%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU343+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 : n018.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 12:48:26 PM UTC 2026
% Result : Theorem 5.13s 1.62s
% Output : Refutation 6.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 202 ( 52 unt; 13 def)
% Number of atoms : 589 ( 159 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 670 ( 283 ~; 298 |; 57 &)
% ( 11 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 8 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-6 aty)
% Number of variables : 239 ( 0 sgn 230 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] :
( ( strict_latt_str(X1)
& latt_str(X1) )
=> ( X1 = boole_lattice(X0)
<=> ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( element(X2,powerset(X0))
=> ! [X3] :
( element(X3,powerset(X0))
=> ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice3) ).
fof(f11,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& join_semilatt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
fof(f12,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& meet_semilatt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattices) ).
fof(f17,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f33,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f34,axiom,
! [X0] :
( latt_str(X0)
=> ( meet_semilatt_str(X0)
& join_semilatt_str(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f38,axiom,
! [X0] :
( meet_semilatt_str(X0)
=> ( function(the_L_meet(X0))
& quasi_total(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& relation_of2_as_subset(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(f40,axiom,
! [X0] :
( join_semilatt_str(X0)
=> ( function(the_L_join(X0))
& quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(f48,axiom,
! [X0] :
( ~ empty_carrier(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(f49,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f71,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ~ empty(X0)
& ~ empty(X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X0,X1),X2)
& relation_of2(X3,cartesian_product2(X0,X1),X2)
& element(X4,X0)
& element(X5,X1) )
=> apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(f72,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_union2(X0,X1,X2) = set_union2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(f73,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f74,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f77,conjecture,
! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( join(boole_lattice(X0),X1,X2) = set_union2(X1,X2)
& meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
fof(f78,negated_conjecture,
~ ! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( join(boole_lattice(X0),X1,X2) = set_union2(X1,X2)
& meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f102,plain,
! [X0,X1] :
( ( X1 = boole_lattice(X0)
<=> ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f103,plain,
! [X0,X1] :
( ( X1 = boole_lattice(X0)
<=> ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ join_semilatt_str(X0) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ meet_semilatt_str(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ meet_semilatt_str(X0) ),
inference(flattening,[],[f106]) ).
fof(f121,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f122,plain,
! [X0] :
( ( meet_semilatt_str(X0)
& join_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f124,plain,
! [X0] :
( ( function(the_L_meet(X0))
& quasi_total(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& relation_of2_as_subset(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0)) )
| ~ meet_semilatt_str(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f125,plain,
! [X0] :
( ( function(the_L_join(X0))
& quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0)) )
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f126,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f127,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f126]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| empty(X0)
| empty(X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ element(X4,X0)
| ~ element(X5,X1) ),
inference(ennf_transformation,[],[f71]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| empty(X0)
| empty(X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ element(X4,X0)
| ~ element(X5,X1) ),
inference(flattening,[],[f143]) ).
fof(f145,plain,
! [X0,X1,X2] :
( subset_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f72]) ).
fof(f146,plain,
! [X0,X1,X2] :
( subset_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f148,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f147]) ).
fof(f149,plain,
? [X0,X1] :
( ? [X2] :
( ( set_union2(X1,X2) != join(boole_lattice(X0),X1,X2)
| set_intersection2(X1,X2) != meet(boole_lattice(X0),X1,X2) )
& element(X2,the_carrier(boole_lattice(X0))) )
& element(X1,the_carrier(boole_lattice(X0))) ),
inference(ennf_transformation,[],[f78]) ).
fof(f160,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3)
| apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(nnf_transformation,[],[f103]) ).
fof(f161,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3)
| apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(flattening,[],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3)
| apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X4] :
( ! [X5] :
( ( apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5)
& apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5) )
| ~ element(X5,powerset(X0)) )
| ~ element(X4,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(rectify,[],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ( ( apply_binary(the_L_join(X1),sK0(X0,X1),sK1(X0,X1)) != subset_union2(X0,sK0(X0,X1),sK1(X0,X1))
| apply_binary(the_L_meet(X1),sK0(X0,X1),sK1(X0,X1)) != subset_intersection2(X0,sK0(X0,X1),sK1(X0,X1)) )
& element(sK1(X0,X1),powerset(X0))
& element(sK0(X0,X1),powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X4] :
( ! [X5] :
( ( apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5)
& apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5) )
| ~ element(X5,powerset(X0)) )
| ~ element(X4,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f162]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f180,plain,
( ( set_union2(sK18,sK19) != join(boole_lattice(sK17),sK18,sK19)
| set_intersection2(sK18,sK19) != meet(boole_lattice(sK17),sK18,sK19) )
& element(sK19,the_carrier(boole_lattice(sK17)))
& element(sK18,the_carrier(boole_lattice(sK17))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f149]) ).
