%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET973+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 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 : Tue Sep 29 12:42:27 PM UTC 2026
% Result : Theorem 9.58s 2.13s
% Output : Refutation 9.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 38
% Syntax : Number of formulae : 280 ( 35 unt; 29 def)
% Number of atoms : 853 ( 107 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 949 ( 376 ~; 460 |; 81 &)
% ( 31 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 22 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-3 aty)
% Number of variables : 319 ( 0 sgn 295 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
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,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
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,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f22,axiom,
! [X0,X1,X2] :
( cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
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(f32,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
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(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f40,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK0(X0,X1,X2),X0)
& ~ in(sK0(X0,X1,X2),X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( in(X6,X0)
& in(X7,X1)
& ordered_pair(X6,X7) = X3 )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( in(X11,X0)
& in(X12,X1)
& ordered_pair(X11,X12) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK1(X0,X1,X2) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1)
& sK1(X0,X1,X2) = ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK4(X0,X1,X8),X0)
& in(sK5(X0,X1,X8),X1)
& ordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK1(X0,X1,X2)),skolemize(X6,sK2(X0,X1,X2)),skolemize(X7,sK3(X0,X1,X2)),skolemize(X11,sK4(X0,X1,X8)),skolemize(X12,sK5(X0,X1,X8))],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X2) )
& ( ( in(sK7(X0,X1,X2),X0)
& ~ in(sK7(X0,X1,X2),X1) )
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f53]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f55]) ).
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(f66,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f69,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f73,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
! [X2,X0,X1,X8] :
( in(sK5(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f47]) ).
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] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f54]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f54]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f54]) ).
fof(f90,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f96,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f97,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f56]) ).
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(f113,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)),singleton(sK4(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f73,f90]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f98,f90]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f97,f90]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f96,f90]) ).
fof(f120,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f69]) ).
fof(f121,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f68]) ).
fof(f122,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f67]) ).
fof(f126,plain,
! [X0,X1,X8] :
( in(sK5(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f74]) ).
fof(f127,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK4(X0,X1,X8),sK5(X0,X1,X8)),singleton(sK4(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f113]) ).
fof(f128,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,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]) ).
fof(f131,definition,
sF14 = cartesian_product2(sK10,sK11),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f132,plain,
cartesian_product2(sK10,sK11) = sF14,
inference(reorient_equations,[],[f131]) ).
fof(f133,definition,
sF15 = cartesian_product2(sK12,sK13),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f134,plain,
cartesian_product2(sK12,sK13) = sF15,
inference(reorient_equations,[],[f133]) ).
fof(f135,definition,
sF16 = set_difference(sF14,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f136,plain,
set_difference(sF14,sF15) = sF16,
inference(reorient_equations,[],[f135]) ).
fof(f137,definition,
sF17 = set_difference(sK10,sK12),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f138,plain,
set_difference(sK10,sK12) = sF17,
inference(reorient_equations,[],[f137]) ).
fof(f139,definition,
sF18 = cartesian_product2(sF17,sK11),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f140,plain,
cartesian_product2(sF17,sK11) = sF18,
inference(reorient_equations,[],[f139]) ).
fof(f141,definition,
sF19 = set_difference(sK11,sK13),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f142,plain,
set_difference(sK11,sK13) = sF19,
inference(reorient_equations,[],[f141]) ).
fof(f143,definition,
sF20 = cartesian_product2(sK10,sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f144,plain,
cartesian_product2(sK10,sF19) = sF20,
inference(reorient_equations,[],[f143]) ).
fof(f145,definition,
sF21 = set_union2(sF18,sF20),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f146,plain,
set_union2(sF18,sF20) = sF21,
inference(reorient_equations,[],[f145]) ).
fof(f147,plain,
sF16 != sF21,
inference(definition_folding,[],[f106,f146,f144,f142,f140,f138,f136,f134,f132]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( in(X3,cartesian_product2(set_difference(X0,X1),X2))
| ~ in(X3,cartesian_product2(X0,X2))
| in(X3,cartesian_product2(X1,X2)) ),
inference(superposition,[],[f128,f105]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( in(X3,cartesian_product2(X0,set_difference(X1,X2)))
| ~ in(X3,cartesian_product2(X0,X1))
| in(X3,cartesian_product2(X0,X2)) ),
inference(superposition,[],[f128,f104]) ).
fof(f170,plain,
! [X0] :
( ~ in(X0,sF14)
| in(X0,sF16)
| in(X0,sF15) ),
inference(superposition,[],[f128,f136]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,cartesian_product2(set_difference(X0,X1),X2))
| in(X3,cartesian_product2(X0,X2)) ),
inference(superposition,[],[f129,f105]) ).
fof(f175,plain,
! [X0] :
( ~ in(X0,sF19)
| in(X0,sK11) ),
inference(superposition,[],[f129,f142]) ).
fof(f176,plain,
! [X0] :
( ~ in(X0,sF16)
| in(X0,sF14) ),
inference(superposition,[],[f129,f136]) ).
fof(f177,plain,
! [X0] :
( ~ in(X0,sF20)
| in(X0,sF21) ),
inference(superposition,[],[f121,f146]) ).
fof(f179,plain,
! [X0] :
( ~ in(X0,sF21)
| in(X0,sF20)
| in(X0,sF18) ),
inference(superposition,[],[f122,f146]) ).
fof(f180,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF14)
| ~ in(X0,sK10)
| ~ in(X1,sK11) ),
inference(superposition,[],[f115,f132]) ).
fof(f181,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF20)
| ~ in(X0,sK10)
| ~ in(X1,sF19) ),
inference(superposition,[],[f115,f144]) ).
fof(f183,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF18)
| ~ in(X0,sF17)
| ~ in(X1,sK11) ),
inference(superposition,[],[f115,f140]) ).
fof(f186,plain,
! [X0] :
( ~ in(X0,sF20)
| unordered_pair(unordered_pair(sK4(sK10,sF19,X0),sK5(sK10,sF19,X0)),singleton(sK4(sK10,sF19,X0))) = X0 ),
inference(superposition,[],[f127,f144]) ).
fof(f187,plain,
! [X0] :
( ~ in(X0,sF15)
| unordered_pair(unordered_pair(sK4(sK12,sK13,X0),sK5(sK12,sK13,X0)),singleton(sK4(sK12,sK13,X0))) = X0 ),
inference(superposition,[],[f127,f134]) ).
