%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU342+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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:26 PM UTC 2026
% Result : Theorem 2.73s 1.27s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 136 ( 15 unt; 6 def)
% Number of atoms : 511 ( 47 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 612 ( 237 ~; 284 |; 65 &)
% ( 11 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 7 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 120 ( 0 sgn 98 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> relation_of_lattice(X0) = a_1_0_filter_1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
fof(f16,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f17,axiom,
! [X0] :
( latt_str(X0)
=> ( meet_semilatt_str(X0)
& join_semilatt_str(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f25,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f30,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( in(X0,a_1_0_filter_1(X1))
<=> ? [X2,X3] :
( element(X2,the_carrier(X1))
& element(X3,the_carrier(X1))
& X0 = ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3)
& below_refl(X1,X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
fof(f34,axiom,
! [X0,X1,X2,X3] :
( ( ~ empty(X0)
& ~ empty(X1)
& element(X2,X0)
& element(X3,X1) )
=> ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(f40,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X0 = X2
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f52,plain,
! [X0] :
( relation_of_lattice(X0) = a_1_0_filter_1(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( relation_of_lattice(X0) = a_1_0_filter_1(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f52]) ).
fof(f57,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f58,plain,
! [X0] :
( ( meet_semilatt_str(X0)
& join_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f59,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f60,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f59]) ).
fof(f63,plain,
! [X0,X1] :
( ( in(X0,a_1_0_filter_1(X1))
<=> ? [X2,X3] :
( element(X2,the_carrier(X1))
& element(X3,the_carrier(X1))
& X0 = ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3)
& below_refl(X1,X2,X3) ) )
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f64,plain,
! [X0,X1] :
( ( in(X0,a_1_0_filter_1(X1))
<=> ? [X2,X3] :
( element(X2,the_carrier(X1))
& element(X3,the_carrier(X1))
& X0 = ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3)
& below_refl(X1,X2,X3) ) )
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(flattening,[],[f65]) ).
fof(f75,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<~> below_refl(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f76,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<~> below_refl(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ( X0 = X2
& X1 = X3 )
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f42]) ).
fof(f86,plain,
! [X0,X1] :
( ( ( in(X0,a_1_0_filter_1(X1))
| ! [X2,X3] :
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) != X0
| ~ below_refl(X1,X2,X3) ) )
& ( ? [X2,X3] :
( element(X2,the_carrier(X1))
& element(X3,the_carrier(X1))
& X0 = ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3)
& below_refl(X1,X2,X3) )
| ~ in(X0,a_1_0_filter_1(X1)) ) )
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(nnf_transformation,[],[f64]) ).
fof(f87,plain,
! [X0,X1] :
( ( ( in(X0,a_1_0_filter_1(X1))
| ! [X2,X3] :
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) != X0
| ~ below_refl(X1,X2,X3) ) )
& ( ? [X4,X5] :
( element(X4,the_carrier(X1))
& element(X5,the_carrier(X1))
& ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X4,X5) = X0
& below_refl(X1,X4,X5) )
| ~ in(X0,a_1_0_filter_1(X1)) ) )
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ( ( in(X0,a_1_0_filter_1(X1))
| ! [X2,X3] :
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) != X0
| ~ below_refl(X1,X2,X3) ) )
& ( ( element(sK5(X0,X1),the_carrier(X1))
& element(sK6(X0,X1),the_carrier(X1))
& ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),sK5(X0,X1),sK6(X0,X1)) = X0
& below_refl(X1,sK5(X0,X1),sK6(X0,X1)) )
| ~ in(X0,a_1_0_filter_1(X1)) ) )
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X4,sK5(X0,X1)),skolemize(X5,sK6(X0,X1))],[f87]) ).
fof(f95,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ below_refl(X0,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& ( below_refl(X0,X1,X2)
| in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f96,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ below_refl(X0,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& ( below_refl(X0,X1,X2)
| in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
( ( ~ below_refl(sK11,sK12,sK13)
| ~ in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),relation_of_lattice(sK11)) )
& ( below_refl(sK11,sK12,sK13)
| in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),relation_of_lattice(sK11)) )
& element(sK13,the_carrier(sK11))
& element(sK12,the_carrier(sK11))
& ~ empty_carrier(sK11)
& lattice(sK11)
& latt_str(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f96]) ).
