%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU176+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:47:35 PM UTC 2026
% Result : Theorem 31.79s 5.34s
% Output : Refutation 32.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 28
% Syntax : Number of formulae : 210 ( 41 unt; 7 def)
% Number of atoms : 711 ( 153 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 836 ( 335 ~; 365 |; 96 &)
% ( 18 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 10 con; 0-3 aty)
% Number of variables : 371 ( 346 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( ( X0 != empty_set
=> ( X1 = set_meet(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) )
& ( X0 = empty_set
=> ( X1 = set_meet(X0)
<=> X1 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f6,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f9,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f13,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f14,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f17,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f18,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f20,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f25,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f26,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f31,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f32,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f39,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f40,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f49,plain,
! [X0,X1] :
( ( ( X1 = set_meet(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 )
& ( ( X1 = set_meet(X0)
<=> X1 = empty_set )
| empty_set != X0 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f52,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f54,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f17]) ).
fof(f55,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f59,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f25]) ).
fof(f60,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f26]) ).
fof(f62,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f31]) ).
fof(f63,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f32]) ).
fof(f64,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f65,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f64]) ).
fof(f69,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f40]) ).
fof(f70,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f72,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f71]) ).
fof(f77,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f78,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( ( ( X1 = set_meet(X0)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 )
& ( ( ( X1 = set_meet(X0)
| empty_set != X1 )
& ( X1 = empty_set
| set_meet(X0) != X1 ) )
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f80,plain,
! [X0,X1] :
( ( ( ( X1 = set_meet(X0)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 )
& ( ( ( X1 = set_meet(X0)
| empty_set != X1 )
& ( X1 = empty_set
| set_meet(X0) != X1 ) )
| empty_set != X0 ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ( ( ( X1 = set_meet(X0)
| ( ( ( ~ in(sK0(X0,X1),sK1(X0,X1))
& in(sK1(X0,X1),X0) )
| ~ in(sK0(X0,X1),X1) )
& ( ! [X4] :
( in(sK0(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK2(X0,X5))
& in(sK2(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 )
& ( ( ( X1 = set_meet(X0)
| empty_set != X1 )
& ( X1 = empty_set
| set_meet(X0) != X1 ) )
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1)),skolemize(X6,sK2(X0,X5))],[f80]) ).
fof(f82,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,[],[f50]) ).
fof(f83,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,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f86,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK4(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK4(X0,X1),X1) )
& ( ( in(sK4(X0,X1),sK5(X0,X1))
& in(sK5(X0,X1),X0) )
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK6(X0,X5))
& in(sK6(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f86]) ).
fof(f88,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,[],[f7]) ).
fof(f89,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,[],[f88]) ).
fof(f90,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,[],[f89]) ).
fof(f91,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))],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(nnf_transformation,[],[f52]) ).
fof(f93,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ( ( ~ in(subset_complement(X0,sK8(X0,X1,X2)),X1)
| ~ in(sK8(X0,X1,X2),X2) )
& ( in(subset_complement(X0,sK8(X0,X1,X2)),X1)
| in(sK8(X0,X1,X2),X2) )
& element(sK8(X0,X1,X2),powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f94]) ).
fof(f101,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f102,plain,
( union_of_subsets(sK14,complements_of_subsets(sK14,sK15)) != subset_difference(sK14,cast_to_subset(sK14),meet_of_subsets(sK14,sK15))
& empty_set != sK15
& element(sK15,powerset(powerset(sK14))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f70]) ).
fof(f106,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
! [X0,X1,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| set_meet(X0) != X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f81]) ).
fof(f110,plain,
! [X0,X1,X5] :
( in(X5,X1)
| in(sK2(X0,X5),X0)
| set_meet(X0) != X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f81]) ).
fof(f111,plain,
! [X0,X1,X5] :
( in(X5,X1)
| ~ in(X5,sK2(X0,X5))
| set_meet(X0) != X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f81]) ).
fof(f115,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f116,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f117,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f118,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f5]) ).
fof(f119,plain,
! [X0,X1,X5] :
( in(sK6(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f87]) ).
fof(f120,plain,
! [X0,X1,X5] :
( in(X5,sK6(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f87]) ).
fof(f121,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X5,X6)
| ~ in(X6,X0)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f87]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f131,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f132,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2)
| ~ element(X4,powerset(X0))
| complements_of_subsets(X0,X1) != X2
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f137,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f138,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f139,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f140,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f142,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f58]) ).
fof(f146,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f147,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f154,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f155,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f63]) ).
fof(f156,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f161,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f163,plain,
element(sK15,powerset(powerset(sK14))),
inference(cnf_transformation,[],[f102]) ).
fof(f164,plain,
empty_set != sK15,
inference(cnf_transformation,[],[f102]) ).
fof(f165,plain,
union_of_subsets(sK14,complements_of_subsets(sK14,sK15)) != subset_difference(sK14,cast_to_subset(sK14),meet_of_subsets(sK14,sK15)),
inference(cnf_transformation,[],[f102]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f174,plain,
! [X0,X5] :
( ~ in(X5,sK2(X0,X5))
| in(X5,set_meet(X0))
| empty_set = X0 ),
inference(equality_resolution,[],[f111]) ).