fof(f190,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF14)
| in(X1,sK11) ),
inference(superposition,[],[f117,f132]) ).
fof(f191,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF20)
| in(X1,sF19) ),
inference(superposition,[],[f117,f144]) ).
fof(f193,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF18)
| in(X1,sK11) ),
inference(superposition,[],[f117,f140]) ).
fof(f195,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF14)
| in(X0,sK10) ),
inference(superposition,[],[f116,f132]) ).
fof(f196,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF20)
| in(X0,sK10) ),
inference(superposition,[],[f116,f144]) ).
fof(f197,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF15)
| in(X0,sK12) ),
inference(superposition,[],[f116,f134]) ).
fof(f198,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF18)
| in(X0,sF17) ),
inference(superposition,[],[f116,f140]) ).
fof(f200,plain,
! [X0] :
( ~ in(X0,sF18)
| in(X0,sF21) ),
inference(superposition,[],[f120,f146]) ).
fof(f204,plain,
! [X0] :
( ~ in(X0,sF17)
| ~ in(X0,sK12) ),
inference(superposition,[],[f130,f138]) ).
fof(f205,plain,
! [X0] :
( ~ in(X0,sF19)
| ~ in(X0,sK13) ),
inference(superposition,[],[f130,f142]) ).
fof(f206,plain,
! [X0] :
( ~ in(X0,sF16)
| ~ in(X0,sF15) ),
inference(superposition,[],[f130,f136]) ).
fof(f213,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF16)
| ~ in(X1,sK11)
| ~ in(X0,sK10)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF15) ),
inference(resolution,[],[f180,f170]) ).
fof(f221,plain,
! [X0] :
( ~ in(sK6(sF16,X0),sF15)
| subset(sF16,X0) ),
inference(resolution,[],[f82,f206]) ).
fof(f222,plain,
! [X0] :
( in(sK6(sF16,X0),sF14)
| subset(sF16,X0) ),
inference(resolution,[],[f82,f176]) ).
fof(f229,plain,
! [X0] :
( in(sK6(sF21,X0),sF20)
| subset(sF21,X0)
| in(sK6(sF21,X0),sF18) ),
inference(resolution,[],[f82,f179]) ).
fof(f249,plain,
! [X0,X1] :
( ~ in(sK5(X1,sF19,X0),sK13)
| ~ in(X0,cartesian_product2(X1,sF19)) ),
inference(resolution,[],[f126,f205]) ).
fof(f300,plain,
! [X0,X1] :
( ~ in(X0,cartesian_product2(sK10,X1))
| in(X0,cartesian_product2(sF17,X1))
| in(X0,cartesian_product2(sK12,X1)) ),
inference(superposition,[],[f166,f138]) ).
fof(f311,plain,
! [X0] :
( ~ in(X0,sF14)
| in(X0,cartesian_product2(sF17,sK11))
| in(X0,cartesian_product2(sK12,sK11)) ),
inference(superposition,[],[f300,f132]) ).
fof(f313,plain,
! [X0] :
( in(X0,cartesian_product2(sK12,sK11))
| ~ in(X0,sF14)
| in(X0,sF18) ),
inference(forward_demodulation,[],[f311,f140]) ).
fof(f320,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21)
| ~ in(X1,sF19)
| ~ in(X0,sK10) ),
inference(resolution,[],[f181,f177]) ).
fof(f325,plain,
! [X0] :
( in(sK6(sF21,X0),sF18)
| subset(sF21,X0)
| sK6(sF21,X0) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,X0)),sK5(sK10,sF19,sK6(sF21,X0))),singleton(sK4(sK10,sF19,sK6(sF21,X0)))) ),
inference(resolution,[],[f186,f229]) ).
fof(f378,plain,
! [X0,X1] :
( ~ in(X0,cartesian_product2(X1,sK11))
| in(X0,cartesian_product2(X1,sF19))
| in(X0,cartesian_product2(X1,sK13)) ),
inference(superposition,[],[f167,f142]) ).
fof(f386,plain,
! [X0] :
( in(X0,cartesian_product2(sK12,sF19))
| in(X0,cartesian_product2(sK12,sK13))
| ~ in(X0,sF14)
| in(X0,sF18) ),
inference(resolution,[],[f378,f313]) ).
fof(f394,plain,
! [X0] :
( in(X0,cartesian_product2(sK12,sF19))
| in(X0,sF15)
| ~ in(X0,sF14)
| in(X0,sF18) ),
inference(forward_demodulation,[],[f386,f134]) ).
fof(f395,plain,
! [X0] :
( ~ in(X0,sF14)
| in(X0,sF15)
| in(X0,sF18)
| unordered_pair(unordered_pair(sK4(sK12,sF19,X0),sK5(sK12,sF19,X0)),singleton(sK4(sK12,sF19,X0))) = X0 ),
inference(resolution,[],[f394,f127]) ).
fof(f397,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF14)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF15)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF18)
| in(X1,sF19) ),
inference(resolution,[],[f394,f117]) ).
fof(f402,plain,
! [X0] :
( in(sK6(sF16,X0),sF15)
| in(sK6(sF16,X0),sF18)
| sK6(sF16,X0) = unordered_pair(unordered_pair(sK4(sK12,sF19,sK6(sF16,X0)),sK5(sK12,sF19,sK6(sF16,X0))),singleton(sK4(sK12,sF19,sK6(sF16,X0))))
| subset(sF16,X0) ),
inference(resolution,[],[f395,f222]) ).
fof(f404,plain,
! [X0] :
( in(sK6(sF16,X0),sF18)
| sK6(sF16,X0) = unordered_pair(unordered_pair(sK4(sK12,sF19,sK6(sF16,X0)),sK5(sK12,sF19,sK6(sF16,X0))),singleton(sK4(sK12,sF19,sK6(sF16,X0))))
| subset(sF16,X0) ),
inference(forward_subsumption_resolution,[],[f402,f221]) ).
fof(f407,plain,
! [X0] :
( in(sK6(sF16,X0),sF21)
| subset(sF16,X0)
| sK6(sF16,X0) = unordered_pair(unordered_pair(sK4(sK12,sF19,sK6(sF16,X0)),sK5(sK12,sF19,sK6(sF16,X0))),singleton(sK4(sK12,sF19,sK6(sF16,X0)))) ),
inference(resolution,[],[f404,f200]) ).
fof(f505,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF18)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF15)
| in(X1,sF19)
| ~ in(X0,sK10)
| ~ in(X1,sK11) ),
inference(resolution,[],[f397,f180]) ).