fof(f110,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| relation_of_lattice(X0) = a_1_0_filter_1(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f113,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f114,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f121,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f126,plain,
! [X0,X1] :
( below_refl(X1,sK5(X0,X1),sK6(X0,X1))
| ~ in(X0,a_1_0_filter_1(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f127,plain,
! [X0,X1] :
( ~ lattice(X1)
| ~ in(X0,a_1_0_filter_1(X1))
| empty_carrier(X1)
| ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),sK5(X0,X1),sK6(X0,X1)) = X0
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f128,plain,
! [X0,X1] :
( element(sK6(X0,X1),the_carrier(X1))
| ~ in(X0,a_1_0_filter_1(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f129,plain,
! [X0,X1] :
( element(sK5(X0,X1),the_carrier(X1))
| ~ in(X0,a_1_0_filter_1(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( in(X0,a_1_0_filter_1(X1))
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3) != X0
| ~ below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f143,plain,
latt_str(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f144,plain,
lattice(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f145,plain,
~ empty_carrier(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f146,plain,
element(sK12,the_carrier(sK11)),
inference(cnf_transformation,[],[f97]) ).
fof(f147,plain,
element(sK13,the_carrier(sK11)),
inference(cnf_transformation,[],[f97]) ).
fof(f148,plain,
( below_refl(sK11,sK12,sK13)
| in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),relation_of_lattice(sK11)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f149,plain,
( ~ below_refl(sK11,sK12,sK13)
| ~ in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),relation_of_lattice(sK11)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f77]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f77]) ).
fof(f155,plain,
! [X2,X3,X1] :
( ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below_refl(X1,X2,X3)
| empty_carrier(X1)
| in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),a_1_0_filter_1(X1))
| ~ latt_str(X1) ),
inference(equality_resolution,[],[f130]) ).
fof(f157,definition,
( spl14_1
<=> in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),relation_of_lattice(sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f158,plain,
( ~ in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),relation_of_lattice(sK11))
| spl14_1 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),relation_of_lattice(sK11))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f161,definition,
( spl14_2
<=> below_refl(sK11,sK12,sK13) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f162,plain,
( ~ below_refl(sK11,sK12,sK13)
| spl14_2 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f163,plain,
( below_refl(sK11,sK12,sK13)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f148,f161,f157]) ).
fof(f165,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f149,f161,f157]) ).
fof(f177,definition,
( spl14_3
<=> empty(the_carrier(sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f178,plain,
( ~ empty(the_carrier(sK11))
| spl14_3 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f179,plain,
( empty(the_carrier(sK11))
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f190,plain,
( empty_carrier(sK11)
| ~ one_sorted_str(sK11)
| ~ spl14_3 ),
inference(resolution,[],[f179,f121]) ).
fof(f192,plain,
( ~ one_sorted_str(sK11)
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f190,f145]) ).
fof(f193,plain,
( empty_carrier(sK11)
| relation_of_lattice(sK11) = a_1_0_filter_1(sK11)
| ~ latt_str(sK11) ),
inference(resolution,[],[f110,f144]) ).
fof(f194,plain,
( relation_of_lattice(sK11) = a_1_0_filter_1(sK11)
| ~ latt_str(sK11) ),
inference(forward_subsumption_resolution,[],[f193,f145]) ).
fof(f195,plain,
relation_of_lattice(sK11) = a_1_0_filter_1(sK11),
inference(forward_subsumption_resolution,[],[f194,f143]) ).
fof(f196,plain,
( ~ join_semilatt_str(sK11)
| ~ spl14_3 ),
inference(resolution,[],[f192,f113]) ).
fof(f200,plain,
( ~ latt_str(sK11)
| ~ spl14_3 ),
inference(resolution,[],[f196,f114]) ).
fof(f201,plain,
( $false
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f200,f143]) ).
fof(f202,plain,
~ spl14_3,
inference(avatar_contradiction_clause,[],[f201]) ).
fof(f215,plain,
( ~ in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),a_1_0_filter_1(sK11))
| spl14_1 ),
inference(superposition,[],[f158,f195]) ).
