%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:00:00 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 14 unt; 4 def)
% Number of atoms : 991 ( 0 equ)
% Maximal formula atoms : 121 ( 14 avg)
% Number of connectives : 1691 ( 770 ~; 534 |; 382 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 201 ( 0 sgn 174 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( r1(X0,X1)
& r1(X1,X2) )
=> r1(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p6(X0)
& ~ p106(X0)
& p105(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p6(X0)
& ~ p106(X0)
& p105(X0) ) ) )
| ~ ( ~ p105(X1)
& p104(X1) ) )
& ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p5(X0)
& ~ p105(X0)
& p104(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p5(X0)
& ~ p105(X0)
& p104(X0) ) ) )
| ~ ( ~ p104(X1)
& p103(X1) ) )
& ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p4(X0)
& ~ p104(X0)
& p103(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p4(X0)
& ~ p104(X0)
& p103(X0) ) ) )
| ~ ( ~ p103(X1)
& p102(X1) ) )
& ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p3(X0)
& ~ p103(X0)
& p102(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p3(X0)
& ~ p103(X0)
& p102(X0) ) ) )
| ~ ( ~ p102(X1)
& p101(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)
| ~ p6(X0)
| ~ p105(X0) )
| p6(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p6(X0)
| ~ p105(X0) )
| ~ p6(X1) ) )
| ~ p105(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p5(X0)
| ~ p104(X0) )
| p5(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p5(X0)
| ~ p104(X0) )
| ~ p5(X1) ) )
| ~ p104(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p4(X0)
| ~ p103(X0) )
| p4(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p4(X0)
| ~ p103(X0) )
| ~ p4(X1) ) )
| ~ p103(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p3(X0)
| ~ p102(X0) )
| p3(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p3(X0)
| ~ p102(X0) )
| ~ p3(X1) ) )
| ~ p102(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) )
& ( p105(X1)
| ~ p106(X1) )
& ( p104(X1)
| ~ p105(X1) )
& ( p103(X1)
| ~ p104(X1) )
& ( p102(X1)
| ~ p103(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p6(X0)
& ~ p106(X0)
& p105(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p6(X0)
& ~ p106(X0)
& p105(X0) ) ) )
| ~ ( ~ p105(X1)
& p104(X1) ) )
& ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p5(X0)
& ~ p105(X0)
& p104(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p5(X0)
& ~ p105(X0)
& p104(X0) ) ) )
