%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 11:55:41 AM UTC 2026
% Result : Theorem 2.71s 1.30s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 22 unt; 6 def)
% Number of atoms : 541 ( 0 equ)
% Maximal formula atoms : 49 ( 8 avg)
% Number of connectives : 952 ( 474 ~; 369 |; 103 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-1 aty)
% Number of variables : 284 ( 0 sgn 257 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X2] :
( ~ r1(X0,X2)
| ~ ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ! [X4] :
( ~ r1(X3,X4)
| ~ p1(X4) ) )
& p1(X2) ) )
& ~ ! [X5] :
( ~ r1(X0,X5)
| p1(X5) ) )
| ( ~ ! [X6] :
( ~ r1(X0,X6)
| p2(X6) )
& ~ ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ~ ( ~ ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| p1(X10) ) )
& ~ ! [X11] :
( ~ r1(X8,X11)
| p1(X11) ) ) ) )
& ~ ! [X12] :
( ~ r1(X0,X12)
| p1(X12) ) )
| ( ~ ! [X13] :
( ~ r1(X0,X13)
| p2(X13) )
& ~ ! [X14] :
( ~ r1(X0,X14)
| ~ ( ~ ! [X15] :
( ~ r1(X14,X15)
| ~ ! [X16] :
( ~ r1(X15,X16)
| ~ ! [X17] :
( ~ r1(X16,X17)
| p1(X17) ) ) )
& ~ ! [X18] :
( ~ r1(X14,X18)
| ~ ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) ) ) )
& ~ ! [X20] :
( ~ r1(X0,X20)
| p1(X20) ) )
| ( ~ ! [X21] :
( ~ r1(X0,X21)
| p2(X21) )
& ~ ! [X22] :
( ~ r1(X0,X22)
| ~ ! [X23] :
( ~ r1(X22,X23)
| $false ) )
& ~ ! [X24] :
( ~ r1(X0,X24)
| p1(X24) ) )
| ! [X25] :
( ~ r1(X0,X25)
| p2(X25) )
| ! [X26] :
( ~ r1(X0,X26)
| ! [X27] :
( ~ r1(X26,X27)
| ~ ! [X28] :
( ~ r1(X27,X28)
| p1(X28) ) )
| ! [X29] :
( ~ r1(X26,X29)
| p1(X29) ) )
| ! [X30] :
( ~ r1(X0,X30)
| p1(X30) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
~ ~ ? [X0] :
~ ( ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X2] :
( ~ r1(X0,X2)
| ~ ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ! [X4] :
( ~ r1(X3,X4)
| ~ p1(X4) ) )
& p1(X2) ) )
& ~ ! [X5] :
( ~ r1(X0,X5)
| p1(X5) ) )
| ( ~ ! [X6] :
( ~ r1(X0,X6)
| p2(X6) )
& ~ ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ~ ( ~ ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| p1(X10) ) )
& ~ ! [X11] :
( ~ r1(X8,X11)
| p1(X11) ) ) ) )
& ~ ! [X12] :
( ~ r1(X0,X12)
| p1(X12) ) )
| ( ~ ! [X13] :
( ~ r1(X0,X13)
| p2(X13) )
& ~ ! [X14] :
( ~ r1(X0,X14)
| ~ ( ~ ! [X15] :
( ~ r1(X14,X15)
| ~ ! [X16] :
( ~ r1(X15,X16)
| ~ ! [X17] :
( ~ r1(X16,X17)
| p1(X17) ) ) )
& ~ ! [X18] :
( ~ r1(X14,X18)
| ~ ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) ) ) )
& ~ ! [X20] :
( ~ r1(X0,X20)
| p1(X20) ) )
| ( ~ ! [X21] :
( ~ r1(X0,X21)
| p2(X21) )
& ~ ! [X22] :
