%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET919+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 02:49:07 PM UTC 2026
% Result : Theorem 4.41s 1.31s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 110 ( 31 unt; 3 def)
% Number of atoms : 507 ( 161 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 398 ( 149 ~; 183 |; 58 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 182 ( 0 sgn 168 !; 14 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,conjecture,
! [X0,X1,X2] :
( in(X0,X1)
=> ( set_intersection2(unordered_pair(X0,X2),X1) = singleton(X0)
| ( X0 != X2
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,X1)
=> ( set_intersection2(unordered_pair(X0,X2),X1) = singleton(X0)
| ( X0 != X2
& in(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,plain,
? [X0,X1,X2] :
( in(X0,X1)
& singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
& ( X0 = X2
| ~ in(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1,X2] :
( in(X0,X1)
& singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
& ( X0 = X2
| ~ in(X2,X1) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| sK1(X0,X1,X2) = X1
| sK1(X0,X1,X2) = X0 )
& ( ~ in(sK1(X0,X1,X2),X2)
| ( sK1(X0,X1,X2) != X1
& sK1(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| ( in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f25]) ).
fof(f29,plain,
( in(sK5,sK6)
& singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6)
& ( sK5 = sK7
| ~ in(sK7,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f15]) ).
fof(f32,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
in(sK5,sK6),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
( sK5 = sK7
| ~ in(sK7,sK6) ),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f34]) ).
fof(f56,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f55]) ).
fof(f57,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f33]) ).
fof(f58,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f39]) ).
fof(f59,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f58]) ).
fof(f62,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f37]) ).
fof(f63,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f45]) ).
fof(f64,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f44]) ).
fof(f65,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f43]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_54,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f56]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f59]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_71,negated_conjecture,
( ( sK7 = sK5 )
| ~ in(sK7,sK6) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_72,negated_conjecture,
set_intersection2(unordered_pair(sK5,sK7),sK6) != singleton(sK5),
inference(cnf_transformation,[],[f53]) ).
tcf(c_73,negated_conjecture,
in(sK5,sK6),
inference(cnf_transformation,[],[f52]) ).
tcf(c_209,plain,
set_intersection2(sK6,unordered_pair(sK5,sK7)) != singleton(sK5),
inference(demodulation,[status(thm)],[c_72,c_51]) ).
tcf(c_478,definition,
iPr_def_10 = unordered_pair(sK5,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_479,definition,
iPr_def_11 = set_intersection2(sK6,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_480,definition,
iPr_def_12 = singleton(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_481,plain,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_209,c_480,c_478,c_479]) ).
tcf(c_482,negated_conjecture,
in(sK5,sK6),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_483,negated_conjecture,
( ( sK7 = sK5 )
| ~ in(sK7,sK6) ),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_778,plain,
in(sK5,iPr_def_12),
inference(superposition,[status(thm)],[c_480,c_54]) ).
tcf(c_780,plain,
in(sK5,iPr_def_10),
inference(superposition,[status(thm)],[c_478,c_59]) ).
tcf(c_781,plain,
set_intersection2(iPr_def_10,sK6) = iPr_def_11,
inference(demodulation,[status(thm)],[c_479,c_51]) ).
tcf(c_811,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_480,c_55]) ).
tcf(c_826,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_781,c_66]) ).
tcf(c_836,plain,
! [X0: $i] :
( in(X0,sK6)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_781,c_67]) ).
tcf(c_848,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK6) ),
inference(superposition,[status(thm)],[c_781,c_65]) ).
tcf(c_881,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ( X0 = sK7 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_478,c_61]) ).
tcf(c_900,plain,
( in(sK5,iPr_def_11)
| ~ in(sK5,sK6) ),
inference(superposition,[status(thm)],[c_780,c_848]) ).
tcf(c_901,plain,
in(sK5,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_900,c_482]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X0),X0)
| ( set_intersection2(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_63]) ).