| ~ ( ~ p104(X1)
& p103(X1) ) )
& ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p4(X0)
& ~ p104(X0)
& p103(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p4(X0)
& ~ p104(X0)
& p103(X0) ) ) )
| ~ ( ~ p103(X1)
& p102(X1) ) )
& ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p3(X0)
& ~ p103(X0)
& p102(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p3(X0)
& ~ p103(X0)
& p102(X0) ) ) )
| ~ ( ~ p102(X1)
& p101(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)
| ~ p6(X0)
| ~ p105(X0) )
| p6(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p6(X0)
| ~ p105(X0) )
| ~ p6(X1) ) )
| ~ p105(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p5(X0)
| ~ p104(X0) )
| p5(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p5(X0)
| ~ p104(X0) )
| ~ p5(X1) ) )
| ~ p104(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p4(X0)
| ~ p103(X0) )
| p4(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p4(X0)
| ~ p103(X0) )
| ~ p4(X1) ) )
| ~ p103(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p3(X0)
| ~ p102(X0) )
| p3(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p3(X0)
| ~ p102(X0) )
| ~ p3(X1) ) )
| ~ p102(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) )
& ( p105(X1)
| ~ p106(X1) )
& ( p104(X1)
| ~ p105(X1) )
& ( p103(X1)
| ~ p104(X1) )
& ( p102(X1)
| ~ p103(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p6(X3)
& ~ p106(X3)
& p105(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p6(X4)
& ~ p106(X4)
& p105(X4) ) ) )
| ~ ( ~ p105(X2)
& p104(X2) ) )
& ( ( ~ ! [X5] :
( ~ r1(X2,X5)
| ~ ( ~ p5(X5)
& ~ p105(X5)
& p104(X5) ) )
& ~ ! [X6] :
( ~ r1(X2,X6)
| ~ ( p5(X6)
& ~ p105(X6)
& p104(X6) ) ) )
| ~ ( ~ p104(X2)
& p103(X2) ) )
& ( ( ~ ! [X7] :
( ~ r1(X2,X7)
| ~ ( ~ p4(X7)
& ~ p104(X7)
& p103(X7) ) )
& ~ ! [X8] :
( ~ r1(X2,X8)
| ~ ( p4(X8)
& ~ p104(X8)
& p103(X8) ) ) )
| ~ ( ~ p103(X2)
& p102(X2) ) )
& ( ( ~ ! [X9] :
( ~ r1(X2,X9)
| ~ ( ~ p3(X9)
& ~ p103(X9)
& p102(X9) ) )
& ~ ! [X10] :
( ~ r1(X2,X10)
| ~ ( p3(X10)
& ~ p103(X10)
& p102(X10) ) ) )
| ~ ( ~ p102(X2)
& p101(X2) ) )
& ( ( ~ ! [X11] :
( ~ r1(X2,X11)
| ~ ( ~ p2(X11)
& ~ p102(X11)
& p101(X11) ) )
& ~ ! [X12] :
( ~ r1(X2,X12)
| ~ ( p2(X12)
& ~ p102(X12)
& p101(X12) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X13] :
( ~ r1(X2,X13)
| ~ p6(X13)
| ~ p105(X13) )
| p6(X2) )
& ( ! [X14] :
( ~ r1(X2,X14)
| p6(X14)
| ~ p105(X14) )
| ~ p6(X2) ) )
| ~ p105(X2) )
& ( ( ( ! [X15] :
( ~ r1(X2,X15)
| ~ p5(X15)
| ~ p104(X15) )
| p5(X2) )
