%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU171+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 : n014.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 02:55:44 PM UTC 2026
% Result : Theorem 10.32s 2.28s
% Output : CNFRefutation 10.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of formulae : 128 ( 49 unt; 2 def)
% Number of atoms : 325 ( 53 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 311 ( 135 ~; 112 |; 37 &)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 182 ( 0 sgn 174 !; 8 ?; 48 :)
% 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(f9,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f35,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f36,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f39,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f60,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f65,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f82,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f89,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f91,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f95,conjecture,
! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f96,negated_conjecture,
~ ! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f99,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f100,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f103,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f104,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f105,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f106,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f126,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f133,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f143,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f148,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f65]) ).
fof(f162,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,powerset(X0))
| ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
inference(ennf_transformation,[],[f89]) ).
fof(f164,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f91]) ).
fof(f166,plain,
? [X0] :
( X0 != empty_set
& ? [X1] :
( element(X1,powerset(X0))
& ? [X2] :
( element(X2,X0)
& ~ in(X2,X1)
& ~ in(X2,subset_complement(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f167,plain,
? [X0] :
( X0 != empty_set
& ? [X1] :
( element(X1,powerset(X0))
& ? [X2] :
( element(X2,X0)
& ~ in(X2,X1)
& ~ in(X2,subset_complement(X0,X1)) ) ) ),
inference(flattening,[],[f166]) ).
fof(f173,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f103]) ).
fof(f174,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f106]) ).
fof(f190,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f191,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f190]) ).
fof(f192,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| subset(sK2(X0,X1),X0) )
& ( ~ in(sK2(X0,X1),X1)
| ~ subset(sK2(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f191]) ).
fof(f193,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( ( ~ element(X1,X0)
| empty(X1) )
& ( ~ empty(X1)
| element(X1,X0) ) ) )
& ( empty(X0)
| ( ( ~ element(X1,X0)
| in(X1,X0) )
& ( ~ in(X1,X0)
| element(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f238,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f238]) ).
fof(f243,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,powerset(X0))
| ( ( ~ disjoint(X1,X2)
| subset(X1,subset_complement(X0,X2)) )
& ( ~ subset(X1,subset_complement(X0,X2))
| disjoint(X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f162]) ).
fof(f245,plain,
( empty_set != sK25
& element(sK26,powerset(sK25))
& element(sK27,sK25)
& ~ in(sK27,sK26)
& ~ in(sK27,subset_complement(sK25,sK26)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X0,sK25),skolemize(X1,sK26),skolemize(X2,sK27)],[f167]) ).
fof(f246,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) != X0
| ~ in(X1,X0) )
& ( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f247,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f252,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f263,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f264,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f269,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f270,plain,
! [X0,X1] :
( empty(X0)
| ~ in(X1,X0)
| element(X1,X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f319,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f320,plain,
empty(empty_set),
inference(cnf_transformation,[],[f36]) ).
fof(f323,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f352,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f360,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f148]) ).
fof(f383,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f239]) ).
fof(f396,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ disjoint(X1,X2)
| subset(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f243]) ).
fof(f399,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f164]) ).
fof(f404,plain,
empty_set != sK25,
inference(cnf_transformation,[],[f245]) ).
fof(f405,plain,
element(sK26,powerset(sK25)),
inference(cnf_transformation,[],[f245]) ).
fof(f406,plain,
element(sK27,sK25),
inference(cnf_transformation,[],[f245]) ).
fof(f407,plain,
~ in(sK27,sK26),
inference(cnf_transformation,[],[f245]) ).
fof(f408,plain,
~ in(sK27,subset_complement(sK25,sK26)),
inference(cnf_transformation,[],[f245]) ).
fof(f412,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f246]) ).
fof(f413,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f100]) ).
fof(f416,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
fof(f417,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f104]) ).
fof(f419,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f420,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f479,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(definition_unfolding,[],[f399,f413]) ).
fof(f482,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) = X0 ),
inference(definition_unfolding,[],[f412,f413]) ).
fof(f493,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f264]) ).
fof(f494,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f263]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f252]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f493]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f494]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_118,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f319]) ).