fof(f190,plain,
! [X0,X1,X4,X5] :
( apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| boole_lattice(X0) != X1
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f191,plain,
! [X0,X1,X4,X5] :
( apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| boole_lattice(X0) != X1
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f192,plain,
! [X0,X1] :
( powerset(X0) = the_carrier(X1)
| boole_lattice(X0) != X1
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f197,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f201,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f209,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f210,plain,
! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f211,plain,
! [X0] :
( ~ latt_str(X0)
| meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f213,plain,
! [X0] :
( relation_of2_as_subset(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f214,plain,
! [X0] :
( quasi_total(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f215,plain,
! [X0] :
( function(the_L_meet(X0))
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f216,plain,
! [X0] :
( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f217,plain,
! [X0] :
( quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f218,plain,
! [X0] :
( function(the_L_join(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f226,plain,
! [X0] : strict_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f227,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f228,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f260,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| empty(X0)
| empty(X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X4,X0)
| ~ element(X5,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f261,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_union2(X0,X1,X2) = set_union2(X1,X2) ),
inference(cnf_transformation,[],[f146]) ).
fof(f262,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(cnf_transformation,[],[f148]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
fof(f267,plain,
element(sK18,the_carrier(boole_lattice(sK17))),
inference(cnf_transformation,[],[f180]) ).
fof(f268,plain,
element(sK19,the_carrier(boole_lattice(sK17))),
inference(cnf_transformation,[],[f180]) ).
fof(f269,plain,
( set_union2(sK18,sK19) != join(boole_lattice(sK17),sK18,sK19)
| set_intersection2(sK18,sK19) != meet(boole_lattice(sK17),sK18,sK19) ),
inference(cnf_transformation,[],[f180]) ).
fof(f280,plain,
! [X0] :
( powerset(X0) = the_carrier(boole_lattice(X0))
| ~ strict_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f192]) ).
fof(f281,plain,
! [X0,X4,X5] :
( subset_union2(X0,X4,X5) = apply_binary(the_L_join(boole_lattice(X0)),X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| ~ strict_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f191]) ).
fof(f282,plain,
! [X0,X4,X5] :
( subset_intersection2(X0,X4,X5) = apply_binary(the_L_meet(boole_lattice(X0)),X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| ~ strict_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f190]) ).
fof(f283,definition,
sF20 = set_union2(sK18,sK19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f284,plain,
set_union2(sK18,sK19) = sF20,
inference(reorient_equations,[],[f283]) ).
fof(f285,definition,
sF21 = boole_lattice(sK17),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f286,plain,
boole_lattice(sK17) = sF21,
inference(reorient_equations,[],[f285]) ).
fof(f287,definition,
sF22 = join(sF21,sK18,sK19),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f288,plain,
join(sF21,sK18,sK19) = sF22,
inference(reorient_equations,[],[f287]) ).
fof(f289,definition,
sF23 = set_intersection2(sK18,sK19),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f290,plain,
set_intersection2(sK18,sK19) = sF23,
inference(reorient_equations,[],[f289]) ).
fof(f291,definition,
sF24 = meet(sF21,sK18,sK19),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f292,plain,
meet(sF21,sK18,sK19) = sF24,
inference(reorient_equations,[],[f291]) ).
fof(f293,plain,
( sF20 != sF22
| sF23 != sF24 ),
inference(definition_folding,[],[f269,f292,f286,f290,f288,f286,f284]) ).
fof(f294,definition,
sF25 = the_carrier(sF21),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f295,plain,
the_carrier(sF21) = sF25,
inference(reorient_equations,[],[f294]) ).
fof(f296,plain,
element(sK19,sF25),
inference(definition_folding,[],[f268,f295,f286]) ).
fof(f297,plain,
element(sK18,sF25),
inference(definition_folding,[],[f267,f295,f286]) ).
fof(f299,definition,
( spl26_1
<=> sF23 = sF24 ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f301,plain,
( sF23 != sF24
| spl26_1 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f303,definition,
( spl26_2
<=> sF20 = sF22 ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f305,plain,
( sF20 != sF22
| spl26_2 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f306,plain,
( ~ spl26_1
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f293,f303,f299]) ).