fof(f226,plain,
! [X0] :
( ~ in(X0,a_1_0_filter_1(sK11))
| empty_carrier(sK11)
| ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK5(X0,sK11),sK6(X0,sK11)) = X0
| ~ latt_str(sK11) ),
inference(resolution,[],[f127,f144]) ).
fof(f227,plain,
! [X0] :
( ~ in(X0,a_1_0_filter_1(sK11))
| ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK5(X0,sK11),sK6(X0,sK11)) = X0
| ~ latt_str(sK11) ),
inference(forward_subsumption_resolution,[],[f226,f145]) ).
fof(f228,plain,
! [X0] :
( ~ in(X0,a_1_0_filter_1(sK11))
| ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK5(X0,sK11),sK6(X0,sK11)) = X0 ),
inference(forward_subsumption_resolution,[],[f227,f143]) ).
fof(f248,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK11))
| ~ element(X1,the_carrier(sK11))
| ~ below_refl(sK11,X0,X1)
| empty_carrier(sK11)
| in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),X0,X1),a_1_0_filter_1(sK11))
| ~ latt_str(sK11) ),
inference(resolution,[],[f155,f144]) ).
fof(f249,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK11))
| ~ element(X1,the_carrier(sK11))
| ~ below_refl(sK11,X0,X1)
| in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),X0,X1),a_1_0_filter_1(sK11))
| ~ latt_str(sK11) ),
inference(forward_subsumption_resolution,[],[f248,f145]) ).
fof(f250,plain,
! [X0,X1] :
( ~ below_refl(sK11,X0,X1)
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11))
| in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),X0,X1),a_1_0_filter_1(sK11)) ),
inference(forward_subsumption_resolution,[],[f249,f143]) ).
fof(f252,plain,
( ~ element(sK13,the_carrier(sK11))
| ~ element(sK12,the_carrier(sK11))
| in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),a_1_0_filter_1(sK11))
| ~ spl14_2 ),
inference(resolution,[],[f250,f163]) ).
fof(f261,plain,
( ~ element(sK12,the_carrier(sK11))
| in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),a_1_0_filter_1(sK11))
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f252,f147]) ).
fof(f265,plain,
( in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),a_1_0_filter_1(sK11))
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f261,f146]) ).
fof(f290,plain,
( $false
| spl14_1
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f265,f215]) ).
fof(f291,plain,
( spl14_1
| ~ spl14_2 ),
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f294,plain,
( in(ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK12,sK13),a_1_0_filter_1(sK11))
| ~ spl14_1 ),
inference(forward_demodulation,[],[f159,f195]) ).
fof(f314,plain,
( in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| empty(the_carrier(sK11))
| empty(the_carrier(sK11))
| ~ element(sK12,the_carrier(sK11))
| ~ element(sK13,the_carrier(sK11))
| ~ spl14_1 ),
inference(superposition,[],[f294,f135]) ).
fof(f315,plain,
( in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| empty(the_carrier(sK11))
| ~ element(sK12,the_carrier(sK11))
| ~ element(sK13,the_carrier(sK11))
| ~ spl14_1 ),
inference(duplicate_literal_removal,[],[f314]) ).
fof(f316,plain,
( in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| ~ element(sK12,the_carrier(sK11))
| ~ element(sK13,the_carrier(sK11))
| ~ spl14_1
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f315,f178]) ).
fof(f317,plain,
( in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| ~ element(sK13,the_carrier(sK11))
| ~ spl14_1
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f316,f146]) ).
fof(f318,plain,
( in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| ~ spl14_1
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f317,f147]) ).
fof(f324,plain,
( ordered_pair(sK12,sK13) = ordered_pair_as_product_element(the_carrier(sK11),the_carrier(sK11),sK5(ordered_pair(sK12,sK13),sK11),sK6(ordered_pair(sK12,sK13),sK11))
| ~ spl14_1
| spl14_3 ),
inference(resolution,[],[f318,f228]) ).
fof(f401,plain,
( ordered_pair(sK12,sK13) = ordered_pair(sK5(ordered_pair(sK12,sK13),sK11),sK6(ordered_pair(sK12,sK13),sK11))
| empty(the_carrier(sK11))
| empty(the_carrier(sK11))
| ~ element(sK5(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| ~ element(sK6(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| ~ spl14_1
| spl14_3 ),
inference(superposition,[],[f324,f135]) ).