fof(f704,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF15)
| in(X1,sF19)
| ~ in(X0,sK10)
| ~ in(X1,sK11)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21) ),
inference(resolution,[],[f505,f200]) ).
fof(f707,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21)
| ~ in(X0,sK10)
| ~ in(X1,sK11)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF15) ),
inference(forward_subsumption_resolution,[],[f704,f320]) ).
fof(f797,plain,
( subset(sF16,sF21)
| sK6(sF16,sF21) = unordered_pair(unordered_pair(sK4(sK12,sF19,sK6(sF16,sF21)),sK5(sK12,sF19,sK6(sF16,sF21))),singleton(sK4(sK12,sF19,sK6(sF16,sF21))))
| subset(sF16,sF21) ),
inference(resolution,[],[f407,f83]) ).
fof(f799,plain,
( subset(sF16,sF21)
| sK6(sF16,sF21) = unordered_pair(unordered_pair(sK4(sK12,sF19,sK6(sF16,sF21)),sK5(sK12,sF19,sK6(sF16,sF21))),singleton(sK4(sK12,sF19,sK6(sF16,sF21)))) ),
inference(duplicate_literal_removal,[],[f797]) ).
fof(f801,definition,
( spl22_39
<=> sK6(sF16,sF21) = unordered_pair(unordered_pair(sK4(sK12,sF19,sK6(sF16,sF21)),sK5(sK12,sF19,sK6(sF16,sF21))),singleton(sK4(sK12,sF19,sK6(sF16,sF21)))) ),
introduced(definition,[new_symbols(definition,[spl22_39])],[avatar_definition]) ).
fof(f803,plain,
( sK6(sF16,sF21) = unordered_pair(unordered_pair(sK4(sK12,sF19,sK6(sF16,sF21)),sK5(sK12,sF19,sK6(sF16,sF21))),singleton(sK4(sK12,sF19,sK6(sF16,sF21))))
| ~ spl22_39 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f805,definition,
( spl22_40
<=> subset(sF16,sF21) ),
introduced(definition,[new_symbols(definition,[spl22_40])],[avatar_definition]) ).
fof(f806,plain,
( ~ subset(sF16,sF21)
| spl22_40 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f807,plain,
( subset(sF16,sF21)
| ~ spl22_40 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f808,plain,
( spl22_39
| spl22_40 ),
inference(avatar_split_clause,[],[f799,f805,f801]) ).
fof(f816,plain,
( ~ in(sK6(sF16,sF21),sF14)
| in(sK5(sK12,sF19,sK6(sF16,sF21)),sK11)
| ~ spl22_39 ),
inference(superposition,[],[f190,f803]) ).
fof(f820,plain,
( ~ in(sK6(sF16,sF21),sF14)
| in(sK4(sK12,sF19,sK6(sF16,sF21)),sK10)
| ~ spl22_39 ),
inference(superposition,[],[f195,f803]) ).
fof(f838,plain,
( in(sK6(sF16,sF21),sF21)
| ~ in(sK4(sK12,sF19,sK6(sF16,sF21)),sK10)
| ~ in(sK5(sK12,sF19,sK6(sF16,sF21)),sK11)
| in(sK6(sF16,sF21),sF15)
| ~ spl22_39 ),
inference(superposition,[],[f707,f803]) ).
fof(f945,definition,
( spl22_53
<=> in(sK6(sF16,sF21),sF15) ),
introduced(definition,[new_symbols(definition,[spl22_53])],[avatar_definition]) ).
fof(f947,plain,
( in(sK6(sF16,sF21),sF15)
| ~ spl22_53 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f949,definition,
( spl22_54
<=> in(sK5(sK12,sF19,sK6(sF16,sF21)),sK11) ),
introduced(definition,[new_symbols(definition,[spl22_54])],[avatar_definition]) ).
fof(f953,definition,
( spl22_55
<=> in(sK4(sK12,sF19,sK6(sF16,sF21)),sK10) ),
introduced(definition,[new_symbols(definition,[spl22_55])],[avatar_definition]) ).
fof(f957,definition,
( spl22_56
<=> in(sK6(sF16,sF21),sF21) ),
introduced(definition,[new_symbols(definition,[spl22_56])],[avatar_definition]) ).
fof(f959,plain,
( in(sK6(sF16,sF21),sF21)
| ~ spl22_56 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f960,plain,
( spl22_53
| ~ spl22_54
| ~ spl22_55
| spl22_56
| ~ spl22_39 ),
inference(avatar_split_clause,[],[f838,f801,f957,f953,f949,f945]) ).
fof(f987,definition,
( spl22_62
<=> in(sK6(sF16,sF21),sF14) ),
introduced(definition,[new_symbols(definition,[spl22_62])],[avatar_definition]) ).
fof(f989,plain,
( ~ in(sK6(sF16,sF21),sF14)
| spl22_62 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f1010,plain,
( spl22_55
| ~ spl22_62
| ~ spl22_39 ),
inference(avatar_split_clause,[],[f820,f801,f987,f953]) ).
fof(f1014,plain,
( spl22_54
| ~ spl22_62
| ~ spl22_39 ),
inference(avatar_split_clause,[],[f816,f801,f987,f949]) ).
fof(f1033,plain,
( subset(sF16,sF21)
| spl22_62 ),
inference(resolution,[],[f989,f222]) ).
fof(f1034,plain,
( ~ subset(sF21,sF16)
| sF16 = sF21
| ~ spl22_40 ),
inference(resolution,[],[f807,f66]) ).
fof(f1035,plain,
( ~ subset(sF21,sF16)
| ~ spl22_40 ),
inference(forward_subsumption_resolution,[],[f1034,f147]) ).
fof(f1431,plain,
! [X0,X1] :
( ~ in(X0,cartesian_product2(sF17,X1))
| in(X0,cartesian_product2(sK10,X1)) ),
inference(superposition,[],[f172,f138]) ).
fof(f1442,plain,
! [X0] :
( ~ in(X0,sF18)
| in(X0,cartesian_product2(sK10,sK11)) ),
inference(superposition,[],[f1431,f140]) ).
fof(f1443,plain,
! [X0] :
( ~ in(X0,sF18)
| in(X0,sF14) ),
inference(forward_demodulation,[],[f1442,f132]) ).
fof(f1445,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF14)
| ~ in(X0,sF17)
| ~ in(X1,sK11) ),
inference(resolution,[],[f1443,f183]) ).
