%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET944+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 02:49:10 PM UTC 2026
% Result : Theorem 7.20s 2.27s
% Output : CNFRefutation 7.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 18 unt; 5 def)
% Number of atoms : 393 ( 41 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 340 ( 136 ~; 154 |; 43 &)
% ( 6 <=>; 1 =>; 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 : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 194 ( 0 sgn 180 !; 14 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f10,conjecture,
! [X0,X1] : subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] : subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f16,plain,
? [X0,X1] : ~ subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
inference(ennf_transformation,[],[f11]) ).
fof(f17,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,[],[f15]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
fof(f20,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,[],[f4]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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,[],[f21]) ).
fof(f23,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(sK1(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK4(X0,X5),X0)
& in(X5,sK4(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| ( in(sK3(X0,X1),X0)
& in(sK2(X0,X1),sK3(X0,X1)) ) )
& ( ~ in(sK2(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK2(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f25]) ).
fof(f29,plain,
~ subset(union(set_intersection2(sK7,sK8)),set_intersection2(union(sK7),union(sK8))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f16]) ).
fof(f31,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK4(X0,X5),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK4(X0,X5)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f51,plain,
~ subset(union(set_intersection2(sK7,sK8)),set_intersection2(union(sK7),union(sK8))),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f37]) ).
fof(f53,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f36]) ).
fof(f54,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f35]) ).
fof(f55,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f43]) ).
fof(f56,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK4(X0,X5)) ),
inference(equality_resolution,[],[f42]) ).
fof(f57,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK4(X0,X5),X0) ),
inference(equality_resolution,[],[f41]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( in(X0,sK4(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(sK4(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_70,negated_conjecture,
~ subset(union(set_intersection2(sK7,sK8)),set_intersection2(union(sK7),union(sK8))),
inference(cnf_transformation,[],[f51]) ).
tcf(c_558,definition,
iPr_def_10 = set_intersection2(sK7,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_559,definition,
iPr_def_11 = union(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_560,definition,
iPr_def_12 = union(sK7),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_561,definition,
iPr_def_13 = union(sK8),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_562,definition,
iPr_def_14 = set_intersection2(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_563,negated_conjecture,
~ subset(iPr_def_11,iPr_def_14),
inference(demodulation,[status(thm)],[c_70,c_561,c_560,c_562,c_558,c_559]) ).
tcf(c_878,plain,
! [X0: $i] :
( in(X0,sK7)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_558,c_58]) ).
tcf(c_930,plain,
! [X0: $i] :
( in(X0,sK8)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_558,c_59]) ).
tcf(c_931,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_562,c_59]) ).
tcf(c_990,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ in(X1,union(X0))
| ~ subset(sK4(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_64,c_53]) ).
tcf(c_1007,plain,
! [X0: $i] :
( in(sK4(iPr_def_10,X0),sK8)
| ~ in(X0,union(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_65,c_930]) ).
tcf(c_1008,plain,
! [X0: $i] :
( in(sK4(iPr_def_10,X0),sK7)
| ~ in(X0,union(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_65,c_878]) ).
tcf(c_1015,plain,
! [X0: $i] :
( in(sK4(iPr_def_10,X0),sK7)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1008,c_559]) ).
tcf(c_1018,plain,
! [X0: $i] :
( in(sK4(iPr_def_10,X0),sK8)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1007,c_559]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK0(X0,X2),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_52,c_63]) ).
tcf(c_1092,plain,
! [X0: $i] :
( in(X0,iPr_def_14)
| ~ in(X0,iPr_def_13)
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_562,c_57]) ).
tcf(c_1457,plain,
! [X0: $i,X1: $i] :
( in(sK1(X0,X1,X0),X0)
| ( set_intersection2(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_55]) ).
tcf(c_2815,plain,
! [X0: $i] :
( in(sK1(iPr_def_14,X0,iPr_def_14),iPr_def_13)
| ( set_intersection2(iPr_def_14,X0) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1457,c_931]) ).
tcf(c_3496,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_1044,c_51]) ).
tcf(c_3641,plain,
! [X0: $i] :
( subset(X0,iPr_def_12)
| ~ in(X0,sK7) ),
inference(superposition,[status(thm)],[c_560,c_3496]) ).
tcf(c_3642,plain,
! [X0: $i] :
( subset(X0,iPr_def_13)
| ~ in(X0,sK8) ),
inference(superposition,[status(thm)],[c_561,c_3496]) ).
tcf(c_3694,plain,
! [X0: $i] :
( subset(sK4(iPr_def_10,X0),iPr_def_12)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1015,c_3641]) ).