fof(f307,plain,
! [X0,X4,X5] :
( subset_intersection2(X0,X4,X5) = apply_binary(the_L_meet(boole_lattice(X0)),X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f282,f226]) ).
fof(f308,plain,
! [X0,X4,X5] :
( subset_union2(X0,X4,X5) = apply_binary(the_L_join(boole_lattice(X0)),X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f281,f226]) ).
fof(f309,plain,
! [X0] :
( powerset(X0) = the_carrier(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f280,f226]) ).
fof(f310,plain,
! [X0,X4,X5] :
( ~ element(X5,powerset(X0))
| subset_intersection2(X0,X4,X5) = apply_binary(the_L_meet(boole_lattice(X0)),X4,X5)
| ~ element(X4,powerset(X0)) ),
inference(forward_subsumption_resolution,[],[f307,f201]) ).
fof(f311,plain,
! [X0,X4,X5] :
( ~ element(X5,powerset(X0))
| subset_union2(X0,X4,X5) = apply_binary(the_L_join(boole_lattice(X0)),X4,X5)
| ~ element(X4,powerset(X0)) ),
inference(forward_subsumption_resolution,[],[f308,f201]) ).
fof(f312,plain,
! [X0] : powerset(X0) = the_carrier(boole_lattice(X0)),
inference(forward_subsumption_resolution,[],[f309,f201]) ).
fof(f313,plain,
latt_str(sF21),
inference(superposition,[],[f201,f286]) ).
fof(f315,plain,
the_carrier(sF21) = powerset(sK17),
inference(superposition,[],[f312,f286]) ).
fof(f316,plain,
sF25 = powerset(sK17),
inference(forward_demodulation,[],[f315,f295]) ).
fof(f317,plain,
~ empty_carrier(sF21),
inference(superposition,[],[f227,f286]) ).
fof(f319,plain,
join_semilatt_str(sF21),
inference(resolution,[],[f210,f313]) ).
fof(f321,plain,
meet_semilatt_str(sF21),
inference(resolution,[],[f211,f313]) ).
fof(f322,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| join(sF21,X1,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X1,X0)
| ~ element(X1,sF25)
| empty_carrier(sF21)
| ~ join_semilatt_str(sF21) ),
inference(superposition,[],[f196,f295]) ).
fof(f325,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| join(sF21,X1,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X1,X0)
| ~ element(X1,sF25)
| ~ join_semilatt_str(sF21) ),
inference(forward_subsumption_resolution,[],[f322,f317]) ).
fof(f327,plain,
! [X0,X1] :
( ~ element(X1,sF25)
| join(sF21,X1,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X1,X0)
| ~ element(X0,sF25) ),
inference(forward_subsumption_resolution,[],[f325,f319]) ).
fof(f328,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| meet(sF21,X1,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X1,X0)
| ~ element(X1,sF25)
| empty_carrier(sF21)
| ~ meet_semilatt_str(sF21) ),
inference(superposition,[],[f197,f295]) ).
fof(f331,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| meet(sF21,X1,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X1,X0)
| ~ element(X1,sF25)
| ~ meet_semilatt_str(sF21) ),
inference(forward_subsumption_resolution,[],[f328,f317]) ).
fof(f333,plain,
! [X0,X1] :
( ~ element(X1,sF25)
| meet(sF21,X1,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X1,X0)
| ~ element(X0,sF25) ),
inference(forward_subsumption_resolution,[],[f331,f321]) ).
fof(f376,plain,
one_sorted_str(sF21),
inference(resolution,[],[f319,f209]) ).
fof(f378,plain,
! [X0] :
( relation_of2(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(resolution,[],[f216,f263]) ).
fof(f383,plain,
! [X0] :
( relation_of2(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ meet_semilatt_str(X0) ),
inference(resolution,[],[f213,f263]) ).
fof(f388,plain,
! [X0] :
( ~ element(X0,sF25)
| meet(sF21,sK18,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),sK18,X0) ),
inference(resolution,[],[f333,f297]) ).
fof(f393,plain,
meet(sF21,sK18,sK19) = apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),sK18,sK19),
inference(resolution,[],[f388,f296]) ).
fof(f396,plain,
sF24 = apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),sK18,sK19),
inference(forward_demodulation,[],[f393,f292]) ).
fof(f401,plain,
! [X0] :
( ~ element(X0,sF25)
| join(sF21,sK18,X0) = apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),sK18,X0) ),
inference(resolution,[],[f327,f297]) ).
