%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET075-6 : 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 : n014.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 14.91s 2.82s
% Output : CNFRefutation 14.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 58 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 20 ~; 22 |; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
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(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
fof(f102,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
fof(f103,plain,
null_class = unordered_pair(x,y),
inference(reorient_equations,[],[f102]) ).
fof(f108,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(f114,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f14,f108]) ).
fof(f152,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(definition_unfolding,[],[f101,f108]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_145,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_195,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_217,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(cnf_transformation,[],[f152]) ).
tcf(c_218,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(cnf_transformation,[],[f103]) ).
tcf(c_3556,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(superposition,[status(thm)],[c_218,c_150]) ).
tcf(c_3816,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = null_class )
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_195,c_160]) ).
tcf(c_6850,plain,
member(x,u),
inference(superposition,[status(thm)],[c_217,c_153]) ).
tcf(c_7365,plain,
! [X0: $i] :
( member(x,X0)
| ~ subclass(u,X0) ),
inference(superposition,[status(thm)],[c_6850,c_142]) ).
tcf(c_7391,plain,
member(x,universal_class),
inference(superposition,[status(thm)],[c_145,c_7365]) ).
tcf(c_10289,plain,
member(x,null_class),
inference(global_subsumption_just,[status(thm)],[c_3556,c_3556,c_7391]) ).
tcf(c_14000,plain,
! [X0: $i] :
( member(x,X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_10289,c_3816]) ).
tcf(c_15205,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(x,X0) ),
inference(superposition,[status(thm)],[c_14000,c_163]) ).
tcf(c_17212,plain,
complement(null_class) = null_class,
inference(superposition,[status(thm)],[c_10289,c_15205]) ).
tcf(c_17586,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(superposition,[status(thm)],[c_17212,c_163]) ).
tcf(c_17627,plain,
$false,
inference(superposition,[status(thm)],[c_10289,c_17586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 09:36:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 14.91/2.82 % SZS status Started for theBenchmark.p
% 14.91/2.82 % SZS status Unsatisfiable for theBenchmark.p
% 14.91/2.82
% 14.91/2.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.91/2.82
% 14.91/2.82 % ------ iProver source info
% 14.91/2.82
% 14.91/2.82 % git: date: 2026-07-19 20:42:38 +0200
% 14.91/2.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.91/2.82 % git: non_committed_changes: false
% 14.91/2.82
% 14.91/2.82 % ------ Parsing...% successful
% 14.91/2.82
% 14.91/2.82
% 14.91/2.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.91/2.82
% 14.91/2.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 14.91/2.82
% 14.91/2.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.91/2.82
% 14.91/2.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.91/2.82 % ------ Proving...
% 14.91/2.82 % ------ Problem Properties
% 14.91/2.82
% 14.91/2.82 %
% 14.91/2.82 % clauses 69
% 14.91/2.82 % conjectures 2
% 14.91/2.82 % EPR 12
% 14.91/2.82 % Horn 61
% 14.91/2.82 % unary 17
% 14.91/2.82 % binary 32
% 14.91/2.82 % lits 147
% 14.91/2.82 % lits eq 21
% 14.91/2.82 % fd_pure 0
% 14.91/2.82 % fd_pseudo 0
% 14.91/2.82 % fd_cond 3
% 14.91/2.82 % fd_pseudo_cond 3
% 14.91/2.82 % AC symbols 0
% 14.91/2.82
% 14.91/2.82 % ------ Input Options Time Limit: Unbounded
% 14.91/2.82
% 14.91/2.82
% 14.91/2.82 % ------
% 14.91/2.82 % Current options:
% 14.91/2.82 % ------
% 14.91/2.82
% 14.91/2.82
% 14.91/2.82 %
% 14.91/2.82
% 14.91/2.82 % ------ Proving...
% 14.91/2.82 %
% 14.91/2.82
% 14.91/2.82 % SZS status Unsatisfiable for theBenchmark.p
% 14.91/2.82
% 14.91/2.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.91/2.82
% 14.91/2.82
%------------------------------------------------------------------------------