fof(f408,plain,
( ordered_pair(sK12,sK13) = ordered_pair(sK5(ordered_pair(sK12,sK13),sK11),sK6(ordered_pair(sK12,sK13),sK11))
| empty(the_carrier(sK11))
| ~ element(sK5(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| ~ element(sK6(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| ~ spl14_1
| spl14_3 ),
inference(duplicate_literal_removal,[],[f401]) ).
fof(f411,plain,
( ordered_pair(sK12,sK13) = ordered_pair(sK5(ordered_pair(sK12,sK13),sK11),sK6(ordered_pair(sK12,sK13),sK11))
| ~ element(sK5(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| ~ element(sK6(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| ~ spl14_1
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f408,f178]) ).
fof(f413,definition,
( spl14_15
<=> element(sK6(ordered_pair(sK12,sK13),sK11),the_carrier(sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
fof(f415,plain,
( ~ element(sK6(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| spl14_15 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f417,definition,
( spl14_16
<=> element(sK5(ordered_pair(sK12,sK13),sK11),the_carrier(sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
fof(f419,plain,
( ~ element(sK5(ordered_pair(sK12,sK13),sK11),the_carrier(sK11))
| spl14_16 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f426,definition,
( spl14_18
<=> ordered_pair(sK12,sK13) = ordered_pair(sK5(ordered_pair(sK12,sK13),sK11),sK6(ordered_pair(sK12,sK13),sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
fof(f428,plain,
( ordered_pair(sK12,sK13) = ordered_pair(sK5(ordered_pair(sK12,sK13),sK11),sK6(ordered_pair(sK12,sK13),sK11))
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f430,plain,
( ~ spl14_15
| ~ spl14_16
| spl14_18
| ~ spl14_1
| spl14_3 ),
inference(avatar_split_clause,[],[f411,f177,f157,f426,f417,f413]) ).
fof(f435,plain,
( ~ in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| empty_carrier(sK11)
| ~ lattice(sK11)
| ~ latt_str(sK11)
| spl14_15 ),
inference(resolution,[],[f415,f128]) ).
fof(f437,plain,
( empty_carrier(sK11)
| ~ lattice(sK11)
| ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| spl14_15 ),
inference(forward_subsumption_resolution,[],[f435,f318]) ).
fof(f438,plain,
( ~ lattice(sK11)
| ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| spl14_15 ),
inference(forward_subsumption_resolution,[],[f437,f145]) ).
fof(f439,plain,
( ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| spl14_15 ),
inference(forward_subsumption_resolution,[],[f438,f144]) ).
fof(f440,plain,
( $false
| ~ spl14_1
| spl14_3
| spl14_15 ),
inference(forward_subsumption_resolution,[],[f439,f143]) ).
fof(f441,plain,
( ~ spl14_1
| spl14_3
| spl14_15 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f449,plain,
( ~ in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| empty_carrier(sK11)
| ~ lattice(sK11)
| ~ latt_str(sK11)
| spl14_16 ),
inference(resolution,[],[f419,f129]) ).
fof(f451,plain,
( empty_carrier(sK11)
| ~ lattice(sK11)
| ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| spl14_16 ),
inference(forward_subsumption_resolution,[],[f449,f318]) ).
fof(f452,plain,
( ~ lattice(sK11)
| ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| spl14_16 ),
inference(forward_subsumption_resolution,[],[f451,f145]) ).
fof(f453,plain,
( ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| spl14_16 ),
inference(forward_subsumption_resolution,[],[f452,f144]) ).
fof(f454,plain,
( $false
| ~ spl14_1
| spl14_3
| spl14_16 ),
inference(forward_subsumption_resolution,[],[f453,f143]) ).
fof(f455,plain,
( ~ spl14_1
| spl14_3
| spl14_16 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f712,plain,
( ! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(sK12,sK13)
| sK6(ordered_pair(sK12,sK13),sK11) = X1 )
| ~ spl14_18 ),
inference(superposition,[],[f150,f428]) ).
