%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET973+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 : n017.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 02:49:14 PM UTC 2026
% Result : Theorem 148.14s 32.54s
% Output : CNFRefutation 148.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 119 ( 66 unt; 0 def)
% Number of atoms : 337 ( 83 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 315 ( 126 ~; 128 |; 53 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 302 ( 1 sgn 290 !; 12 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f15,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f21,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f22,axiom,
! [X0,X1,X2] :
( cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
fof(f23,conjecture,
! [X0,X1,X2,X3] : set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = set_union2(cartesian_product2(set_difference(X0,X2),X1),cartesian_product2(X0,set_difference(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
fof(f24,negated_conjecture,
~ ! [X0,X1,X2,X3] : set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = set_union2(cartesian_product2(set_difference(X0,X2),X1),cartesian_product2(X0,set_difference(X1,X3))),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f27,axiom,
! [X0,X1,X2] : set_difference(X0,set_intersection2(X1,X2)) = set_union2(set_difference(X0,X1),set_difference(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
fof(f29,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f15]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f37,plain,
? [X0,X1,X2,X3] : set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) != set_union2(cartesian_product2(set_difference(X0,X2),X1),cartesian_product2(X0,set_difference(X1,X3))),
inference(ennf_transformation,[],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f40,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ( ~ in(sK0(X0,X1,X2),X1)
& ~ in(sK0(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f43]) ).
fof(f48,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,[],[f32]) ).
fof(f49,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,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK6(X0,X1),X0)
& ~ in(sK6(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK7(X0,X1,X2),X2)
| ( ~ in(sK7(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X0) ) )
& ( ~ in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f53]) ).
fof(f59,plain,
set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)) != set_union2(cartesian_product2(set_difference(sK10,sK12),sK11),cartesian_product2(sK10,set_difference(sK11,sK13))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f37]) ).
fof(f62,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f63,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f81,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f82,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f83,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f84,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f95,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f29]) ).
fof(f103,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f21]) ).
fof(f104,plain,
! [X2,X0,X1] : cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[],[f22]) ).
fof(f105,plain,
! [X2,X0,X1] : cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
fof(f106,plain,
set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)) != set_union2(cartesian_product2(set_difference(sK10,sK12),sK11),cartesian_product2(sK10,set_difference(sK11,sK13))),
inference(cnf_transformation,[],[f59]) ).
fof(f107,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f109,plain,
! [X2,X0,X1] : set_difference(X0,set_intersection2(X1,X2)) = set_union2(set_difference(X0,X1),set_difference(X0,X2)),
inference(cnf_transformation,[],[f27]) ).
fof(f120,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f69]) ).
fof(f128,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f86]) ).
fof(f129,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f85]) ).
fof(f130,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f84]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f62]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f63]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_83,plain,
! [X0: $i] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f95]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
inference(cnf_transformation,[],[f103]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) = cartesian_product2(set_difference(X0,X2),X1),
inference(cnf_transformation,[],[f105]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) = cartesian_product2(X0,set_difference(X1,X2)),
inference(cnf_transformation,[],[f104]) ).
tcf(c_94,negated_conjecture,
set_union2(cartesian_product2(set_difference(sK10,sK12),sK11),cartesian_product2(sK10,set_difference(sK11,sK13))) != set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)),
inference(cnf_transformation,[],[f106]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f107]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(set_difference(X0,X1),set_difference(X0,X2)) = set_difference(X0,set_intersection2(X1,X2)),
inference(cnf_transformation,[],[f109]) ).
tcf(c_323,plain,
set_union2(cartesian_product2(sK10,set_difference(sK11,sK13)),cartesian_product2(set_difference(sK10,sK12),sK11)) != set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)),
inference(demodulation,[status(thm)],[c_94,c_51]) ).
tcf(c_1100,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_52,c_95]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK6(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_59,c_70]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| in(sK6(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_71,c_77]) ).
tcf(c_1155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X2,X0),set_intersection2(X3,X1)),
inference(superposition,[status(thm)],[c_91,c_52]) ).
tcf(c_1159,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| ~ in(sK6(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_71,c_78]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK6(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_71,c_72]) ).
tcf(c_1171,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_95,c_53]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_1100,c_53]) ).
tcf(c_1281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = cartesian_product2(set_intersection2(X1,X0),set_intersection2(X3,X2)),
inference(superposition,[status(thm)],[c_1155,c_91]) ).