fof(f175,plain,
! [X0,X5] :
( in(sK2(X0,X5),X0)
| in(X5,set_meet(X0))
| empty_set = X0 ),
inference(equality_resolution,[],[f110]) ).
fof(f176,plain,
! [X0,X7,X5] :
( ~ in(X5,set_meet(X0))
| ~ in(X7,X0)
| in(X5,X7)
| empty_set = X0 ),
inference(equality_resolution,[],[f109]) ).
fof(f181,plain,
! [X0,X6,X5] :
( in(X5,union(X0))
| ~ in(X5,X6)
| ~ in(X6,X0) ),
inference(equality_resolution,[],[f121]) ).
fof(f182,plain,
! [X0,X5] :
( in(X5,sK6(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f120]) ).
fof(f183,plain,
! [X0,X5] :
( in(sK6(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f119]) ).
fof(f184,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f127]) ).
fof(f185,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f126]) ).
fof(f186,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f125]) ).
fof(f188,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(X4,powerset(X0))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f132]) ).
fof(f189,definition,
sF16 = complements_of_subsets(sK14,sK15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f190,plain,
complements_of_subsets(sK14,sK15) = sF16,
inference(reorient_equations,[],[f189]) ).
fof(f191,definition,
sF17 = union_of_subsets(sK14,sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f192,plain,
union_of_subsets(sK14,sF16) = sF17,
inference(reorient_equations,[],[f191]) ).
fof(f193,definition,
sF18 = cast_to_subset(sK14),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f194,plain,
cast_to_subset(sK14) = sF18,
inference(reorient_equations,[],[f193]) ).
fof(f195,definition,
sF19 = meet_of_subsets(sK14,sK15),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f196,plain,
meet_of_subsets(sK14,sK15) = sF19,
inference(reorient_equations,[],[f195]) ).
fof(f197,definition,
sF20 = subset_difference(sK14,sF18,sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f198,plain,
subset_difference(sK14,sF18,sF19) = sF20,
inference(reorient_equations,[],[f197]) ).
fof(f199,plain,
sF17 != sF20,
inference(definition_folding,[],[f165,f198,f196,f194,f192,f190]) ).
fof(f200,definition,
sF21 = powerset(sK14),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f201,plain,
powerset(sK14) = sF21,
inference(reorient_equations,[],[f200]) ).
fof(f202,definition,
sF22 = powerset(sF21),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f203,plain,
powerset(sF21) = sF22,
inference(reorient_equations,[],[f202]) ).
fof(f204,plain,
element(sK15,sF22),
inference(definition_folding,[],[f163,f203,f201]) ).
fof(f205,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f188,f167]) ).
fof(f207,plain,
! [X0] : element(X0,powerset(X0)),
inference(backward_demodulation,[],[f137,f118]) ).
fof(f208,plain,
sK14 = sF18,
inference(forward_demodulation,[],[f194,f118]) ).
fof(f209,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ in(X4,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X4),X1) ),
inference(forward_subsumption_resolution,[],[f205,f142]) ).
fof(f210,plain,
sF20 = subset_difference(sK14,sK14,sF19),
inference(backward_demodulation,[],[f198,f208]) ).
fof(f212,plain,
( sK15 = complements_of_subsets(sK14,sF16)
| ~ element(sK15,powerset(powerset(sK14))) ),
inference(superposition,[],[f147,f190]) ).
fof(f213,plain,
( element(sF16,powerset(powerset(sK14)))
| ~ element(sK15,powerset(powerset(sK14))) ),
inference(superposition,[],[f142,f190]) ).
fof(f214,plain,
( element(sF16,powerset(sF21))
| ~ element(sK15,powerset(powerset(sK14))) ),
inference(forward_demodulation,[],[f213,f201]) ).
fof(f215,plain,
( ~ element(sK15,powerset(sF21))
| sK15 = complements_of_subsets(sK14,sF16) ),
inference(forward_demodulation,[],[f212,f201]) ).
fof(f216,plain,
( element(sF16,sF22)
| ~ element(sK15,powerset(powerset(sK14))) ),
inference(forward_demodulation,[],[f214,f203]) ).
fof(f217,plain,
( ~ element(sK15,sF22)
| sK15 = complements_of_subsets(sK14,sF16) ),
inference(forward_demodulation,[],[f215,f203]) ).
fof(f218,plain,
( ~ element(sK15,powerset(sF21))
| element(sF16,sF22) ),
inference(forward_demodulation,[],[f216,f201]) ).
fof(f219,plain,
sK15 = complements_of_subsets(sK14,sF16),
inference(forward_subsumption_resolution,[],[f217,f204]) ).
fof(f220,plain,
( ~ element(sK15,sF22)
| element(sF16,sF22) ),
inference(forward_demodulation,[],[f218,f203]) ).
fof(f221,plain,
element(sF16,sF22),
inference(forward_subsumption_resolution,[],[f220,f204]) ).
fof(f226,plain,
( element(sF17,powerset(sK14))
| ~ element(sF16,powerset(powerset(sK14))) ),
inference(superposition,[],[f139,f192]) ).
