%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET108-7 : 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 : 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 02:46:38 PM UTC 2026
% Result : Unsatisfiable 2.51s 6.29s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 12 unt; 0 def)
% Number of atoms : 18 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 14 ( 0 sgn 14 !; 0 ?; 3 :)
% 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(f174,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).
fof(f175,negated_conjecture,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).
fof(f176,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(f177,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f174,f176]) ).
fof(f178,plain,
~ member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f175,f176,f176,f176]) ).
fof(f201,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,f176]) ).
tcf(c_203,negated_conjecture,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f177]) ).
tcf(c_204,negated_conjecture,
~ member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f178]) ).
tcf(c_227,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,[],[f201]) ).
tcf(c_2946,plain,
unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))) = unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),
inference(superposition,[status(thm)],[c_203,c_227]) ).
tcf(c_2951,plain,
~ member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(demodulation,[status(thm)],[c_204,c_2946]) ).
tcf(c_2952,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2951,c_203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET108-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.38 % Computer : n016.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Thu Sep 24 09:56:19 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 2.51/6.29 % SZS status Started for theBenchmark.p
% 2.51/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.51/6.29
% 2.51/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.51/6.29
% 2.51/6.29 % ------ iProver source info
% 2.51/6.29
% 2.51/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.51/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.51/6.29 % git: non_committed_changes: false
% 2.51/6.29
% 2.51/6.29 % ------ Parsing...% successful
% 2.51/6.29
% 2.51/6.29
% 2.51/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.51/6.29
% 2.51/6.29 % ------ 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 %
% 2.51/6.29
% 2.51/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.51/6.29
% 2.51/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.51/6.29 % ------ Proving...
% 2.51/6.29 % ------ Problem Properties
% 2.51/6.29
% 2.51/6.29 %
% 2.51/6.29 % clauses 51
% 2.51/6.29 % conjectures 2
% 2.51/6.29 % EPR 9
% 2.51/6.29 % Horn 41
% 2.51/6.29 % unary 15
% 2.51/6.29 % binary 19
% 2.51/6.29 % lits 105
% 2.51/6.29 % lits eq 34
% 2.51/6.29 % fd_pure 0
% 2.51/6.29 % fd_pseudo 0
% 2.51/6.29 % fd_cond 1
% 2.51/6.29 % fd_pseudo_cond 11
% 2.51/6.29 % AC symbols 0
% 2.51/6.29
% 2.51/6.29 % ------ Schedule dynamic 5 is on
% 2.51/6.29
% 2.51/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.51/6.29
% 2.51/6.29
% 2.51/6.29 % ------
% 2.51/6.29 % Current options:
% 2.51/6.29 % ------
% 2.51/6.29
% 2.51/6.29
% 2.51/6.29 %
% 2.51/6.29
% 2.51/6.29 % ------ Proving...
% 2.51/6.29 %
% 2.51/6.29
% 2.51/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.51/6.29
% 2.51/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.51/6.29
% 2.51/6.29
%------------------------------------------------------------------------------