tcf(c_1405,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_1141,c_70]) ).
tcf(c_1409,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ subset(X0,set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_1405,c_53]) ).
tcf(c_1532,plain,
! [X0: $i,X1: $i,X2: $i] : cartesian_product2(X0,set_intersection2(X1,X2)) = cartesian_product2(X0,set_intersection2(X2,X1)),
inference(superposition,[status(thm)],[c_83,c_1281]) ).
tcf(c_1939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_union2(cartesian_product2(X0,set_difference(X1,X2)),set_difference(cartesian_product2(X0,X1),X3)) = set_difference(cartesian_product2(X0,X1),set_intersection2(cartesian_product2(X0,X2),X3)),
inference(superposition,[status(thm)],[c_93,c_97]) ).
tcf(c_2926,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_71,c_1137]) ).
tcf(c_2936,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_51,c_2926]) ).
tcf(c_2939,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(X0,X1),set_difference(X0,set_intersection2(X1,X2))),
inference(superposition,[status(thm)],[c_97,c_2926]) ).
tcf(c_2951,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(X0,X1),set_difference(X0,set_intersection2(X2,X1))),
inference(superposition,[status(thm)],[c_97,c_2936]) ).
tcf(c_6374,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X0),X1),
inference(superposition,[status(thm)],[c_1141,c_1159]) ).
tcf(c_6375,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| ~ subset(set_difference(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_1165,c_1159]) ).
tcf(c_6400,plain,
! [X0: $i,X1: $i] : set_intersection2(set_difference(X0,X0),X1) = set_difference(X0,X0),
inference(superposition,[status(thm)],[c_6374,c_1171]) ).
tcf(c_6402,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,set_difference(X1,X1)) = set_difference(X1,X1),
inference(superposition,[status(thm)],[c_6374,c_1173]) ).
tcf(c_6706,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(X0,X1),set_difference(X0,set_difference(X2,X2))),
inference(superposition,[status(thm)],[c_6400,c_2951]) ).
tcf(c_6816,plain,
! [X0: $i,X1: $i] : set_difference(X0,X0) = set_difference(X1,X1),
inference(superposition,[status(thm)],[c_6402,c_6400]) ).
tcf(c_6817,plain,
! [X0: $i] : set_difference(X0,X0) = iPr_def_10,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_6816]) ).
tcf(c_6838,plain,
! [X0: $i] : subset(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_6374,c_6817]) ).
tcf(c_6842,plain,
! [X0: $i] : set_intersection2(X0,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_6402,c_6817]) ).
tcf(c_6847,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_difference(X0,iPr_def_10)),
inference(demodulation,[status(thm)],[c_6706,c_6817]) ).
tcf(c_6849,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ subset(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_6838,c_53]) ).
tcf(c_7001,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_intersection2(X0,X1)) = set_union2(iPr_def_10,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_6817,c_97]) ).
tcf(c_7008,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,iPr_def_10)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_6817,c_78]) ).
tcf(c_7015,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_intersection2(X0,X1),X0),iPr_def_10),
inference(superposition,[status(thm)],[c_6817,c_2939]) ).
tcf(c_8122,plain,
! [X0: $i,X1: $i] : set_difference(set_intersection2(X0,X1),X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_7015,c_6849]) ).
tcf(c_8172,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8122,c_77]) ).
tcf(c_8872,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_8172,c_7008]) ).
tcf(c_9883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_difference(cartesian_product2(X0,X1),cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3))) = set_union2(iPr_def_10,set_difference(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),
inference(superposition,[status(thm)],[c_91,c_7001]) ).
tcf(c_9884,plain,
! [X0: $i] : set_union2(iPr_def_10,set_difference(X0,iPr_def_10)) = set_difference(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_6842,c_7001]) ).
tcf(c_12562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_union2(cartesian_product2(X0,set_difference(X1,X2)),cartesian_product2(set_difference(X0,X3),X1)) = set_difference(cartesian_product2(X0,X1),set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X3,X1))),
inference(superposition,[status(thm)],[c_92,c_1939]) ).
tcf(c_12624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_union2(cartesian_product2(X0,set_difference(X1,X2)),cartesian_product2(set_difference(X0,X3),X1)) = set_difference(cartesian_product2(X0,X1),cartesian_product2(set_intersection2(X3,X0),set_intersection2(X1,X2))),
inference(demodulation,[status(thm)],[c_12562,c_1155]) ).
