%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET021-7 : 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 : n016.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 02:46:07 PM UTC 2026
% Result : Unsatisfiable 3.75s 1.18s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 50 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
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(f104,axiom,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f173,axiom,
! [X2,X3,X0,X1] :
( X1 = X3
| ~ member(X1,universal_class)
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
fof(f174,axiom,
! [X0,X1] :
( member(ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1))),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_1) ).
fof(f179,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_1) ).
fof(f180,negated_conjecture,
second(ordered_pair(u,v)) != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_2) ).
fof(f181,plain,
v != second(ordered_pair(u,v)),
inference(reorient_equations,[],[f180]) ).
fof(f182,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f183,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f179,f182]) ).
fof(f184,plain,
v != second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),
inference(definition_unfolding,[],[f181,f182]) ).
fof(f189,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ~ member(X1,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))) ),
inference(definition_unfolding,[],[f173,f182,f182]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f104,f182]) ).
fof(f211,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f174,f182,f182,f182,f182]) ).
fof(f212,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f182]) ).
tcf(c_208,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f183]) ).
tcf(c_209,negated_conjecture,
second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) != v,
inference(cnf_transformation,[],[f184]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ member(X1,universal_class)
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))) ) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_3131,plain,
( ( unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) = unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))) )
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_3306,plain,
! [X0: $i,X1: $i] :
( ( second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = v )
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class)
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) != unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(v,v))) ) ),
inference(instantiation,[status(thm)],[c_214]) ).
tcf(c_3310,plain,
( member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_4389,plain,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class)
| ~ member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_225]) ).
tcf(c_5563,plain,
( ( second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = v )
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class)
| ( unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) != unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))) ) ),
inference(instantiation,[status(thm)],[c_3306]) ).
tcf(c_5564,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5563,c_4389,c_3310,c_3131,c_209,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET021-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 09:18:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 3.75/1.18 % SZS status Started for theBenchmark.p
% 3.75/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.75/1.18
% 3.75/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.75/1.18
% 3.75/1.18 % ------ iProver source info
% 3.75/1.18
% 3.75/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.75/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.75/1.18 % git: non_committed_changes: false
% 3.75/1.18
% 3.75/1.18 % ------ Parsing...% successful
% 3.75/1.18
% 3.75/1.18
% 3.75/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.75/1.18
% 3.75/1.18 % ------ 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 %
% 3.75/1.18
% 3.75/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.75/1.18
% 3.75/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.75/1.18 % ------ Proving...
% 3.75/1.18 % ------ Problem Properties
% 3.75/1.18
% 3.75/1.18 %
% 3.75/1.18 % clauses 56
% 3.75/1.18 % conjectures 2
% 3.75/1.18 % EPR 9
% 3.75/1.18 % Horn 42
% 3.75/1.18 % unary 15
% 3.75/1.18 % binary 24
% 3.75/1.18 % lits 115
% 3.75/1.18 % lits eq 41
% 3.75/1.18 % fd_pure 0
% 3.75/1.18 % fd_pseudo 0
% 3.75/1.18 % fd_cond 1
% 3.75/1.18 % fd_pseudo_cond 11
% 3.75/1.18 % AC symbols 0
% 3.75/1.18
% 3.75/1.18 % ------ Schedule dynamic 5 is on
% 3.75/1.18
% 3.75/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.75/1.18
% 3.75/1.18
% 3.75/1.18 % ------
% 3.75/1.18 % Current options:
% 3.75/1.18 % ------
% 3.75/1.18
% 3.75/1.18
% 3.75/1.18 %
% 3.75/1.18
% 3.75/1.18 % ------ Proving...
% 3.75/1.18 %
% 3.75/1.18
% 3.75/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.75/1.18
% 3.75/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.19
% 3.75/1.19
%------------------------------------------------------------------------------