fof(f406,plain,
join(sF21,sK18,sK19) = apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),sK18,sK19),
inference(resolution,[],[f401,f296]) ).
fof(f409,plain,
sF22 = apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),sK18,sK19),
inference(forward_demodulation,[],[f406,f288]) ).
fof(f414,plain,
! [X0,X1] :
( ~ element(X1,sF25)
| ~ element(X0,sF25)
| set_intersection2(X1,X0) = subset_intersection2(sK17,X1,X0) ),
inference(superposition,[],[f262,f316]) ).
fof(f415,plain,
! [X0] :
( ~ element(X0,sF25)
| set_intersection2(sK18,X0) = subset_intersection2(sK17,sK18,X0) ),
inference(resolution,[],[f414,f297]) ).
fof(f420,plain,
set_intersection2(sK18,sK19) = subset_intersection2(sK17,sK18,sK19),
inference(resolution,[],[f415,f296]) ).
fof(f423,plain,
sF23 = subset_intersection2(sK17,sK18,sK19),
inference(forward_demodulation,[],[f420,f290]) ).
fof(f447,definition,
( spl26_3
<=> empty(sF25) ),
introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition]) ).
fof(f448,plain,
( ~ empty(sF25)
| spl26_3 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f449,plain,
( empty(sF25)
| ~ spl26_3 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f484,plain,
( relation_of2(the_L_join(sF21),cartesian_product2(sF25,sF25),sF25)
| ~ join_semilatt_str(sF21) ),
inference(superposition,[],[f378,f295]) ).
fof(f487,plain,
relation_of2(the_L_join(sF21),cartesian_product2(sF25,sF25),sF25),
inference(forward_subsumption_resolution,[],[f484,f319]) ).
fof(f489,plain,
( relation_of2(the_L_meet(sF21),cartesian_product2(sF25,sF25),sF25)
| ~ meet_semilatt_str(sF21) ),
inference(superposition,[],[f383,f295]) ).
fof(f492,plain,
relation_of2(the_L_meet(sF21),cartesian_product2(sF25,sF25),sF25),
inference(forward_subsumption_resolution,[],[f489,f321]) ).
fof(f493,plain,
( quasi_total(the_L_join(sF21),cartesian_product2(sF25,sF25),sF25)
| ~ join_semilatt_str(sF21) ),
inference(superposition,[],[f217,f295]) ).
fof(f496,plain,
quasi_total(the_L_join(sF21),cartesian_product2(sF25,sF25),sF25),
inference(forward_subsumption_resolution,[],[f493,f319]) ).
fof(f500,plain,
( quasi_total(the_L_meet(sF21),cartesian_product2(sF25,sF25),sF25)
| ~ meet_semilatt_str(sF21) ),
inference(superposition,[],[f214,f295]) ).
fof(f503,plain,
quasi_total(the_L_meet(sF21),cartesian_product2(sF25,sF25),sF25),
inference(forward_subsumption_resolution,[],[f500,f321]) ).
fof(f504,plain,
( ~ empty(sF25)
| empty_carrier(sF21)
| ~ one_sorted_str(sF21) ),
inference(superposition,[],[f228,f295]) ).
fof(f506,plain,
( empty_carrier(sF21)
| ~ one_sorted_str(sF21)
| ~ spl26_3 ),
inference(forward_subsumption_resolution,[],[f504,f449]) ).
fof(f507,plain,
( ~ one_sorted_str(sF21)
| ~ spl26_3 ),
inference(forward_subsumption_resolution,[],[f506,f317]) ).
fof(f508,plain,
( $false
| ~ spl26_3 ),
inference(forward_subsumption_resolution,[],[f507,f376]) ).
fof(f509,plain,
~ spl26_3,
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f518,plain,
! [X0,X1] :
( empty(sF25)
| empty(sF25)
| ~ function(the_L_meet(sF21))
| ~ quasi_total(the_L_meet(sF21),cartesian_product2(sF25,sF25),sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X0,X1) = apply_binary(the_L_meet(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) ),
inference(resolution,[],[f492,f260]) ).
fof(f520,plain,
! [X0,X1] :
( empty(sF25)
| ~ function(the_L_meet(sF21))
| ~ quasi_total(the_L_meet(sF21),cartesian_product2(sF25,sF25),sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X0,X1) = apply_binary(the_L_meet(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) ),
inference(duplicate_literal_removal,[],[f518]) ).
