%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET075-7 : 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 : n009.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 02:46:25 PM UTC 2026
% Result : Unsatisfiable 2.95s 1.09s
% Output : CNFRefutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 27 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
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(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(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f128,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
fof(f129,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
fof(f130,plain,
null_class = unordered_pair(x,y),
inference(reorient_equations,[],[f129]) ).
fof(f131,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(f132,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(definition_unfolding,[],[f128,f131]) ).
fof(f135,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,f131]) ).
tcf(c_166,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(cnf_transformation,[],[f132]) ).
tcf(c_167,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(cnf_transformation,[],[f130]) ).
tcf(c_170,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,[],[f135]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_190,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f113]) ).
tcf(c_966,plain,
( member(y,null_class)
| ~ member(y,universal_class) ),
inference(superposition,[status(thm)],[c_167,c_184]) ).
tcf(c_967,plain,
~ member(y,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_966,c_190]) ).
tcf(c_1407,plain,
( member(y,universal_class)
| ~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)) ),
inference(instantiation,[status(thm)],[c_170]) ).
tcf(c_1408,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1407,c_967,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 09:37:29 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.95/1.09 % SZS status Started for theBenchmark.p
% 2.95/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 2.95/1.09
% 2.95/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.95/1.09
% 2.95/1.09 % ------ iProver source info
% 2.95/1.09
% 2.95/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 2.95/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.95/1.09 % git: non_committed_changes: false
% 2.95/1.09
% 2.95/1.09 % ------ Parsing...% successful
% 2.95/1.09
% 2.95/1.09
% 2.95/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.95/1.09
% 2.95/1.09 % ------ 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 %
% 2.95/1.09
% 2.95/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.95/1.09
% 2.95/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.95/1.09 % ------ Proving...
% 2.95/1.09 % ------ Problem Properties
% 2.95/1.09
% 2.95/1.09 %
% 2.95/1.09 % clauses 30
% 2.95/1.09 % conjectures 2
% 2.95/1.09 % EPR 9
% 2.95/1.09 % Horn 26
% 2.95/1.09 % unary 11
% 2.95/1.09 % binary 11
% 2.95/1.09 % lits 57
% 2.95/1.09 % lits eq 13
% 2.95/1.09 % fd_pure 0
% 2.95/1.09 % fd_pseudo 0
% 2.95/1.09 % fd_cond 1
% 2.95/1.09 % fd_pseudo_cond 4
% 2.95/1.09 % AC symbols 0
% 2.95/1.09
% 2.95/1.09 % ------ Schedule dynamic 5 is on
% 2.95/1.09
% 2.95/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.95/1.09
% 2.95/1.09
% 2.95/1.09 % ------
% 2.95/1.09 % Current options:
% 2.95/1.09 % ------
% 2.95/1.09
% 2.95/1.09
% 2.95/1.09 %
% 2.95/1.09
% 2.95/1.09 % ------ Proving...
% 2.95/1.09 %
% 2.95/1.09
% 2.95/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 2.95/1.09
% 2.95/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.95/1.09
% 2.95/1.09
%------------------------------------------------------------------------------