%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 11:53:13 AM UTC 2026
% Result : Theorem 1.83s 1.11s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 10 unt; 5 def)
% Number of atoms : 681 ( 0 equ)
% Maximal formula atoms : 69 ( 17 avg)
% Number of connectives : 1143 ( 500 ~; 400 |; 239 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 145 ( 0 sgn 122 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p2(X0)
& ~ p102(X0)
& p101(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p2(X0)
& ~ p102(X0)
& p101(X0) ) ) )
| ~ ( ~ p101(X1)
& p100(X1) ) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ~ p101(X0) )
| p2(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ p101(X0) )
| ~ p2(X1) ) )
| ~ p101(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0)
| ~ p100(X0) )
| p1(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0)
| ~ p100(X0) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) ) ) )
& ( ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ p2(X1)
& ~ p102(X1)
& p101(X1) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ~ p102(X1)
& p101(X1) ) ) )
| ~ ( ~ p101(X0)
& p100(X0) ) )
& ( ( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ~ p101(X1) )
| p2(X0) )
& ( ! [X1] :
( ~ r1(X0,X1)
| p2(X1)
| ~ p101(X1) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1)
| ~ p100(X1) )
| p1(X0) )
& ( ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ p100(X1) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p101(X0)
| ~ p102(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p2(X0)
& ~ p102(X0)
& p101(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p2(X0)
& ~ p102(X0)
& p101(X0) ) ) )
| ~ ( ~ p101(X1)
& p100(X1) ) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ~ p101(X0) )
| p2(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ p101(X0) )
| ~ p2(X1) ) )
| ~ p101(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0)
| ~ p100(X0) )
| p1(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0)
| ~ p100(X0) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) ) ) )
& ( ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ p2(X1)
& ~ p102(X1)
& p101(X1) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ~ p102(X1)
& p101(X1) ) ) )
| ~ ( ~ p101(X0)
& p100(X0) ) )
& ( ( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ~ p101(X1) )
| p2(X0) )
& ( ! [X1] :
( ~ r1(X0,X1)
| p2(X1)
| ~ p101(X1) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1)
| ~ p100(X1) )
| p1(X0) )
& ( ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ p100(X1) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p101(X0)
| ~ p102(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p2(X3)
& ~ p102(X3)
& p101(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p2(X4)
& ~ p102(X4)
& p101(X4) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ p2(X9)
& ~ p102(X9)
& p101(X9) ) )
& ~ ! [X10] :
( ~ r1(X0,X10)
| ~ ( p2(X10)
& ~ p102(X10)
& p101(X10) ) ) )
| ~ ( ~ p101(X0)
& p100(X0) ) )
& ( ( ( ! [X11] :
( ~ r1(X0,X11)
| ~ p2(X11)
| ~ p101(X11) )
| p2(X0) )
& ( ! [X12] :
( ~ r1(X0,X12)
| p2(X12)
| ~ p101(X12) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X13] :
( ~ r1(X0,X13)
| ~ p1(X13)
| ~ p100(X13) )
| p1(X0) )
& ( ! [X14] :
( ~ r1(X0,X14)
| p1(X14)
| ~ p100(X14) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p101(X0)
| ~ p102(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p2(X3)
& ~ p102(X3)
& p101(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p2(X4)
& ~ p102(X4)
& p101(X4) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ p2(X9)
& ~ p102(X9)
& p101(X9) ) )
& ~ ! [X10] :
( ~ r1(X0,X10)
| ~ ( p2(X10)
& ~ p102(X10)
& p101(X10) ) ) )
| ~ ( ~ p101(X0)
& p100(X0) ) )
& ( ( ( ! [X11] :
( ~ r1(X0,X11)
| ~ p2(X11)
| ~ p101(X11) )
| p2(X0) )
& ( ! [X12] :
( ~ r1(X0,X12)
| p2(X12)
| ~ p101(X12) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X13] :
( ~ r1(X0,X13)
| ~ p1(X13)
| ~ p100(X13) )
| p1(X0) )