fof(f1449,plain,
! [X0] :
( in(sK6(sF21,X0),sF14)
| subset(sF21,X0)
| sK6(sF21,X0) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,X0)),sK5(sK10,sF19,sK6(sF21,X0))),singleton(sK4(sK10,sF19,sK6(sF21,X0)))) ),
inference(resolution,[],[f1443,f325]) ).
fof(f1481,plain,
! [X0] :
( in(sK6(sF21,X0),sF16)
| sK6(sF21,X0) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,X0)),sK5(sK10,sF19,sK6(sF21,X0))),singleton(sK4(sK10,sF19,sK6(sF21,X0))))
| subset(sF21,X0)
| in(sK6(sF21,X0),sF15) ),
inference(resolution,[],[f1449,f170]) ).
fof(f1494,plain,
( sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16))))
| subset(sF21,sF16)
| in(sK6(sF21,sF16),sF15)
| subset(sF21,sF16) ),
inference(resolution,[],[f1481,f83]) ).
fof(f1500,plain,
( sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16))))
| subset(sF21,sF16)
| in(sK6(sF21,sF16),sF15) ),
inference(duplicate_literal_removal,[],[f1494]) ).
fof(f1502,plain,
( sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16))))
| in(sK6(sF21,sF16),sF15)
| ~ spl22_40 ),
inference(forward_subsumption_resolution,[],[f1500,f1035]) ).
fof(f1504,definition,
( spl22_81
<=> in(sK6(sF21,sF16),sF15) ),
introduced(definition,[new_symbols(definition,[spl22_81])],[avatar_definition]) ).
fof(f1505,plain,
( ~ in(sK6(sF21,sF16),sF15)
| spl22_81 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f1506,plain,
( in(sK6(sF21,sF16),sF15)
| ~ spl22_81 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f1508,definition,
( spl22_82
<=> sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16)))) ),
introduced(definition,[new_symbols(definition,[spl22_82])],[avatar_definition]) ).
fof(f1509,plain,
( sK6(sF21,sF16) != unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16))))
| spl22_82 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f1510,plain,
( sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16))))
| ~ spl22_82 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f1511,plain,
( spl22_81
| spl22_82
| ~ spl22_40 ),
inference(avatar_split_clause,[],[f1502,f805,f1508,f1504]) ).
fof(f1515,plain,
( $false
| spl22_40
| spl22_62 ),
inference(forward_subsumption_resolution,[],[f1033,f806]) ).
fof(f1516,plain,
( spl22_40
| spl22_62 ),
inference(avatar_contradiction_clause,[],[f1515]) ).
fof(f1533,plain,
( subset(sF16,sF21)
| ~ spl22_56 ),
inference(resolution,[],[f959,f83]) ).
fof(f1535,plain,
( $false
| spl22_40
| ~ spl22_56 ),
inference(forward_subsumption_resolution,[],[f1533,f806]) ).
fof(f1536,plain,
( spl22_40
| ~ spl22_56 ),
inference(avatar_contradiction_clause,[],[f1535]) ).
fof(f1545,definition,
( spl22_83
<=> subset(sF21,sF16) ),
introduced(definition,[new_symbols(definition,[spl22_83])],[avatar_definition]) ).
fof(f1546,plain,
( ~ subset(sF21,sF16)
| spl22_83 ),
inference(avatar_component_clause,[],[f1545]) ).
fof(f1549,plain,
( sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK12,sK13,sK6(sF21,sF16)),sK5(sK12,sK13,sK6(sF21,sF16))),singleton(sK4(sK12,sK13,sK6(sF21,sF16))))
| ~ spl22_81 ),
inference(resolution,[],[f1506,f187]) ).
fof(f1554,plain,
( subset(sF16,sF21)
| ~ spl22_53 ),
inference(resolution,[],[f947,f221]) ).
fof(f1556,plain,
( $false
| spl22_40
| ~ spl22_53 ),
inference(forward_subsumption_resolution,[],[f1554,f806]) ).
fof(f1557,plain,
( spl22_40
| ~ spl22_53 ),
inference(avatar_contradiction_clause,[],[f1556]) ).
fof(f1558,plain,
( ~ spl22_83
| ~ spl22_40 ),
inference(avatar_split_clause,[],[f1035,f805,f1545]) ).
fof(f1584,plain,
( ~ in(sK6(sF21,sF16),sF15)
| in(sK4(sK12,sK13,sK6(sF21,sF16)),sK12)
| ~ spl22_81 ),
inference(superposition,[],[f197,f1549]) ).
fof(f1585,plain,
( ~ in(sK6(sF21,sF16),sF18)
| in(sK4(sK12,sK13,sK6(sF21,sF16)),sF17)
| ~ spl22_81 ),
inference(superposition,[],[f198,f1549]) ).
fof(f1720,definition,
( spl22_97
<=> in(sK4(sK12,sK13,sK6(sF21,sF16)),sF17) ),
introduced(definition,[new_symbols(definition,[spl22_97])],[avatar_definition]) ).
fof(f1721,plain,
( in(sK4(sK12,sK13,sK6(sF21,sF16)),sF17)
| ~ spl22_97 ),
inference(avatar_component_clause,[],[f1720]) ).
fof(f1724,definition,
( spl22_98
<=> in(sK6(sF21,sF16),sF14) ),
introduced(definition,[new_symbols(definition,[spl22_98])],[avatar_definition]) ).
fof(f1742,definition,
( spl22_102
<=> in(sK6(sF21,sF16),sF20) ),
introduced(definition,[new_symbols(definition,[spl22_102])],[avatar_definition]) ).
fof(f1743,plain,
( ~ in(sK6(sF21,sF16),sF20)
| spl22_102 ),
inference(avatar_component_clause,[],[f1742]) ).
fof(f1744,plain,
( in(sK6(sF21,sF16),sF20)
| ~ spl22_102 ),
inference(avatar_component_clause,[],[f1742]) ).
fof(f1754,definition,
( spl22_104
<=> in(sK4(sK12,sK13,sK6(sF21,sF16)),sK12) ),
introduced(definition,[new_symbols(definition,[spl22_104])],[avatar_definition]) ).
fof(f1756,plain,
( in(sK4(sK12,sK13,sK6(sF21,sF16)),sK12)
| ~ spl22_104 ),
inference(avatar_component_clause,[],[f1754]) ).
fof(f1758,definition,
( spl22_105
<=> in(sK6(sF21,sF16),sF18) ),
introduced(definition,[new_symbols(definition,[spl22_105])],[avatar_definition]) ).
