%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL638+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 SAT
% Computer : n016.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 11:59:05 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 9 unt; 2 def)
% Number of atoms : 330 ( 0 equ)
% Maximal formula atoms : 31 ( 7 avg)
% Number of connectives : 616 ( 329 ~; 229 |; 56 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-1 aty)
% Number of variables : 186 ( 0 sgn 165 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ~ p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(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)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ~ p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(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)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| p1(X3) ) )
& ~ p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ~ ( ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X5,X6)
| ~ p1(X6) ) )
& p1(X4) ) )
| ~ ! [X7] :
( ~ r1(X0,X7)
| ~ ( ~ ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| ~ p1(X10) ) ) )
& ! [X11] :
( ~ r1(X7,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) ) )
| ~ ! [X13] :
( ~ r1(X0,X13)
| ~ ( ~ ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
& ! [X16] :
( ~ r1(X13,X16)
| p1(X16) ) ) )
| ~ ! [X17] :
( ~ r1(X0,X17)
| ~ ! [X18] :
( ~ r1(X17,X18)
| $false ) )
| ! [X19] :
( ~ r1(X0,X19)
| p1(X19)
| ~ ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| p1(X3) ) )
& ~ p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ~ ( ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X5,X6)
| ~ p1(X6) ) )
& p1(X4) ) )
| ~ ! [X7] :
( ~ r1(X0,X7)
| ~ ( ~ ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| ~ p1(X10) ) ) )
& ! [X11] :
( ~ r1(X7,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) ) )
| ~ ! [X13] :
( ~ r1(X0,X13)
| ~ ( ~ ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
& ! [X16] :
( ~ r1(X13,X16)
| p1(X16) ) ) )
| ~ ! [X17] :
( ~ r1(X0,X17)
| ~ ! [X18] : ~ r1(X17,X18) )
| ! [X19] :
( ~ r1(X0,X19)
| p1(X19)
| ~ ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(true_and_false_elimination,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| p1(X3) ) )
& ~ p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ~ ( ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X5,X6)
| ~ p1(X6) ) )
& p1(X4) ) )
| ~ ! [X7] :
( ~ r1(X0,X7)
| ~ ( ~ ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| ~ p1(X10) ) ) )
& ! [X11] :
( ~ r1(X7,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) ) )
| ~ ! [X13] :
( ~ r1(X0,X13)
| ~ ( ~ ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
& ! [X16] :
( ~ r1(X13,X16)
| p1(X16) ) ) )
| ~ ! [X17] :
( ~ r1(X0,X17)
| ~ ! [X18] : ~ r1(X17,X18) )
| ! [X19] :
( ~ r1(X0,X19)
| p1(X19)
| ~ ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& ~ p1(X3) ) )
| p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ? [X6] :
( r1(X5,X6)
& p1(X6) ) )
| ~ p1(X4) )
& ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ? [X10] :
( r1(X9,X10)
& p1(X10) ) ) )
| ? [X11] :
( r1(X7,X11)
& ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) )
& ! [X13] :
( ~ r1(X0,X13)
| ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
| ? [X16] :
( r1(X13,X16)
& ~ p1(X16) ) )
& ! [X17] :
( ~ r1(X0,X17)
| ? [X18] : r1(X17,X18) )
& ? [X19] :
( r1(X0,X19)
& ~ p1(X19)
& ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& ~ p1(X3) ) )
| p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ? [X6] :
( r1(X5,X6)
& p1(X6) ) )
| ~ p1(X4) )
& ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ? [X10] :
( r1(X9,X10)
& p1(X10) ) ) )
| ? [X11] :
( r1(X7,X11)
& ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) )
& ! [X13] :
( ~ r1(X0,X13)
| ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
| ? [X16] :
( r1(X13,X16)
& ~ p1(X16) ) )
& ! [X17] :
( ~ r1(X0,X17)
| ? [X18] : r1(X17,X18) )
& ? [X19] :
( r1(X0,X19)
& ~ p1(X19)
& ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
( ! [X1] :
( ~ r1(sK0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ( r1(X2,sK1(X2))
& ~ p1(sK1(X2)) ) )
| p1(X1) )
& ! [X4] :
( ~ r1(sK0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ( r1(X5,sK2(X5))
& p1(sK2(X5)) ) )
| ~ p1(X4) )
& ! [X7] :
( ~ r1(sK0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ( r1(X9,sK3(X9))
& p1(sK3(X9)) ) ) )
| ( r1(X7,sK4(X7))
& ! [X12] :
( ~ r1(sK4(X7),X12)
| ~ p1(X12) ) ) )
& ! [X13] :
( ~ r1(sK0,X13)
| ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
| ( r1(X13,sK5(X13))
& ~ p1(sK5(X13)) ) )
& ! [X17] :
( ~ r1(sK0,X17)
| r1(X17,sK6(X17)) )
& r1(sK0,sK7)
& ~ p1(sK7)
& ! [X20] :
( ~ r1(sK7,X20)
| p1(X20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X3,sK1(X2)),skolemize(X6,sK2(X5)),skolemize(X10,sK3(X9)),skolemize(X11,sK4(X7)),skolemize(X16,sK5(X13)),skolemize(X18,sK6(X17)),skolemize(X19,sK7)],[f7]) ).