& ( ! [X16] :
( ~ r1(X2,X16)
| p5(X16)
| ~ p104(X16) )
| ~ p5(X2) ) )
| ~ p104(X2) )
& ( ( ( ! [X17] :
( ~ r1(X2,X17)
| ~ p4(X17)
| ~ p103(X17) )
| p4(X2) )
& ( ! [X18] :
( ~ r1(X2,X18)
| p4(X18)
| ~ p103(X18) )
| ~ p4(X2) ) )
| ~ p103(X2) )
& ( ( ( ! [X19] :
( ~ r1(X2,X19)
| ~ p3(X19)
| ~ p102(X19) )
| p3(X2) )
& ( ! [X20] :
( ~ r1(X2,X20)
| p3(X20)
| ~ p102(X20) )
| ~ p3(X2) ) )
| ~ p102(X2) )
& ( ( ( ! [X21] :
( ~ r1(X2,X21)
| ~ p2(X21)
| ~ p101(X21) )
| p2(X2) )
& ( ! [X22] :
( ~ r1(X2,X22)
| p2(X22)
| ~ p101(X22) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X23] :
( ~ r1(X2,X23)
| ~ p1(X23)
| ~ p100(X23) )
| p1(X2) )
& ( ! [X24] :
( ~ r1(X2,X24)
| p1(X24)
| ~ p100(X24) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p105(X2)
| ~ p106(X2) )
& ( p104(X2)
| ~ p105(X2) )
& ( p103(X2)
| ~ p104(X2) )
& ( p102(X2)
| ~ p103(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p6(X3)
& ~ p106(X3)
& p105(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p6(X4)
& ~ p106(X4)
& p105(X4) ) ) )
| ~ ( ~ p105(X2)
& p104(X2) ) )
& ( ( ~ ! [X5] :
( ~ r1(X2,X5)
| ~ ( ~ p5(X5)
& ~ p105(X5)
& p104(X5) ) )
& ~ ! [X6] :
( ~ r1(X2,X6)
| ~ ( p5(X6)
& ~ p105(X6)
& p104(X6) ) ) )
| ~ ( ~ p104(X2)
& p103(X2) ) )
& ( ( ~ ! [X7] :
( ~ r1(X2,X7)
| ~ ( ~ p4(X7)
& ~ p104(X7)
& p103(X7) ) )
& ~ ! [X8] :
( ~ r1(X2,X8)
| ~ ( p4(X8)
& ~ p104(X8)
& p103(X8) ) ) )
| ~ ( ~ p103(X2)
& p102(X2) ) )
& ( ( ~ ! [X9] :
( ~ r1(X2,X9)
| ~ ( ~ p3(X9)
& ~ p103(X9)
& p102(X9) ) )
& ~ ! [X10] :
( ~ r1(X2,X10)
| ~ ( p3(X10)
& ~ p103(X10)
& p102(X10) ) ) )
| ~ ( ~ p102(X2)
& p101(X2) ) )
& ( ( ~ ! [X11] :
( ~ r1(X2,X11)
| ~ ( ~ p2(X11)
& ~ p102(X11)
& p101(X11) ) )
& ~ ! [X12] :
( ~ r1(X2,X12)
| ~ ( p2(X12)
& ~ p102(X12)
& p101(X12) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X13] :
( ~ r1(X2,X13)
| ~ p6(X13)
| ~ p105(X13) )
| p6(X2) )
& ( ! [X14] :
( ~ r1(X2,X14)
| p6(X14)
| ~ p105(X14) )
| ~ p6(X2) ) )
| ~ p105(X2) )
& ( ( ( ! [X15] :
( ~ r1(X2,X15)
| ~ p5(X15)
| ~ p104(X15) )
| p5(X2) )
& ( ! [X16] :
( ~ r1(X2,X16)
| p5(X16)
| ~ p104(X16) )
| ~ p5(X2) ) )
| ~ p104(X2) )
& ( ( ( ! [X17] :
( ~ r1(X2,X17)
| ~ p4(X17)
| ~ p103(X17) )
| p4(X2) )
& ( ! [X18] :
( ~ r1(X2,X18)
| p4(X18)
| ~ p103(X18) )
| ~ p4(X2) ) )
| ~ p103(X2) )
& ( ( ( ! [X19] :
( ~ r1(X2,X19)
| ~ p3(X19)
| ~ p102(X19) )
| p3(X2) )
& ( ! [X20] :
( ~ r1(X2,X20)
| p3(X20)
| ~ p102(X20) )
| ~ p3(X2) ) )
| ~ p102(X2) )
& ( ( ( ! [X21] :
( ~ r1(X2,X21)
| ~ p2(X21)
| ~ p101(X21) )
| p2(X2) )
