%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET162-6 : 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 : n010.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 02:46:48 PM UTC 2026
% Result : Unsatisfiable 3.83s 2.26s
% Output : CNFRefutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 80 ( 24 unt; 4 def)
% Number of atoms : 227 ( 26 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 132 ( 59 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 64 :)
% 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(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
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(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f122,negated_conjecture,
union(null_class,x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_with_null_class_1) ).
fof(f123,plain,
x != union(null_class,x),
inference(reorient_equations,[],[f122]) ).
fof(f186,plain,
x != complement(intersection(complement(null_class),complement(x))),
inference(definition_unfolding,[],[f123,f26]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_165,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_214,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_255,negated_conjecture,
complement(intersection(complement(null_class),complement(x))) != x,
inference(cnf_transformation,[],[f186]) ).
tcf(c_2974,definition,
iPr_def_10 = complement(null_class),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2975,definition,
iPr_def_11 = complement(x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2976,definition,
iPr_def_12 = intersection(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2977,definition,
iPr_def_13 = complement(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2978,negated_conjecture,
iPr_def_13 != x,
inference(demodulation,[status(thm)],[c_255,c_2975,c_2974,c_2976,c_2977]) ).
tcf(c_3922,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2976,c_181]) ).
tcf(c_3940,plain,
! [X0: $i] :
( subclass(iPr_def_12,X0)
| member(not_subclass_element(iPr_def_12,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_163,c_3922]) ).
tcf(c_3951,plain,
subclass(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_3940,c_164]) ).
tcf(c_3960,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_163,c_183]) ).
tcf(c_3961,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_214,c_183]) ).
tcf(c_3963,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2975,c_183]) ).
tcf(c_3978,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_3961]) ).
tcf(c_4024,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_165,c_162]) ).
tcf(c_4093,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_163,c_4024]) ).
tcf(c_4201,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2974,c_184]) ).
tcf(c_4202,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,x)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2975,c_184]) ).
tcf(c_4203,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| member(X0,iPr_def_12)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2977,c_184]) ).
tcf(c_4232,plain,
! [X0: $i] :
( ( X0 = universal_class )
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_165,c_168]) ).
tcf(c_4241,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ subclass(iPr_def_11,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3951,c_168]) ).
tcf(c_4378,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2976,c_182]) ).
tcf(c_4421,plain,
( ( iPr_def_13 = x )
| ~ subclass(iPr_def_13,x)
| ~ subclass(x,iPr_def_13) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_4834,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_11)
| member(not_subclass_element(X0,X1),x) ),
inference(superposition,[status(thm)],[c_4093,c_4202]) ).
tcf(c_4987,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_4093,c_3960]) ).
tcf(c_4990,plain,
! [X0: $i] :
( subclass(complement(iPr_def_12),X0)
| ~ member(not_subclass_element(iPr_def_13,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_2977,c_3960]) ).
tcf(c_4991,plain,
! [X0: $i] :
( subclass(iPr_def_13,X0)
| ~ member(not_subclass_element(iPr_def_13,X0),iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_4990,c_2977]) ).
tcf(c_5174,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_4987,c_162]) ).
tcf(c_5193,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(superposition,[status(thm)],[c_214,c_5174]) ).
tcf(c_5196,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_5193]) ).
tcf(c_5207,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_5193,c_3978,c_5196]) ).
tcf(c_5210,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(demodulation,[status(thm)],[c_5174,c_5207]) ).
tcf(c_5222,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_5207,c_183]) ).
tcf(c_5250,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_5210,c_4024,c_5210,c_5222]) ).
tcf(c_5256,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,universal_class) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4201,c_5250]) ).
tcf(c_5270,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| member(not_subclass_element(universal_class,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_163,c_5256]) ).
tcf(c_5278,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4093,c_5256]) ).
tcf(c_5375,plain,
subclass(universal_class,iPr_def_10),
inference(superposition,[status(thm)],[c_5270,c_164]) ).
tcf(c_5381,plain,
universal_class = iPr_def_10,
inference(superposition,[status(thm)],[c_5375,c_4232]) ).
tcf(c_5390,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| member(X0,iPr_def_12)
| ~ member(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_4203,c_5381]) ).