fof(f9,plain,
! [X20] :
( ~ r1(sK7,X20)
| p1(X20) ),
inference(cnf_transformation,[],[f8]) ).
fof(f10,plain,
~ p1(sK7),
inference(cnf_transformation,[],[f8]) ).
fof(f11,plain,
r1(sK0,sK7),
inference(cnf_transformation,[],[f8]) ).
fof(f12,plain,
! [X17] :
( ~ r1(sK0,X17)
| r1(X17,sK6(X17)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
! [X14,X15,X13] :
( ~ p1(sK5(X13))
| ~ r1(X13,X14)
| ~ r1(X14,X15)
| p1(X15)
| ~ r1(sK0,X13) ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X14,X15,X13] :
( ~ r1(sK0,X13)
| ~ r1(X13,X14)
| ~ r1(X14,X15)
| p1(X15)
| r1(X13,sK5(X13)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f21,plain,
! [X2,X1] :
( ~ p1(sK1(X2))
| ~ r1(X1,X2)
| ~ r1(sK0,X1)
| p1(X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X2,X1] :
( ~ r1(sK0,X1)
| ~ r1(X1,X2)
| r1(X2,sK1(X2))
| p1(X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
r1(sK7,sK6(sK7)),
inference(resolution,[],[f12,f11]) ).
fof(f35,plain,
! [X0] :
( ~ r1(sK7,X0)
| r1(X0,sK1(X0))
| p1(sK7) ),
inference(resolution,[],[f22,f11]) ).
fof(f36,plain,
! [X0] :
( ~ r1(sK7,X0)
| r1(X0,sK1(X0)) ),
inference(forward_subsumption_resolution,[],[f35,f10]) ).
fof(f37,plain,
r1(sK6(sK7),sK1(sK6(sK7))),
inference(resolution,[],[f36,f23]) ).
fof(f38,plain,
! [X0,X1] :
( ~ r1(sK7,X0)
| ~ r1(X0,X1)
| p1(X1)
| r1(sK7,sK5(sK7)) ),
inference(resolution,[],[f14,f11]) ).
fof(f40,definition,
( spl8_3
<=> r1(sK7,sK5(sK7)) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f42,plain,
( r1(sK7,sK5(sK7))
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f44,definition,
( spl8_4
<=> ! [X0,X1] :
( ~ r1(sK7,X0)
| p1(X1)
| ~ r1(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f45,plain,
( ! [X0,X1] :
( ~ r1(sK7,X0)
| p1(X1)
| ~ r1(X0,X1) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f38,f44,f40]) ).
fof(f48,plain,
( p1(sK5(sK7))
| ~ spl8_3 ),
inference(resolution,[],[f42,f9]) ).
fof(f58,plain,
( ! [X0,X1] :
( ~ r1(sK7,X0)
| ~ r1(X0,X1)
| p1(X1)
| ~ r1(sK0,sK7) )
| ~ spl8_3 ),
inference(resolution,[],[f48,f13]) ).
fof(f73,plain,
( ! [X0,X1] :
( ~ r1(sK7,X0)
| ~ r1(X0,X1)
| p1(X1) )
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f58,f11]) ).
fof(f74,plain,
( spl8_4
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f73,f40,f44]) ).
fof(f98,plain,
( ! [X0] :
( ~ r1(sK6(sK7),X0)
| p1(X0) )
| ~ spl8_4 ),
inference(resolution,[],[f45,f23]) ).
fof(f101,plain,
( p1(sK1(sK6(sK7)))
| ~ spl8_4 ),
inference(resolution,[],[f98,f37]) ).
fof(f103,plain,
( ! [X0] :
( ~ r1(X0,sK6(sK7))
| ~ r1(sK0,X0)
| p1(X0) )
| ~ spl8_4 ),
inference(resolution,[],[f101,f21]) ).
fof(f311,plain,
( ~ r1(sK0,sK7)
| p1(sK7)
| ~ spl8_4 ),
inference(resolution,[],[f103,f23]) ).
fof(f312,plain,
( p1(sK7)
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f311,f11]) ).
fof(f313,plain,
( $false
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f312,f10]) ).
fof(f314,plain,
~ spl8_4,
inference(avatar_contradiction_clause,[],[f313]) ).
cnf(s2,plain,
( spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f46]) ).
cnf(s6,plain,
( ~ spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f74]) ).
cnf(s31,plain,
~ spl8_4,
inference(sat_conversion,[],[f314]) ).
cnf(s32,plain,
~ spl8_3,
inference(rat,[],[s6,s31]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s2,s31,s32]) ).
fof(f315,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 16:13:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 % (2818290)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (2818300)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1310293076:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (2818300) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2818290-2818300"...
% 0.10/0.44 % (2818300)...printing done.
% 0.10/0.44 % (2818300)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (2818300)------------------------------
% 0.10/0.44 % (2818300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (2818300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (2818300)CaDiCaL version: 2.1.3
% 0.10/0.44 % (2818300)Termination reason: Refutation
% 0.10/0.44 % (2818300)Time elapsed: 0.004 s
% 0.10/0.44 % (2818300)Peak memory usage: 12 MB
% 0.10/0.44 % (2818300)Instructions burned: 8 (million)
% 0.10/0.44 % (2818290)Success in time 0.025 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------