%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:55:35 PM UTC 2026
% Result : Theorem 10.84s 7.32s
% Output : CNFRefutation 10.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 118 ( 32 unt; 0 def)
% Number of atoms : 287 ( 104 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 292 ( 123 ~; 136 |; 22 &)
% ( 7 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 161 ( 1 sgn 153 !; 8 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f11,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f22,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f29,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f31,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f32,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f49,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f50,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f62,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f64,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f65,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f67,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f72,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f78,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f87,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f38]) ).
fof(f104,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f64]) ).
fof(f105,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f108,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f109,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f108]) ).
fof(f124,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f125,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK4(X0,X1),X0)
& ~ in(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f125]) ).
fof(f136,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f138,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f139,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
( ( subset(sK7,singleton(sK8))
| sK7 = singleton(sK8)
| empty_set = sK7 )
& ( ~ subset(sK7,singleton(sK8))
| ( sK7 != singleton(sK8)
& empty_set != sK7 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f139]) ).
fof(f145,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f152,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f156,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f175,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f176,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f193,plain,
empty(empty_set),
inference(cnf_transformation,[],[f22]) ).
fof(f201,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f204,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f205,plain,
( subset(sK7,singleton(sK8))
| sK7 = singleton(sK8)
| empty_set = sK7 ),
inference(cnf_transformation,[],[f140]) ).
fof(f206,plain,
( ~ subset(sK7,singleton(sK8))
| sK7 != singleton(sK8) ),
inference(cnf_transformation,[],[f140]) ).
fof(f207,plain,
( ~ subset(sK7,singleton(sK8))
| empty_set != sK7 ),
inference(cnf_transformation,[],[f140]) ).
fof(f210,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f72]) ).
fof(f212,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f87]) ).
fof(f224,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f49]) ).
fof(f225,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f226,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f241,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f243,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f244,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f65]) ).
fof(f247,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f264,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f201,f241]) ).
fof(f266,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0) ),
inference(definition_unfolding,[],[f204,f241]) ).
fof(f267,plain,
( ~ subset(sK7,unordered_pair(sK8,sK8))
| empty_set != sK7 ),
inference(definition_unfolding,[],[f207,f241]) ).
fof(f268,plain,
( ~ subset(sK7,unordered_pair(sK8,sK8))
| sK7 != unordered_pair(sK8,sK8) ),
inference(definition_unfolding,[],[f206,f241,f241]) ).
fof(f269,plain,
( subset(sK7,unordered_pair(sK8,sK8))
| sK7 = unordered_pair(sK8,sK8)
| empty_set = sK7 ),
inference(definition_unfolding,[],[f205,f241,f241]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f152]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_93,plain,
empty(empty_set),
inference(cnf_transformation,[],[f193]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_105,negated_conjecture,
( ~ subset(sK7,unordered_pair(sK8,sK8))
| ( empty_set != sK7 ) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_106,negated_conjecture,
( ~ subset(sK7,unordered_pair(sK8,sK8))
| ( unordered_pair(sK8,sK8) != sK7 ) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_107,negated_conjecture,
( subset(sK7,unordered_pair(sK8,sK8))
| ( empty_set = sK7 )
| ( unordered_pair(sK8,sK8) = sK7 ) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_110,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f210]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f224]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f244]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_1518,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1520,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| ~ subset(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1526,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2948,plain,
! [X0: $i,X1: $i] :
( subset(sK7,unordered_pair(sK8,sK8))
| ~ subset(X1,X0)
| ( sK7 != X1 )
| ( unordered_pair(sK8,sK8) != X0 ) ),
inference(instantiation,[status(thm)],[c_1525]) ).
tcf(c_2955,plain,
( ( unordered_pair(sK8,sK8) = sK7 )
| ~ subset(sK7,unordered_pair(sK8,sK8))
| ~ subset(unordered_pair(sK8,sK8),sK7) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_3008,plain,
( subset(unordered_pair(sK8,sK8),sK7)
| ~ in(sK8,sK7) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_3025,plain,
! [X0: $i] :
( empty(sK7)
| ~ empty(X0)
| ( sK7 != X0 ) ),
inference(instantiation,[status(thm)],[c_1526]) ).
tcf(c_3028,plain,
( empty(sK7)
| ~ empty(empty_set)
| ( sK7 != empty_set ) ),
inference(instantiation,[status(thm)],[c_3025]) ).