& ( ! [X14] :
( ~ r1(X0,X14)
| p1(X14)
| ~ p100(X14) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p101(X0)
| ~ p102(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p2(X3)
& p101(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p2(X4)
& p101(X4) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ p2(X9)
& p101(X9) ) )
& ~ ! [X10] :
( ~ r1(X0,X10)
| ~ ( p2(X10)
& p101(X10) ) ) )
| ~ ( ~ p101(X0)
& p100(X0) ) )
& ( ( ( ! [X11] :
( ~ r1(X0,X11)
| ~ p2(X11)
| ~ p101(X11) )
| p2(X0) )
& ( ! [X12] :
( ~ r1(X0,X12)
| p2(X12)
| ~ p101(X12) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X13] :
( ~ r1(X0,X13)
| ~ p1(X13)
| ~ p100(X13) )
| p1(X0) )
& ( ! [X14] :
( ~ r1(X0,X14)
| p1(X14)
| ~ p100(X14) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ) ),
inference(pure_predicate_removal,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ? [X3] :
( r1(X2,X3)
& ~ p2(X3)
& p101(X3) )
& ? [X4] :
( r1(X2,X4)
& p2(X4)
& p101(X4) ) )
| p101(X2)
| ~ p100(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( ? [X9] :
( r1(X0,X9)
& ~ p2(X9)
& p101(X9) )
& ? [X10] :
( r1(X0,X10)
& p2(X10)
& p101(X10) ) )
| p101(X0)
| ~ p100(X0) )
& ( ( ( ! [X11] :
( ~ r1(X0,X11)
| ~ p2(X11)
| ~ p101(X11) )
| p2(X0) )
& ( ! [X12] :
( ~ r1(X0,X12)
| p2(X12)
| ~ p101(X12) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X13] :
( ~ r1(X0,X13)
| ~ p1(X13)
| ~ p100(X13) )
| p1(X0) )
& ( ! [X14] :
( ~ r1(X0,X14)
| p1(X14)
| ~ p100(X14) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ? [X3] :
( r1(X2,X3)
& ~ p2(X3)
& p101(X3) )
& ? [X4] :
( r1(X2,X4)
& p2(X4)
& p101(X4) ) )
| p101(X2)
| ~ p100(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( ? [X9] :
( r1(X0,X9)
& ~ p2(X9)
& p101(X9) )
& ? [X10] :
( r1(X0,X10)
& p2(X10)
& p101(X10) ) )
| p101(X0)
| ~ p100(X0) )
& ( ( ( ! [X11] :
( ~ r1(X0,X11)
| ~ p2(X11)
| ~ p101(X11) )
| p2(X0) )
& ( ! [X12] :
( ~ r1(X0,X12)
| p2(X12)
| ~ p101(X12) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X13] :
( ~ r1(X0,X13)
| ~ p1(X13)
| ~ p100(X13) )
| p1(X0) )
& ( ! [X14] :
( ~ r1(X0,X14)
| p1(X14)
| ~ p100(X14) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ),
inference(flattening,[],[f6]) ).
fof(f8,definition,
! [X2] :
( ( ? [X3] :
( r1(X2,X3)
& ~ p2(X3)
& p101(X3) )
& ? [X4] :
( r1(X2,X4)
& p2(X4)
& p101(X4) ) )
| p101(X2)
| ~ p100(X2)
| ~ sP0(X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f9,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( sP0(X2)
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( ? [X9] :
( r1(X0,X9)
& ~ p2(X9)
& p101(X9) )
& ? [X10] :
( r1(X0,X10)
& p2(X10)
& p101(X10) ) )
| p101(X0)
| ~ p100(X0) )
& ( ( ( ! [X11] :
( ~ r1(X0,X11)
| ~ p2(X11)
| ~ p101(X11) )
| p2(X0) )
& ( ! [X12] :
( ~ r1(X0,X12)
| p2(X12)
| ~ p101(X12) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X13] :
( ~ r1(X0,X13)
| ~ p1(X13)
| ~ p100(X13) )
| p1(X0) )
& ( ! [X14] :
( ~ r1(X0,X14)
| p1(X14)
| ~ p100(X14) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ),
inference(definition_folding,[],[f7,f8]) ).
fof(f13,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( sP0(X2)
& ( ( ( ! [X3] :
( ~ r1(X2,X3)
| ~ p2(X3)
| ~ p101(X3) )
| p2(X2) )
& ( ! [X4] :
( ~ r1(X2,X4)
| p2(X4)
| ~ p101(X4) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p1(X5)
| ~ p100(X5) )
| p1(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p1(X6)
| ~ p100(X6) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( ? [X7] :
( r1(X0,X7)
& ~ p2(X7)
& p101(X7) )
& ? [X8] :
( r1(X0,X8)
& p2(X8)
& p101(X8) ) )
| p101(X0)
| ~ p100(X0) )
& ( ( ( ! [X9] :
( ~ r1(X0,X9)
| ~ p2(X9)
| ~ p101(X9) )
| p2(X0) )
& ( ! [X10] :
( ~ r1(X0,X10)
| p2(X10)
| ~ p101(X10) )
| ~ p2(X0) ) )
| ~ p101(X0) )
& ( ( ( ! [X11] :
( ~ r1(X0,X11)
| ~ p1(X11)
| ~ p100(X11) )
| p1(X0) )
& ( ! [X12] :
( ~ r1(X0,X12)
| p1(X12)
| ~ p100(X12) )
| ~ p1(X0) ) )
| ~ p100(X0) )
& ( p100(X0)
| ~ p101(X0) )
& ~ p101(X0)
& p100(X0) ),
inference(rectify,[],[f9]) ).
