%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:38:58 AM UTC 2026
% Result : Unsatisfiable 2.51s 1.12s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 16 unt; 3 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 27 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ follows(X0,X1)
| succeeds(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',direct_success) ).
fof(f2,axiom,
! [X2,X0,X1] :
( succeeds(X0,X1)
| ~ succeeds(X0,X2)
| ~ succeeds(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_success) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ labels(X2,X0)
| ~ has(X1,goto(X2))
| succeeds(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goto_success) ).
fof(f8,axiom,
labels(loop,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',label_state_3) ).
fof(f13,axiom,
follows(p6,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_3_to_6) ).
fof(f15,axiom,
follows(p7,p6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_6_to_7) ).
fof(f17,axiom,
follows(p8,p7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_7_to_8) ).
fof(f18,axiom,
has(p8,goto(loop)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_8) ).
fof(f19,negated_conjecture,
~ succeeds(p3,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_loop_through_p3) ).
fof(f23,plain,
succeeds(p6,p3),
inference(resolution,[],[f1,f13]) ).
fof(f24,plain,
succeeds(p7,p6),
inference(resolution,[],[f1,f15]) ).
fof(f25,plain,
succeeds(p8,p7),
inference(resolution,[],[f1,f17]) ).
fof(f27,plain,
! [X0] :
( ~ succeeds(p3,X0)
| ~ succeeds(X0,p3) ),
inference(resolution,[],[f2,f19]) ).
fof(f28,plain,
! [X0,X1] :
( ~ succeeds(X0,p3)
| ~ succeeds(p3,X1)
| ~ succeeds(X1,X0) ),
inference(resolution,[],[f27,f2]) ).
fof(f33,plain,
! [X0] :
( succeeds(p3,X0)
| ~ has(X0,goto(loop)) ),
inference(resolution,[],[f3,f8]) ).
fof(f65,plain,
( ~ succeeds(p6,p3)
| ~ succeeds(p3,p7) ),
inference(resolution,[],[f28,f24]) ).
fof(f74,definition,
( spl0_1
<=> succeeds(p3,p8) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f75,plain,
( ~ succeeds(p3,p8)
| spl0_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f81,definition,
( spl0_3
<=> succeeds(p3,p7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f82,plain,
( ~ succeeds(p3,p7)
| spl0_3 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_4
<=> succeeds(p6,p3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f85,plain,
( ~ succeeds(p6,p3)
| spl0_4 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f65,f84,f81]) ).
fof(f94,plain,
( ~ has(p8,goto(loop))
| spl0_1 ),
inference(resolution,[],[f75,f33]) ).
fof(f97,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f85,f23]) ).
fof(f100,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f102,plain,
( ! [X0] :
( ~ succeeds(p3,X0)
| ~ succeeds(X0,p7) )
| spl0_3 ),
inference(resolution,[],[f82,f2]) ).
fof(f106,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f94,f18]) ).
fof(f107,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f121,plain,
( ~ succeeds(p3,p8)
| spl0_3 ),
inference(resolution,[],[f102,f25]) ).
fof(f122,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f121,f81,f74]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f100]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f107]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f122]) ).
cnf(s8,plain,
spl0_3,
inference(rat,[],[s7,s5]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s4,s8]) ).
fof(f123,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n008.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 21:43:10 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.22 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
% 2.51/1.12 % (2683058)Input is clausal, will run a generic CNF schedule.
% 2.51/1.12 % (2683069)dis-21_1_sil=8000:lcm=predicate:random_seed=2040512162:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.51/1.12 % (2683069)First to succeed.
% 2.51/1.12 % (2683069)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2683058"
% 2.51/1.12 % (2683063)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=4226296501:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.51/1.12 % (2683068)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4096705773:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.51/1.12 % (2683066)lrs+10_1_sil=8000:sp=occurrence:random_seed=2179019055:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.51/1.12 % (2683067)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=185724919:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.51/1.12 % (2683065)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3136159570:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.51/1.12 % (2683064)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4169795214:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.51/1.12 % (2683068)Also succeeded, but the first one will report.
% 2.51/1.12 % (2683066)Also succeeded, but the first one will report.
% 2.51/1.12 % (2683067)Also succeeded, but the first one will report.
% 2.51/1.12 % (2683069)Refutation found. Thanks to Tanya!
% 2.51/1.12 % SZS status Unsatisfiable for theBenchmark
% 2.51/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/1.12 % (2683069)------------------------------
% 2.51/1.12 % (2683069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.12 % (2683069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.12 % (2683069)CaDiCaL version: 2.1.3
% 2.51/1.12 % (2683069)Termination reason: Refutation
% 2.51/1.12 % (2683069)Time elapsed: 0.002 s
% 2.51/1.12 % (2683069)Peak memory usage: 89 MB
% 2.51/1.12 % (2683069)Instructions burned: 2 (million)
% 2.51/1.12 % (2683069)------------------------------
% 2.51/1.12 % (2683069)------------------------------
% 2.51/1.12 % (2683058)Success in time 0.27 s
% 2.51/1.12 % Vampire exiting
%------------------------------------------------------------------------------