fof(f1759,plain,
( ~ in(sK6(sF21,sF16),sF18)
| spl22_105 ),
inference(avatar_component_clause,[],[f1758]) ).
fof(f1762,plain,
( spl22_97
| ~ spl22_105
| ~ spl22_81 ),
inference(avatar_split_clause,[],[f1585,f1504,f1758,f1720]) ).
fof(f1763,plain,
( in(sK4(sK12,sK13,sK6(sF21,sF16)),sK12)
| ~ spl22_81 ),
inference(forward_subsumption_resolution,[],[f1584,f1506]) ).
fof(f1773,plain,
( spl22_104
| ~ spl22_81 ),
inference(avatar_split_clause,[],[f1763,f1504,f1754]) ).
fof(f1779,plain,
( ! [X0,X1] :
( ~ in(sK6(sF21,sF16),cartesian_product2(X0,X1))
| in(sK5(sK10,sF19,sK6(sF21,sF16)),X1) )
| ~ spl22_82 ),
inference(superposition,[],[f117,f1510]) ).
fof(f1785,plain,
( ~ in(sK6(sF21,sF16),sF20)
| in(sK5(sK10,sF19,sK6(sF21,sF16)),sF19)
| ~ spl22_82 ),
inference(superposition,[],[f191,f1510]) ).
fof(f1787,plain,
( ~ in(sK6(sF21,sF16),sF18)
| in(sK5(sK10,sF19,sK6(sF21,sF16)),sK11)
| ~ spl22_82 ),
inference(superposition,[],[f193,f1510]) ).
fof(f1788,plain,
( ~ in(sK6(sF21,sF16),sF14)
| in(sK4(sK10,sF19,sK6(sF21,sF16)),sK10)
| ~ spl22_82 ),
inference(superposition,[],[f195,f1510]) ).
fof(f1789,plain,
( ~ in(sK6(sF21,sF16),sF20)
| in(sK4(sK10,sF19,sK6(sF21,sF16)),sK10)
| ~ spl22_82 ),
inference(superposition,[],[f196,f1510]) ).
fof(f1791,plain,
( ~ in(sK6(sF21,sF16),sF18)
| in(sK4(sK10,sF19,sK6(sF21,sF16)),sF17)
| ~ spl22_82 ),
inference(superposition,[],[f198,f1510]) ).
fof(f1792,plain,
( in(sK6(sF21,sF16),sF16)
| ~ in(sK5(sK10,sF19,sK6(sF21,sF16)),sK11)
| ~ in(sK4(sK10,sF19,sK6(sF21,sF16)),sK10)
| in(sK6(sF21,sF16),sF15)
| ~ spl22_82 ),
inference(superposition,[],[f213,f1510]) ).
fof(f1807,plain,
( in(sK6(sF21,sF16),sF14)
| ~ in(sK4(sK10,sF19,sK6(sF21,sF16)),sF17)
| ~ in(sK5(sK10,sF19,sK6(sF21,sF16)),sK11)
| ~ spl22_82 ),
inference(superposition,[],[f1445,f1510]) ).
fof(f1922,definition,
( spl22_118
<=> in(sK5(sK10,sF19,sK6(sF21,sF16)),sK11) ),
introduced(definition,[new_symbols(definition,[spl22_118])],[avatar_definition]) ).
fof(f1924,plain,
( ~ in(sK5(sK10,sF19,sK6(sF21,sF16)),sK11)
| spl22_118 ),
inference(avatar_component_clause,[],[f1922]) ).
fof(f1926,definition,
( spl22_119
<=> in(sK4(sK10,sF19,sK6(sF21,sF16)),sF17) ),
introduced(definition,[new_symbols(definition,[spl22_119])],[avatar_definition]) ).
fof(f1929,plain,
( ~ spl22_118
| ~ spl22_119
| spl22_98
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f1807,f1508,f1724,f1926,f1922]) ).
fof(f1935,definition,
( spl22_120
<=> in(sK5(sK10,sF19,sK6(sF21,sF16)),sK13) ),
introduced(definition,[new_symbols(definition,[spl22_120])],[avatar_definition]) ).
fof(f1936,plain,
( ~ in(sK5(sK10,sF19,sK6(sF21,sF16)),sK13)
| spl22_120 ),
inference(avatar_component_clause,[],[f1935]) ).
fof(f1937,plain,
( in(sK5(sK10,sF19,sK6(sF21,sF16)),sK13)
| ~ spl22_120 ),
inference(avatar_component_clause,[],[f1935]) ).
fof(f1939,definition,
( spl22_121
<=> in(sK4(sK10,sF19,sK6(sF21,sF16)),sK10) ),
introduced(definition,[new_symbols(definition,[spl22_121])],[avatar_definition]) ).
fof(f1949,definition,
( spl22_122
<=> in(sK5(sK10,sF19,sK6(sF21,sF16)),sF19) ),
introduced(definition,[new_symbols(definition,[spl22_122])],[avatar_definition]) ).
fof(f1950,plain,
( in(sK5(sK10,sF19,sK6(sF21,sF16)),sF19)
| ~ spl22_122 ),
inference(avatar_component_clause,[],[f1949]) ).
fof(f1958,plain,
( in(sK6(sF21,sF16),sF16)
| ~ in(sK5(sK10,sF19,sK6(sF21,sF16)),sK11)
| ~ in(sK4(sK10,sF19,sK6(sF21,sF16)),sK10)
| spl22_81
| ~ spl22_82 ),
inference(forward_subsumption_resolution,[],[f1792,f1505]) ).
fof(f1959,plain,
( spl22_119
| ~ spl22_105
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f1791,f1508,f1758,f1926]) ).
fof(f1960,plain,
( spl22_121
| ~ spl22_102
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f1789,f1508,f1742,f1939]) ).
fof(f1961,plain,
( spl22_121
| ~ spl22_98
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f1788,f1508,f1724,f1939]) ).
fof(f1962,plain,
( spl22_118
| ~ spl22_105
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f1787,f1508,f1758,f1922]) ).
fof(f1963,plain,
( spl22_122
| ~ spl22_102
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f1785,f1508,f1742,f1949]) ).
fof(f1976,definition,
( spl22_124
<=> in(sK6(sF21,sF16),sF16) ),
introduced(definition,[new_symbols(definition,[spl22_124])],[avatar_definition]) ).