fof(f227,plain,
( element(sF17,sF21)
| ~ element(sF16,powerset(powerset(sK14))) ),
inference(forward_demodulation,[],[f226,f201]) ).
fof(f228,plain,
( ~ element(sF16,powerset(sF21))
| element(sF17,sF21) ),
inference(forward_demodulation,[],[f227,f201]) ).
fof(f229,plain,
( ~ element(sF16,sF22)
| element(sF17,sF21) ),
inference(forward_demodulation,[],[f228,f203]) ).
fof(f230,plain,
element(sF17,sF21),
inference(forward_subsumption_resolution,[],[f229,f221]) ).
fof(f231,plain,
( element(sF19,powerset(sK14))
| ~ element(sK15,powerset(powerset(sK14))) ),
inference(superposition,[],[f140,f196]) ).
fof(f232,plain,
( element(sF19,sF21)
| ~ element(sK15,powerset(powerset(sK14))) ),
inference(forward_demodulation,[],[f231,f201]) ).
fof(f233,plain,
( ~ element(sK15,powerset(sF21))
| element(sF19,sF21) ),
inference(forward_demodulation,[],[f232,f201]) ).
fof(f234,plain,
( ~ element(sK15,sF22)
| element(sF19,sF21) ),
inference(forward_demodulation,[],[f233,f203]) ).
fof(f235,plain,
element(sF19,sF21),
inference(forward_subsumption_resolution,[],[f234,f204]) ).
fof(f238,plain,
( sF17 = union(sF16)
| ~ element(sF16,powerset(powerset(sK14))) ),
inference(superposition,[],[f192,f154]) ).
fof(f240,plain,
( ~ element(sF16,powerset(sF21))
| sF17 = union(sF16) ),
inference(forward_demodulation,[],[f238,f201]) ).
fof(f242,plain,
( ~ element(sF16,sF22)
| sF17 = union(sF16) ),
inference(forward_demodulation,[],[f240,f203]) ).
fof(f244,plain,
sF17 = union(sF16),
inference(forward_subsumption_resolution,[],[f242,f221]) ).
fof(f260,plain,
( sF19 = set_meet(sK15)
| ~ element(sK15,powerset(powerset(sK14))) ),
inference(superposition,[],[f196,f155]) ).
fof(f262,plain,
( ~ element(sK15,powerset(sF21))
| sF19 = set_meet(sK15) ),
inference(forward_demodulation,[],[f260,f201]) ).
fof(f264,plain,
( ~ element(sK15,sF22)
| sF19 = set_meet(sK15) ),
inference(forward_demodulation,[],[f262,f203]) ).
fof(f266,plain,
sF19 = set_meet(sK15),
inference(forward_subsumption_resolution,[],[f264,f204]) ).
fof(f287,plain,
! [X0,X1] :
( set_difference(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0))
| ~ element(subset_complement(X0,X1),powerset(X0)) ),
inference(superposition,[],[f146,f131]) ).
fof(f289,plain,
! [X0,X1] :
( set_difference(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(forward_subsumption_resolution,[],[f287,f138]) ).
fof(f296,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF21))
| ~ in(X1,complements_of_subsets(sK14,X0))
| in(subset_complement(sK14,X1),X0) ),
inference(superposition,[],[f209,f201]) ).
fof(f298,plain,
! [X0,X1] :
( ~ in(X1,complements_of_subsets(sK14,X0))
| ~ element(X0,sF22)
| in(subset_complement(sK14,X1),X0) ),
inference(forward_demodulation,[],[f296,f203]) ).
fof(f301,plain,
( sF20 = set_difference(sK14,sF19)
| ~ element(sK14,powerset(sK14))
| ~ element(sF19,powerset(sK14)) ),
inference(superposition,[],[f210,f156]) ).
fof(f302,plain,
( sF20 = set_difference(sK14,sF19)
| ~ element(sF19,powerset(sK14)) ),
inference(forward_subsumption_resolution,[],[f301,f207]) ).
fof(f304,plain,
( ~ element(sF19,sF21)
| sF20 = set_difference(sK14,sF19) ),
inference(forward_demodulation,[],[f302,f201]) ).
fof(f306,plain,
sF20 = set_difference(sK14,sF19),
inference(forward_subsumption_resolution,[],[f304,f235]) ).
fof(f321,plain,
! [X0] :
( ~ in(X0,sF16)
| ~ element(sK15,sF22)
| in(subset_complement(sK14,X0),sK15) ),
inference(superposition,[],[f298,f190]) ).
fof(f322,plain,
! [X0] :
( ~ in(X0,sK15)
| ~ element(sF16,sF22)
| in(subset_complement(sK14,X0),sF16) ),
inference(superposition,[],[f298,f219]) ).
fof(f325,plain,
! [X0] :
( in(subset_complement(sK14,X0),sF16)
| ~ in(X0,sK15) ),
inference(forward_subsumption_resolution,[],[f322,f221]) ).
fof(f326,plain,
! [X0] :
( in(subset_complement(sK14,X0),sK15)
| ~ in(X0,sF16) ),
inference(forward_subsumption_resolution,[],[f321,f204]) ).