& ( ! [X22] :
( ~ r1(X2,X22)
| p2(X22)
| ~ p101(X22) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X23] :
( ~ r1(X2,X23)
| ~ p1(X23)
| ~ p100(X23) )
| p1(X2) )
& ( ! [X24] :
( ~ r1(X2,X24)
| p1(X24)
| ~ p100(X24) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p105(X2)
| ~ p106(X2) )
& ( p104(X2)
| ~ p105(X2) )
& ( p103(X2)
| ~ p104(X2) )
& ( p102(X2)
| ~ p103(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p6(X3)
& p105(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p6(X4)
& p105(X4) ) ) )
| ~ ( ~ p105(X2)
& p104(X2) ) )
& ( ( ~ ! [X5] :
( ~ r1(X2,X5)
| ~ ( ~ p5(X5)
& ~ p105(X5)
& p104(X5) ) )
& ~ ! [X6] :
( ~ r1(X2,X6)
| ~ ( p5(X6)
& ~ p105(X6)
& p104(X6) ) ) )
| ~ ( ~ p104(X2)
& p103(X2) ) )
& ( ( ~ ! [X7] :
( ~ r1(X2,X7)
| ~ ( ~ p4(X7)
& ~ p104(X7)
& p103(X7) ) )
& ~ ! [X8] :
( ~ r1(X2,X8)
| ~ ( p4(X8)
& ~ p104(X8)
& p103(X8) ) ) )
| ~ ( ~ p103(X2)
& p102(X2) ) )
& ( ( ~ ! [X9] :
( ~ r1(X2,X9)
| ~ ( ~ p3(X9)
& ~ p103(X9)
& p102(X9) ) )
& ~ ! [X10] :
( ~ r1(X2,X10)
| ~ ( p3(X10)
& ~ p103(X10)
& p102(X10) ) ) )
| ~ ( ~ p102(X2)
& p101(X2) ) )
& ( ( ~ ! [X11] :
( ~ r1(X2,X11)
| ~ ( ~ p2(X11)
& ~ p102(X11)
& p101(X11) ) )
& ~ ! [X12] :
( ~ r1(X2,X12)
| ~ ( p2(X12)
& ~ p102(X12)
& p101(X12) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X13] :
( ~ r1(X2,X13)
| ~ p6(X13)
| ~ p105(X13) )
| p6(X2) )
& ( ! [X14] :
( ~ r1(X2,X14)
| p6(X14)
| ~ p105(X14) )
| ~ p6(X2) ) )
| ~ p105(X2) )
& ( ( ( ! [X15] :
( ~ r1(X2,X15)
| ~ p5(X15)
| ~ p104(X15) )
| p5(X2) )
& ( ! [X16] :
( ~ r1(X2,X16)
| p5(X16)
| ~ p104(X16) )
| ~ p5(X2) ) )
| ~ p104(X2) )
& ( ( ( ! [X17] :
( ~ r1(X2,X17)
| ~ p4(X17)
| ~ p103(X17) )
| p4(X2) )
& ( ! [X18] :
( ~ r1(X2,X18)
| p4(X18)
| ~ p103(X18) )
| ~ p4(X2) ) )
| ~ p103(X2) )
& ( ( ( ! [X19] :
( ~ r1(X2,X19)
| ~ p3(X19)
| ~ p102(X19) )
| p3(X2) )
& ( ! [X20] :
( ~ r1(X2,X20)
| p3(X20)
| ~ p102(X20) )
| ~ p3(X2) ) )
| ~ p102(X2) )
& ( ( ( ! [X21] :
( ~ r1(X2,X21)
| ~ p2(X21)
| ~ p101(X21) )
| p2(X2) )
& ( ! [X22] :
( ~ r1(X2,X22)
| p2(X22)
| ~ p101(X22) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X23] :
( ~ r1(X2,X23)
| ~ p1(X23)
| ~ p100(X23) )
| p1(X2) )
& ( ! [X24] :
( ~ r1(X2,X24)
| p1(X24)
| ~ p100(X24) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p104(X2)
| ~ p105(X2) )
& ( p103(X2)
| ~ p104(X2) )
& ( p102(X2)
| ~ p103(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( r1(X0,X2)
| ~ r1(X0,X1)
| ~ r1(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( r1(X0,X2)
| ~ r1(X0,X1)