fof(f1978,plain,
( in(sK6(sF21,sF16),sF16)
| ~ spl22_124 ),
inference(avatar_component_clause,[],[f1976]) ).
fof(f1982,plain,
( subset(sF21,sF16)
| in(sK6(sF21,sF16),sF18)
| spl22_102 ),
inference(resolution,[],[f1743,f229]) ).
fof(f1983,plain,
( in(sK6(sF21,sF16),sF18)
| spl22_83
| spl22_102 ),
inference(forward_subsumption_resolution,[],[f1982,f1546]) ).
fof(f1984,plain,
( $false
| spl22_83
| spl22_102
| spl22_105 ),
inference(forward_subsumption_resolution,[],[f1983,f1759]) ).
fof(f1985,plain,
( spl22_83
| spl22_102
| spl22_105 ),
inference(avatar_contradiction_clause,[],[f1984]) ).
fof(f2183,plain,
( ~ spl22_121
| ~ spl22_118
| spl22_124
| spl22_81
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f1958,f1508,f1504,f1976,f1922,f1939]) ).
fof(f2269,plain,
( subset(sF21,sF16)
| ~ spl22_124 ),
inference(resolution,[],[f1978,f83]) ).
fof(f2272,plain,
( $false
| spl22_83
| ~ spl22_124 ),
inference(forward_subsumption_resolution,[],[f2269,f1546]) ).
fof(f2273,plain,
( spl22_83
| ~ spl22_124 ),
inference(avatar_contradiction_clause,[],[f2272]) ).
fof(f2276,plain,
( subset(sF21,sF16)
| sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16))))
| spl22_105 ),
inference(resolution,[],[f1759,f325]) ).
fof(f2287,plain,
( ~ in(sK6(sF21,sF16),sF15)
| in(sK5(sK10,sF19,sK6(sF21,sF16)),sK13)
| ~ spl22_82 ),
inference(superposition,[],[f1779,f134]) ).
fof(f2353,plain,
( ~ in(sK4(sK12,sK13,sK6(sF21,sF16)),sK12)
| ~ spl22_97 ),
inference(resolution,[],[f1721,f204]) ).
fof(f2355,plain,
( $false
| ~ spl22_97
| ~ spl22_104 ),
inference(forward_subsumption_resolution,[],[f2353,f1756]) ).
fof(f2356,plain,
( ~ spl22_97
| ~ spl22_104 ),
inference(avatar_contradiction_clause,[],[f2355]) ).
fof(f2422,plain,
( ~ in(sK6(sF21,sF16),cartesian_product2(sK10,sF19))
| ~ spl22_120 ),
inference(resolution,[],[f1937,f249]) ).
fof(f2423,plain,
( ~ in(sK6(sF21,sF16),sF20)
| ~ spl22_120 ),
inference(forward_demodulation,[],[f2422,f144]) ).
fof(f2424,plain,
( $false
| ~ spl22_102
| ~ spl22_120 ),
inference(forward_subsumption_resolution,[],[f2423,f1744]) ).
fof(f2425,plain,
( ~ spl22_102
| ~ spl22_120 ),
inference(avatar_contradiction_clause,[],[f2424]) ).
fof(f2435,plain,
( in(sK5(sK10,sF19,sK6(sF21,sF16)),sK11)
| ~ spl22_122 ),
inference(resolution,[],[f1950,f175]) ).
fof(f2436,plain,
( $false
| spl22_118
| ~ spl22_122 ),
inference(forward_subsumption_resolution,[],[f2435,f1924]) ).
fof(f2437,plain,
( spl22_118
| ~ spl22_122 ),
inference(avatar_contradiction_clause,[],[f2436]) ).
fof(f2442,plain,
( in(sK5(sK10,sF19,sK6(sF21,sF16)),sK13)
| ~ spl22_81
| ~ spl22_82 ),
inference(forward_subsumption_resolution,[],[f2287,f1506]) ).
fof(f2448,plain,
( $false
| ~ spl22_81
| ~ spl22_82
| spl22_120 ),
inference(forward_subsumption_resolution,[],[f2442,f1936]) ).
fof(f2449,plain,
( ~ spl22_81
| ~ spl22_82
| spl22_120 ),
inference(avatar_contradiction_clause,[],[f2448]) ).
fof(f2453,plain,
( sK6(sF21,sF16) = unordered_pair(unordered_pair(sK4(sK10,sF19,sK6(sF21,sF16)),sK5(sK10,sF19,sK6(sF21,sF16))),singleton(sK4(sK10,sF19,sK6(sF21,sF16))))
| spl22_83
| spl22_105 ),
inference(forward_subsumption_resolution,[],[f2276,f1546]) ).
fof(f2454,plain,
( $false
| spl22_82
| spl22_83
| spl22_105 ),
inference(forward_subsumption_resolution,[],[f2453,f1509]) ).
fof(f2455,plain,
( spl22_82
| spl22_83
| spl22_105 ),
inference(avatar_contradiction_clause,[],[f2454]) ).
cnf(s52,plain,
( spl22_39
| spl22_40 ),
inference(sat_conversion,[],[f808]) ).
cnf(s80,plain,
( ~ spl22_39
| spl22_53
| ~ spl22_54
| ~ spl22_55
| spl22_56 ),
inference(sat_conversion,[],[f960]) ).
cnf(s98,plain,
( ~ spl22_39
| spl22_55
| ~ spl22_62 ),
inference(sat_conversion,[],[f1010]) ).
cnf(s102,plain,
( ~ spl22_39
| spl22_54
| ~ spl22_62 ),
inference(sat_conversion,[],[f1014]) ).
cnf(s116,plain,
( ~ spl22_40
| spl22_81
| spl22_82 ),
inference(sat_conversion,[],[f1511]) ).
cnf(s117,plain,
( spl22_40
| spl22_62 ),
inference(sat_conversion,[],[f1516]) ).
cnf(s121,plain,
( spl22_40
| ~ spl22_56 ),
inference(sat_conversion,[],[f1536]) ).
cnf(s124,plain,
( spl22_40
| ~ spl22_53 ),
inference(sat_conversion,[],[f1557]) ).
cnf(s125,plain,
( ~ spl22_40
| ~ spl22_83 ),
inference(sat_conversion,[],[f1558]) ).
cnf(s159,plain,
( ~ spl22_81
| spl22_97
| ~ spl22_105 ),
inference(sat_conversion,[],[f1762]) ).