tcf(c_1395,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_12,X0) = iPr_def_12 )
| ( sK2(iPr_def_12,X0,iPr_def_12) = sK5 ) ),
inference(superposition,[status(thm)],[c_1112,c_811]) ).
tcf(c_1397,plain,
! [X0: $i] :
( in(sK2(iPr_def_11,X0,iPr_def_11),iPr_def_10)
| ( set_intersection2(iPr_def_11,X0) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1112,c_826]) ).
tcf(c_1547,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_11,X0) = iPr_def_11 )
| ( sK2(iPr_def_11,X0,iPr_def_11) = sK5 )
| ( sK2(iPr_def_11,X0,iPr_def_11) = sK7 ) ),
inference(superposition,[status(thm)],[c_1397,c_881]) ).
tcf(c_1862,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_12,X0) = iPr_def_12 )
| ~ in(sK5,X0)
| ~ in(sK2(iPr_def_12,X0,iPr_def_12),iPr_def_12) ),
inference(superposition,[status(thm)],[c_1395,c_62]) ).
tcf(c_2584,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_12,X0) = iPr_def_12 )
| ~ in(sK5,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1862,c_1112]) ).
tcf(c_2595,plain,
set_intersection2(iPr_def_12,sK6) = iPr_def_12,
inference(superposition,[status(thm)],[c_482,c_2584]) ).
tcf(c_2598,plain,
set_intersection2(iPr_def_12,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_901,c_2584]) ).
tcf(c_2630,plain,
! [X0: $i] :
( in(X0,sK6)
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2595,c_67]) ).
tcf(c_2727,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_12,X1),sK6)
| in(sK2(X0,iPr_def_12,X1),X1)
| ( set_intersection2(X0,iPr_def_12) = X1 ) ),
inference(superposition,[status(thm)],[c_64,c_2630]) ).
tcf(c_2728,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_12,X0,X1),sK6)
| in(sK2(iPr_def_12,X0,X1),X1)
| ( set_intersection2(iPr_def_12,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_63,c_2630]) ).
tcf(c_3081,plain,
set_intersection2(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2598,c_51]) ).
tcf(c_3096,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3081,c_66]) ).
tcf(c_3333,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_12,iPr_def_11),sK6)
| ( set_intersection2(X0,iPr_def_12) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_2727,c_836]) ).
tcf(c_3414,plain,
! [X0: $i] :
( in(sK2(iPr_def_12,X0,iPr_def_11),sK6)
| ( set_intersection2(iPr_def_12,X0) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_2728,c_836]) ).
tcf(c_3939,plain,
( ( set_intersection2(iPr_def_12,sK6) = iPr_def_11 )
| ~ in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_12)
| ~ in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3414,c_62]) ).
tcf(c_3942,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_12)
| ~ in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3939,c_2595]) ).
tcf(c_3943,plain,
( ~ in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_12)
| ~ in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3942,c_481]) ).
tcf(c_4214,plain,
~ in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_3943,c_3096]) ).
tcf(c_4215,plain,
( in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_11)
| ( set_intersection2(iPr_def_12,sK6) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_63,c_4214]) ).
tcf(c_4216,plain,
( in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_11)
| ( iPr_def_11 = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_4215,c_2595]) ).
tcf(c_4217,plain,
in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_4216,c_481]) ).
tcf(c_4220,plain,
in(sK2(iPr_def_12,sK6,iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_4217,c_826]) ).
tcf(c_4715,plain,
( in(sK7,sK6)
| ( set_intersection2(iPr_def_11,iPr_def_12) = iPr_def_11 )
| ( sK2(iPr_def_11,iPr_def_12,iPr_def_11) = sK5 ) ),
inference(superposition,[status(thm)],[c_1547,c_3333]) ).
tcf(c_4716,plain,
( in(sK7,sK6)
| ( iPr_def_11 = iPr_def_12 )
| ( sK2(iPr_def_11,iPr_def_12,iPr_def_11) = sK5 ) ),
inference(light_normalisation,[status(thm)],[c_4715,c_3081]) ).
