%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN108-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:49:41 PM UTC 2026
% Result : Unsatisfiable 0.19s 1.14s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 10 unt; 3 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 24 ~; 20 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
s0(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f37,axiom,
n0(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
fof(f39,axiom,
! [X0,X1] :
( k1(X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_001) ).
fof(f150,axiom,
! [X0] :
( q1(X0,X0,X0)
| ~ k1(X0)
| ~ s0(b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_112) ).
fof(f167,axiom,
! [X0,X1] :
( ~ q1(X1,X0,X0)
| k2(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_129) ).
fof(f369,negated_conjecture,
! [X0] : ~ k2(a,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f1170,definition,
( spl0_201
<=> s0(b) ),
introduced(definition,[new_symbols(definition,[spl0_201])],[avatar_definition]) ).
fof(f1203,definition,
( spl0_209
<=> ! [X0] :
( q1(X0,X0,X0)
| ~ k1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_209])],[avatar_definition]) ).
fof(f1204,plain,
( ! [X0] :
( q1(X0,X0,X0)
| ~ k1(X0) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1205,plain,
( ~ spl0_201
| spl0_209 ),
inference(avatar_split_clause,[],[f150,f1203,f1170]) ).
fof(f1448,definition,
( spl0_268
<=> k1(a) ),
introduced(definition,[new_symbols(definition,[spl0_268])],[avatar_definition]) ).
fof(f1449,plain,
( k1(a)
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f1450,plain,
( ~ k1(a)
| spl0_268 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f1567,plain,
spl0_201,
inference(avatar_split_clause,[],[f5,f1170]) ).
fof(f1657,plain,
( ! [X0] : ~ n0(X0,a)
| spl0_268 ),
inference(resolution,[],[f39,f1450]) ).
fof(f1667,plain,
( $false
| spl0_268 ),
inference(resolution,[],[f1657,f37]) ).
fof(f1668,plain,
spl0_268,
inference(avatar_contradiction_clause,[],[f1667]) ).
fof(f1782,plain,
( ! [X0] :
( k2(X0,X0)
| ~ k1(X0) )
| ~ spl0_209 ),
inference(resolution,[],[f1204,f167]) ).
fof(f1791,plain,
( ~ k1(a)
| ~ spl0_209 ),
inference(resolution,[],[f1782,f369]) ).
fof(f1792,plain,
( $false
| ~ spl0_209
| ~ spl0_268 ),
inference(forward_subsumption_resolution,[],[f1791,f1449]) ).
fof(f1793,plain,
( ~ spl0_209
| ~ spl0_268 ),
inference(avatar_contradiction_clause,[],[f1792]) ).
cnf(s99,plain,
( ~ spl0_201
| spl0_209 ),
inference(sat_conversion,[],[f1205]) ).
cnf(s167,plain,
spl0_201,
inference(sat_conversion,[],[f1567]) ).
cnf(s201,plain,
spl0_268,
inference(sat_conversion,[],[f1668]) ).
cnf(s246,plain,
( ~ spl0_209
| ~ spl0_268 ),
inference(sat_conversion,[],[f1793]) ).
cnf(s249,plain,
~ spl0_209,
inference(rat,[],[s246,s201]) ).
cnf(s302,plain,
$false,
inference(rat,[],[s99,s249,s167]) ).
fof(f1795,plain,
$false,
inference(avatar_sat_refutation,[],[s302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN108-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:34:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 0.19/1.14 % (1855725)Input is clausal, will run a generic CNF schedule.
% 0.19/1.14 % (1855735)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1263726179:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.14 % (1855735)First to succeed.
% 0.19/1.14 % (1855735)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1855725"
% 0.19/1.14 % (1855730)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=5900306:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.14 % (1855736)dis-21_1_sil=8000:lcm=predicate:random_seed=1786773839: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)
% 0.19/1.14 % (1855732)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1219605032:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.14 % (1855731)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3252763421:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.14 % (1855733)lrs+10_1_sil=8000:sp=occurrence:random_seed=3454236875:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.14 % (1855734)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1091719314:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.14 % (1855733)Also succeeded, but the first one will report.
% 0.19/1.14 % (1855734)Also succeeded, but the first one will report.
% 0.19/1.14 % (1855736)Also succeeded, but the first one will report.
% 0.19/1.14 % (1855735)Refutation found. Thanks to Tanya!
% 0.19/1.14 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.14 % (1855735)------------------------------
% 0.19/1.14 % (1855735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.14 % (1855735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.14 % (1855735)CaDiCaL version: 2.1.3
% 0.19/1.14 % (1855735)Termination reason: Refutation
% 0.19/1.14 % (1855735)Time elapsed: 0.009 s
% 0.19/1.14 % (1855735)Peak memory usage: 90 MB
% 0.19/1.14 % (1855735)Instructions burned: 23 (million)
% 0.19/1.14 % (1855735)------------------------------
% 0.19/1.14 % (1855735)------------------------------
% 0.19/1.14 % (1855725)Success in time 0.292 s
% 0.19/1.14 % Vampire exiting
%------------------------------------------------------------------------------