%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET020-7 : 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 : n019.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 6.89s 1.74s
% Output : CNFRefutation 6.89s
% 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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f103,axiom,
! [X2,X3,X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f172,axiom,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ member(X0,universal_class)
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
fof(f180,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
fof(f181,plain,
u != first(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,
u != first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),
inference(definition_unfolding,[],[f181,f182]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ member(X0,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,[],[f172,f182,f182]) ).
fof(f201,plain,
! [X2,X3,X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f103,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,
first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) != u,
inference(cnf_transformation,[],[f184]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ member(X0,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,[],[f190]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f201]) ).
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_3308,plain,
! [X0: $i,X1: $i] :
( ( first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u )
| ~ member(first(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(X0,X0))) != unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(X1,X1))) ) ),
inference(instantiation,[status(thm)],[c_215]) ).
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_4376,plain,
( member(first(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_226]) ).
tcf(c_10089,plain,
( ( first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u )
| ~ member(first(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_3308]) ).
tcf(c_10090,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10089,c_4376,c_3310,c_3131,c_209,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:13:04 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 6.89/1.74 % SZS status Started for theBenchmark.p
% 6.89/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 6.89/1.74
% 6.89/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.89/1.74
% 6.89/1.74 % ------ iProver source info
% 6.89/1.74
% 6.89/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 6.89/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.89/1.74 % git: non_committed_changes: false
% 6.89/1.74
% 6.89/1.74 % ------ Parsing...% successful
% 6.89/1.74
% 6.89/1.74
% 6.89/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.89/1.74
% 6.89/1.74 % ------ 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 %
% 6.89/1.74
% 6.89/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.89/1.74
% 6.89/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.89/1.74 % ------ Proving...
% 6.89/1.74 % ------ Problem Properties
% 6.89/1.74
% 6.89/1.74 %
% 6.89/1.74 % clauses 56
% 6.89/1.74 % conjectures 2
% 6.89/1.74 % EPR 9
% 6.89/1.74 % Horn 42
% 6.89/1.74 % unary 15
% 6.89/1.74 % binary 24
% 6.89/1.74 % lits 115
% 6.89/1.74 % lits eq 41
% 6.89/1.74 % fd_pure 0
% 6.89/1.74 % fd_pseudo 0
% 6.89/1.74 % fd_cond 1
% 6.89/1.74 % fd_pseudo_cond 11
% 6.89/1.74 % AC symbols 0
% 6.89/1.74
% 6.89/1.74 % ------ Schedule dynamic 5 is on
% 6.89/1.74
% 6.89/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.89/1.74
% 6.89/1.74
% 6.89/1.74 % ------
% 6.89/1.74 % Current options:
% 6.89/1.74 % ------
% 6.89/1.74
% 6.89/1.74
% 6.89/1.74 %
% 6.89/1.74
% 6.89/1.74 % ------ Proving...
% 6.89/1.74 %
% 6.89/1.74
% 6.89/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 6.89/1.74
% 6.89/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.89/1.75
% 6.89/1.75
%------------------------------------------------------------------------------