fof(f337,plain,
! [X0,X1] :
( ~ in(X0,sF19)
| ~ in(X1,sK15)
| in(X0,X1)
| empty_set = sK15 ),
inference(superposition,[],[f176,f266]) ).
fof(f338,plain,
! [X0,X1] :
( ~ in(X1,sK15)
| ~ in(X0,sF19)
| in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f337,f164]) ).
fof(f339,plain,
! [X0,X1] :
( in(X0,subset_complement(sK14,X1))
| ~ in(X0,sF19)
| ~ in(X1,sF16) ),
inference(resolution,[],[f338,f326]) ).
fof(f341,plain,
! [X0,X1] :
( in(X1,set_difference(sK14,X0))
| ~ in(X1,sF19)
| ~ in(X0,sF16)
| ~ element(X0,powerset(sK14)) ),
inference(superposition,[],[f339,f131]) ).
fof(f342,plain,
! [X0,X1] :
( in(X1,set_difference(sK14,X0))
| ~ element(X0,sF21)
| ~ in(X1,sF19)
| ~ in(X0,sF16) ),
inference(forward_demodulation,[],[f341,f201]) ).
fof(f406,plain,
! [X0] :
( ~ in(X0,sK14)
| in(X0,sF20)
| in(X0,sF19) ),
inference(superposition,[],[f184,f306]) ).
fof(f430,plain,
! [X2,X0,X1] :
( in(X1,subset_complement(X2,X0))
| ~ in(X1,X2)
| in(X1,X0)
| ~ element(X0,powerset(X2)) ),
inference(superposition,[],[f184,f289]) ).
fof(f461,plain,
! [X0,X1] :
( ~ element(X0,sF22)
| ~ in(X1,X0)
| element(X1,sF21) ),
inference(superposition,[],[f167,f203]) ).
fof(f692,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,sF21)
| ~ in(X0,sF19)
| ~ in(X1,sF16) ),
inference(resolution,[],[f186,f342]) ).
fof(f694,plain,
! [X0] :
( ~ in(X0,sF20)
| ~ in(X0,sF19) ),
inference(superposition,[],[f186,f306]) ).
fof(f1174,plain,
! [X0,X1] :
( ~ in(X1,sF16)
| ~ in(X0,X1)
| in(X0,sF17) ),
inference(superposition,[],[f181,f244]) ).
fof(f1175,plain,
! [X0,X1] :
( ~ in(X0,subset_complement(sK14,X1))
| in(X0,sF17)
| ~ in(X1,sK15) ),
inference(resolution,[],[f1174,f325]) ).
fof(f1290,plain,
! [X0] :
( ~ in(X0,sK15)
| element(X0,sF21) ),
inference(resolution,[],[f461,f204]) ).
fof(f1292,plain,
! [X0] :
( ~ in(X0,sF16)
| element(X0,sF21) ),
inference(resolution,[],[f461,f221]) ).
fof(f1423,plain,
! [X0] :
( ~ in(sK3(sF20,X0),sF19)
| subset(sF20,X0) ),
inference(resolution,[],[f694,f116]) ).
fof(f1437,plain,
! [X0] :
( ~ in(X0,sF20)
| in(X0,sK14) ),
inference(superposition,[],[f185,f306]) ).
fof(f1445,plain,
! [X0] :
( in(sK3(sF20,X0),sK14)
| subset(sF20,X0) ),
inference(resolution,[],[f1437,f116]) ).
fof(f1488,plain,
! [X0,X1] :
( ~ in(X1,sF16)
| ~ in(X0,sF19)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f692,f1292]) ).
fof(f1585,plain,
! [X0,X1] :
( ~ in(X0,sF19)
| ~ in(X0,sK6(sF16,X1))
| ~ in(X1,union(sF16)) ),
inference(resolution,[],[f1488,f183]) ).
fof(f1957,plain,
! [X0] :
( ~ element(X0,sF21)
| subset(X0,sK14) ),
inference(superposition,[],[f161,f201]) ).
fof(f2638,plain,
! [X0,X1] :
( in(X0,sF17)
| ~ in(X1,sK15)
| ~ in(X0,sK14)
| in(X0,X1)
| ~ element(X1,powerset(sK14)) ),
inference(resolution,[],[f1175,f430]) ).
fof(f2652,plain,
! [X0,X1] :
( ~ element(X1,sF21)
| in(X0,sF17)
| ~ in(X1,sK15)
| ~ in(X0,sK14)
| in(X0,X1) ),
inference(forward_demodulation,[],[f2638,f201]) ).
fof(f2653,plain,
! [X0,X1] :
( ~ in(X1,sK15)
| in(X0,sF17)
| ~ in(X0,sK14)
| in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f2652,f1290]) ).
fof(f2669,plain,
! [X0,X1] :
( in(X0,sF17)
| ~ in(X0,sK14)
| in(X0,sK2(sK15,X1))
| in(X1,set_meet(sK15))
| empty_set = sK15 ),
inference(resolution,[],[f2653,f175]) ).
