%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET239-6 : 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 : n014.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 1.95s 11.29s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 17 unt; 2 def)
% Number of atoms : 32 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
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_restriction_alternate_defn2_1) ).
fof(f123,negated_conjecture,
~ member(z,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn2_2) ).
fof(f143,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f186,plain,
member(z,intersection(xr,cross_product(x,y))),
inference(definition_unfolding,[],[f122,f28]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f143]) ).
tcf(c_256,negated_conjecture,
member(z,intersection(xr,cross_product(x,y))),
inference(cnf_transformation,[],[f186]) ).
tcf(c_257,negated_conjecture,
~ member(z,xr),
inference(cnf_transformation,[],[f123]) ).
tcf(c_2980,definition,
iPr_def_10 = cross_product(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2981,definition,
iPr_def_11 = intersection(xr,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2982,negated_conjecture,
~ member(z,xr),
inference(demodulation,[status(thm)],[c_257]) ).
tcf(c_2983,negated_conjecture,
member(z,iPr_def_11),
inference(demodulation,[status(thm)],[c_256,c_2980,c_2981]) ).
tcf(c_3834,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = intersection(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2980,c_186]) ).
tcf(c_3837,plain,
intersection(iPr_def_10,xr) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2981,c_3834]) ).
tcf(c_3948,plain,
! [X0: $i] :
( member(X0,xr)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3837,c_182]) ).
tcf(c_3978,plain,
member(z,xr),
inference(superposition,[status(thm)],[c_2983,c_3948]) ).
tcf(c_3979,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3978,c_2982]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET239-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n014.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 10:21:31 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 0.14/10.43
% 0.14/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.43
% 0.14/10.43 % Detected problem language: tptp
% 0.14/10.44 % Proving...
% 1.95/11.29 % SZS status Started for theBenchmark.p
% 1.95/11.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.95/11.29
% 1.95/11.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.95/11.29
% 1.95/11.29 % ------ iProver source info
% 1.95/11.29
% 1.95/11.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.95/11.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.95/11.29 % git: non_committed_changes: false
% 1.95/11.29
% 1.95/11.29 % ------ Parsing...% successful
% 1.95/11.29
% 1.95/11.29
% 1.95/11.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.95/11.29
% 1.95/11.29 % ------ 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 %
% 1.95/11.29
% 1.95/11.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.95/11.29
% 1.95/11.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.95/11.29 % ------ Proving...
% 1.95/11.29 % ------ Problem Properties
% 1.95/11.29
% 1.95/11.29 %
% 1.95/11.29 % clauses 85
% 1.95/11.29 % conjectures 2
% 1.95/11.29 % EPR 14
% 1.95/11.29 % Horn 77
% 1.95/11.29 % unary 24
% 1.95/11.29 % binary 40
% 1.95/11.29 % lits 173
% 1.95/11.29 % lits eq 27
% 1.95/11.29 % fd_pure 0
% 1.95/11.29 % fd_pseudo 0
% 1.95/11.29 % fd_cond 3
% 1.95/11.29 % fd_pseudo_cond 7
% 1.95/11.29 % AC symbols 0
% 1.95/11.29
% 1.95/11.29 % ------ Schedule dynamic 5 is on
% 1.95/11.29
% 1.95/11.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.95/11.29
% 1.95/11.29
% 1.95/11.29 % ------
% 1.95/11.29 % Current options:
% 1.95/11.29 % ------
% 1.95/11.29
% 1.95/11.29
% 1.95/11.29 %
% 1.95/11.29
% 1.95/11.29 % ------ Proving...
% 1.95/11.29 %
% 1.95/11.29
% 1.95/11.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.95/11.29
% 1.95/11.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.95/11.29
% 1.95/11.29
%------------------------------------------------------------------------------