| ~ r1(X1,X2) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ? [X3] :
( r1(X2,X3)
& ~ p6(X3)
& p105(X3) )
& ? [X4] :
( r1(X2,X4)
& p6(X4)
& p105(X4) ) )
| p105(X2)
| ~ p104(X2) )
& ( ( ? [X5] :
( r1(X2,X5)
& ~ p5(X5)
& ~ p105(X5)
& p104(X5) )
& ? [X6] :
( r1(X2,X6)
& p5(X6)
& ~ p105(X6)
& p104(X6) ) )
| p104(X2)
| ~ p103(X2) )
& ( ( ? [X7] :
( r1(X2,X7)
& ~ p4(X7)
& ~ p104(X7)
& p103(X7) )
& ? [X8] :
( r1(X2,X8)
& p4(X8)
& ~ p104(X8)
& p103(X8) ) )
| p103(X2)
| ~ p102(X2) )
& ( ( ? [X9] :
( r1(X2,X9)
& ~ p3(X9)
& ~ p103(X9)
& p102(X9) )
& ? [X10] :
( r1(X2,X10)
& p3(X10)
& ~ p103(X10)
& p102(X10) ) )
| p102(X2)
| ~ p101(X2) )
& ( ( ? [X11] :
( r1(X2,X11)
& ~ p2(X11)
& ~ p102(X11)
& p101(X11) )
& ? [X12] :
( r1(X2,X12)
& p2(X12)
& ~ p102(X12)
& p101(X12) ) )
| p101(X2)
| ~ p100(X2) )
& ( ( ( ! [X13] :
( ~ r1(X2,X13)
| ~ p6(X13)
| ~ p105(X13) )
| p6(X2) )
& ( ! [X14] :
( ~ r1(X2,X14)
| p6(X14)
| ~ p105(X14) )
| ~ p6(X2) ) )
| ~ p105(X2) )
& ( ( ( ! [X15] :
( ~ r1(X2,X15)
| ~ p5(X15)
| ~ p104(X15) )
| p5(X2) )
& ( ! [X16] :
( ~ r1(X2,X16)
| p5(X16)
| ~ p104(X16) )
| ~ p5(X2) ) )
| ~ p104(X2) )
& ( ( ( ! [X17] :
( ~ r1(X2,X17)
| ~ p4(X17)
| ~ p103(X17) )
| p4(X2) )
& ( ! [X18] :
( ~ r1(X2,X18)
| p4(X18)
| ~ p103(X18) )
| ~ p4(X2) ) )
| ~ p103(X2) )
& ( ( ( ! [X19] :
( ~ r1(X2,X19)
| ~ p3(X19)
| ~ p102(X19) )
| p3(X2) )
& ( ! [X20] :
( ~ r1(X2,X20)
| p3(X20)
| ~ p102(X20) )
| ~ p3(X2) ) )
| ~ p102(X2) )
& ( ( ( ! [X21] :
( ~ r1(X2,X21)
| ~ p2(X21)
| ~ p101(X21) )
| p2(X2) )
& ( ! [X22] :
( ~ r1(X2,X22)
| p2(X22)
| ~ p101(X22) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X23] :
( ~ r1(X2,X23)
| ~ p1(X23)
| ~ p100(X23) )
| p1(X2) )
& ( ! [X24] :
( ~ r1(X2,X24)
| p1(X24)
| ~ p100(X24) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p104(X2)
| ~ p105(X2) )
& ( p103(X2)
| ~ p104(X2) )
& ( p102(X2)
| ~ p103(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ? [X3] :
( r1(X2,X3)
& ~ p6(X3)
& p105(X3) )
& ? [X4] :
( r1(X2,X4)
& p6(X4)
& p105(X4) ) )
| p105(X2)
| ~ p104(X2) )
& ( ( ? [X5] :
( r1(X2,X5)
& ~ p5(X5)
& ~ p105(X5)
& p104(X5) )
& ? [X6] :
( r1(X2,X6)
& p5(X6)
& ~ p105(X6)
& p104(X6) ) )
| p104(X2)
| ~ p103(X2) )
& ( ( ? [X7] :
( r1(X2,X7)
& ~ p4(X7)
& ~ p104(X7)
& p103(X7) )
& ? [X8] :
( r1(X2,X8)
& p4(X8)
& ~ p104(X8)
& p103(X8) ) )
| p103(X2)
| ~ p102(X2) )
& ( ( ? [X9] :
( r1(X2,X9)
& ~ p3(X9)
& ~ p103(X9)
& p102(X9) )
& ? [X10] :
( r1(X2,X10)
& p3(X10)
& ~ p103(X10)
& p102(X10) ) )
| p102(X2)
| ~ p101(X2) )