tcf(c_5414,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,X1) ),
inference(demodulation,[status(thm)],[c_4024,c_5381]) ).
tcf(c_6530,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4378,c_5414]) ).
tcf(c_6537,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| member(not_subclass_element(iPr_def_11,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_163,c_6530]) ).
tcf(c_6559,plain,
subclass(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_6537,c_164]) ).
tcf(c_6569,plain,
iPr_def_11 = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_4241,c_6559]) ).
tcf(c_6573,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_5390,c_6569]) ).
tcf(c_6574,plain,
! [X0: $i] :
( subclass(iPr_def_13,X0)
| ~ member(not_subclass_element(iPr_def_13,X0),iPr_def_11) ),
inference(demodulation,[status(thm)],[c_4991,c_6569]) ).
tcf(c_7011,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_13)
| member(not_subclass_element(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5278,c_6573]) ).
tcf(c_13870,plain,
! [X0: $i] :
( subclass(X0,x)
| member(not_subclass_element(X0,x),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4834,c_164]) ).
tcf(c_13895,plain,
subclass(iPr_def_13,x),
inference(superposition,[status(thm)],[c_13870,c_6574]) ).
tcf(c_13913,plain,
( ( x = iPr_def_13 )
| ~ subclass(x,iPr_def_13) ),
inference(superposition,[status(thm)],[c_13895,c_168]) ).
tcf(c_14121,plain,
~ subclass(x,iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_13913,c_2978,c_4421,c_13895]) ).
tcf(c_15747,plain,
! [X0: $i] :
( subclass(X0,iPr_def_13)
| member(not_subclass_element(X0,iPr_def_13),iPr_def_11) ),
inference(superposition,[status(thm)],[c_7011,c_164]) ).
tcf(c_15771,plain,
! [X0: $i] :
( subclass(X0,iPr_def_13)
| ~ member(not_subclass_element(X0,iPr_def_13),x) ),
inference(superposition,[status(thm)],[c_15747,c_3963]) ).
tcf(c_15792,plain,
subclass(x,iPr_def_13),
inference(superposition,[status(thm)],[c_163,c_15771]) ).
tcf(c_15800,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15792,c_14121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 10:06:28 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.83/2.26 % SZS status Started for theBenchmark.p
% 3.83/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 3.83/2.26
% 3.83/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.83/2.26
% 3.83/2.26 % ------ iProver source info
% 3.83/2.26
% 3.83/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 3.83/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.83/2.26 % git: non_committed_changes: false
% 3.83/2.26
% 3.83/2.26 % ------ Parsing...% successful
% 3.83/2.26
% 3.83/2.26
% 3.83/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.83/2.26
% 3.83/2.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.83/2.26
% 3.83/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.83/2.26
% 3.83/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.83/2.26 % ------ Proving...
% 3.83/2.26 % ------ Problem Properties
% 3.83/2.26
% 3.83/2.26 %
% 3.83/2.26 % clauses 86
% 3.83/2.26 % conjectures 1
% 3.83/2.26 % EPR 13
% 3.83/2.26 % Horn 78
% 3.83/2.26 % unary 25
% 3.83/2.26 % binary 40
% 3.83/2.26 % lits 174
% 3.83/2.26 % lits eq 30
% 3.83/2.26 % fd_pure 0
% 3.83/2.26 % fd_pseudo 0
% 3.83/2.26 % fd_cond 3
% 3.83/2.26 % fd_pseudo_cond 7
% 3.83/2.26 % AC symbols 0
% 3.83/2.26
% 3.83/2.26 % ------ Schedule dynamic 5 is on
% 3.83/2.26
% 3.83/2.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.83/2.26
% 3.83/2.26
% 3.83/2.26 % ------
% 3.83/2.26 % Current options:
% 3.83/2.26 % ------
% 3.83/2.26
% 3.83/2.26
% 3.83/2.26 %
% 3.83/2.26
% 3.83/2.26 % ------ Proving...
% 3.83/2.26 %
% 3.83/2.26
% 3.83/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 3.83/2.26
% 3.83/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.83/2.26
% 3.83/2.26
%------------------------------------------------------------------------------