%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET098-7 : 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 4.15s 1.30s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 21 unt; 0 def)
% Number of atoms : 91 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 41 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 68 !; 0 ?; 38 :)
% 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(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(f117,axiom,
! [X0] :
( member(not_subclass_element(X0,null_class),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f118,plain,
! [X0] :
( member(not_subclass_element(X0,null_class),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f117]) ).
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(f158,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_1) ).
fof(f159,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_2) ).
fof(f160,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f159]) ).
fof(f161,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_3) ).
fof(f162,plain,
null_class != x,
inference(reorient_equations,[],[f161]) ).
fof(f164,plain,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x),
inference(definition_unfolding,[],[f158,f12]) ).
fof(f165,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f160,f12]) ).
fof(f167,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| null_class = X0
| ~ subclass(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f155,f12,f12]) ).
fof(f178,plain,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X1,X0)),
inference(definition_unfolding,[],[f122,f12]) ).
tcf(c_193,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),x),
inference(cnf_transformation,[],[f164]) ).
tcf(c_194,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[],[f165]) ).
tcf(c_195,negated_conjecture,
null_class != x,
inference(cnf_transformation,[],[f162]) ).
tcf(c_197,plain,
! [X0: $i] :
( member(not_subclass_element(X0,null_class),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( ( X0 = null_class )
| ( unordered_pair(X1,X1) = X0 )
| ~ subclass(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_215,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,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_227,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f113]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] : subclass(unordered_pair(X0,X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f178]) ).
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_2008,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,X1),null_class),X1)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_197,c_216]) ).
tcf(c_2049,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_2008,c_193]) ).
tcf(c_2162,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_236,c_237]) ).
tcf(c_2164,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,unordered_pair(X2,X1))
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_229,c_237]) ).
tcf(c_2392,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_2049,c_215]) ).
tcf(c_2403,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_2392,c_227]) ).
tcf(c_2611,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_218,c_2403]) ).
tcf(c_2634,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_2611,c_2162]) ).
tcf(c_2645,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2634,c_2164]) ).
tcf(c_2682,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_2645,c_202]) ).
tcf(c_3019,plain,
! [X0: $i] : subclass(x,unordered_pair(X0,not_subclass_element(x,null_class))),
inference(superposition,[status(thm)],[c_203,c_2682]) ).
tcf(c_3220,plain,
( ( null_class = x )
| ( unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) = x ) ),
inference(superposition,[status(thm)],[c_3019,c_204]) ).
tcf(c_3223,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3220,c_195,c_194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 09:47:13 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 4.15/1.30 % SZS status Started for theBenchmark.p
% 4.15/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.15/1.30
% 4.15/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.15/1.30
% 4.15/1.30 % ------ iProver source info
% 4.15/1.30
% 4.15/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.15/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.15/1.30 % git: non_committed_changes: false
% 4.15/1.30
% 4.15/1.30 % ------ Parsing...% successful
% 4.15/1.30
% 4.15/1.30
% 4.15/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.15/1.30
% 4.15/1.30 % ------ 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 %
% 4.15/1.30
% 4.15/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.15/1.30
% 4.15/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.15/1.30 % ------ Proving...
% 4.15/1.30 % ------ Problem Properties
% 4.15/1.30
% 4.15/1.30 %
% 4.15/1.30 % clauses 57
% 4.15/1.30 % conjectures 3
% 4.15/1.30 % EPR 10
% 4.15/1.30 % Horn 44
% 4.15/1.30 % unary 15
% 4.15/1.30 % binary 23
% 4.15/1.30 % lits 119
% 4.15/1.30 % lits eq 34
% 4.15/1.30 % fd_pure 0
% 4.15/1.30 % fd_pseudo 0
% 4.15/1.30 % fd_cond 2
% 4.15/1.30 % fd_pseudo_cond 12
% 4.15/1.30 % AC symbols 0
% 4.15/1.30
% 4.15/1.30 % ------ Schedule dynamic 5 is on
% 4.15/1.30
% 4.15/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.15/1.30
% 4.15/1.30
% 4.15/1.30 % ------
% 4.15/1.30 % Current options:
% 4.15/1.30 % ------
% 4.15/1.30
% 4.15/1.30
% 4.15/1.30 %
% 4.15/1.30
% 4.15/1.30 % ------ Proving...
% 4.15/1.30 %
% 4.15/1.30
% 4.15/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.15/1.30
% 4.15/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.15/1.30
% 4.15/1.30
%------------------------------------------------------------------------------