& ( ( ? [X11] :
( r1(X2,X11)
& ~ p2(X11)
& ~ p102(X11)
& p101(X11) )
& ? [X12] :
( r1(X2,X12)
& p2(X12)
& ~ p102(X12)
& p101(X12) ) )
| p101(X2)
| ~ p100(X2) )
& ( ( ( ! [X13] :
( ~ r1(X2,X13)
| ~ p6(X13)
| ~ p105(X13) )
| p6(X2) )
& ( ! [X14] :
( ~ r1(X2,X14)
| p6(X14)
| ~ p105(X14) )
| ~ p6(X2) ) )
| ~ p105(X2) )
& ( ( ( ! [X15] :
( ~ r1(X2,X15)
| ~ p5(X15)
| ~ p104(X15) )
| p5(X2) )
& ( ! [X16] :
( ~ r1(X2,X16)
| p5(X16)
| ~ p104(X16) )
| ~ p5(X2) ) )
| ~ p104(X2) )
& ( ( ( ! [X17] :
( ~ r1(X2,X17)
| ~ p4(X17)
| ~ p103(X17) )
| p4(X2) )
& ( ! [X18] :
( ~ r1(X2,X18)
| p4(X18)
| ~ p103(X18) )
| ~ p4(X2) ) )
| ~ p103(X2) )
& ( ( ( ! [X19] :
( ~ r1(X2,X19)
| ~ p3(X19)
| ~ p102(X19) )
| p3(X2) )
& ( ! [X20] :
( ~ r1(X2,X20)
| p3(X20)
| ~ p102(X20) )
| ~ p3(X2) ) )
| ~ p102(X2) )
& ( ( ( ! [X21] :
( ~ r1(X2,X21)
| ~ p2(X21)
| ~ p101(X21) )
| p2(X2) )
& ( ! [X22] :
( ~ r1(X2,X22)
| p2(X22)
| ~ p101(X22) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X23] :
( ~ r1(X2,X23)
| ~ p1(X23)
| ~ p100(X23) )
| p1(X2) )
& ( ! [X24] :
( ~ r1(X2,X24)
| p1(X24)
| ~ p100(X24) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p104(X2)
| ~ p105(X2) )
& ( p103(X2)
| ~ p104(X2) )
& ( p102(X2)
| ~ p103(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f13,plain,
! [X2,X0,X1] :
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| r1(X0,X2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f50,plain,
! [X2] :
( ~ p101(X2)
| p102(X2)
| ~ p3(sK4(X2))
| ~ r1(sK0,X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f51,plain,
! [X2] :
( ~ p101(X2)
| p102(X2)
| r1(X2,sK4(X2))
| ~ r1(sK0,X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f56,plain,
! [X2] :
( ~ p100(X2)
| p101(X2)
| p101(sK2(X2))
| ~ r1(sK0,X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f57,plain,
! [X2] :
( ~ p100(X2)
| p101(X2)
| ~ p102(sK2(X2))
| ~ r1(sK0,X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f59,plain,
! [X2] :
( ~ p100(X2)
| p101(X2)
| r1(X2,sK2(X2))
| ~ r1(sK0,X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f69,plain,
! [X1] :
( ~ r1(sK0,X1)
| p3(X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f70,plain,
p100(sK0),
inference(cnf_transformation,[],[f11]) ).
fof(f71,plain,
~ p101(sK0),
inference(cnf_transformation,[],[f11]) ).
fof(f72,plain,
p101(sK0),
inference(consistent_polarity_flipping,[],[f71]) ).
fof(f82,plain,
! [X2] :
( ~ r1(sK0,X2)
| ~ p101(X2)
| r1(X2,sK2(X2))
| ~ p100(X2) ),
inference(consistent_polarity_flipping,[],[f59]) ).