fof(f2673,plain,
! [X0,X1] :
( in(X0,sF17)
| ~ in(X0,sK14)
| in(X0,sK2(sK15,X1))
| in(X1,set_meet(sK15)) ),
inference(forward_subsumption_resolution,[],[f2669,f164]) ).
fof(f2674,plain,
! [X0,X1] :
( in(X0,sK2(sK15,X1))
| in(X0,sF17)
| ~ in(X0,sK14)
| in(X1,sF19) ),
inference(forward_demodulation,[],[f2673,f266]) ).
fof(f3148,plain,
subset(sF17,sK14),
inference(resolution,[],[f1957,f230]) ).
fof(f3157,plain,
! [X0] :
( ~ in(X0,sF17)
| in(X0,sK14) ),
inference(resolution,[],[f3148,f115]) ).
fof(f3164,plain,
! [X0] :
( in(sK3(sF17,X0),sK14)
| subset(sF17,X0) ),
inference(resolution,[],[f3157,f116]) ).
fof(f3344,plain,
! [X0,X1] :
( ~ in(X0,sK6(sF16,X1))
| ~ in(X0,sF19)
| ~ in(X1,sF17) ),
inference(forward_demodulation,[],[f1585,f244]) ).
fof(f3479,plain,
! [X0] :
( in(X0,sF17)
| ~ in(X0,sK14)
| in(X0,sF19)
| in(X0,set_meet(sK15))
| empty_set = sK15 ),
inference(resolution,[],[f2674,f174]) ).
fof(f3490,plain,
! [X0] :
( in(X0,sF17)
| ~ in(X0,sK14)
| in(X0,sF19)
| in(X0,set_meet(sK15)) ),
inference(forward_subsumption_resolution,[],[f3479,f164]) ).
fof(f3491,plain,
! [X0] :
( in(X0,sF19)
| in(X0,sF17)
| ~ in(X0,sK14)
| in(X0,sF19) ),
inference(forward_demodulation,[],[f3490,f266]) ).
fof(f3492,plain,
! [X0] :
( ~ in(X0,sK14)
| in(X0,sF17)
| in(X0,sF19) ),
inference(duplicate_literal_removal,[],[f3491]) ).
fof(f3577,plain,
! [X0] :
( subset(sF20,X0)
| in(sK3(sF20,X0),sF17)
| in(sK3(sF20,X0),sF19) ),
inference(resolution,[],[f1445,f3492]) ).
fof(f3583,plain,
! [X0] :
( in(sK3(sF20,X0),sF17)
| subset(sF20,X0) ),
inference(forward_subsumption_resolution,[],[f3577,f1423]) ).
fof(f3585,plain,
( subset(sF20,sF17)
| subset(sF20,sF17) ),
inference(resolution,[],[f3583,f117]) ).
fof(f3591,plain,
subset(sF20,sF17),
inference(duplicate_literal_removal,[],[f3585]) ).
fof(f3593,plain,
~ subset(sF17,sF20),
inference(unit_resulting_resolution,[],[f106,f199,f3591]) ).
fof(f3650,plain,
in(sK3(sF17,sF20),sK14),
inference(unit_resulting_resolution,[],[f3164,f3593]) ).
fof(f3652,plain,
~ in(sK3(sF17,sF20),sF20),
inference(unit_resulting_resolution,[],[f117,f3593]) ).
fof(f3653,plain,
in(sK3(sF17,sF20),sF17),
inference(unit_resulting_resolution,[],[f116,f3593]) ).
fof(f3697,plain,
in(sK3(sF17,sF20),sF19),
inference(unit_resulting_resolution,[],[f406,f3652,f3650]) ).
fof(f3781,plain,
! [X0] :
( ~ in(X0,sF19)
| ~ in(X0,sF17)
| ~ in(X0,union(sF16)) ),
inference(resolution,[],[f3344,f182]) ).
fof(f3788,plain,
! [X0] :
( ~ in(X0,sF17)
| ~ in(X0,sF19)
| ~ in(X0,sF17) ),
inference(forward_demodulation,[],[f3781,f244]) ).
fof(f3789,plain,
! [X0] :
( ~ in(X0,sF19)
| ~ in(X0,sF17) ),
inference(duplicate_literal_removal,[],[f3788]) ).
fof(f3792,plain,
$false,
inference(unit_resulting_resolution,[],[f3789,f3653,f3697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU176+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:52:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.80/3.04 % (787072)Detected formulas, will run a generic FOF schedule.
% 15.80/3.04 % (787079)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=2979416820:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 15.80/3.04 % (787078)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=3569933514:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 15.80/3.04 % (787077)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=3214497254:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 15.80/3.04 % (787083)dis-21_1_sil=8000:lcm=predicate:random_seed=3534081329: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)
% 15.80/3.04 % (787082)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1816721199:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 15.80/3.04 % (787081)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2184032211:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 15.80/3.04 % (787080)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2534213451:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 15.80/3.04 % (787080)Refutation not found, incomplete strategy
% 15.80/3.04 % (787080)------------------------------
% 15.80/3.04 % (787080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.04 % (787080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.04 % (787080)CaDiCaL version: 2.1.3
% 15.80/3.04 % (787080)Termination reason: Refutation not found, incomplete strategy
% 15.80/3.04 % (787080)Time elapsed: 0.002 s
% 15.80/3.04 % (787080)Peak memory usage: 88 MB
% 15.80/3.04 % (787080)Instructions burned: 2 (million)
% 15.80/3.04 % (787081)Instruction limit reached!