fof(f521,plain,
( ! [X0,X1] :
( ~ function(the_L_meet(sF21))
| ~ quasi_total(the_L_meet(sF21),cartesian_product2(sF25,sF25),sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X0,X1) = apply_binary(the_L_meet(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) )
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f520,f448]) ).
fof(f522,plain,
( ! [X0,X1] :
( ~ function(the_L_meet(sF21))
| apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X0,X1) = apply_binary(the_L_meet(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) )
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f521,f503]) ).
fof(f524,definition,
( spl26_8
<=> ! [X0,X1] :
( apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X0,X1) = apply_binary(the_L_meet(sF21),X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) ) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
fof(f525,plain,
( ! [X0,X1] :
( ~ element(X1,sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X0,X1) = apply_binary(the_L_meet(sF21),X0,X1)
| ~ element(X0,sF25) )
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f527,definition,
( spl26_9
<=> function(the_L_meet(sF21)) ),
introduced(definition,[new_symbols(definition,[spl26_9])],[avatar_definition]) ).
fof(f529,plain,
( ~ function(the_L_meet(sF21))
| spl26_9 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f530,plain,
( spl26_8
| ~ spl26_9
| spl26_3 ),
inference(avatar_split_clause,[],[f522,f447,f527,f524]) ).
fof(f531,plain,
( ~ meet_semilatt_str(sF21)
| spl26_9 ),
inference(resolution,[],[f529,f215]) ).
fof(f532,plain,
( $false
| spl26_9 ),
inference(forward_subsumption_resolution,[],[f531,f321]) ).
fof(f533,plain,
spl26_9,
inference(avatar_contradiction_clause,[],[f532]) ).
fof(f535,plain,
( ! [X0] :
( ~ element(X0,sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),X0,sK19) = apply_binary(the_L_meet(sF21),X0,sK19) )
| ~ spl26_8 ),
inference(resolution,[],[f525,f296]) ).
fof(f553,plain,
( apply_binary_as_element(sF25,sF25,sF25,the_L_meet(sF21),sK18,sK19) = apply_binary(the_L_meet(sF21),sK18,sK19)
| ~ spl26_8 ),
inference(resolution,[],[f535,f297]) ).
fof(f558,plain,
( sF24 = apply_binary(the_L_meet(sF21),sK18,sK19)
| ~ spl26_8 ),
inference(forward_demodulation,[],[f553,f396]) ).
fof(f559,plain,
! [X0,X1] :
( empty(sF25)
| empty(sF25)
| ~ function(the_L_join(sF21))
| ~ quasi_total(the_L_join(sF21),cartesian_product2(sF25,sF25),sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X0,X1) = apply_binary(the_L_join(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) ),
inference(resolution,[],[f487,f260]) ).
fof(f561,plain,
! [X0,X1] :
( empty(sF25)
| ~ function(the_L_join(sF21))
| ~ quasi_total(the_L_join(sF21),cartesian_product2(sF25,sF25),sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X0,X1) = apply_binary(the_L_join(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) ),
inference(duplicate_literal_removal,[],[f559]) ).
fof(f562,plain,
( ! [X0,X1] :
( ~ function(the_L_join(sF21))
| ~ quasi_total(the_L_join(sF21),cartesian_product2(sF25,sF25),sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X0,X1) = apply_binary(the_L_join(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) )
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f561,f448]) ).
fof(f563,plain,
( ! [X0,X1] :
( ~ function(the_L_join(sF21))
| apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X0,X1) = apply_binary(the_L_join(sF21),X0,X1)
| ~ element(X0,sF25)
| ~ element(X1,sF25) )
| spl26_3 ),
inference(forward_subsumption_resolution,[],[f562,f496]) ).
fof(f565,definition,
( spl26_12
<=> ! [X0,X1] :
( apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X0,X1) = apply_binary(the_L_join(sF21),X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) ) ),
introduced(definition,[new_symbols(definition,[spl26_12])],[avatar_definition]) ).
fof(f566,plain,
( ! [X0,X1] :
( ~ element(X1,sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X0,X1) = apply_binary(the_L_join(sF21),X0,X1)
| ~ element(X0,sF25) )
| ~ spl26_12 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f568,definition,
( spl26_13
<=> function(the_L_join(sF21)) ),
introduced(definition,[new_symbols(definition,[spl26_13])],[avatar_definition]) ).
fof(f570,plain,
( ~ function(the_L_join(sF21))
| spl26_13 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f571,plain,
( spl26_12
| ~ spl26_13
| spl26_3 ),
inference(avatar_split_clause,[],[f563,f447,f568,f565]) ).