fof(f84,plain,
! [X2] :
( p102(sK2(X2))
| ~ p101(X2)
| ~ p100(X2)
| ~ r1(sK0,X2) ),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f85,plain,
! [X2] :
( ~ p101(sK2(X2))
| ~ p101(X2)
| ~ p100(X2)
| ~ r1(sK0,X2) ),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f90,plain,
! [X2] :
( ~ r1(sK0,X2)
| ~ p102(X2)
| r1(X2,sK4(X2))
| p101(X2) ),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f91,plain,
! [X2] :
( ~ p3(sK4(X2))
| ~ p102(X2)
| p101(X2)
| ~ r1(sK0,X2) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f135,plain,
( ~ p101(sK0)
| r1(sK0,sK2(sK0))
| ~ p100(sK0) ),
inference(resolution,[],[f12,f82]) ).
fof(f221,plain,
( r1(sK0,sK2(sK0))
| ~ p100(sK0) ),
inference(forward_subsumption_resolution,[],[f135,f72]) ).
fof(f238,plain,
r1(sK0,sK2(sK0)),
inference(forward_subsumption_resolution,[],[f221,f70]) ).
fof(f269,plain,
( ~ p102(sK2(sK0))
| r1(sK2(sK0),sK4(sK2(sK0)))
| p101(sK2(sK0)) ),
inference(resolution,[],[f238,f90]) ).
fof(f283,plain,
! [X0] :
( ~ r1(sK2(sK0),X0)
| r1(sK0,X0) ),
inference(resolution,[],[f238,f13]) ).
fof(f285,definition,
( spl11_22
<=> p102(sK2(sK0)) ),
introduced(definition,[new_symbols(definition,[spl11_22])],[avatar_definition]) ).
fof(f286,plain,
( ~ p102(sK2(sK0))
| spl11_22 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f287,plain,
( p102(sK2(sK0))
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f325,definition,
( spl11_32
<=> p101(sK2(sK0)) ),
introduced(definition,[new_symbols(definition,[spl11_32])],[avatar_definition]) ).
fof(f326,plain,
( ~ p101(sK2(sK0))
| spl11_32 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f327,plain,
( p101(sK2(sK0))
| ~ spl11_32 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f375,definition,
( spl11_43
<=> r1(sK2(sK0),sK4(sK2(sK0))) ),
introduced(definition,[new_symbols(definition,[spl11_43])],[avatar_definition]) ).
fof(f377,plain,
( r1(sK2(sK0),sK4(sK2(sK0)))
| ~ spl11_43 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f378,plain,
( spl11_32
| spl11_43
| ~ spl11_22 ),
inference(avatar_split_clause,[],[f269,f285,f375,f325]) ).
fof(f586,plain,
( ~ p101(sK0)
| ~ p100(sK0)
| ~ r1(sK0,sK0)
| ~ spl11_32 ),
inference(resolution,[],[f327,f85]) ).
fof(f587,plain,
( ~ p100(sK0)
| ~ r1(sK0,sK0)
| ~ spl11_32 ),
inference(forward_subsumption_resolution,[],[f586,f72]) ).
fof(f588,plain,
( ~ r1(sK0,sK0)
| ~ spl11_32 ),
inference(forward_subsumption_resolution,[],[f587,f70]) ).
fof(f589,plain,
( $false
| ~ spl11_32 ),
inference(forward_subsumption_resolution,[],[f588,f12]) ).
fof(f590,plain,
~ spl11_32,
inference(avatar_contradiction_clause,[],[f589]) ).
fof(f591,plain,
( ~ p101(sK0)
| ~ p100(sK0)
| ~ r1(sK0,sK0)
| spl11_22 ),
inference(resolution,[],[f286,f84]) ).
fof(f592,plain,
( ~ p100(sK0)
| ~ r1(sK0,sK0)
| spl11_22 ),
inference(forward_subsumption_resolution,[],[f591,f72]) ).
fof(f593,plain,
( ~ r1(sK0,sK0)
| spl11_22 ),
inference(forward_subsumption_resolution,[],[f592,f70]) ).
fof(f594,plain,
( $false
| spl11_22 ),
inference(forward_subsumption_resolution,[],[f593,f12]) ).
