%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET411-6 : 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 : n003.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 02:47:13 PM UTC 2026
% Result : Unsatisfiable 4.20s 1.18s
% Output : CNFRefutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 32 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 14 :)
% 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(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(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',element_relation1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f113,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-1.ax',compose_can_define_singleton) ).
fof(f122,negated_conjecture,
member(ordered_pair(x,y),singleton_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_1) ).
fof(f123,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compose_condition_for_singleton_membership1_2) ).
tcf(c_163,negated_conjecture,
member(ordered_pair(x,y),singleton_relation),
inference(cnf_transformation,[],[f122]) ).
tcf(c_164,negated_conjecture,
~ member(x,universal_class),
inference(cnf_transformation,[],[f123]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_168,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(cnf_transformation,[],[f113]) ).
tcf(c_172,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_792,plain,
! [X0: $i] :
( member(X0,element_relation)
| ~ member(X0,singleton_relation) ),
inference(superposition,[status(thm)],[c_168,c_174]) ).
tcf(c_820,plain,
member(ordered_pair(x,y),element_relation),
inference(superposition,[status(thm)],[c_163,c_792]) ).
tcf(c_837,plain,
! [X0: $i] :
( member(ordered_pair(x,y),X0)
| ~ subclass(element_relation,X0) ),
inference(superposition,[status(thm)],[c_820,c_184]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i] :
( member(x,X0)
| ~ subclass(element_relation,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_837,c_167]) ).
tcf(c_907,plain,
( member(x,universal_class)
| ~ subclass(element_relation,cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_886]) ).
tcf(c_908,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_907,c_172,c_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 10:53:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.20/1.18 % SZS status Started for theBenchmark.p
% 4.20/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 4.20/1.18
% 4.20/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.20/1.18
% 4.20/1.18 % ------ iProver source info
% 4.20/1.18
% 4.20/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 4.20/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.20/1.18 % git: non_committed_changes: false
% 4.20/1.18
% 4.20/1.18 % ------ Parsing...% successful
% 4.20/1.18
% 4.20/1.18
% 4.20/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.20/1.18
% 4.20/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.20/1.18
% 4.20/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.20/1.18
% 4.20/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.20/1.18 % ------ Proving...
% 4.20/1.18 % ------ Problem Properties
% 4.20/1.18
% 4.20/1.18 %
% 4.20/1.18 % clauses 19
% 4.20/1.18 % conjectures 2
% 4.20/1.18 % EPR 5
% 4.20/1.18 % Horn 18
% 4.20/1.18 % unary 7
% 4.20/1.18 % binary 6
% 4.20/1.18 % lits 37
% 4.20/1.18 % lits eq 2
% 4.20/1.18 % fd_pure 0
% 4.20/1.18 % fd_pseudo 0
% 4.20/1.18 % fd_cond 0
% 4.20/1.18 % fd_pseudo_cond 1
% 4.20/1.18 % AC symbols 0
% 4.20/1.18
% 4.20/1.18 % ------ Schedule dynamic 5 is on
% 4.20/1.18
% 4.20/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.20/1.18
% 4.20/1.18
% 4.20/1.18 % ------
% 4.20/1.18 % Current options:
% 4.20/1.18 % ------
% 4.20/1.18
% 4.20/1.18
% 4.20/1.18 %
% 4.20/1.18
% 4.20/1.18 % ------ Proving...
% 4.20/1.18 %
% 4.20/1.18
% 4.20/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 4.20/1.18
% 4.20/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.20/1.18
% 4.20/1.18
%------------------------------------------------------------------------------