fof(f572,plain,
( ~ join_semilatt_str(sF21)
| spl26_13 ),
inference(resolution,[],[f570,f218]) ).
fof(f573,plain,
( $false
| spl26_13 ),
inference(forward_subsumption_resolution,[],[f572,f319]) ).
fof(f574,plain,
spl26_13,
inference(avatar_contradiction_clause,[],[f573]) ).
fof(f576,plain,
( ! [X0] :
( ~ element(X0,sF25)
| apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),X0,sK19) = apply_binary(the_L_join(sF21),X0,sK19) )
| ~ spl26_12 ),
inference(resolution,[],[f566,f296]) ).
fof(f594,plain,
( apply_binary_as_element(sF25,sF25,sF25,the_L_join(sF21),sK18,sK19) = apply_binary(the_L_join(sF21),sK18,sK19)
| ~ spl26_12 ),
inference(resolution,[],[f576,f297]) ).
fof(f599,plain,
( sF22 = apply_binary(the_L_join(sF21),sK18,sK19)
| ~ spl26_12 ),
inference(forward_demodulation,[],[f594,f409]) ).
fof(f607,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| subset_union2(sK17,X1,X0) = apply_binary(the_L_join(boole_lattice(sK17)),X1,X0)
| ~ element(X1,sF25) ),
inference(superposition,[],[f311,f316]) ).
fof(f608,plain,
! [X0,X1] :
( ~ element(X1,sF25)
| ~ element(X0,sF25)
| subset_union2(sK17,X1,X0) = apply_binary(the_L_join(sF21),X1,X0) ),
inference(forward_demodulation,[],[f607,f286]) ).
fof(f609,plain,
! [X0] :
( ~ element(X0,sF25)
| subset_union2(sK17,sK18,X0) = apply_binary(the_L_join(sF21),sK18,X0) ),
inference(resolution,[],[f608,f297]) ).
fof(f614,plain,
apply_binary(the_L_join(sF21),sK18,sK19) = subset_union2(sK17,sK18,sK19),
inference(resolution,[],[f609,f296]) ).
fof(f617,plain,
( sF22 = subset_union2(sK17,sK18,sK19)
| ~ spl26_12 ),
inference(forward_demodulation,[],[f614,f599]) ).
fof(f656,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| subset_intersection2(sK17,X1,X0) = apply_binary(the_L_meet(boole_lattice(sK17)),X1,X0)
| ~ element(X1,sF25) ),
inference(superposition,[],[f310,f316]) ).
fof(f657,plain,
! [X0,X1] :
( ~ element(X1,sF25)
| ~ element(X0,sF25)
| subset_intersection2(sK17,X1,X0) = apply_binary(the_L_meet(sF21),X1,X0) ),
inference(forward_demodulation,[],[f656,f286]) ).
fof(f658,plain,
! [X0] :
( ~ element(X0,sF25)
| subset_intersection2(sK17,sK18,X0) = apply_binary(the_L_meet(sF21),sK18,X0) ),
inference(resolution,[],[f657,f297]) ).
fof(f663,plain,
subset_intersection2(sK17,sK18,sK19) = apply_binary(the_L_meet(sF21),sK18,sK19),
inference(resolution,[],[f658,f296]) ).
fof(f668,plain,
( sF24 = subset_intersection2(sK17,sK18,sK19)
| ~ spl26_8 ),
inference(forward_demodulation,[],[f663,f558]) ).
fof(f670,plain,
( sF23 = sF24
| ~ spl26_8 ),
inference(forward_demodulation,[],[f668,f423]) ).
fof(f672,plain,
( $false
| spl26_1
| ~ spl26_8 ),
inference(forward_subsumption_resolution,[],[f670,f301]) ).
fof(f673,plain,
( spl26_1
| ~ spl26_8 ),
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f1465,plain,
! [X0,X1] :
( ~ element(X1,sF25)
| ~ element(X0,sF25)
| set_union2(X1,X0) = subset_union2(sK17,X1,X0) ),
inference(superposition,[],[f261,f316]) ).
fof(f1476,plain,
! [X0] :
( ~ element(X0,sF25)
| subset_union2(sK17,sK18,X0) = set_union2(sK18,X0) ),
inference(resolution,[],[f1465,f297]) ).
fof(f1493,plain,
set_union2(sK18,sK19) = subset_union2(sK17,sK18,sK19),
inference(resolution,[],[f1476,f296]) ).