tcf(c_3794,plain,
! [X0: $i] :
( subset(sK4(iPr_def_10,X0),iPr_def_13)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1018,c_3642]) ).
tcf(c_5271,plain,
( ( set_intersection2(iPr_def_14,iPr_def_13) = iPr_def_14 )
| ~ in(sK1(iPr_def_14,iPr_def_13,iPr_def_14),iPr_def_14) ),
inference(superposition,[status(thm)],[c_2815,c_54]) ).
tcf(c_7938,plain,
( ( set_intersection2(iPr_def_13,iPr_def_14) = iPr_def_14 )
| ~ in(sK1(iPr_def_14,iPr_def_13,iPr_def_14),iPr_def_14) ),
inference(demodulation,[status(thm)],[c_5271,c_50]) ).
tcf(c_7948,plain,
( ( set_intersection2(iPr_def_14,iPr_def_13) = iPr_def_14 )
| ( set_intersection2(iPr_def_13,iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1457,c_7938]) ).
tcf(c_7960,plain,
set_intersection2(iPr_def_13,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_7948,c_50]) ).
tcf(c_8250,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,iPr_def_11)
| ~ in(X0,union(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3694,c_990]) ).
tcf(c_8252,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,iPr_def_11)
| ~ in(X0,union(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3794,c_990]) ).
tcf(c_8254,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_8252,c_559]) ).
tcf(c_8257,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_8250,c_559]) ).
tcf(c_8514,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| in(sK0(iPr_def_11,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_52,c_8254]) ).
tcf(c_8615,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| in(sK0(iPr_def_11,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_52,c_8257]) ).
tcf(c_8809,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_11,X1)
| in(sK0(iPr_def_11,X1),X0)
| ~ subset(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_8514,c_53]) ).
tcf(c_8831,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| in(sK0(iPr_def_11,X0),iPr_def_14)
| ~ in(sK0(iPr_def_11,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_8615,c_1092]) ).
tcf(c_10126,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(iPr_def_11,X2)
| in(sK0(iPr_def_11,X2),X1)
| ~ subset(iPr_def_13,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_8809,c_59]) ).
tcf(c_23430,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| in(sK0(iPr_def_11,X0),iPr_def_14)
| ~ subset(iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_7960,c_10126]) ).
tcf(c_23465,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| in(sK0(iPr_def_11,X0),iPr_def_14) ),
inference(global_subsumption_just,[status(thm)],[c_23430,c_8514,c_8831]) ).
tcf(c_23475,plain,
subset(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_23465,c_51]) ).
tcf(c_23478,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23475,c_563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET944+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:26:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 7.20/2.27 % SZS status Started for theBenchmark.p
% 7.20/2.27 % SZS status Theorem for theBenchmark.p
% 7.20/2.27
% 7.20/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.20/2.27
% 7.20/2.27 % ------ iProver source info
% 7.20/2.27
% 7.20/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 7.20/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.20/2.27 % git: non_committed_changes: false
% 7.20/2.27
% 7.20/2.27 % ------ Parsing...
% 7.20/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.20/2.27
% 7.20/2.27 % ------ Preprocessing... sup_sim: 0 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 %
% 7.20/2.27
% 7.20/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.20/2.27
% 7.20/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.20/2.27 % ------ Proving...
% 7.20/2.27 % ------ Problem Properties
% 7.20/2.27
% 7.20/2.27 %
% 7.20/2.27 % clauses 26
% 7.20/2.27 % conjectures 1
% 7.20/2.27 % EPR 5
% 7.20/2.27 % Horn 21
% 7.20/2.27 % unary 10
% 7.20/2.27 % binary 7
% 7.20/2.27 % lits 53
% 7.20/2.27 % lits eq 14
% 7.20/2.27 % fd_pure 0
% 7.20/2.27 % fd_pseudo 0
% 7.20/2.27 % fd_cond 0
% 7.20/2.27 % fd_pseudo_cond 6
% 7.20/2.27 % AC symbols 0
% 7.20/2.27
% 7.20/2.27 % ------ Schedule dynamic 5 is on
% 7.20/2.27
% 7.20/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.20/2.27
% 7.20/2.27
% 7.20/2.27 % ------
% 7.20/2.27 % Current options:
% 7.20/2.27 % ------
% 7.20/2.27
% 7.20/2.27
% 7.20/2.27 %
% 7.20/2.27
% 7.20/2.27 % ------ Proving...
% 7.20/2.27 %
% 7.20/2.27
% 7.20/2.27 % SZS status Theorem for theBenchmark.p
% 7.20/2.27
% 7.20/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.20/2.28
% 7.20/2.28
%------------------------------------------------------------------------------