%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET382-6 : 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 : n012.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 02:47:11 PM UTC 2026
% Result : Unsatisfiable 2.77s 0.97s
% Output : CNFRefutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 21 unt; 2 def)
% Number of atoms : 90 ( 18 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn 49 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
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(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f122,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_relation_property2_1) ).
fof(f123,negated_conjecture,
restrict(x,universal_class,universal_class) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_relation_property2_2) ).
fof(f124,plain,
x != restrict(x,universal_class,universal_class),
inference(reorient_equations,[],[f123]) ).
fof(f144,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f187,plain,
x != intersection(x,cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f124,f28]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
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,[],[f144]) ).
tcf(c_256,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_257,negated_conjecture,
intersection(x,cross_product(universal_class,universal_class)) != x,
inference(cnf_transformation,[],[f187]) ).
tcf(c_2981,definition,
iPr_def_10 = cross_product(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2982,definition,
iPr_def_11 = intersection(x,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2983,negated_conjecture,
iPr_def_11 != x,
inference(demodulation,[status(thm)],[c_257,c_2981,c_2982]) ).
tcf(c_2984,negated_conjecture,
subclass(x,iPr_def_10),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_3890,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2982,c_181]) ).
tcf(c_3904,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| member(not_subclass_element(iPr_def_11,X0),x) ),
inference(superposition,[status(thm)],[c_164,c_3890]) ).
tcf(c_3915,plain,
subclass(iPr_def_11,x),
inference(superposition,[status(thm)],[c_3904,c_165]) ).
tcf(c_3970,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = intersection(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2981,c_186]) ).
tcf(c_3984,plain,
intersection(iPr_def_10,x) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2982,c_3970]) ).
tcf(c_4015,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2984,c_163]) ).
tcf(c_4239,plain,
( ( x = iPr_def_11 )
| ~ subclass(x,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3915,c_169]) ).
tcf(c_4430,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_3984,c_183]) ).
tcf(c_5965,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,x) ),
inference(global_subsumption_just,[status(thm)],[c_4430,c_4015,c_4430]) ).
tcf(c_5972,plain,
! [X0: $i] :
( subclass(x,X0)
| member(not_subclass_element(x,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_164,c_5965]) ).
tcf(c_5994,plain,
subclass(x,iPr_def_11),
inference(superposition,[status(thm)],[c_5972,c_165]) ).
tcf(c_6001,plain,
x = iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_4239,c_5994]) ).
tcf(c_6015,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_2983,c_6001]) ).
tcf(c_6017,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_6015]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET382-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 10:46:21 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.03/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 2.77/0.97 % SZS status Started for theBenchmark.p
% 2.77/0.97 % SZS status Unsatisfiable for theBenchmark.p
% 2.77/0.97
% 2.77/0.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.77/0.97
% 2.77/0.97 % ------ iProver source info
% 2.77/0.97
% 2.77/0.97 % git: date: 2026-07-19 20:42:38 +0200
% 2.77/0.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.77/0.97 % git: non_committed_changes: false
% 2.77/0.97
% 2.77/0.97 % ------ Parsing...% successful
% 2.77/0.97
% 2.77/0.97
% 2.77/0.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.77/0.97
% 2.77/0.97 % ------ 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 %
% 2.77/0.97
% 2.77/0.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.77/0.97
% 2.77/0.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.77/0.97 % ------ Proving...
% 2.77/0.97 % ------ Problem Properties
% 2.77/0.97
% 2.77/0.97 %
% 2.77/0.97 % clauses 85
% 2.77/0.97 % conjectures 2
% 2.77/0.97 % EPR 14
% 2.77/0.97 % Horn 77
% 2.77/0.97 % unary 24
% 2.77/0.97 % binary 40
% 2.77/0.97 % lits 173
% 2.77/0.97 % lits eq 28
% 2.77/0.97 % fd_pure 0
% 2.77/0.97 % fd_pseudo 0
% 2.77/0.97 % fd_cond 3
% 2.77/0.97 % fd_pseudo_cond 7
% 2.77/0.97 % AC symbols 0
% 2.77/0.97
% 2.77/0.97 % ------ Schedule dynamic 5 is on
% 2.77/0.97
% 2.77/0.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.77/0.97
% 2.77/0.97
% 2.77/0.97 % ------
% 2.77/0.97 % Current options:
% 2.77/0.97 % ------
% 2.77/0.97
% 2.77/0.97
% 2.77/0.97 %
% 2.77/0.97
% 2.77/0.97 % ------ Proving...
% 2.77/0.97 %
% 2.77/0.97
% 2.77/0.97 % SZS status Unsatisfiable for theBenchmark.p
% 2.77/0.97
% 2.77/0.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.77/0.97
% 2.77/0.97
%------------------------------------------------------------------------------