fof(f1498,plain,
( set_union2(sK18,sK19) = sF22
| ~ spl26_12 ),
inference(forward_demodulation,[],[f1493,f617]) ).
fof(f1501,plain,
( sF20 = sF22
| ~ spl26_12 ),
inference(forward_demodulation,[],[f1498,f284]) ).
fof(f1502,plain,
( $false
| spl26_2
| ~ spl26_12 ),
inference(forward_subsumption_resolution,[],[f1501,f305]) ).
fof(f1503,plain,
( spl26_2
| ~ spl26_12 ),
inference(avatar_contradiction_clause,[],[f1502]) ).
cnf(s1,plain,
( ~ spl26_1
| ~ spl26_2 ),
inference(sat_conversion,[],[f306]) ).
cnf(s6,plain,
~ spl26_3,
inference(sat_conversion,[],[f509]) ).
cnf(s7,plain,
( spl26_3
| spl26_8
| ~ spl26_9 ),
inference(sat_conversion,[],[f530]) ).
cnf(s8,plain,
spl26_9,
inference(sat_conversion,[],[f533]) ).
cnf(s10,plain,
( spl26_3
| spl26_12
| ~ spl26_13 ),
inference(sat_conversion,[],[f571]) ).
cnf(s11,plain,
spl26_13,
inference(sat_conversion,[],[f574]) ).
cnf(s13,plain,
( spl26_1
| ~ spl26_8 ),
inference(sat_conversion,[],[f673]) ).
cnf(s16,plain,
( spl26_2
| ~ spl26_12 ),
inference(sat_conversion,[],[f1503]) ).
cnf(s19,plain,
( spl26_3
| spl26_12 ),
inference(rat,[],[s10,s11]) ).
cnf(s22,plain,
( spl26_3
| spl26_8 ),
inference(rat,[],[s7,s8]) ).
cnf(s23,plain,
spl26_12,
inference(rat,[],[s19,s6]) ).
cnf(s24,plain,
spl26_8,
inference(rat,[],[s22,s6]) ).
cnf(s25,plain,
spl26_2,
inference(rat,[],[s16,s23]) ).
cnf(s26,plain,
spl26_1,
inference(rat,[],[s13,s24]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s1,s25,s26]) ).
fof(f1504,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU343+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 04:51:10 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 5.13/1.62 % (2996881)Detected formulas, will run a generic FOF schedule.
% 5.13/1.62 % (2996886)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=884546607:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.13/1.62 % (2996887)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=4039072337:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.13/1.62 % (2996890)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3991697852:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.13/1.62 % (2996888)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=2500593498:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.13/1.62 % (2996889)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3083020507:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.13/1.62 % (2996889)Refutation not found, incomplete strategy
% 5.13/1.62 % (2996889)------------------------------
% 5.13/1.62 % (2996889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996889)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996889)Termination reason: Refutation not found, incomplete strategy
% 5.13/1.62 % (2996889)Time elapsed: 0.002 s
% 5.13/1.62 % (2996889)Peak memory usage: 88 MB
% 5.13/1.62 % (2996889)Instructions burned: 1 (million)
% 5.13/1.62 % (2996891)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4224433824:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.13/1.62 % (2996892)dis-21_1_sil=8000:lcm=predicate:random_seed=2582490175: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)
% 5.13/1.62 % (2996890)Instruction limit reached!
% 5.13/1.62 % (2996890)------------------------------
% 5.13/1.62 % (2996890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996890)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996890)Termination reason: Instruction limit
% 5.13/1.62 % (2996890)Termination phase: Saturation
% 5.13/1.62 % (2996890)Time elapsed: 0.069 s
% 5.13/1.62 % (2996890)Peak memory usage: 88 MB
% 5.13/1.62 % (2996890)Instructions burned: 120 (million)
% 5.13/1.62 % (2996892)Instruction limit reached!
% 5.13/1.62 % (2996892)------------------------------
% 5.13/1.62 % (2996892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996892)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996892)Termination reason: Instruction limit
% 5.13/1.62 % (2996892)Termination phase: Saturation
% 5.13/1.62 % (2996892)Time elapsed: 0.078 s
% 5.13/1.62 % (2996892)Peak memory usage: 90 MB
% 5.13/1.62 % (2996892)Instructions burned: 131 (million)
% 5.13/1.62 % (2996891)Instruction limit reached!
