%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET238-6 : 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 : n004.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 3.90s 1.27s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 16 unt; 0 def)
% Number of atoms : 24 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
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(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,
member(z,restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_1) ).
fof(f123,negated_conjecture,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_2) ).
fof(f125,plain,
member(z,intersection(cross_product(x,y),xr)),
inference(definition_unfolding,[],[f122,f29]) ).
fof(f126,plain,
~ member(ordered_pair(first(z),second(z)),intersection(cross_product(x,y),xr)),
inference(definition_unfolding,[],[f123,f29]) ).
fof(f129,plain,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = intersection(cross_product(X1,X2),X0),
inference(definition_unfolding,[],[f28,f29]) ).
tcf(c_163,negated_conjecture,
member(z,intersection(cross_product(x,y),xr)),
inference(cnf_transformation,[],[f125]) ).
tcf(c_164,negated_conjecture,
~ member(ordered_pair(first(z),second(z)),intersection(cross_product(x,y),xr)),
inference(cnf_transformation,[],[f126]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f129]) ).
tcf(c_171,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_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_396,plain,
member(z,intersection(xr,cross_product(x,y))),
inference(demodulation,[status(thm)],[c_163,c_167]) ).
tcf(c_397,plain,
~ member(ordered_pair(first(z),second(z)),intersection(xr,cross_product(x,y))),
inference(demodulation,[status(thm)],[c_164,c_167]) ).
tcf(c_975,plain,
member(z,cross_product(x,y)),
inference(superposition,[status(thm)],[c_396,c_181]) ).
tcf(c_1104,plain,
ordered_pair(first(z),second(z)) = z,
inference(superposition,[status(thm)],[c_975,c_171]) ).
tcf(c_1106,plain,
~ member(z,intersection(xr,cross_product(x,y))),
inference(demodulation,[status(thm)],[c_397,c_1104]) ).
tcf(c_1107,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1106,c_396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET238-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 10:20:37 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 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
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.90/1.27 % SZS status Started for theBenchmark.p
% 3.90/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.90/1.27
% 3.90/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.90/1.27
% 3.90/1.27 % ------ iProver source info
% 3.90/1.27
% 3.90/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.90/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.90/1.27 % git: non_committed_changes: false
% 3.90/1.27
% 3.90/1.27 % ------ Parsing...% successful
% 3.90/1.27
% 3.90/1.27
% 3.90/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.90/1.27
% 3.90/1.27 % ------ Preprocessing... sup_sim: 2 sf_s rm: 11 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.90/1.27
% 3.90/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.90/1.27
% 3.90/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.90/1.27 % ------ Proving...
% 3.90/1.27 % ------ Problem Properties
% 3.90/1.27
% 3.90/1.27 %
% 3.90/1.27 % clauses 21
% 3.90/1.27 % conjectures 0
% 3.90/1.27 % EPR 4
% 3.90/1.27 % Horn 20
% 3.90/1.27 % unary 6
% 3.90/1.27 % binary 8
% 3.90/1.27 % lits 43
% 3.90/1.27 % lits eq 6
% 3.90/1.27 % fd_pure 0
% 3.90/1.27 % fd_pseudo 0
% 3.90/1.27 % fd_cond 0
% 3.90/1.27 % fd_pseudo_cond 2
% 3.90/1.27 % AC symbols 0
% 3.90/1.27
% 3.90/1.27 % ------ Schedule dynamic 5 is on
% 3.90/1.27
% 3.90/1.27 % ------ no conjectures: strip conj schedule
% 3.90/1.27
% 3.90/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.90/1.27
% 3.90/1.27
% 3.90/1.27 % ------
% 3.90/1.27 % Current options:
% 3.90/1.27 % ------
% 3.90/1.27
% 3.90/1.27
% 3.90/1.27 %
% 3.90/1.27
% 3.90/1.27 % ------ Proving...
% 3.90/1.27 %
% 3.90/1.27
% 3.90/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.90/1.27
% 3.90/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.90/1.27
% 3.90/1.27
%------------------------------------------------------------------------------