cnf(s168,plain,
( ~ spl22_81
| spl22_104 ),
inference(sat_conversion,[],[f1773]) ).
cnf(s196,plain,
( ~ spl22_82
| spl22_98
| ~ spl22_118
| ~ spl22_119 ),
inference(sat_conversion,[],[f1929]) ).
cnf(s203,plain,
( ~ spl22_82
| ~ spl22_105
| spl22_119 ),
inference(sat_conversion,[],[f1959]) ).
cnf(s204,plain,
( ~ spl22_82
| ~ spl22_102
| spl22_121 ),
inference(sat_conversion,[],[f1960]) ).
cnf(s205,plain,
( ~ spl22_82
| ~ spl22_98
| spl22_121 ),
inference(sat_conversion,[],[f1961]) ).
cnf(s206,plain,
( ~ spl22_82
| ~ spl22_105
| spl22_118 ),
inference(sat_conversion,[],[f1962]) ).
cnf(s207,plain,
( ~ spl22_82
| ~ spl22_102
| spl22_122 ),
inference(sat_conversion,[],[f1963]) ).
cnf(s220,plain,
( spl22_83
| spl22_102
| spl22_105 ),
inference(sat_conversion,[],[f1985]) ).
cnf(s255,plain,
( spl22_81
| ~ spl22_82
| ~ spl22_118
| ~ spl22_121
| spl22_124 ),
inference(sat_conversion,[],[f2183]) ).
cnf(s257,plain,
( spl22_83
| ~ spl22_124 ),
inference(sat_conversion,[],[f2273]) ).
cnf(s262,plain,
( ~ spl22_97
| ~ spl22_104 ),
inference(sat_conversion,[],[f2356]) ).
cnf(s269,plain,
( ~ spl22_102
| ~ spl22_120 ),
inference(sat_conversion,[],[f2425]) ).
cnf(s270,plain,
( spl22_118
| ~ spl22_122 ),
inference(sat_conversion,[],[f2437]) ).
cnf(s274,plain,
( ~ spl22_81
| ~ spl22_82
| spl22_120 ),
inference(sat_conversion,[],[f2449]) ).
cnf(s276,plain,
( spl22_82
| spl22_83
| spl22_105 ),
inference(sat_conversion,[],[f2455]) ).
cnf(s277,plain,
( ~ spl22_105
| spl22_98
| ~ spl22_82 ),
inference(rat,[],[s196,s203,s206]) ).
cnf(s278,plain,
( ~ spl22_102
| ~ spl22_82
| spl22_81
| spl22_124 ),
inference(rat,[],[s255,s270,s204,s207]) ).
cnf(s279,plain,
( spl22_81
| ~ spl22_40 ),
inference(rat,[],[s205,s255,s277,s206,s220,s278,s116,s257,s125]) ).
cnf(s280,plain,
~ spl22_40,
inference(rat,[],[s274,s269,s276,s220,s159,s262,s168,s279,s125]) ).
cnf(s281,plain,
~ spl22_53,
inference(rat,[],[s124,s280]) ).
cnf(s282,plain,
~ spl22_56,
inference(rat,[],[s121,s280]) ).
cnf(s285,plain,
spl22_62,
inference(rat,[],[s117,s280]) ).
cnf(s286,plain,
spl22_39,
inference(rat,[],[s52,s280]) ).
cnf(s287,plain,
spl22_54,
inference(rat,[],[s102,s286,s285]) ).
cnf(s288,plain,
spl22_55,
inference(rat,[],[s98,s286,s285]) ).
cnf(s289,plain,
$false,
inference(rat,[],[s80,s282,s281,s286,s288,s287]) ).
fof(f2456,plain,
$false,
inference(avatar_sat_refutation,[],[s289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET973+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:12:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.83/2.13 % (3174366)Detected formulas, will run a generic FOF schedule.
% 8.83/2.13 % (3174373)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2347588505:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.83/2.13 % (3174371)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2187002268:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.83/2.13 % (3174377)dis-21_1_sil=8000:lcm=predicate:random_seed=2664194443:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 8.83/2.13 % (3174372)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3452101843:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.83/2.13 % (3174374)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3602477713:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.83/2.13 % (3174375)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2863622230:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.83/2.13 % (3174374)Refutation not found, incomplete strategy
% 8.83/2.13 % (3174374)------------------------------
% 8.83/2.13 % (3174374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174374)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174374)Termination reason: Refutation not found, incomplete strategy
% 8.83/2.13 % (3174374)Time elapsed: 0.002 s
% 8.83/2.13 % (3174374)Peak memory usage: 88 MB
% 8.83/2.13 % (3174374)Instructions burned: 1 (million)
% 8.83/2.13 % (3174376)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=309553674:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.83/2.13 % (3174375)Instruction limit reached!
% 8.83/2.13 % (3174375)------------------------------
% 8.83/2.13 % (3174375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174375)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174375)Termination reason: Instruction limit
% 8.83/2.13 % (3174375)Termination phase: Saturation
% 8.83/2.13 % (3174375)Time elapsed: 0.074 s
% 8.83/2.13 % (3174375)Peak memory usage: 89 MB
% 8.83/2.13 % (3174375)Instructions burned: 121 (million)
% 8.83/2.13 % (3174377)Instruction limit reached!
% 8.83/2.13 % (3174377)------------------------------
% 8.83/2.13 % (3174377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174377)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174377)Termination reason: Instruction limit
% 8.83/2.13 % (3174377)Termination phase: Saturation
% 8.83/2.13 % (3174377)Time elapsed: 0.074 s
% 8.83/2.13 % (3174377)Peak memory usage: 89 MB
% 8.83/2.13 % (3174377)Instructions burned: 130 (million)
% 8.83/2.13 % (3174376)Instruction limit reached!
% 8.83/2.13 % (3174376)------------------------------
% 8.83/2.13 % (3174376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174376)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174376)Termination reason: Instruction limit
% 8.83/2.13 % (3174376)Termination phase: Saturation
% 8.83/2.13 % (3174376)Time elapsed: 0.095 s
% 8.83/2.13 % (3174376)Peak memory usage: 90 MB
% 8.83/2.13 % (3174376)Instructions burned: 139 (million)
% 8.83/2.13 % (3174385)lrs+10_1_sil=8000:sp=occurrence:random_seed=2533483857:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.83/2.13 % (3174386)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3763544517:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.83/2.13 % (3174387)lrs+1011_1_sil=32000:sp=occurrence:random_seed=736826053:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.83/2.13 % (3174374)------------------------------
% 8.83/2.13 % (3174374)------------------------------
% 8.83/2.13 % (3174386)Instruction limit reached!
