%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET113-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:46:39 PM UTC 2026
% Result : Unsatisfiable 2.29s 0.98s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 18 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?; 1 :)
% 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(f175,axiom,
! [X0] :
( first(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f181,negated_conjecture,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets1_1) ).
fof(f182,negated_conjecture,
first(x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).
fof(f183,plain,
x != first(x),
inference(reorient_equations,[],[f182]) ).
fof(f184,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(f185,plain,
~ member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f181,f184]) ).
fof(f208,plain,
! [X0] :
( first(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f175,f184]) ).
tcf(c_210,negated_conjecture,
~ member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f185]) ).
tcf(c_211,negated_conjecture,
first(x) != x,
inference(cnf_transformation,[],[f183]) ).
tcf(c_234,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| ( first(X0) = X0 ) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_3116,plain,
( member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class))
| ( first(x) = x ) ),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_3117,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3116,c_210,c_211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET113-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Thu Sep 24 09:53:06 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.34 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 2.29/0.98 % SZS status Started for theBenchmark.p
% 2.29/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 2.29/0.98
% 2.29/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.29/0.98
% 2.29/0.98 % ------ iProver source info
% 2.29/0.98
% 2.29/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 2.29/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.29/0.98 % git: non_committed_changes: false
% 2.29/0.98
% 2.29/0.98 % ------ Parsing...% successful
% 2.29/0.98
% 2.29/0.98
% 2.29/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.29/0.98
% 2.29/0.98 % ------ 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 %
% 2.29/0.98
% 2.29/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.29/0.98
% 2.29/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.29/0.98 % ------ Proving...
% 2.29/0.98 % ------ Problem Properties
% 2.29/0.98
% 2.29/0.98 %
% 2.29/0.98 % clauses 58
% 2.29/0.98 % conjectures 2
% 2.29/0.98 % EPR 9
% 2.29/0.98 % Horn 44
% 2.29/0.98 % unary 15
% 2.29/0.98 % binary 26
% 2.29/0.98 % lits 119
% 2.29/0.98 % lits eq 43
% 2.29/0.98 % fd_pure 0
% 2.29/0.98 % fd_pseudo 0
% 2.29/0.98 % fd_cond 1
% 2.29/0.98 % fd_pseudo_cond 11
% 2.29/0.98 % AC symbols 0
% 2.29/0.98
% 2.29/0.98 % ------ Schedule dynamic 5 is on
% 2.29/0.98
% 2.29/0.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.29/0.98
% 2.29/0.98
% 2.29/0.98 % ------
% 2.29/0.98 % Current options:
% 2.29/0.98 % ------
% 2.29/0.98
% 2.29/0.98
% 2.29/0.98 %
% 2.29/0.98
% 2.29/0.98 % ------ Proving...
% 2.29/0.98 %
% 2.29/0.98
% 2.29/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 2.29/0.98
% 2.29/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.29/0.98
% 2.29/0.98
%------------------------------------------------------------------------------