tcf(c_12634,plain,
set_difference(cartesian_product2(sK10,sK11),cartesian_product2(set_intersection2(sK12,sK10),set_intersection2(sK11,sK13))) != set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)),
inference(demodulation,[status(thm)],[c_323,c_12624]) ).
tcf(c_12635,plain,
set_union2(iPr_def_10,set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13))) != set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)),
inference(demodulation,[status(thm)],[c_12634,c_1281,c_1532,c_9883]) ).
tcf(c_24500,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,iPr_def_10)),X1),
inference(superposition,[status(thm)],[c_6847,c_6375]) ).
tcf(c_24742,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_24500,c_6849]) ).
tcf(c_24795,plain,
! [X0: $i,X1: $i] :
( in(X0,iPr_def_10)
| in(X0,set_difference(X1,iPr_def_10))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_24742,c_76]) ).
tcf(c_24821,plain,
! [X0: $i,X1: $i] :
( in(X0,set_difference(X1,iPr_def_10))
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24795,c_8872]) ).
tcf(c_26709,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,iPr_def_10))
| ~ in(sK6(X0,set_difference(X1,iPr_def_10)),X1) ),
inference(superposition,[status(thm)],[c_24821,c_70]) ).
tcf(c_113993,plain,
! [X0: $i] : subset(X0,set_difference(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_71,c_26709]) ).
tcf(c_114138,plain,
! [X0: $i] : set_difference(X0,iPr_def_10) = X0,
inference(superposition,[status(thm)],[c_113993,c_1409]) ).
tcf(c_114208,plain,
! [X0: $i] : set_union2(iPr_def_10,X0) = X0,
inference(demodulation,[status(thm)],[c_9884,c_114138]) ).
tcf(c_114271,plain,
set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)) != set_difference(cartesian_product2(sK10,sK11),cartesian_product2(sK12,sK13)),
inference(demodulation,[status(thm)],[c_12635,c_114208]) ).
tcf(c_114285,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_114271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET973+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.37 % Computer : n017.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Thu Sep 24 12:24:45 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 148.14/32.54 % SZS status Started for theBenchmark.p
% 148.14/32.54 % SZS status Theorem for theBenchmark.p
% 148.14/32.54
% 148.14/32.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 148.14/32.54
% 148.14/32.54 % ------ iProver source info
% 148.14/32.54
% 148.14/32.54 % git: date: 2026-07-19 20:42:38 +0200
% 148.14/32.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 148.14/32.54 % git: non_committed_changes: false
% 148.14/32.54
% 148.14/32.54 % ------ Parsing...
% 148.14/32.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 148.14/32.54
% 148.14/32.54 % ------ Preprocessing... sup_sim: 8 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 %
% 148.14/32.54
% 148.14/32.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 148.14/32.54
% 148.14/32.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 148.14/32.54 % ------ Proving...
% 148.14/32.54 % ------ Problem Properties
% 148.14/32.54
% 148.14/32.54 %
% 148.14/32.54 % clauses 46
% 148.14/32.54 % conjectures 0
% 148.14/32.54 % EPR 6
% 148.14/32.54 % Horn 36
% 148.14/32.54 % unary 15
% 148.14/32.54 % binary 15
% 148.14/32.54 % lits 97
% 148.14/32.54 % lits eq 24
% 148.14/32.54 % fd_pure 0
% 148.14/32.54 % fd_pseudo 0
% 148.14/32.54 % fd_cond 0
% 148.14/32.54 % fd_pseudo_cond 11
% 148.14/32.54 % AC symbols 0
% 148.14/32.54
% 148.14/32.54 % ------ Input Options Time Limit: Unbounded
% 148.14/32.54
% 148.14/32.54
% 148.14/32.54 % ------
% 148.14/32.54 % Current options:
% 148.14/32.54 % ------
% 148.14/32.54
% 148.14/32.54
% 148.14/32.54 %
% 148.14/32.54
% 148.14/32.54 % ------ Proving...
% 148.14/32.54 %
% 148.14/32.54
% 148.14/32.54 % SZS status Theorem for theBenchmark.p
% 148.14/32.54
% 148.14/32.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 148.14/32.54
% 148.14/32.54
%------------------------------------------------------------------------------