tcf(c_3052,plain,
! [X0: $i] :
( ( sK7 = X0 )
| ~ subset(sK7,X0)
| ~ subset(X0,sK7) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_3059,plain,
( ( sK7 = empty_set )
| ~ subset(sK7,empty_set)
| ~ subset(empty_set,sK7) ),
inference(instantiation,[status(thm)],[c_3052]) ).
tcf(c_3063,plain,
! [X0: $i] :
( subset(sK7,unordered_pair(sK8,sK8))
| ~ subset(sK7,X0)
| ( sK7 != sK7 )
| ( unordered_pair(sK8,sK8) != X0 ) ),
inference(instantiation,[status(thm)],[c_2948]) ).
tcf(c_3065,plain,
! [X0: $i,X1: $i] :
( ( sK7 = X0 )
| ( sK7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1520]) ).
tcf(c_3192,plain,
! [X0: $i] :
( ( sK7 = X0 )
| ( sK7 != sK7 )
| ( X0 != sK7 ) ),
inference(instantiation,[status(thm)],[c_3065]) ).
tcf(c_3193,plain,
( ( sK7 = empty_set )
| ( sK7 != sK7 )
| ( empty_set != sK7 ) ),
inference(instantiation,[status(thm)],[c_3192]) ).
tcf(c_3258,plain,
! [X0: $i] :
( in(sK8,sK7)
| ~ subset(X0,sK7)
| ~ in(sK8,X0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_3878,plain,
( subset(sK7,unordered_pair(sK8,sK8))
| ~ subset(sK7,sK7)
| ( sK7 != sK7 )
| ( unordered_pair(sK8,sK8) != sK7 ) ),
inference(instantiation,[status(thm)],[c_3063]) ).
tcf(c_4501,plain,
( ( empty_set = sK7 )
| ( unordered_pair(sK8,sK8) = sK7 )
| ( set_difference(sK7,unordered_pair(sK8,sK8)) = empty_set ) ),
inference(superposition,[status(thm)],[c_107,c_125]) ).
tcf(c_4666,plain,
( subset(empty_set,sK7)
| ( empty_set = sK7 )
| ( unordered_pair(sK8,sK8) = sK7 ) ),
inference(superposition,[status(thm)],[c_4501,c_124]) ).
tcf(c_5067,plain,
( ( empty_set = sK7 )
| ( unordered_pair(sK8,sK8) = sK7 )
| ( set_difference(sK7,unordered_pair(sK8,sK8)) = empty_set ) ),
inference(superposition,[status(thm)],[c_107,c_125]) ).
tcf(c_5200,plain,
sK7 = sK7,
inference(instantiation,[status(thm)],[c_1518]) ).
tcf(c_5337,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[c_141,c_76]) ).
tcf(c_5436,plain,
( ~ empty(sK7)
| ( empty_set != sK7 ) ),
inference(resolution,[status(thm)],[c_5337,c_105]) ).
tcf(c_5438,plain,
empty_set != sK7,
inference(global_subsumption_just,[status(thm)],[c_5436,c_93,c_3028,c_3193,c_5200,c_5436]) ).
tcf(c_5746,plain,
( ( set_difference(sK7,unordered_pair(sK8,sK8)) = empty_set )
| ( unordered_pair(sK8,sK8) = sK7 ) ),
inference(global_subsumption_just,[status(thm)],[c_5067,c_4501,c_5438]) ).
tcf(c_5747,plain,
( ( unordered_pair(sK8,sK8) = sK7 )
| ( set_difference(sK7,unordered_pair(sK8,sK8)) = empty_set ) ),
inference(renaming,[status(thm)],[c_5746]) ).
tcf(c_5751,plain,
( subset(sK7,unordered_pair(sK8,sK8))
| ( unordered_pair(sK8,sK8) = sK7 ) ),
inference(superposition,[status(thm)],[c_5747,c_126]) ).
tcf(c_5753,plain,
( subset(empty_set,sK7)
| ( unordered_pair(sK8,sK8) = sK7 ) ),
inference(superposition,[status(thm)],[c_5747,c_124]) ).
tcf(c_5784,plain,
subset(sK7,sK7),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_5848,plain,
subset(empty_set,sK7),
inference(global_subsumption_just,[status(thm)],[c_5753,c_93,c_106,c_107,c_3028,c_3193,c_3878,c_4666,c_5200,c_5436,c_5784]) ).
