%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET082-6 : 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 : n005.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 02:46:30 PM UTC 2026
% Result : Unsatisfiable 4.27s 1.50s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 15 unt; 1 def)
% Number of atoms : 57 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 34 ( 17 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?; 10 :)
% 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(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f101,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_1) ).
fof(f102,negated_conjecture,
singleton(x) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_2) ).
fof(f103,plain,
null_class != singleton(x),
inference(reorient_equations,[],[f102]) ).
fof(f152,plain,
null_class != unordered_pair(x,x),
inference(definition_unfolding,[],[f103,f12]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_145,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_194,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_217,negated_conjecture,
~ member(x,universal_class),
inference(cnf_transformation,[],[f101]) ).
tcf(c_218,negated_conjecture,
unordered_pair(x,x) != null_class,
inference(cnf_transformation,[],[f152]) ).
tcf(c_2644,definition,
iPr_def_10 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2645,negated_conjecture,
iPr_def_10 != null_class,
inference(demodulation,[status(thm)],[c_218,c_2644]) ).
tcf(c_2646,negated_conjecture,
~ member(x,universal_class),
inference(demodulation,[status(thm)],[c_217]) ).
tcf(c_4129,plain,
! [X0: $i] :
( ( X0 = x )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2644,c_149]) ).
tcf(c_4192,plain,
( ( null_class = iPr_def_10 )
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_194,c_4129]) ).
tcf(c_4233,plain,
( member(x,iPr_def_10)
| ( null_class = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4192,c_194]) ).
tcf(c_4253,plain,
! [X0: $i] :
( member(x,X0)
| ( null_class = iPr_def_10 )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4233,c_142]) ).
tcf(c_4332,plain,
( member(x,universal_class)
| ( null_class = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_145,c_4253]) ).
tcf(c_4336,plain,
null_class = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_4332,c_2646]) ).
tcf(c_4351,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_2645,c_4336]) ).
tcf(c_4352,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_4351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET082-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.57 % Computer : n005.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Thu Sep 24 09:39:48 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.15/0.63
% 0.15/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.63
% 0.15/0.63 % Detected problem language: tptp
% 0.15/0.65 % Proving...
% 4.27/1.50 % SZS status Started for theBenchmark.p
% 4.27/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.27/1.50
% 4.27/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.27/1.50
% 4.27/1.50 % ------ iProver source info
% 4.27/1.50
% 4.27/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 4.27/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.27/1.50 % git: non_committed_changes: false
% 4.27/1.50
% 4.27/1.50 % ------ Parsing...% successful
% 4.27/1.50
% 4.27/1.50
% 4.27/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.27/1.50
% 4.27/1.50 % ------ 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 %
% 4.27/1.50
% 4.27/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.27/1.50
% 4.27/1.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.27/1.50 % ------ Proving...
% 4.27/1.50 % ------ Problem Properties
% 4.27/1.50
% 4.27/1.50 %
% 4.27/1.50 % clauses 70
% 4.27/1.50 % conjectures 2
% 4.27/1.50 % EPR 14
% 4.27/1.50 % Horn 62
% 4.27/1.50 % unary 18
% 4.27/1.50 % binary 32
% 4.27/1.50 % lits 148
% 4.27/1.50 % lits eq 22
% 4.27/1.50 % fd_pure 0
% 4.27/1.50 % fd_pseudo 0
% 4.27/1.50 % fd_cond 3
% 4.27/1.50 % fd_pseudo_cond 3
% 4.27/1.50 % AC symbols 0
% 4.27/1.50
% 4.27/1.50 % ------ Schedule dynamic 5 is on
% 4.27/1.50
% 4.27/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.27/1.50
% 4.27/1.50
% 4.27/1.50 % ------
% 4.27/1.50 % Current options:
% 4.27/1.50 % ------
% 4.27/1.50
% 4.27/1.50
% 4.27/1.50 %
% 4.27/1.50
% 4.27/1.50 % ------ Proving...
% 4.27/1.50 %
% 4.27/1.50
% 4.27/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.27/1.50
% 4.27/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.27/1.50
% 4.27/1.50
%------------------------------------------------------------------------------