.14/6.88
% 7.14/6.88 % git: date: 2026-07-19 20:42:38 +0200
% 7.14/6.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.14/6.88 % git: non_committed_changes: false
% 7.14/6.88
% 7.14/6.88 % ------ Parsing...% successful
% 7.14/6.88
% 7.14/6.88
% 7.14/6.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.14/6.88
% 7.14/6.88 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.14/6.88
% 7.14/6.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.14/6.88
% 7.14/6.88 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.14/6.88 % ------ Proving...
% 7.14/6.88 % ------ Problem Properties
% 7.14/6.88
% 7.14/6.88 %
% 7.14/6.88 % clauses 22
% 7.14/6.88 % conjectures 2
% 7.14/6.88 % EPR 4
% 7.14/6.88 % Horn 20
% 7.14/6.88 % unary 6
% 7.14/6.88 % binary 9
% 7.14/6.88 % lits 46
% 7.14/6.88 % lits eq 5
% 7.14/6.88 % fd_pure 0
% 7.14/6.88 % fd_pseudo 0
% 7.14/6.88 % fd_cond 0
% 7.14/6.88 % fd_pseudo_cond 1
% 7.14/6.88 % AC symbols 0
% 7.14/6.88
% 7.14/6.88 % ------ Schedule dynamic 5 is on
% 7.14/6.88
% 7.14/6.88 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.14/6.88
% 7.14/6.88
% 7.14/6.88 % ------
% 7.14/6.88 % Current options:
% 7.14/6.88 % ------
% 7.14/6.88
% 7.14/6.88
% 7.14/6.88 %
% 7.14/6.88
% 7.14/6.88 % ------ Proving...
% 7.14/6.88 %
% 7.14/6.88
% 7.14/6.88 % SZS status Unsatisfiable for theBenchmark.p
% 7.14/6.88
% 7.14/6.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.14/6.89
% 7.14/6.89
%------------------------------------------------------------------------------