tcf(c_4717,plain,
( in(sK7,sK6)
| ( sK2(iPr_def_11,iPr_def_12,iPr_def_11) = sK5 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4716,c_481]) ).
tcf(c_4809,plain,
( ( sK7 = sK5 )
| ( sK2(iPr_def_11,iPr_def_12,iPr_def_11) = sK5 ) ),
inference(superposition,[status(thm)],[c_4717,c_483]) ).
tcf(c_4842,plain,
( ( sK7 = sK5 )
| ( set_intersection2(iPr_def_11,iPr_def_12) = iPr_def_11 )
| ~ in(sK5,iPr_def_12)
| ~ in(sK2(iPr_def_11,iPr_def_12,iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4809,c_62]) ).
tcf(c_4862,plain,
( ( iPr_def_11 = iPr_def_12 )
| ( sK7 = sK5 )
| ~ in(sK5,iPr_def_12)
| ~ in(sK2(iPr_def_11,iPr_def_12,iPr_def_11),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_4842,c_3081]) ).
tcf(c_4863,plain,
( ( sK7 = sK5 )
| ~ in(sK2(iPr_def_11,iPr_def_12,iPr_def_11),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4862,c_481,c_778]) ).
tcf(c_4876,plain,
( ( sK7 = sK5 )
| ~ in(sK5,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4809,c_4863]) ).
tcf(c_4877,plain,
sK7 = sK5,
inference(forward_subsumption_resolution,[status(thm)],[c_4876,c_901]) ).
tcf(c_4887,plain,
! [X0: $i] :
( ( X0 = sK5 )
| ~ in(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_881,c_4877]) ).
tcf(c_4958,plain,
sK2(iPr_def_12,sK6,iPr_def_11) = sK5,
inference(superposition,[status(thm)],[c_4220,c_4887]) ).
tcf(c_4999,plain,
~ in(sK5,iPr_def_12),
inference(demodulation,[status(thm)],[c_4214,c_4958]) ).
tcf(c_5000,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4999,c_778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET919+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 12:24:20 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 4.41/1.31 % SZS status Started for theBenchmark.p
% 4.41/1.31 % SZS status Theorem for theBenchmark.p
% 4.41/1.31
% 4.41/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.41/1.31
% 4.41/1.31 % ------ iProver source info
% 4.41/1.31
% 4.41/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.41/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.41/1.31 % git: non_committed_changes: false
% 4.41/1.31
% 4.41/1.31 % ------ Parsing...
% 4.41/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.41/1.31
% 4.41/1.31 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.41/1.31
% 4.41/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.41/1.31
% 4.41/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.41/1.31 % ------ Proving...
% 4.41/1.31 % ------ Problem Properties
% 4.41/1.31
% 4.41/1.31 %
% 4.41/1.31 % clauses 27
% 4.41/1.31 % conjectures 2
% 4.41/1.31 % EPR 5
% 4.41/1.31 % Horn 22
% 4.41/1.31 % unary 12
% 4.41/1.31 % binary 5
% 4.41/1.31 % lits 54
% 4.41/1.31 % lits eq 26
% 4.41/1.31 % fd_pure 0
% 4.41/1.31 % fd_pseudo 0
% 4.41/1.31 % fd_cond 0
% 4.41/1.31 % fd_pseudo_cond 8
% 4.41/1.31 % AC symbols 0
% 4.41/1.31
% 4.41/1.31 % ------ Schedule dynamic 5 is on
% 4.41/1.31
% 4.41/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.41/1.31
% 4.41/1.31
% 4.41/1.31 % ------
% 4.41/1.31 % Current options:
% 4.41/1.31 % ------
% 4.41/1.31
% 4.41/1.31
% 4.41/1.31 %
% 4.41/1.31
% 4.41/1.31 % ------ Proving...
% 4.41/1.31 %
% 4.41/1.31
% 4.41/1.31 % SZS status Theorem for theBenchmark.p
% 4.41/1.31
% 4.41/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.41/1.31
% 4.41/1.31
%------------------------------------------------------------------------------