% 15.80/3.04 % (787081)------------------------------
% 15.80/3.04 % (787081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.04 % (787081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.04 % (787081)CaDiCaL version: 2.1.3
% 15.80/3.04 % (787081)Termination reason: Instruction limit
% 15.80/3.04 % (787081)Termination phase: Saturation
% 15.80/3.04 % (787081)Time elapsed: 0.074 s
% 15.80/3.04 % (787081)Peak memory usage: 88 MB
% 15.80/3.04 % (787081)Instructions burned: 119 (million)
% 15.80/3.04 % (787083)Instruction limit reached!
% 15.80/3.04 % (787083)------------------------------
% 15.80/3.04 % (787083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.04 % (787083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.04 % (787083)CaDiCaL version: 2.1.3
% 15.80/3.04 % (787083)Termination reason: Instruction limit
% 15.80/3.04 % (787083)Termination phase: Saturation
% 15.80/3.04 % (787083)Time elapsed: 0.076 s
% 15.80/3.04 % (787083)Peak memory usage: 90 MB
% 15.80/3.04 % (787083)Instructions burned: 130 (million)
% 15.80/3.04 % (787082)Instruction limit reached!
% 15.80/3.04 % (787082)------------------------------
% 15.80/3.04 % (787082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.04 % (787082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.04 % (787082)CaDiCaL version: 2.1.3
% 15.80/3.04 % (787082)Termination reason: Instruction limit
% 15.80/3.04 % (787082)Termination phase: Saturation
% 15.80/3.04 % (787082)Time elapsed: 0.096 s
% 15.80/3.04 % (787082)Peak memory usage: 89 MB
% 15.80/3.04 % (787082)Instructions burned: 140 (million)
% 15.80/3.04 % (787091)lrs+10_1_sil=8000:sp=occurrence:random_seed=332244223:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 15.80/3.04 % (787092)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1304006543:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 15.80/3.04 % (787093)lrs+1011_1_sil=32000:sp=occurrence:random_seed=431874211:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 15.80/3.04 % (787080)------------------------------
% 15.80/3.04 % (787080)------------------------------
% 15.80/3.04 % (787092)Instruction limit reached!
% 15.80/3.04 % (787092)------------------------------
% 15.80/3.04 % (787092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.04 % (787092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.30/3.98 % (787092)CaDiCaL version: 2.1.3
% 21.30/3.98 % (787092)Termination reason: Instruction limit
% 21.30/3.98 % (787092)Termination phase: Saturation
% 21.30/3.98 % (787092)Time elapsed: 0.078 s
% 21.30/3.98 % (787092)Peak memory usage: 91 MB
% 21.30/3.98 % (787092)Instructions burned: 158 (million)
% 21.30/3.98 % (787097)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=3067558189:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 21.30/3.98 % (787091)Instruction limit reached!
% 21.30/3.98 % (787091)------------------------------
% 21.30/3.98 % (787091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.30/3.98 % (787091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.30/3.98 % (787091)CaDiCaL version: 2.1.3
% 21.30/3.98 % (787091)Termination reason: Instruction limit
% 21.30/3.98 % (787091)Termination phase: Saturation
% 21.30/3.98 % (787091)Time elapsed: 0.178 s
% 21.30/3.98 % (787091)Peak memory usage: 91 MB
% 21.30/3.98 % (787091)Instructions burned: 286 (million)
% 21.30/3.98 % (787098)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3859339906:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 21.30/3.98 % (787093)Instruction limit reached!
% 21.30/3.98 % (787093)------------------------------
% 21.30/3.98 % (787093)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.30/3.98 % (787093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.30/3.98 % (787093)CaDiCaL version: 2.1.3
% 21.30/3.98 % (787093)Termination reason: Instruction limit
% 21.30/3.98 % (787093)Termination phase: Saturation
% 21.30/3.98 % (787093)Time elapsed: 0.221 s
% 21.30/3.98 % (787093)Peak memory usage: 91 MB
% 21.30/3.98 % (787093)Instructions burned: 325 (million)
% 21.30/3.98 % (787100)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2248925091:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 21.30/3.98 % (787097)Instruction limit reached!
% 21.30/3.98 % (787097)------------------------------
% 21.30/3.98 % (787097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.30/3.98 % (787097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.30/3.98 % (787097)CaDiCaL version: 2.1.3
% 21.30/3.98 % (787097)Termination reason: Instruction limit
% 21.30/3.98 % (787097)Termination phase: Saturation
% 21.30/3.98 % (787097)Time elapsed: 0.142 s
% 21.30/3.98 % (787097)Peak memory usage: 92 MB
% 21.30/3.98 % (787097)Instructions burned: 248 (million)
% 21.30/3.98 % (787102)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4120705498:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 21.30/3.98 % (787098)Instruction limit reached!
