%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET099-7 : 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 : n002.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 02:46:35 PM UTC 2026
% Result : Unsatisfiable 4.84s 1.50s
% Output : CNFRefutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 20 unt; 0 def)
% Number of atoms : 55 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 22 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/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/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(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f156,axiom,
! [X0] :
( X0 = null_class
| singleton(not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_of_elements_in_class) ).
fof(f157,plain,
! [X0] :
( null_class = X0
| singleton(not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0)) ),
inference(reorient_equations,[],[f156]) ).
fof(f158,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
fof(f159,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(reorient_equations,[],[f158]) ).
fof(f160,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).
fof(f161,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f160]) ).
fof(f162,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
fof(f163,plain,
null_class != x,
inference(reorient_equations,[],[f162]) ).
fof(f165,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(definition_unfolding,[],[f159,f12]) ).
fof(f166,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f161,f12]) ).
fof(f167,plain,
! [X0] :
( null_class = X0
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0)) ),
inference(definition_unfolding,[],[f157,f12,f12,f12]) ).
tcf(c_193,negated_conjecture,
not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(cnf_transformation,[],[f165]) ).
tcf(c_194,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[],[f166]) ).
tcf(c_195,negated_conjecture,
null_class != x,
inference(cnf_transformation,[],[f163]) ).
tcf(c_196,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0))
| ( X0 = null_class )
| ( unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0 ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_236,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_2043,plain,
( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| ( null_class = x )
| ( unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) = x ) ),
inference(superposition,[status(thm)],[c_193,c_196]) ).
tcf(c_2052,plain,
member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(forward_subsumption_resolution,[status(thm)],[c_2043,c_195,c_194]) ).
tcf(c_2131,plain,
member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))),
inference(superposition,[status(thm)],[c_2052,c_217]) ).
tcf(c_2147,plain,
~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
inference(superposition,[status(thm)],[c_2131,c_219]) ).
tcf(c_2229,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_236,c_237]) ).
tcf(c_2267,plain,
member(not_subclass_element(x,null_class),universal_class),
inference(superposition,[status(thm)],[c_2131,c_2229]) ).
tcf(c_2292,plain,
~ member(not_subclass_element(x,null_class),universal_class),
inference(superposition,[status(thm)],[c_249,c_2147]) ).
tcf(c_2294,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2292,c_2267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.41 % Computer : n002.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Thu Sep 24 09:50:34 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.48 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
% 0.24/0.49
% 0.24/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.49
% 0.24/0.50 % Detected problem language: tptp
% 0.24/0.51 % Proving...
% 4.84/1.50 % SZS status Started for theBenchmark.p
% 4.84/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.84/1.50
% 4.84/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.84/1.50
% 4.84/1.50 % ------ iProver source info
% 4.84/1.50
% 4.84/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 4.84/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.84/1.50 % git: non_committed_changes: false
% 4.84/1.50
% 4.84/1.50 % ------ Parsing...% successful
% 4.84/1.50
% 4.84/1.50
% 4.84/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.84/1.50
% 4.84/1.50 % ------ 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 %
% 4.84/1.50
% 4.84/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.84/1.50
% 4.84/1.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.84/1.50 % ------ Proving...
% 4.84/1.50 % ------ Problem Properties
% 4.84/1.50
% 4.84/1.50 %
% 4.84/1.50 % clauses 57
% 4.84/1.50 % conjectures 3
% 4.84/1.50 % EPR 10
% 4.84/1.50 % Horn 44
% 4.84/1.50 % unary 15
% 4.84/1.50 % binary 23
% 4.84/1.50 % lits 119
% 4.84/1.50 % lits eq 35
% 4.84/1.50 % fd_pure 0
% 4.84/1.50 % fd_pseudo 0
% 4.84/1.50 % fd_cond 2
% 4.84/1.50 % fd_pseudo_cond 12
% 4.84/1.50 % AC symbols 0
% 4.84/1.50
% 4.84/1.50 % ------ Schedule dynamic 5 is on
% 4.84/1.50
% 4.84/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.84/1.50
% 4.84/1.50
% 4.84/1.50 % ------
% 4.84/1.50 % Current options:
% 4.84/1.50 % ------
% 4.84/1.50
% 4.84/1.50
% 4.84/1.50 %
% 4.84/1.50
% 4.84/1.50 % ------ Proving...
% 4.84/1.50 %
% 4.84/1.50
% 4.84/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.84/1.50
% 4.84/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.84/1.51
% 4.84/1.51
%------------------------------------------------------------------------------