fof(f595,plain,
spl11_22,
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f657,plain,
( r1(sK0,sK4(sK2(sK0)))
| ~ spl11_43 ),
inference(resolution,[],[f283,f377]) ).
fof(f845,definition,
( spl11_117
<=> p3(sK4(sK2(sK0))) ),
introduced(definition,[new_symbols(definition,[spl11_117])],[avatar_definition]) ).
fof(f847,plain,
( p3(sK4(sK2(sK0)))
| ~ spl11_117 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f978,plain,
( p3(sK4(sK2(sK0)))
| ~ spl11_43 ),
inference(resolution,[],[f657,f69]) ).
fof(f1115,plain,
( spl11_117
| ~ spl11_43 ),
inference(avatar_split_clause,[],[f978,f375,f845]) ).
fof(f1128,plain,
( ~ p102(sK2(sK0))
| p101(sK2(sK0))
| ~ r1(sK0,sK2(sK0))
| ~ spl11_117 ),
inference(resolution,[],[f847,f91]) ).
fof(f1129,plain,
( p101(sK2(sK0))
| ~ r1(sK0,sK2(sK0))
| ~ spl11_22
| ~ spl11_117 ),
inference(forward_subsumption_resolution,[],[f1128,f287]) ).
fof(f1130,plain,
( ~ r1(sK0,sK2(sK0))
| ~ spl11_22
| spl11_32
| ~ spl11_117 ),
inference(forward_subsumption_resolution,[],[f1129,f326]) ).
fof(f1131,plain,
( $false
| ~ spl11_22
| spl11_32
| ~ spl11_117 ),
inference(forward_subsumption_resolution,[],[f1130,f238]) ).
fof(f1132,plain,
( ~ spl11_22
| spl11_32
| ~ spl11_117 ),
inference(avatar_contradiction_clause,[],[f1131]) ).
cnf(s32,plain,
( ~ spl11_22
| spl11_32
| spl11_43 ),
inference(sat_conversion,[],[f378]) ).
cnf(s68,plain,
~ spl11_32,
inference(sat_conversion,[],[f590]) ).
cnf(s69,plain,
spl11_22,
inference(sat_conversion,[],[f595]) ).
cnf(s149,plain,
( ~ spl11_43
| spl11_117 ),
inference(sat_conversion,[],[f1115]) ).
cnf(s152,plain,
( ~ spl11_22
| spl11_32
| ~ spl11_117 ),
inference(sat_conversion,[],[f1132]) ).
cnf(s154,plain,
~ spl11_117,
inference(rat,[],[s152,s69,s68]) ).
cnf(s156,plain,
~ spl11_43,
inference(rat,[],[s149,s154]) ).
cnf(s173,plain,
$false,
inference(rat,[],[s32,s156,s68,s69]) ).
fof(f1133,plain,
$false,
inference(avatar_sat_refutation,[],[s173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 16:36:46 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % (3768883)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (3768889)% WARNING: option uhcvi not known.
% 0.12/0.45 % (3768889)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2452030751:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % (3768889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3768883-3768889"...
% 0.12/0.45 % (3768890)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3762470743:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (3768888)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3536580340_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.45 % (3768891)dis+10_1_sil=32000:sp=arity:random_seed=2678034225:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % (3768893)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=235296262:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.45 % (3768892)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=788767868:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (3768889)...printing done.
% 0.12/0.45 % (3768894)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3782281346:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (3768889)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (3768889)------------------------------
% 0.12/0.46 % (3768889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (3768889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (3768889)CaDiCaL version: 2.1.3
% 0.12/0.46 % (3768889)Termination reason: Refutation
% 0.12/0.46 % (3768889)Time elapsed: 0.007 s
% 0.12/0.46 % (3768889)Peak memory usage: 13 MB
% 0.12/0.46 % (3768889)Instructions burned: 18 (million)
% 0.12/0.46 % (3768883)Success in time 0.033 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------