( ~ r1(X0,X22)
| ~ ! [X23] : ~ r1(X22,X23) )
& ~ ! [X24] :
( ~ r1(X0,X24)
| p1(X24) ) )
| ! [X25] :
( ~ r1(X0,X25)
| p2(X25) )
| ! [X26] :
( ~ r1(X0,X26)
| ! [X27] :
( ~ r1(X26,X27)
| ~ ! [X28] :
( ~ r1(X27,X28)
| p1(X28) ) )
| ! [X29] :
( ~ r1(X26,X29)
| p1(X29) ) )
| ! [X30] :
( ~ r1(X0,X30)
| p1(X30) ) ),
inference(true_and_false_elimination,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ~ ! [X2] :
( ~ r1(X0,X2)
| ~ ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ! [X4] :
( ~ r1(X3,X4)
| ~ p1(X4) ) )
& p1(X2) ) )
& ~ ! [X5] :
( ~ r1(X0,X5)
| p1(X5) ) )
| ( ~ ! [X6] :
( ~ r1(X0,X6)
| p2(X6) )
& ~ ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ~ ( ~ ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| p1(X10) ) )
& ~ ! [X11] :
( ~ r1(X8,X11)
| p1(X11) ) ) ) )
& ~ ! [X12] :
( ~ r1(X0,X12)
| p1(X12) ) )
| ( ~ ! [X13] :
( ~ r1(X0,X13)
| p2(X13) )
& ~ ! [X14] :
( ~ r1(X0,X14)
| ~ ( ~ ! [X15] :
( ~ r1(X14,X15)
| ~ ! [X16] :
( ~ r1(X15,X16)
| ~ ! [X17] :
( ~ r1(X16,X17)
| p1(X17) ) ) )
& ~ ! [X18] :
( ~ r1(X14,X18)
| ~ ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) ) ) )
& ~ ! [X20] :
( ~ r1(X0,X20)
| p1(X20) ) )
| ( ~ ! [X21] :
( ~ r1(X0,X21)
| p2(X21) )
& ~ ! [X22] :
( ~ r1(X0,X22)
| ~ ! [X23] : ~ r1(X22,X23) )
& ~ ! [X24] :
( ~ r1(X0,X24)
| p1(X24) ) )
| ! [X25] :
( ~ r1(X0,X25)
| p2(X25) )
| ! [X26] :
( ~ r1(X0,X26)
| ! [X27] :
( ~ r1(X26,X27)
| ~ ! [X28] :
( ~ r1(X27,X28)
| p1(X28) ) )
| ! [X29] :
( ~ r1(X26,X29)
| p1(X29) ) )
| ! [X30] :
( ~ r1(X0,X30)
| p1(X30) ) ),
inference(flattening,[],[f6]) ).
fof(f10,plain,
? [X0] :
( ( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X2] :
( ~ r1(X0,X2)
| ! [X3] :
( ~ r1(X2,X3)
| ? [X4] :
( r1(X3,X4)
& p1(X4) ) )
| ~ p1(X2) )
| ! [X5] :
( ~ r1(X0,X5)
| p1(X5) ) )
& ( ! [X6] :
( ~ r1(X0,X6)
| p2(X6) )
| ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ? [X10] :
( r1(X9,X10)
& ~ p1(X10) ) )
| ! [X11] :
( ~ r1(X8,X11)
| p1(X11) ) ) )
| ! [X12] :
( ~ r1(X0,X12)
| p1(X12) ) )
& ( ! [X13] :
( ~ r1(X0,X13)
| p2(X13) )
| ! [X14] :
( ~ r1(X0,X14)
| ! [X15] :
( ~ r1(X14,X15)
| ? [X16] :
( r1(X15,X16)
& ! [X17] :
( ~ r1(X16,X17)
| p1(X17) ) ) )
| ! [X18] :
( ~ r1(X14,X18)
| ? [X19] :
( r1(X18,X19)
& ~ p1(X19) ) ) )
| ! [X20] :
( ~ r1(X0,X20)
| p1(X20) ) )
& ( ! [X21] :
( ~ r1(X0,X21)
| p2(X21) )
| ! [X22] :
( ~ r1(X0,X22)
| ? [X23] : r1(X22,X23) )
| ! [X24] :
( ~ r1(X0,X24)
| p1(X24) ) )
& ? [X25] :
( r1(X0,X25)
& ~ p2(X25) )
& ? [X26] :
( r1(X0,X26)
& ? [X27] :
( r1(X26,X27)
& ! [X28] :
( ~ r1(X27,X28)