fof(f714,plain,
( ! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(sK12,sK13)
| sK5(ordered_pair(sK12,sK13),sK11) = X0 )
| ~ spl14_18 ),
inference(superposition,[],[f151,f428]) ).
fof(f721,plain,
( sK13 = sK6(ordered_pair(sK12,sK13),sK11)
| ~ spl14_18 ),
inference(equality_resolution,[],[f712]) ).
fof(f1113,plain,
( sK12 = sK5(ordered_pair(sK12,sK13),sK11)
| ~ spl14_18 ),
inference(equality_resolution,[],[f714]) ).
fof(f1126,plain,
( below_refl(sK11,sK12,sK6(ordered_pair(sK12,sK13),sK11))
| ~ in(ordered_pair(sK12,sK13),a_1_0_filter_1(sK11))
| empty_carrier(sK11)
| ~ lattice(sK11)
| ~ latt_str(sK11)
| ~ spl14_18 ),
inference(superposition,[],[f126,f1113]) ).
fof(f1128,plain,
( below_refl(sK11,sK12,sK6(ordered_pair(sK12,sK13),sK11))
| empty_carrier(sK11)
| ~ lattice(sK11)
| ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| ~ spl14_18 ),
inference(forward_subsumption_resolution,[],[f1126,f318]) ).
fof(f1135,plain,
( below_refl(sK11,sK12,sK6(ordered_pair(sK12,sK13),sK11))
| ~ lattice(sK11)
| ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| ~ spl14_18 ),
inference(forward_subsumption_resolution,[],[f1128,f145]) ).
fof(f1139,plain,
( below_refl(sK11,sK12,sK6(ordered_pair(sK12,sK13),sK11))
| ~ latt_str(sK11)
| ~ spl14_1
| spl14_3
| ~ spl14_18 ),
inference(forward_subsumption_resolution,[],[f1135,f144]) ).
fof(f1141,plain,
( below_refl(sK11,sK12,sK6(ordered_pair(sK12,sK13),sK11))
| ~ spl14_1
| spl14_3
| ~ spl14_18 ),
inference(forward_subsumption_resolution,[],[f1139,f143]) ).
fof(f1143,plain,
( below_refl(sK11,sK12,sK13)
| ~ spl14_1
| spl14_3
| ~ spl14_18 ),
inference(forward_demodulation,[],[f1141,f721]) ).
fof(f1144,plain,
( $false
| ~ spl14_1
| spl14_2
| spl14_3
| ~ spl14_18 ),
inference(forward_subsumption_resolution,[],[f1143,f162]) ).
fof(f1145,plain,
( ~ spl14_1
| spl14_2
| spl14_3
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f1144]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f164]) ).
cnf(s2,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f165]) ).
cnf(s5,plain,
~ spl14_3,
inference(sat_conversion,[],[f202]) ).
cnf(s9,plain,
( spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f291]) ).
cnf(s20,plain,
( ~ spl14_1
| spl14_3
| ~ spl14_15
| ~ spl14_16
| spl14_18 ),
inference(sat_conversion,[],[f430]) ).
cnf(s21,plain,
( ~ spl14_1
| spl14_3
| spl14_15 ),
inference(sat_conversion,[],[f441]) ).
cnf(s22,plain,
( ~ spl14_1
| spl14_3
| spl14_16 ),
inference(sat_conversion,[],[f455]) ).
cnf(s61,plain,
( ~ spl14_1
| spl14_2
| spl14_3
| ~ spl14_18 ),
inference(sat_conversion,[],[f1145]) ).
cnf(s70,plain,
spl14_1,
inference(rat,[],[s1,s9]) ).
cnf(s76,plain,
spl14_16,
inference(rat,[],[s22,s5,s70]) ).
cnf(s77,plain,
spl14_15,
inference(rat,[],[s21,s5,s70]) ).
cnf(s78,plain,
~ spl14_2,
inference(rat,[],[s2,s70]) ).
cnf(s91,plain,
spl14_18,
inference(rat,[],[s20,s70,s76,s5,s77]) ).
cnf(s93,plain,
$false,
inference(rat,[],[s61,s70,s5,s91,s78]) ).
fof(f1146,plain,
$false,
inference(avatar_sat_refutation,[],[s93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU342+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:44:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.73/1.27 % (3211354)Detected formulas, will run a generic FOF schedule.