% 8.83/2.13 % (3174386)------------------------------
% 8.83/2.13 % (3174386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174386)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174386)Termination reason: Instruction limit
% 8.83/2.13 % (3174386)Termination phase: Saturation
% 8.83/2.13 % (3174386)Time elapsed: 0.078 s
% 8.83/2.13 % (3174386)Peak memory usage: 89 MB
% 8.83/2.13 % (3174386)Instructions burned: 157 (million)
% 8.83/2.13 % (3174391)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2479933547:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.83/2.13 % (3174385)Instruction limit reached!
% 8.83/2.13 % (3174385)------------------------------
% 8.83/2.13 % (3174385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174385)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174385)Termination reason: Instruction limit
% 8.83/2.13 % (3174385)Termination phase: Saturation
% 8.83/2.13 % (3174385)Time elapsed: 0.180 s
% 8.83/2.13 % (3174385)Peak memory usage: 92 MB
% 8.83/2.13 % (3174385)Instructions burned: 285 (million)
% 8.83/2.13 % (3174392)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=847767007:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.83/2.13 % (3174392)Refutation not found, incomplete strategy
% 8.83/2.13 % (3174392)------------------------------
% 8.83/2.13 % (3174392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174392)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174392)Termination reason: Refutation not found, incomplete strategy
% 8.83/2.13 % (3174392)Time elapsed: 0.003 s
% 8.83/2.13 % (3174392)Peak memory usage: 88 MB
% 8.83/2.13 % (3174392)Instructions burned: 2 (million)
% 8.83/2.13 % (3174387)Instruction limit reached!
% 8.83/2.13 % (3174387)------------------------------
% 8.83/2.13 % (3174387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174387)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174387)Termination reason: Instruction limit
% 8.83/2.13 % (3174387)Termination phase: Saturation
% 8.83/2.13 % (3174387)Time elapsed: 0.204 s
% 8.83/2.13 % (3174387)Peak memory usage: 92 MB
% 8.83/2.13 % (3174387)Instructions burned: 327 (million)
% 8.83/2.13 % (3174394)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2091782723:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.83/2.13 % (3174391)Instruction limit reached!
% 8.83/2.13 % (3174391)------------------------------
% 8.83/2.13 % (3174391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174391)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174391)Termination reason: Instruction limit
% 8.83/2.13 % (3174391)Termination phase: Saturation
% 8.83/2.13 % (3174391)Time elapsed: 0.152 s
% 8.83/2.13 % (3174391)Peak memory usage: 91 MB
% 8.83/2.13 % (3174391)Instructions burned: 248 (million)
% 8.83/2.13 % (3174396)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=485066944:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.83/2.13 % (3174396)Instruction limit reached!
% 8.83/2.13 % (3174396)------------------------------
% 8.83/2.13 % (3174396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174396)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174396)Termination reason: Instruction limit
% 8.83/2.13 % (3174396)Termination phase: Saturation
% 8.83/2.13 % (3174396)Time elapsed: 0.065 s
% 8.83/2.13 % (3174396)Peak memory usage: 89 MB
% 8.83/2.13 % (3174396)Instructions burned: 114 (million)
% 8.83/2.13 % (3174392)------------------------------
% 8.83/2.13 % (3174392)------------------------------
% 8.83/2.13 % (3174398)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1099106304:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.83/2.13 % (3174398)Refutation not found, incomplete strategy
% 8.83/2.13 % (3174398)------------------------------
% 8.83/2.13 % (3174398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174398)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174398)Termination reason: Refutation not found, incomplete strategy
% 8.83/2.13 % (3174398)Time elapsed: 0.002 s
% 8.83/2.13 % (3174398)Peak memory usage: 88 MB
% 8.83/2.13 % (3174398)Instructions burned: 2 (million)
% 8.83/2.13 % (3174400)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3239121922:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 8.83/2.13 % (3174401)lrs+10_1_sil=8000:sp=occurrence:random_seed=3446725959:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.83/2.13 % (3174400)Instruction limit reached!
% 8.83/2.13 % (3174400)------------------------------
% 8.83/2.13 % (3174400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174400)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174400)Termination reason: Instruction limit
% 8.83/2.13 % (3174400)Termination phase: Saturation
% 8.83/2.13 % (3174400)Time elapsed: 0.068 s
% 8.83/2.13 % (3174400)Peak memory usage: 89 MB
% 8.83/2.13 % (3174400)Instructions burned: 114 (million)
% 8.83/2.13 % (3174371)First to succeed.
% 8.83/2.13 % (3174371)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3174366"
% 8.83/2.13 % (3174398)------------------------------
% 8.83/2.13 % (3174398)------------------------------
% 8.83/2.13 % (3174405)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3337308992:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.83/2.13 % (3174405)Refutation not found, incomplete strategy
% 8.83/2.13 % (3174405)------------------------------
% 8.83/2.13 % (3174405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.13 % (3174405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.13 % (3174405)CaDiCaL version: 2.1.3
% 8.83/2.13 % (3174405)Termination reason: Refutation not found, incomplete strategy
% 8.83/2.13 % (3174405)Time elapsed: 0.002 s
% 8.83/2.13 % (3174405)Peak memory usage: 88 MB
% 8.83/2.13 % (3174405)Instructions burned: 3 (million)
% 8.83/2.13 % (3174406)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3180748541:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 9.58/2.13 % (3174371)Refutation found. Thanks to Tanya!
% 9.58/2.13 % SZS status Theorem for theBenchmark
% 9.58/2.13 % SZS output start Proof for theBenchmark
% See solution above
% 9.75/2.33 % (3174371)------------------------------
% 9.75/2.33 % (3174371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.75/2.33 % (3174371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.75/2.33 % (3174371)CaDiCaL version: 2.1.3
% 9.75/2.33 % (3174371)Termination reason: Refutation
% 9.75/2.33 % (3174371)Time elapsed: 0.878 s
% 9.75/2.33 % (3174371)Peak memory usage: 133 MB
% 9.75/2.33 % (3174371)Instructions burned: 1334 (million)
% 9.75/2.33 % (3174371)------------------------------
% 9.75/2.33 % (3174371)------------------------------
% 9.75/2.33 % (3174366)Success in time 1.291 s
% 9.75/2.33 % Vampire exiting
%------------------------------------------------------------------------------