| p1(X28) ) )
& ? [X29] :
( r1(X26,X29)
& ~ p1(X29) ) )
& ? [X30] :
( r1(X0,X30)
& ~ p1(X30) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
? [X0] :
( ( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X2] :
( ~ r1(X0,X2)
| ! [X3] :
( ~ r1(X2,X3)
| ? [X4] :
( r1(X3,X4)
& p1(X4) ) )
| ~ p1(X2) )
| ! [X5] :
( ~ r1(X0,X5)
| p1(X5) ) )
& ( ! [X6] :
( ~ r1(X0,X6)
| p2(X6) )
| ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ? [X10] :
( r1(X9,X10)
& ~ p1(X10) ) )
| ! [X11] :
( ~ r1(X8,X11)
| p1(X11) ) ) )
| ! [X12] :
( ~ r1(X0,X12)
| p1(X12) ) )
& ( ! [X13] :
( ~ r1(X0,X13)
| p2(X13) )
| ! [X14] :
( ~ r1(X0,X14)
| ! [X15] :
( ~ r1(X14,X15)
| ? [X16] :
( r1(X15,X16)
& ! [X17] :
( ~ r1(X16,X17)
| p1(X17) ) ) )
| ! [X18] :
( ~ r1(X14,X18)
| ? [X19] :
( r1(X18,X19)
& ~ p1(X19) ) ) )
| ! [X20] :
( ~ r1(X0,X20)
| p1(X20) ) )
& ( ! [X21] :
( ~ r1(X0,X21)
| p2(X21) )
| ! [X22] :
( ~ r1(X0,X22)
| ? [X23] : r1(X22,X23) )
| ! [X24] :
( ~ r1(X0,X24)
| p1(X24) ) )
& ? [X25] :
( r1(X0,X25)
& ~ p2(X25) )
& ? [X26] :
( r1(X0,X26)
& ? [X27] :
( r1(X26,X27)
& ! [X28] :
( ~ r1(X27,X28)
| p1(X28) ) )
& ? [X29] :
( r1(X26,X29)
& ~ p1(X29) ) )
& ? [X30] :
( r1(X0,X30)
& ~ p1(X30) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
( ( ! [X1] :
( ~ r1(sK0,X1)
| p2(X1) )
| ! [X2] :
( ~ r1(sK0,X2)
| ! [X3] :
( ~ r1(X2,X3)
| ( r1(X3,sK1(X3))
& p1(sK1(X3)) ) )
| ~ p1(X2) )
| ! [X5] :
( ~ r1(sK0,X5)
| p1(X5) ) )
& ( ! [X6] :
( ~ r1(sK0,X6)
| p2(X6) )
| ! [X7] :
( ~ r1(sK0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ( r1(X9,sK2(X9))
& ~ p1(sK2(X9)) ) )
| ! [X11] :
( ~ r1(X8,X11)
| p1(X11) ) ) )
| ! [X12] :
( ~ r1(sK0,X12)
| p1(X12) ) )
& ( ! [X13] :
( ~ r1(sK0,X13)
| p2(X13) )
| ! [X14] :
( ~ r1(sK0,X14)
| ! [X15] :
( ~ r1(X14,X15)
| ( r1(X15,sK3(X15))
& ! [X17] :
( ~ r1(sK3(X15),X17)
| p1(X17) ) ) )
| ! [X18] :
( ~ r1(X14,X18)
| ( r1(X18,sK4(X18))
& ~ p1(sK4(X18)) ) ) )
| ! [X20] :
( ~ r1(sK0,X20)
| p1(X20) ) )
& ( ! [X21] :
( ~ r1(sK0,X21)
| p2(X21) )
| ! [X22] :
( ~ r1(sK0,X22)
| r1(X22,sK5(X22)) )
| ! [X24] :
( ~ r1(sK0,X24)
| p1(X24) ) )
& r1(sK0,sK6)
& ~ p2(sK6)
& r1(sK0,sK7)
& r1(sK7,sK8)
& ! [X28] :
( ~ r1(sK8,X28)
| p1(X28) )
& r1(sK7,sK9)
& ~ p1(sK9)
& r1(sK0,sK10)
& ~ p1(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10]),skolemize(X0,sK0),skolemize(X4,sK1(X3)),skolemize(X10,sK2(X9)),skolemize(X16,sK3(X15)),skolemize(X19,sK4(X18)),skolemize(X23,sK5(X22)),skolemize(X25,sK6),skolemize(X26,sK7),skolemize(X27,sK8),skolemize(X29,sK9),skolemize(X30,sK10)],[f11]) ).