% 21.30/3.98 % (787098)------------------------------
% 21.30/3.98 % (787098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.30/3.98 % (787098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.30/3.98 % (787098)CaDiCaL version: 2.1.3
% 21.30/3.98 % (787098)Termination reason: Instruction limit
% 21.30/3.98 % (787098)Termination phase: Saturation
% 21.30/3.98 % (787098)Time elapsed: 0.184 s
% 21.30/3.98 % (787098)Peak memory usage: 90 MB
% 21.30/3.98 % (787098)Instructions burned: 295 (million)
% 21.30/3.98 % (787104)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=554624927:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 21.30/3.98 % (787102)Instruction limit reached!
% 21.30/3.98 % (787102)------------------------------
% 21.30/3.98 % (787102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.30/3.98 % (787102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.30/3.98 % (787102)CaDiCaL version: 2.1.3
% 21.30/3.98 % (787102)Termination reason: Instruction limit
% 21.30/3.98 % (787102)Termination phase: Saturation
% 21.30/3.98 % (787102)Time elapsed: 0.078 s
% 21.30/3.98 % (787102)Peak memory usage: 89 MB
% 21.30/3.98 % (787102)Instructions burned: 114 (million)
% 21.30/3.98 % (787104)Instruction limit reached!
% 21.30/3.98 % (787104)------------------------------
% 21.30/3.98 % (787104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.30/3.98 % (787104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.30/3.98 % (787104)CaDiCaL version: 2.1.3
% 21.30/3.98 % (787104)Termination reason: Instruction limit
% 21.30/3.98 % (787104)Termination phase: Saturation
% 21.30/3.98 % (787104)Time elapsed: 0.065 s
% 31.79/5.34 % (787104)Peak memory usage: 89 MB
% 31.79/5.34 % (787104)Instructions burned: 128 (million)
% 31.79/5.34 % (787106)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=450481994:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 31.79/5.34 % (787108)lrs+10_1_sil=8000:sp=occurrence:random_seed=3643003452:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 31.79/5.34 % (787106)Instruction limit reached!
% 31.79/5.34 % (787106)------------------------------
% 31.79/5.34 % (787106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787106)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787106)Termination reason: Instruction limit
% 31.79/5.34 % (787106)Termination phase: Saturation
% 31.79/5.34 % (787106)Time elapsed: 0.064 s
% 31.79/5.34 % (787106)Peak memory usage: 89 MB
% 31.79/5.34 % (787106)Instructions burned: 115 (million)
% 31.79/5.34 % (787109)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1022851727:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 31.79/5.34 % (787112)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=205601898:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 31.79/5.34 % (787109)Instruction limit reached!
% 31.79/5.34 % (787109)------------------------------
% 31.79/5.34 % (787109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787109)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787109)Termination reason: Instruction limit
% 31.79/5.34 % (787109)Termination phase: Saturation
% 31.79/5.34 % (787109)Time elapsed: 0.265 s
% 31.79/5.34 % (787109)Peak memory usage: 90 MB
% 31.79/5.34 % (787109)Instructions burned: 438 (million)
% 31.79/5.34 % (787115)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=711260548:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 31.79/5.34 % (787115)Instruction limit reached!
% 31.79/5.34 % (787115)------------------------------
% 31.79/5.34 % (787115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787115)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787115)Termination reason: Instruction limit
% 31.79/5.34 % (787115)Termination phase: Saturation
% 31.79/5.34 % (787115)Time elapsed: 0.074 s
% 31.79/5.34 % (787115)Peak memory usage: 90 MB
% 31.79/5.34 % (787115)Instructions burned: 136 (million)
% 31.79/5.34 % (787108)Instruction limit reached!
% 31.79/5.34 % (787108)------------------------------
% 31.79/5.34 % (787108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787108)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787108)Termination reason: Instruction limit
% 31.79/5.34 % (787108)Termination phase: Saturation
% 31.79/5.34 % (787108)Time elapsed: 0.536 s
% 31.79/5.34 % (787108)Peak memory usage: 97 MB
% 31.79/5.34 % (787108)Instructions burned: 907 (million)
% 31.79/5.34 % (787117)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3487261581:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 31.79/5.34 % (787118)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3861083036:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 31.79/5.34 % (787117)Instruction limit reached!
% 31.79/5.34 % (787117)------------------------------
% 31.79/5.34 % (787117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787117)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787117)Termination reason: Instruction limit
% 31.79/5.34 % (787117)Termination phase: Saturation
% 31.79/5.34 % (787117)Time elapsed: 0.388 s
% 31.79/5.34 % (787117)Peak memory usage: 96 MB
% 31.79/5.34 % (787117)Instructions burned: 593 (million)
% 31.79/5.34 % (787121)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=3815411232:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/125Mi)
% 31.79/5.34 % (787121)Instruction limit reached!