tcf(c_5871,plain,
subset(sK7,unordered_pair(sK8,sK8)),
inference(global_subsumption_just,[status(thm)],[c_5751,c_107,c_3878,c_5200,c_5438,c_5784]) ).
tcf(c_6475,plain,
( ( empty_set = sK7 )
| ~ empty(sK7)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_13427,negated_conjecture,
subset(sK7,unordered_pair(sK8,sK8)),
inference(global_subsumption_just,[status(thm)],[c_107,c_5871]) ).
tcf(c_13469,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_52,c_142]) ).
tcf(c_13635,plain,
set_difference(sK7,unordered_pair(sK8,sK8)) = empty_set,
inference(superposition,[status(thm)],[c_13427,c_125]) ).
tcf(c_13651,plain,
subset(empty_set,sK7),
inference(superposition,[status(thm)],[c_13635,c_124]) ).
tcf(c_13668,plain,
set_union2(empty_set,sK7) = sK7,
inference(superposition,[status(thm)],[c_13651,c_112]) ).
tcf(c_13888,plain,
subset(sK7,sK7),
inference(superposition,[status(thm)],[c_13668,c_13469]) ).
tcf(c_14459,plain,
! [X0: $i] :
( subset(X0,empty_set)
| in(sK8,X0)
| ~ subset(X0,sK7) ),
inference(superposition,[status(thm)],[c_13635,c_104]) ).
tcf(c_14578,plain,
! [X0: $i] :
( subset(X0,empty_set)
| ~ subset(X0,sK7) ),
inference(global_subsumption_just,[status(thm)],[c_14459,c_93,c_106,c_107,c_2955,c_3008,c_3028,c_3193,c_3258,c_3878,c_5200,c_5436,c_5784,c_14459]) ).
tcf(c_14587,plain,
subset(sK7,empty_set),
inference(superposition,[status(thm)],[c_13888,c_14578]) ).
tcf(c_14591,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14587,c_6475,c_5848,c_5438,c_3059,c_3028,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n015.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Thu Sep 24 13:00:02 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 10.84/7.32 % SZS status Started for theBenchmark.p
% 10.84/7.32 % SZS status Theorem for theBenchmark.p
% 10.84/7.32
% 10.84/7.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.84/7.32
% 10.84/7.32 % ------ iProver source info
% 10.84/7.32
% 10.84/7.32 % git: date: 2026-07-19 20:42:38 +0200
% 10.84/7.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.84/7.32 % git: non_committed_changes: false
% 10.84/7.32
% 10.84/7.32 % ------ Parsing...
% 10.84/7.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.84/7.32
% 10.84/7.32 % ------ Preprocessing... sup_sim: 3 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 %
% 10.84/7.32
% 10.84/7.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.84/7.32
% 10.84/7.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.84/7.32 % ------ Proving...
% 10.84/7.32 % ------ Problem Properties
% 10.84/7.32
% 10.84/7.32 %
% 10.84/7.32 % clauses 89
% 10.84/7.32 % conjectures 3
% 10.84/7.32 % EPR 21
% 10.84/7.32 % Horn 69
% 10.84/7.32 % unary 22
% 10.84/7.32 % binary 36
% 10.84/7.32 % lits 191
% 10.84/7.32 % lits eq 54
% 10.84/7.32 % fd_pure 0
% 10.84/7.32 % fd_pseudo 0
% 10.84/7.32 % fd_cond 3
% 10.84/7.32 % fd_pseudo_cond 19
% 10.84/7.32 % AC symbols 0
% 10.84/7.32
% 10.84/7.32 % ------ Input Options Time Limit: Unbounded
% 10.84/7.32
% 10.84/7.32
% 10.84/7.32 % ------
% 10.84/7.32 % Current options:
% 10.84/7.32 % ------
% 10.84/7.32
% 10.84/7.32
% 10.84/7.32 %
% 10.84/7.32
% 10.84/7.32 % ------ Proving...
% 10.84/7.32 %
% 10.84/7.32
% 10.84/7.32 % SZS status Theorem for theBenchmark.p
% 10.84/7.32
% 10.84/7.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.84/7.32
% 10.84/7.32
%------------------------------------------------------------------------------