% 5.13/1.62 % (2996891)------------------------------
% 5.13/1.62 % (2996891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996891)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996891)Termination reason: Instruction limit
% 5.13/1.62 % (2996891)Termination phase: Saturation
% 5.13/1.62 % (2996891)Time elapsed: 0.091 s
% 5.13/1.62 % (2996891)Peak memory usage: 90 MB
% 5.13/1.62 % (2996891)Instructions burned: 140 (million)
% 5.13/1.62 % (2996901)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1344296839:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.13/1.62 % (2996900)lrs+10_1_sil=8000:sp=occurrence:random_seed=1115739038:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.13/1.62 % (2996901)Refutation not found, incomplete strategy
% 5.13/1.62 % (2996901)------------------------------
% 5.13/1.62 % (2996901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996901)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996901)Termination reason: Refutation not found, incomplete strategy
% 5.13/1.62 % (2996901)Time elapsed: 0.007 s
% 5.13/1.62 % (2996901)Peak memory usage: 89 MB
% 5.13/1.62 % (2996901)Instructions burned: 10 (million)
% 5.13/1.62 % (2996902)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3224091815:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.13/1.62 % (2996889)------------------------------
% 5.13/1.62 % (2996889)------------------------------
% 5.13/1.62 % (2996900)Instruction limit reached!
% 5.13/1.62 % (2996900)------------------------------
% 5.13/1.62 % (2996900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996900)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996900)Termination reason: Instruction limit
% 5.13/1.62 % (2996900)Termination phase: Saturation
% 5.13/1.62 % (2996900)Time elapsed: 0.160 s
% 5.13/1.62 % (2996900)Peak memory usage: 92 MB
% 5.13/1.62 % (2996900)Instructions burned: 286 (million)
% 5.13/1.62 % (2996906)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=90567821:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.13/1.62 % (2996902)Instruction limit reached!
% 5.13/1.62 % (2996902)------------------------------
% 5.13/1.62 % (2996902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996902)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996902)Termination reason: Instruction limit
% 5.13/1.62 % (2996902)Termination phase: Saturation
% 5.13/1.62 % (2996902)Time elapsed: 0.197 s
% 5.13/1.62 % (2996902)Peak memory usage: 92 MB
% 5.13/1.62 % (2996902)Instructions burned: 325 (million)
% 5.13/1.62 % (2996901)------------------------------
% 5.13/1.62 % (2996901)------------------------------
% 5.13/1.62 % (2996886)First to succeed.
% 5.13/1.62 % (2996886)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2996881"
% 5.13/1.62 % (2996907)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1445336324:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.13/1.62 % (2996907)Refutation not found, incomplete strategy
% 5.13/1.62 % (2996907)------------------------------
% 5.13/1.62 % (2996907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996907)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996907)Termination reason: Refutation not found, incomplete strategy
% 5.13/1.62 % (2996907)Time elapsed: 0.008 s
% 5.13/1.62 % (2996907)Peak memory usage: 89 MB
% 5.13/1.62 % (2996907)Instructions burned: 10 (million)
% 5.13/1.62 % (2996906)Instruction limit reached!
% 5.13/1.62 % (2996906)------------------------------
% 5.13/1.62 % (2996906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.62 % (2996906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.62 % (2996906)CaDiCaL version: 2.1.3
% 5.13/1.62 % (2996906)Termination reason: Instruction limit
% 5.13/1.62 % (2996906)Termination phase: Saturation
% 5.13/1.62 % (2996906)Time elapsed: 0.131 s
% 5.13/1.62 % (2996906)Peak memory usage: 92 MB
% 5.13/1.62 % (2996906)Instructions burned: 248 (million)
% 5.13/1.62 % (2996909)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1051074355:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.13/1.62 % (2996910)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1810010347:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.13/1.62 % (2996886)Refutation found. Thanks to Tanya!
% 5.13/1.62 % SZS status Theorem for theBenchmark
% 5.13/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 6.08/1.82 % (2996886)------------------------------
% 6.08/1.82 % (2996886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.82 % (2996886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.82 % (2996886)CaDiCaL version: 2.1.3
% 6.08/1.82 % (2996886)Termination reason: Refutation
% 6.08/1.82 % (2996886)Time elapsed: 0.489 s
% 6.08/1.82 % (2996886)Peak memory usage: 133 MB
% 6.08/1.82 % (2996886)Instructions burned: 1288 (million)
% 6.08/1.82 % (2996886)------------------------------
% 6.08/1.82 % (2996886)------------------------------
% 6.08/1.82 % (2996881)Success in time 0.77 s
% 6.08/1.82 % Vampire exiting
%------------------------------------------------------------------------------