%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT227_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:37:16 PM UTC 2026
% Result : Theorem 2.36s 1.15s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 99 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 38 ~; 39 |; 4 &)
% ( 6 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 3 prp; 0-5 aty)
% Number of functors : 30 ( 30 usr; 11 con; 0-5 aty)
% Number of variables : 65 ( 0 sgn 63 !; 2 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
arrow_159774573e_indi: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_9,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).
tff(func_def_1,type,
arrow_610318064e_Prof: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),bool) ).
tff(func_def_2,type,
arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_3,type,
arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_4,type,
arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_5,type,
arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_6,type,
comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_7,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_8,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_9,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_10,type,
product_prod_case:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_11,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_12,type,
id_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_13,type,
converse:
!>[X0: $tType,X1: $tType] : fun(fun(product_prod(X0,X1),bool),fun(product_prod(X1,X0),bool)) ).
tff(func_def_14,type,
inv_image:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X1,X0) ) > fun(product_prod(X1,X1),bool) ) ).
tff(func_def_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_19,type,
p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_20,type,
p1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_21,type,
a: arrow_411405190le_alt ).
tff(func_def_22,type,
b: arrow_411405190le_alt ).
tff(func_def_23,type,
c: arrow_411405190le_alt ).
tff(func_def_24,type,
sK0: arrow_159774573e_indi ).
tff(func_def_25,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_26,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_27,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_2,type,
arrow_987702531ctator: ( fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).
tff(pred_def_3,type,
arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_4,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_5,type,
antisym:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_6,type,
irrefl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_7,type,
total_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_8,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_9,type,
pp: bool > $o ).
tff(pred_def_10,type,
sP4: arrow_411405190le_alt > $o ).
tff(pred_def_11,type,
sP5: arrow_411405190le_alt > $o ).
tff(pred_def_12,type,
sP6: arrow_411405190le_alt > $o ).
tff(f6,axiom,
! [X0: arrow_159774573e_indi] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,X0))
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_iff) ).
tff(f9,axiom,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
( member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
<=> member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_converse__iff) ).
tff(f14,axiom,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
( member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
=> member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_converseD) ).
tff(f58,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,X0),X6: fun(X0,X1)] :
( ( comp(X0,X1,X2,X6,X5) = X4 )
=> ( aa(X0,X1,X6,aa(X2,X0,X5,X3)) = aa(X2,X1,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_o__eq__dest__lhs) ).
tff(f98,conjecture,
! [X0: arrow_159774573e_indi] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),X0))
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f99,negated_conjecture,
~ ! [X0: arrow_159774573e_indi] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),X0))
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
tff(f100,plain,
? [X0: arrow_159774573e_indi] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),X0))
<~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
inference(ennf_transformation,[],[f99]) ).
tff(f102,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,X0),X6: fun(X0,X1)] :
( ( aa(X0,X1,X6,aa(X2,X0,X5,X3)) = aa(X2,X1,X4,X3) )
| ( comp(X0,X1,X2,X6,X5) != X4 ) ),
inference(ennf_transformation,[],[f58]) ).
tff(f106,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
( member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2)
| ~ member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2)) ),
inference(ennf_transformation,[],[f14]) ).
tff(f109,plain,
? [X0: arrow_159774573e_indi] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),X0)) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),X0)) ) ),
inference(nnf_transformation,[],[f100]) ).
tff(f110,plain,
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),sK0)) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f109]) ).
tff(f113,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
( ( member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
| ~ member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2) )
& ( member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2)
| ~ member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2)) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f115,plain,
! [X0: arrow_159774573e_indi] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,X0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,X0)) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f116,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),sK0)) ),
inference(cnf_transformation,[],[f110]) ).
tff(f117,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p1),sK0)) ),
inference(cnf_transformation,[],[f110]) ).
tff(f119,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X6: fun(X0,X1),X4: fun(X2,X1),X5: fun(X2,X0)] :
( ( aa(X2,X1,X4,X3) = aa(X0,X1,X6,aa(X2,X0,X5,X3)) )
| ( comp(X0,X1,X2,X6,X5) != X4 ) ),
inference(cnf_transformation,[],[f102]) ).
tff(f130,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
( ~ member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
| member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2) ),
inference(cnf_transformation,[],[f106]) ).
tff(f133,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
( member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
| ~ member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2) ),
inference(cnf_transformation,[],[f113]) ).
tff(f135,plain,
! [X0: arrow_159774573e_indi] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,X0))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
inference(cnf_transformation,[],[f115]) ).