fof(f13,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
~ p1(sK10),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
r1(sK0,sK10),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
~ p1(sK9),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
r1(sK7,sK9),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X28] :
( ~ r1(sK8,X28)
| p1(X28) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
r1(sK7,sK8),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
r1(sK0,sK7),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
~ p2(sK6),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
r1(sK0,sK6),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X11,X8,X6,X9,X7,X12] :
( ~ r1(sK0,X6)
| p2(X6)
| ~ r1(sK0,X7)
| ~ r1(X7,X8)
| ~ r1(X8,X9)
| ~ p1(sK2(X9))
| ~ r1(X8,X11)
| p1(X11)
| ~ r1(sK0,X12)
| p1(X12) ),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X11,X8,X6,X9,X7,X12] :
( ~ r1(sK0,X6)
| p2(X6)
| ~ r1(sK0,X7)
| ~ r1(X7,X8)
| ~ r1(X8,X9)
| r1(X9,sK2(X9))
| ~ r1(X8,X11)
| p1(X11)
| ~ r1(sK0,X12)
| p1(X12) ),
inference(cnf_transformation,[],[f12]) ).
fof(f34,definition,
( spl11_1
<=> ! [X24] :
( ~ r1(sK0,X24)
| p1(X24) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f35,plain,
( ! [X24] :
( p1(X24)
| ~ r1(sK0,X24) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f40,definition,
( spl11_3
<=> ! [X21] :
( ~ r1(sK0,X21)
| p2(X21) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f41,plain,
( ! [X21] :
( p2(X21)
| ~ r1(sK0,X21) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f60,definition,
( spl11_8
<=> ! [X11,X9,X8,X7] :
( ~ r1(sK0,X7)
| p1(X11)
| ~ r1(X8,X11)
| ~ p1(sK2(X9))
| ~ r1(X8,X9)
| ~ r1(X7,X8) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f61,plain,
( ! [X11,X8,X9,X7] :
( ~ p1(sK2(X9))
| p1(X11)
| ~ r1(X8,X11)
| ~ r1(sK0,X7)
| ~ r1(X8,X9)
| ~ r1(X7,X8) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( spl11_1
| spl11_8
| spl11_3 ),
inference(avatar_split_clause,[],[f29,f40,f60,f34]) ).
fof(f64,definition,
( spl11_9
<=> ! [X11,X9,X8,X7] :
( ~ r1(sK0,X7)
| p1(X11)
| ~ r1(X8,X11)
| r1(X9,sK2(X9))
| ~ r1(X8,X9)
| ~ r1(X7,X8) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f65,plain,
( ! [X11,X8,X9,X7] :
( r1(X9,sK2(X9))
| p1(X11)
| ~ r1(X8,X11)
| ~ r1(sK0,X7)
| ~ r1(X8,X9)
| ~ r1(X7,X8) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( spl11_1
| spl11_9
| spl11_3 ),
inference(avatar_split_clause,[],[f30,f40,f64,f34]) ).
fof(f75,plain,
( ~ r1(sK0,sK6)
| ~ spl11_3 ),
inference(resolution,[],[f41,f22]) ).
fof(f76,plain,
( $false
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f75,f23]) ).
fof(f77,plain,
~ spl11_3,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f78,plain,
( ~ r1(sK0,sK10)
| ~ spl11_1 ),
inference(resolution,[],[f35,f15]) ).
fof(f80,plain,
( $false
| ~ spl11_1 ),
inference(forward_subsumption_resolution,[],[f78,f16]) ).
fof(f81,plain,
~ spl11_1,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f114,plain,
( ! [X2,X0,X1] :
( p1(X0)
| ~ r1(X1,X0)
| ~ r1(sK0,X2)
| ~ r1(X1,sK8)
| ~ r1(X2,X1)
| p1(sK2(sK8)) )
| ~ spl11_9 ),
inference(resolution,[],[f65,f19]) ).
fof(f115,plain,
( ! [X2,X0,X1] :
( ~ r1(X1,sK8)
| ~ r1(X1,X0)
| ~ r1(sK0,X2)
| p1(X0)
| ~ r1(X2,X1) )
| ~ spl11_8
| ~ spl11_9 ),
inference(forward_subsumption_resolution,[],[f114,f61]) ).
fof(f118,plain,
( ! [X0,X1] :
( ~ r1(sK7,X0)
| ~ r1(sK0,X1)
| p1(X0)
| ~ r1(X1,sK7) )
| ~ spl11_8
| ~ spl11_9 ),
inference(resolution,[],[f115,f20]) ).
