%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET097-7 : 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 : n011.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 0.61s 1.29s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 22 unt; 0 def)
% Number of atoms : 86 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 42 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 60 ( 0 sgn 60 !; 0 ?; 33 :)
% 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(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f115,axiom,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f116,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class) ),
inference(reorient_equations,[],[f115]) ).
fof(f122,axiom,
! [X0,X1] : subclass(singleton(X0),unordered_pair(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f154,axiom,
! [X0,X1] :
( singleton(X1) = X0
| X0 = null_class
| ~ subclass(X0,singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
fof(f155,plain,
! [X0,X1] :
( singleton(X1) = X0
| null_class = X0
| ~ subclass(X0,singleton(X1)) ),
inference(reorient_equations,[],[f154]) ).
fof(f156,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_1) ).
fof(f157,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).
fof(f158,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f157]) ).
fof(f159,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).
fof(f160,plain,
null_class != x,
inference(reorient_equations,[],[f159]) ).
fof(f162,plain,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(definition_unfolding,[],[f156,f12,f12]) ).
fof(f163,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f158,f12]) ).
fof(f164,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| null_class = X0
| ~ subclass(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f155,f12,f12]) ).
fof(f175,plain,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X1,X0)),
inference(definition_unfolding,[],[f122,f12]) ).
tcf(c_192,negated_conjecture,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(cnf_transformation,[],[f162]) ).
tcf(c_193,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[],[f163]) ).
tcf(c_194,negated_conjecture,
null_class != x,
inference(cnf_transformation,[],[f160]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( ( X0 = null_class )
| ( unordered_pair(X1,X1) = X0 )
| ~ subclass(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_223,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_225,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f113]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] : subclass(unordered_pair(X0,X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f175]) ).
tcf(c_234,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_1930,plain,
subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(superposition,[status(thm)],[c_201,c_192]) ).
tcf(c_1942,plain,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(superposition,[status(thm)],[c_1930,c_223]) ).
tcf(c_2123,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_234,c_235]) ).
tcf(c_2125,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,unordered_pair(X2,X1))
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_227,c_235]) ).
tcf(c_2353,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_1942,c_212]) ).
tcf(c_2364,plain,
! [X0: $i] :
( ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2353,c_225]) ).
tcf(c_2570,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,x)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_216,c_2364]) ).
tcf(c_2595,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2570,c_2123]) ).
tcf(c_2606,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2595,c_2125]) ).
tcf(c_2643,plain,
! [X0: $i,X1: $i] :
( subclass(X0,unordered_pair(X1,not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(X0,unordered_pair(X1,not_subclass_element(x,null_class))),x) ),
inference(superposition,[status(thm)],[c_2606,c_200]) ).
tcf(c_2980,plain,
! [X0: $i] : subclass(x,unordered_pair(X0,not_subclass_element(x,null_class))),
inference(superposition,[status(thm)],[c_201,c_2643]) ).
tcf(c_3181,plain,
( ( null_class = x )
| ( unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) = x ) ),
inference(superposition,[status(thm)],[c_2980,c_202]) ).
tcf(c_3184,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3181,c_194,c_193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET097-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:46:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 0.61/1.29 % SZS status Started for theBenchmark.p
% 0.61/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.61/1.29
% 0.61/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.61/1.29
% 0.61/1.29 % ------ iProver source info
% 0.61/1.29
% 0.61/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.61/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.61/1.29 % git: non_committed_changes: false
% 0.61/1.29
% 0.61/1.29 % ------ Parsing...% successful
% 0.61/1.29
% 0.61/1.29
% 0.61/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.61/1.29
% 0.61/1.29 % ------ 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 %
% 0.61/1.29
% 0.61/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.61/1.29
% 0.61/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.61/1.29 % ------ Proving...
% 0.61/1.29 % ------ Problem Properties
% 0.61/1.29
% 0.61/1.29 %
% 0.61/1.29 % clauses 56
% 0.61/1.29 % conjectures 3
% 0.61/1.29 % EPR 10
% 0.61/1.29 % Horn 44
% 0.61/1.29 % unary 15
% 0.61/1.29 % binary 23
% 0.61/1.29 % lits 116
% 0.61/1.29 % lits eq 32
% 0.61/1.29 % fd_pure 0
% 0.61/1.29 % fd_pseudo 0
% 0.61/1.29 % fd_cond 2
% 0.61/1.29 % fd_pseudo_cond 12
% 0.61/1.29 % AC symbols 0
% 0.61/1.29
% 0.61/1.29 % ------ Schedule dynamic 5 is on
% 0.61/1.29
% 0.61/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.61/1.29
% 0.61/1.29
% 0.61/1.29 % ------
% 0.61/1.29 % Current options:
% 0.61/1.29 % ------
% 0.61/1.29
% 0.61/1.29
% 0.61/1.29 %
% 0.61/1.29
% 0.61/1.29 % ------ Proving...
% 0.61/1.29 %
% 0.61/1.29
% 0.61/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.61/1.29
% 0.61/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.61/1.29
% 0.61/1.29
%------------------------------------------------------------------------------