%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET134-6 : 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 : 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 02:46:42 PM UTC 2026
% Result : Unsatisfiable 5.12s 7.54s
% Output : CNFRefutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 74 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 28 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 11 ( 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 : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox/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,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_member_of_triple_1) ).
fof(f103,negated_conjecture,
set_builder(u,set_builder(y,set_builder(z,null_class))) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_member_of_triple_2) ).
fof(f104,plain,
null_class = set_builder(u,set_builder(y,set_builder(z,null_class))),
inference(reorient_equations,[],[f103]) ).
fof(f110,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f154,plain,
null_class = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))),
inference(definition_unfolding,[],[f104,f110,f110,f110]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_218,negated_conjecture,
member(u,universal_class),
inference(cnf_transformation,[],[f102]) ).
tcf(c_219,negated_conjecture,
complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))) = null_class,
inference(cnf_transformation,[],[f154]) ).
tcf(c_3340,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_219,c_165]) ).
tcf(c_3360,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = null_class )
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_196,c_161]) ).
tcf(c_3542,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_3340,c_162]) ).
tcf(c_3543,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,complement(unordered_pair(u,u)))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_3340,c_161]) ).
tcf(c_3600,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,universal_class)
| ~ member(X0,unordered_pair(u,u)) ),
inference(superposition,[status(thm)],[c_3543,c_164]) ).
tcf(c_3622,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,universal_class)
| ~ member(X0,complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))) ),
inference(superposition,[status(thm)],[c_3542,c_164]) ).
tcf(c_3665,plain,
( member(u,null_class)
| ~ member(u,universal_class) ),
inference(superposition,[status(thm)],[c_151,c_3600]) ).
tcf(c_3793,plain,
member(u,null_class),
inference(global_subsumption_just,[status(thm)],[c_3665,c_218,c_3665]) ).
tcf(c_3833,plain,
! [X0: $i] :
( ~ member(X0,null_class)
| ~ member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))) ),
inference(superposition,[status(thm)],[c_219,c_164]) ).
tcf(c_3846,plain,
! [X0: $i] :
( member(u,X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_3793,c_3360]) ).
tcf(c_4102,plain,
( ( intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))) = null_class )
| ~ member(u,null_class) ),
inference(superposition,[status(thm)],[c_3846,c_3833]) ).
tcf(c_4297,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_219,c_165]) ).
tcf(c_4854,plain,
intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))) = null_class,
inference(global_subsumption_just,[status(thm)],[c_4102,c_218,c_3665,c_4102]) ).
tcf(c_4861,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_4854,c_4297]) ).
tcf(c_4866,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(superposition,[status(thm)],[c_4854,c_3833]) ).
tcf(c_5219,plain,
! [X0: $i] : ~ member(X0,universal_class),
inference(global_subsumption_just,[status(thm)],[c_3622,c_4866,c_4861]) ).
tcf(c_5222,plain,
$false,
inference(superposition,[status(thm)],[c_218,c_5219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET134-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/6.35 % Computer : n012.cluster.edu
% 0.04/6.35 % Model : x86_64 x86_64
% 0.04/6.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/6.35 % Memory : 8046.5625MB
% 0.04/6.35 % OS : Linux 6.8.0-71-generic
% 0.04/6.35 % CPULimit : 300
% 0.04/6.35 % WCLimit : 300
% 0.04/6.35 % DateTime : Thu Sep 24 09:58:37 UTC 2026
% 0.04/6.35 % CPUTime :
% 0.04/6.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/6.37 Running first-order theorem proving
% 0.04/6.37 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
% 0.04/6.37
% 0.04/6.37 % ======== iProver multi-core TPTP/SMT =========
% 0.04/6.37
% 0.04/6.37 % Detected problem language: tptp
% 0.04/6.38 % Proving...
% 5.12/7.54 % SZS status Started for theBenchmark.p
% 5.12/7.54 % SZS status Unsatisfiable for theBenchmark.p
% 5.12/7.54
% 5.12/7.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.12/7.54
% 5.12/7.54 % ------ iProver source info
% 5.12/7.54
% 5.12/7.54 % git: date: 2026-07-19 20:42:38 +0200
% 5.12/7.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.12/7.54 % git: non_committed_changes: false
% 5.12/7.54
% 5.12/7.54 % ------ Parsing...% successful
% 5.12/7.54
% 5.12/7.54
% 5.12/7.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.12/7.54
% 5.12/7.54 % ------ 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 %
% 5.12/7.54
% 5.12/7.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.12/7.54
% 5.12/7.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.12/7.54 % ------ Proving...
% 5.12/7.54 % ------ Problem Properties
% 5.12/7.54
% 5.12/7.54 %
% 5.12/7.54 % clauses 69
% 5.12/7.54 % conjectures 2
% 5.12/7.54 % EPR 13
% 5.12/7.54 % Horn 61
% 5.12/7.54 % unary 17
% 5.12/7.54 % binary 32
% 5.12/7.54 % lits 147
% 5.12/7.54 % lits eq 21
% 5.12/7.54 % fd_pure 0
% 5.12/7.54 % fd_pseudo 0
% 5.12/7.54 % fd_cond 3
% 5.12/7.54 % fd_pseudo_cond 3
% 5.12/7.54 % AC symbols 0
% 5.12/7.54
% 5.12/7.54 % ------ Input Options Time Limit: Unbounded
% 5.12/7.54
% 5.12/7.54
% 5.12/7.54 % ------
% 5.12/7.54 % Current options:
% 5.12/7.54 % ------
% 5.12/7.54
% 5.12/7.54
% 5.12/7.54 %
% 5.12/7.54
% 5.12/7.54 % ------ Proving...
% 5.12/7.54 %
% 5.12/7.54
% 5.12/7.54 % SZS status Unsatisfiable for theBenchmark.p
% 5.12/7.54
% 5.12/7.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.12/7.54
% 5.12/7.54
%------------------------------------------------------------------------------