tcf(c_119,plain,
empty(empty_set),
inference(cnf_transformation,[],[f320]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f360]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f383]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,subset_complement(X1,X2))
| ~ disjoint(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f479]) ).
tcf(c_202,negated_conjecture,
~ in(sK27,subset_complement(sK25,sK26)),
inference(cnf_transformation,[],[f408]) ).
tcf(c_203,negated_conjecture,
~ in(sK27,sK26),
inference(cnf_transformation,[],[f407]) ).
tcf(c_204,negated_conjecture,
element(sK27,sK25),
inference(cnf_transformation,[],[f406]) ).
tcf(c_205,negated_conjecture,
element(sK26,powerset(sK25)),
inference(cnf_transformation,[],[f405]) ).
tcf(c_206,negated_conjecture,
empty_set != sK25,
inference(cnf_transformation,[],[f404]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) = X0 ) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f417]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f420]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_213,c_67]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_309]) ).
tcf(c_2123,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_310]) ).
tcf(c_3847,definition,
iPr_def_10 = powerset(sK25),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3848,definition,
iPr_def_11 = subset_complement(sK25,sK26),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3850,negated_conjecture,
element(sK26,iPr_def_10),
inference(demodulation,[status(thm)],[c_205,c_3847]) ).
tcf(c_3851,negated_conjecture,
element(sK27,sK25),
inference(demodulation,[status(thm)],[c_204]) ).
tcf(c_3852,negated_conjecture,
~ in(sK27,sK26),
inference(demodulation,[status(thm)],[c_203]) ).
tcf(c_3853,negated_conjecture,
~ in(sK27,iPr_def_11),
inference(demodulation,[status(thm)],[c_202,c_3848]) ).
tcf(c_6361,plain,
~ empty(iPr_def_10),
inference(superposition,[status(thm)],[c_3847,c_118]) ).
tcf(c_6496,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_52,c_214]) ).
tcf(c_6532,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ subset(X0,sK25) ),
inference(superposition,[status(thm)],[c_3847,c_65]) ).
tcf(c_6602,plain,
! [X0: $i] :
( subset(X0,sK25)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3847,c_66]) ).
tcf(c_6900,plain,
( empty(sK25)
| in(sK27,sK25) ),
inference(superposition,[status(thm)],[c_3851,c_68]) ).
tcf(c_6901,plain,
( empty(iPr_def_10)
| in(sK26,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3850,c_68]) ).
tcf(c_6912,plain,
in(sK26,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6901,c_6361]) ).
tcf(c_6990,plain,
subset(sK26,sK25),
inference(superposition,[status(thm)],[c_6912,c_6602]) ).
tcf(c_7339,plain,
( ( empty_set = sK25 )
| ~ empty(sK25)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_7988,plain,
set_union2(sK26,sK25) = sK25,
inference(superposition,[status(thm)],[c_6990,c_159]) ).
tcf(c_8084,plain,
set_union2(sK25,sK26) = sK25,
inference(demodulation,[status(thm)],[c_7988,c_52]) ).
tcf(c_8091,plain,
( empty(sK26)
| ~ empty(sK25) ),
inference(superposition,[status(thm)],[c_8084,c_122]) ).
tcf(c_8102,plain,
~ empty(sK25),
inference(global_subsumption_just,[status(thm)],[c_8091,c_119,c_206,c_7339]) ).
tcf(c_8107,plain,
in(sK27,sK25),
inference(backward_subsumption_resolution,[status(thm)],[c_6900,c_8102]) ).
tcf(c_9558,plain,
set_difference(sK26,unordered_pair(sK27,sK27)) = sK26,
inference(superposition,[status(thm)],[c_209,c_3852]) ).
tcf(c_9816,plain,
disjoint(sK26,unordered_pair(sK27,sK27)),
inference(superposition,[status(thm)],[c_9558,c_215]) ).
tcf(c_9914,plain,
disjoint(unordered_pair(sK27,sK27),sK26),
inference(superposition,[status(thm)],[c_9816,c_151]) ).