% 31.79/5.34 % (787121)------------------------------
% 31.79/5.34 % (787121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787121)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787121)Termination reason: Instruction limit
% 31.79/5.34 % (787121)Termination phase: Saturation
% 31.79/5.34 % (787121)Time elapsed: 0.076 s
% 31.79/5.34 % (787121)Peak memory usage: 90 MB
% 31.79/5.34 % (787121)Instructions burned: 126 (million)
% 31.79/5.34 % (787100)Instruction limit reached!
% 31.79/5.34 % (787100)------------------------------
% 31.79/5.34 % (787100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787100)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787100)Termination reason: Instruction limit
% 31.79/5.34 % (787100)Termination phase: Saturation
% 31.79/5.34 % (787100)Time elapsed: 1.531 s
% 31.79/5.34 % (787100)Peak memory usage: 142 MB
% 31.79/5.34 % (787100)Instructions burned: 2351 (million)
% 31.79/5.34 % (787123)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2090511328:i=134:gtgl=5:slsql=off:gtg=exists_sym_2978 on theBenchmark for (2978ds/134Mi)
% 31.79/5.34 % (787124)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3975614761:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2977 on theBenchmark for (2977ds/141Mi)
% 31.79/5.34 % (787123)Instruction limit reached!
% 31.79/5.34 % (787123)------------------------------
% 31.79/5.34 % (787123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787123)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787123)Termination reason: Instruction limit
% 31.79/5.34 % (787123)Termination phase: Saturation
% 31.79/5.34 % (787123)Time elapsed: 0.091 s
% 31.79/5.34 % (787123)Peak memory usage: 90 MB
% 31.79/5.34 % (787123)Instructions burned: 135 (million)
% 31.79/5.34 % (787124)Instruction limit reached!
% 31.79/5.34 % (787124)------------------------------
% 31.79/5.34 % (787124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787124)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787124)Termination reason: Instruction limit
% 31.79/5.34 % (787124)Termination phase: Saturation
% 31.79/5.34 % (787124)Time elapsed: 0.074 s
% 31.79/5.34 % (787124)Peak memory usage: 91 MB
% 31.79/5.34 % (787124)Instructions burned: 141 (million)
% 31.79/5.34 % (787127)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1690217385:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2976 on theBenchmark for (2976ds/431Mi)
% 31.79/5.34 % (787128)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=150242541:i=6060:aac=none:ins=25_2975 on theBenchmark for (2975ds/6060Mi)
% 31.79/5.34 % (787127)Instruction limit reached!
% 31.79/5.34 % (787127)------------------------------
% 31.79/5.34 % (787127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787127)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787127)Termination reason: Instruction limit
% 31.79/5.34 % (787127)Termination phase: Saturation
% 31.79/5.34 % (787127)Time elapsed: 0.256 s
% 31.79/5.34 % (787127)Peak memory usage: 91 MB
% 31.79/5.34 % (787127)Instructions burned: 431 (million)
% 31.79/5.34 % (787131)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=2240142274:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2972 on theBenchmark for (2972ds/150Mi)
% 31.79/5.34 % (787131)Instruction limit reached!
% 31.79/5.34 % (787131)------------------------------
% 31.79/5.34 % (787131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787131)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787131)Termination reason: Instruction limit
% 31.79/5.34 % (787131)Termination phase: Saturation
% 31.79/5.34 % (787131)Time elapsed: 0.094 s
% 31.79/5.34 % (787131)Peak memory usage: 91 MB
% 31.79/5.34 % (787131)Instructions burned: 151 (million)
% 31.79/5.34 % (787133)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=2606501690:i=14155:bd=all_2969 on theBenchmark for (2969ds/14155Mi)
% 31.79/5.34 % (787133)First to succeed.
% 31.79/5.34 % (787133)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-787072"
% 31.79/5.34 % (787112)Instruction limit reached!
% 31.79/5.34 % (787112)------------------------------
% 31.79/5.34 % (787112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.79/5.34 % (787112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.79/5.34 % (787112)CaDiCaL version: 2.1.3
% 31.79/5.34 % (787112)Termination reason: Instruction limit
% 31.79/5.34 % (787112)Termination phase: Saturation
% 31.79/5.34 % (787112)Time elapsed: 3.280 s
% 31.79/5.34 % (787112)Peak memory usage: 164 MB
% 31.79/5.34 % (787112)Instructions burned: 5204 (million)
% 31.79/5.34 % (787133)Refutation found. Thanks to Tanya!
% 31.79/5.34 % SZS status Theorem for theBenchmark
% 31.79/5.34 % SZS output start Proof for theBenchmark
% See solution above
% 32.33/5.54 % (787133)------------------------------
% 32.33/5.54 % (787133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.33/5.54 % (787133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.33/5.54 % (787133)CaDiCaL version: 2.1.3
% 32.33/5.54 % (787133)Termination reason: Refutation
% 32.33/5.54 % (787133)Time elapsed: 1.083 s
% 32.33/5.54 % (787133)Peak memory usage: 135 MB
% 32.33/5.54 % (787133)Instructions burned: 1618 (million)
% 32.33/5.54 % (787133)------------------------------
% 32.33/5.54 % (787133)------------------------------
% 32.33/5.54 % (787072)Success in time 4.48 s
% 32.33/5.54 % Vampire exiting
%------------------------------------------------------------------------------