fof(f131,definition,
( spl11_20
<=> ! [X1] :
( ~ r1(sK0,X1)
| ~ r1(X1,sK7) ) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
fof(f132,plain,
( ! [X1] :
( ~ r1(X1,sK7)
| ~ r1(sK0,X1) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl11_21
<=> ! [X0] :
( ~ r1(sK7,X0)
| p1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition]) ).
fof(f135,plain,
( ! [X0] :
( p1(X0)
| ~ r1(sK7,X0) )
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( spl11_20
| spl11_21
| ~ spl11_8
| ~ spl11_9 ),
inference(avatar_split_clause,[],[f118,f64,f60,f134,f131]) ).
fof(f155,plain,
( ~ r1(sK0,sK7)
| ~ spl11_20 ),
inference(resolution,[],[f13,f132]) ).
fof(f156,plain,
( $false
| ~ spl11_20 ),
inference(forward_subsumption_resolution,[],[f155,f21]) ).
fof(f157,plain,
~ spl11_20,
inference(avatar_contradiction_clause,[],[f156]) ).
fof(f162,plain,
( ~ r1(sK7,sK9)
| ~ spl11_21 ),
inference(resolution,[],[f135,f17]) ).
fof(f164,plain,
( $false
| ~ spl11_21 ),
inference(forward_subsumption_resolution,[],[f162,f18]) ).
fof(f165,plain,
~ spl11_21,
inference(avatar_contradiction_clause,[],[f164]) ).
cnf(s6,plain,
( spl11_1
| spl11_3
| spl11_8 ),
inference(sat_conversion,[],[f62]) ).
cnf(s7,plain,
( spl11_1
| spl11_3
| spl11_9 ),
inference(sat_conversion,[],[f66]) ).
cnf(s10,plain,
~ spl11_3,
inference(sat_conversion,[],[f77]) ).
cnf(s11,plain,
~ spl11_1,
inference(sat_conversion,[],[f81]) ).
cnf(s16,plain,
( ~ spl11_8
| ~ spl11_9
| spl11_20
| spl11_21 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
~ spl11_20,
inference(sat_conversion,[],[f157]) ).
cnf(s20,plain,
~ spl11_21,
inference(sat_conversion,[],[f165]) ).
cnf(s21,plain,
( ~ spl11_8
| ~ spl11_9 ),
inference(rat,[],[s16,s20,s19]) ).
cnf(s24,plain,
spl11_9,
inference(rat,[],[s7,s10,s11]) ).
cnf(s25,plain,
~ spl11_8,
inference(rat,[],[s21,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s6,s25,s10,s11]) ).
fof(f166,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n008.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 16:29:56 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.44 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
% 2.71/1.30 % (1431992)Detected formulas, will run a generic FOF schedule.
% 2.71/1.30 % (1431997)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=2105967233:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.30 % (1431998)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=4043019075:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.30 % (1432000)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=778787398:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.30 % (1431999)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=1649451553:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.30 % (1432001)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1589808780:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.30 % (1432003)dis-21_1_sil=8000:lcm=predicate:random_seed=2870926243: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)
% 2.71/1.30 % (1432002)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4252295621:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.30 % (1432002)First to succeed.
% 2.71/1.30 % (1432002)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1431992"
% 2.71/1.30 % (1432003)Also succeeded, but the first one will report.
% 2.71/1.30 % (1432000)Also succeeded, but the first one will report.
% 2.71/1.30 % (1432001)Also succeeded, but the first one will report.
% 2.71/1.30 % (1432002)Refutation found. Thanks to Tanya!
% 2.71/1.30 % SZS status Theorem for theBenchmark
% 2.71/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.49 % (1432002)------------------------------
% 3.51/1.49 % (1432002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.49 % (1432002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.49 % (1432002)CaDiCaL version: 2.1.3
% 3.51/1.49 % (1432002)Termination reason: Refutation
% 3.51/1.49 % (1432002)Time elapsed: 0.006 s
% 3.51/1.49 % (1432002)Peak memory usage: 89 MB
% 3.51/1.49 % (1432002)Instructions burned: 6 (million)
% 3.51/1.49 % (1432002)------------------------------
% 3.51/1.49 % (1432002)------------------------------
% 3.51/1.49 % (1431992)Success in time 0.426 s
% 3.51/1.50 % Vampire exiting
%------------------------------------------------------------------------------