tcf(c_12638,plain,
set_union2(unordered_pair(sK27,sK27),sK25) = sK25,
inference(superposition,[status(thm)],[c_8107,c_198]) ).
tcf(c_13325,plain,
set_union2(sK25,unordered_pair(sK27,sK27)) = sK25,
inference(demodulation,[status(thm)],[c_12638,c_52]) ).
tcf(c_13327,plain,
subset(unordered_pair(sK27,sK27),sK25),
inference(superposition,[status(thm)],[c_13325,c_6496]) ).
tcf(c_13870,plain,
in(unordered_pair(sK27,sK27),iPr_def_10),
inference(superposition,[status(thm)],[c_13327,c_6532]) ).
tcf(c_13950,plain,
element(unordered_pair(sK27,sK27),iPr_def_10),
inference(superposition,[status(thm)],[c_13870,c_2123]) ).
tcf(c_22417,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ disjoint(X0,sK26)
| ~ element(sK26,powerset(sK25))
| ~ element(X0,powerset(sK25)) ),
inference(superposition,[status(thm)],[c_3848,c_196]) ).
tcf(c_22446,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ element(sK26,iPr_def_10)
| ~ disjoint(X0,sK26)
| ~ element(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_22417,c_3847]) ).
tcf(c_22447,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ disjoint(X0,sK26)
| ~ element(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22446,c_3850]) ).
tcf(c_22784,plain,
( subset(unordered_pair(sK27,sK27),iPr_def_11)
| ~ disjoint(unordered_pair(sK27,sK27),sK26) ),
inference(superposition,[status(thm)],[c_13950,c_22447]) ).
tcf(c_22796,plain,
subset(unordered_pair(sK27,sK27),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_22784,c_9914]) ).
tcf(c_23790,plain,
in(sK27,iPr_def_11),
inference(superposition,[status(thm)],[c_22796,c_184]) ).
tcf(c_23797,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23790,c_3853]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU171+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.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 13:02:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 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
% 0.10/0.44 % Proving...
% 10.32/2.28 % SZS status Started for theBenchmark.p
% 10.32/2.28 % SZS status Theorem for theBenchmark.p
% 10.32/2.28
% 10.32/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.32/2.28
% 10.32/2.28 % ------ iProver source info
% 10.32/2.28
% 10.32/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 10.32/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.32/2.28 % git: non_committed_changes: false
% 10.32/2.28
% 10.32/2.28 % ------ Parsing...
% 10.32/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.32/2.28
% 10.32/2.28 % ------ Preprocessing... sup_sim: 5 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 %
% 10.32/2.28
% 10.32/2.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.32/2.28
% 10.32/2.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.32/2.28 % ------ Proving...
% 10.32/2.28 % ------ Problem Properties
% 10.32/2.28
% 10.32/2.28 %
% 10.32/2.28 % clauses 157
% 10.32/2.28 % conjectures 5
% 10.32/2.28 % EPR 30
% 10.32/2.28 % Horn 126
% 10.32/2.28 % unary 38
% 10.32/2.28 % binary 65
% 10.32/2.28 % lits 339
% 10.32/2.28 % lits eq 86
% 10.32/2.28 % fd_pure 0
% 10.32/2.28 % fd_pseudo 0
% 10.32/2.28 % fd_cond 3
% 10.32/2.28 % fd_pseudo_cond 35
% 10.32/2.28 % AC symbols 0
% 10.32/2.28
% 10.32/2.28 % ------ Schedule dynamic 5 is on
% 10.32/2.28
% 10.32/2.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.32/2.28
% 10.32/2.28
% 10.32/2.28 % ------
% 10.32/2.28 % Current options:
% 10.32/2.28 % ------
% 10.32/2.28
% 10.32/2.28
% 10.32/2.28 %
% 10.32/2.28
% 10.32/2.28 % ------ Proving...
% 10.32/2.28 %
% 10.32/2.28
% 10.32/2.28 % SZS status Theorem for theBenchmark.p
% 10.32/2.28
% 10.32/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.32/2.28
% 10.32/2.28
%------------------------------------------------------------------------------