tff(f136,plain,
! [X0: arrow_159774573e_indi] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,X0)) ),
inference(cnf_transformation,[],[f115]) ).
tff(f148,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X6: fun(X0,X1),X5: fun(X2,X0)] : ( aa(X0,X1,X6,aa(X2,X0,X5,X3)) = aa(X2,X1,comp(X0,X1,X2,X6,X5),X3) ),
inference(equality_resolution,[],[f119]) ).
tff(f149,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0)))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0)) ),
inference(forward_demodulation,[],[f116,f148]) ).
tff(f150,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0)))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0)) ),
inference(forward_demodulation,[],[f117,f148]) ).
tff(f152,definition,
( spl7_1
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0)) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f153,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0))
| spl7_1 ),
inference(avatar_component_clause,[],[f152]) ).
tff(f154,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f152]) ).
tff(f156,definition,
( spl7_2
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f157,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0)))
| spl7_2 ),
inference(avatar_component_clause,[],[f156]) ).
tff(f158,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0)))
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f156]) ).
tff(f159,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f149,f156,f152]) ).
tff(f160,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f150,f156,f152]) ).
tff(f162,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0))
| ~ spl7_2 ),
inference(resolution,[],[f158,f130]) ).
tff(f165,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0))
| ~ spl7_2 ),
inference(resolution,[],[f162,f135]) ).
tff(f166,plain,
( $false
| spl7_1
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f165,f153]) ).
tff(f167,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_contradiction_clause,[],[f166]) ).
tff(f168,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0))
| ~ spl7_1 ),
inference(resolution,[],[f154,f136]) ).
tff(f170,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p1,sK0))
| spl7_2 ),
inference(resolution,[],[f157,f133]) ).
tff(f174,plain,
( $false
| ~ spl7_1
| spl7_2 ),
inference(forward_subsumption_resolution,[],[f170,f168]) ).
tff(f175,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_contradiction_clause,[],[f174]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f159]) ).
cnf(s2,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f160]) ).
cnf(s3,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f167]) ).
cnf(s5,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f175]) ).
cnf(s6,plain,
spl7_1,
inference(rat,[],[s1,s3]) ).
cnf(s7,plain,
spl7_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
tff(f176,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT227_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.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 00:00:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.36/1.15 % (3464058)Detected formulas, will run a generic FOF schedule.
% 2.36/1.15 % (3464066)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1256664238:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.36/1.15 % (3464066)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.36/1.15 % (3464066)First to succeed.
% 2.36/1.15 % (3464066)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3464058"
% 2.36/1.15 % (3464063)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=1934304955:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.36/1.15 % (3464065)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=2984949542:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.36/1.15 % (3464064)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=4249865907:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.36/1.15 % (3464067)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3103201674:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.36/1.15 % (3464068)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1856523425:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.36/1.15 % (3464069)dis-21_1_sil=8000:lcm=predicate:random_seed=3399959519: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)
% 2.36/1.15 % (3464065)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.36/1.15 % (3464067)Also succeeded, but the first one will report.
% 2.36/1.15 % (3464068)Also succeeded, but the first one will report.
% 2.36/1.15 % (3464069)Instruction limit reached!
% 2.36/1.15 % (3464069)------------------------------
% 2.36/1.15 % (3464069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.36/1.15 % (3464069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.15 % (3464069)CaDiCaL version: 2.1.3
% 2.36/1.15 % (3464069)Termination reason: Instruction limit
% 2.36/1.15 % (3464069)Termination phase: Saturation
% 2.36/1.15 % (3464069)Time elapsed: 0.080 s
% 2.36/1.15 % (3464069)Peak memory usage: 90 MB
% 2.36/1.15 % (3464069)Instructions burned: 129 (million)
% 2.36/1.15 % (3464066)Refutation found. Thanks to Tanya!
% 2.36/1.15 % SZS status Theorem for theBenchmark
% 2.36/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.34 % (3464066)------------------------------
% 2.69/1.34 % (3464066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (3464066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (3464066)CaDiCaL version: 2.1.3
% 2.69/1.34 % (3464066)Termination reason: Refutation
% 2.69/1.34 % (3464066)Time elapsed: 0.004 s
% 2.69/1.34 % (3464066)Peak memory usage: 90 MB
% 2.69/1.34 % (3464066)Instructions burned: 8 (million)
% 2.69/1.34 % (3464066)------------------------------
% 2.69/1.34 % (3464066)------------------------------
% 2.69/1.34 % (3464058)Success in time 0.303 s
% 2.69/1.34 % Vampire exiting
%------------------------------------------------------------------------------