% 2.73/1.27 % (3211362)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1345448963:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.27 % (3211362)Refutation not found, incomplete strategy
% 2.73/1.27 % (3211362)------------------------------
% 2.73/1.27 % (3211362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.27 % (3211362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.27 % (3211362)CaDiCaL version: 2.1.3
% 2.73/1.27 % (3211362)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.27 % (3211362)Time elapsed: 0.001 s
% 2.73/1.27 % (3211362)Peak memory usage: 88 MB
% 2.73/1.27 % (3211362)Instructions burned: 1 (million)
% 2.73/1.27 % (3211365)dis-21_1_sil=8000:lcm=predicate:random_seed=1912634955: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)
% 2.73/1.27 % (3211364)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1560198471:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.27 % (3211361)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=2635209988:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.27 % (3211359)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=958938026:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.27 % (3211360)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=4189652968:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.27 % (3211363)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=348823177:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.27 % (3211363)Refutation not found, incomplete strategy
% 2.73/1.27 % (3211363)------------------------------
% 2.73/1.27 % (3211363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.27 % (3211363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.27 % (3211363)CaDiCaL version: 2.1.3
% 2.73/1.27 % (3211363)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.27 % (3211363)Time elapsed: 0.003 s
% 2.73/1.27 % (3211363)Peak memory usage: 88 MB
% 2.73/1.27 % (3211363)Instructions burned: 3 (million)
% 2.73/1.27 % (3211364)First to succeed.
% 2.73/1.27 % (3211364)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3211354"
% 2.73/1.27 % (3211365)Instruction limit reached!
% 2.73/1.27 % (3211365)------------------------------
% 2.73/1.27 % (3211365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.27 % (3211365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.27 % (3211365)CaDiCaL version: 2.1.3
% 2.73/1.27 % (3211365)Termination reason: Instruction limit
% 2.73/1.27 % (3211365)Termination phase: Saturation
% 2.73/1.27 % (3211365)Time elapsed: 0.075 s
% 2.73/1.27 % (3211365)Peak memory usage: 91 MB
% 2.73/1.27 % (3211365)Instructions burned: 130 (million)
% 2.73/1.27 % (3211362)------------------------------
% 2.73/1.27 % (3211362)------------------------------
% 2.73/1.27 % (3211373)lrs+10_1_sil=8000:sp=occurrence:random_seed=1381840461:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.73/1.27 % (3211374)lrs+10_1_sil=32000:urr=on:br=off:random_seed=174392935:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.73/1.27 % (3211363)------------------------------
% 2.73/1.27 % (3211363)------------------------------
% 2.73/1.27 % (3211374)Instruction limit reached!
% 2.73/1.27 % (3211374)------------------------------
% 2.73/1.27 % (3211374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.27 % (3211374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.27 % (3211374)CaDiCaL version: 2.1.3
% 2.73/1.27 % (3211374)Termination reason: Instruction limit
% 2.73/1.27 % (3211374)Termination phase: Saturation
% 2.73/1.27 % (3211374)Time elapsed: 0.045 s
% 2.73/1.27 % (3211374)Peak memory usage: 90 MB
% 2.73/1.27 % (3211374)Instructions burned: 158 (million)
% 2.73/1.27 % (3211364)Refutation found. Thanks to Tanya!
% 2.73/1.27 % SZS status Theorem for theBenchmark
% 2.73/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.36 % (3211364)------------------------------
% 3.53/1.36 % (3211364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.36 % (3211364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.36 % (3211364)CaDiCaL version: 2.1.3
% 3.53/1.36 % (3211364)Termination reason: Refutation
% 3.53/1.36 % (3211364)Time elapsed: 0.032 s
% 3.53/1.36 % (3211364)Peak memory usage: 90 MB
% 3.53/1.36 % (3211364)Instructions burned: 43 (million)
% 3.53/1.36 % (3211364)------------------------------
% 3.53/1.36 % (3211364)------------------------------
% 3.53/1.36 % (3211354)Success in time 0.429 s
% 3.53/1.36 % Vampire exiting
%------------------------------------------------------------------------------