fof(f14,plain,
( ! [X1] :
( ~ r1(sK3,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(sK3,X2)
| ( sP0(X2)
& ( ( ( ! [X3] :
( ~ r1(X2,X3)
| ~ p2(X3)
| ~ p101(X3) )
| p2(X2) )
& ( ! [X4] :
( ~ r1(X2,X4)
| p2(X4)
| ~ p101(X4) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p1(X5)
| ~ p100(X5) )
| p1(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p1(X6)
| ~ p100(X6) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ( ( r1(sK3,sK4)
& ~ p2(sK4)
& p101(sK4)
& r1(sK3,sK5)
& p2(sK5)
& p101(sK5) )
| p101(sK3)
| ~ p100(sK3) )
& ( ( ( ! [X9] :
( ~ r1(sK3,X9)
| ~ p2(X9)
| ~ p101(X9) )
| p2(sK3) )
& ( ! [X10] :
( ~ r1(sK3,X10)
| p2(X10)
| ~ p101(X10) )
| ~ p2(sK3) ) )
| ~ p101(sK3) )
& ( ( ( ! [X11] :
( ~ r1(sK3,X11)
| ~ p1(X11)
| ~ p100(X11) )
| p1(sK3) )
& ( ! [X12] :
( ~ r1(sK3,X12)
| p1(X12)
| ~ p100(X12) )
| ~ p1(sK3) ) )
| ~ p100(sK3) )
& ( p100(sK3)
| ~ p101(sK3) )
& ~ p101(sK3)
& p100(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X7,sK4),skolemize(X8,sK5)],[f13]) ).
fof(f21,plain,
p100(sK3),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
~ p101(sK3),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
( ~ p2(sK4)
| p101(sK3)
| ~ p100(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
( r1(sK3,sK4)
| p101(sK3)
| ~ p100(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f40,plain,
! [X1] :
( p2(X1)
| ~ r1(sK3,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f42,definition,
( spl6_1
<=> p101(sK3) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f45,definition,
( spl6_2
<=> p100(sK3) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f91,definition,
( spl6_13
<=> p2(sK4) ),
introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition]) ).
fof(f92,plain,
( ~ p2(sK4)
| spl6_13 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( ~ spl6_2
| spl6_1
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f32,f91,f42,f45]) ).
fof(f95,definition,
( spl6_14
<=> r1(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition]) ).
fof(f96,plain,
( r1(sK3,sK4)
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( ~ spl6_2
| spl6_1
| spl6_14 ),
inference(avatar_split_clause,[],[f33,f95,f42,f45]) ).
fof(f98,plain,
spl6_2,
inference(avatar_split_clause,[],[f21,f45]) ).
fof(f99,plain,
( ~ r1(sK3,sK4)
| spl6_13 ),
inference(resolution,[],[f40,f92]) ).
fof(f100,plain,
( $false
| spl6_13
| ~ spl6_14 ),
inference(resolution,[],[f99,f96]) ).
fof(f101,plain,
( spl6_13
| ~ spl6_14 ),
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f102,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f22,f42]) ).
cnf(s10,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_13 ),
inference(sat_conversion,[],[f93]) ).
cnf(s11,plain,
( spl6_1
| ~ spl6_2
| spl6_14 ),
inference(sat_conversion,[],[f97]) ).
cnf(s12,plain,
spl6_2,
inference(sat_conversion,[],[f98]) ).
cnf(s13,plain,
( spl6_13
| ~ spl6_14 ),
inference(sat_conversion,[],[f101]) ).
cnf(s14,plain,
~ spl6_1,
inference(sat_conversion,[],[f102]) ).
cnf(s15,plain,
spl6_14,
inference(rat,[],[s11,s12,s14]) ).
cnf(s16,plain,
spl6_13,
inference(rat,[],[s13,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s10,s16,s12,s14]) ).
fof(f103,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 16:08:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.83/1.11 % (3241109)Detected formulas, will run a generic FOF schedule.
% 1.83/1.11 % (3241127)dis-21_1_sil=8000:lcm=predicate:random_seed=133829770: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)
% 1.83/1.11 % (3241127)First to succeed.
% 1.83/1.11 % (3241127)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3241109"
% 1.83/1.11 % (3241126)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1603843726:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.83/1.11 % (3241125)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4114940426:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.83/1.11 % (3241121)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=1888166594:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.83/1.11 % (3241124)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3411907830:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.83/1.11 % (3241123)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=498270568:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.83/1.11 % (3241122)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=1077307975:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.83/1.11 % (3241125)Also succeeded, but the first one will report.
% 1.83/1.11 % (3241126)Also succeeded, but the first one will report.
% 1.83/1.11 % (3241124)Also succeeded, but the first one will report.
% 1.83/1.11 % (3241127)Refutation found. Thanks to Tanya!
% 1.83/1.11 % SZS status Theorem for theBenchmark
% 1.83/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.31 % (3241127)------------------------------
% 0.18/1.31 % (3241127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.31 % (3241127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.31 % (3241127)CaDiCaL version: 2.1.3
% 0.18/1.31 % (3241127)Termination reason: Refutation
% 0.18/1.31 % (3241127)Time elapsed: 0.002 s
% 0.18/1.31 % (3241127)Peak memory usage: 89 MB
% 0.18/1.31 % (3241127)Instructions burned: 4 (million)
% 0.18/1.31 % (3241127)------------------------------
% 0.18/1.31 % (3241127)------------------------------
% 0.18/1.31 % (3241109)Success in time 0.266 s
% 0.18/1.31 % Vampire exiting
%------------------------------------------------------------------------------