%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN169-1 : 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 : n015.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 01:49:49 PM UTC 2026
% Result : Unsatisfiable 2.82s 1.17s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 13 unt; 5 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 33 ~; 24 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
q0(e,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,axiom,
n0(d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f40,axiom,
! [X0,X1] :
( ~ n0(X1,X0)
| l1(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
fof(f168,axiom,
( k2(e,e)
| ~ l1(e,e) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_130) ).
fof(f290,axiom,
! [X2,X0,X1] :
( p3(X0,X0,X0)
| ~ q0(X1,X0)
| ~ k2(X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_252) ).
fof(f369,negated_conjecture,
! [X0,X1] : ~ p3(X0,d,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f1013,definition,
( spl0_181
<=> l1(e,e) ),
introduced(definition,[new_symbols(definition,[spl0_181])],[avatar_definition]) ).
fof(f1014,plain,
( ~ l1(e,e)
| spl0_181 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f1016,definition,
( spl0_182
<=> k2(e,e) ),
introduced(definition,[new_symbols(definition,[spl0_182])],[avatar_definition]) ).
fof(f1017,plain,
( k2(e,e)
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1018,plain,
( ~ spl0_181
| spl0_182 ),
inference(avatar_split_clause,[],[f168,f1016,f1013]) ).
fof(f1196,definition,
( spl0_233
<=> ! [X2] : ~ k2(X2,X2) ),
introduced(definition,[new_symbols(definition,[spl0_233])],[avatar_definition]) ).
fof(f1197,plain,
( ! [X2] : ~ k2(X2,X2)
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f1196]) ).
fof(f1199,definition,
( spl0_234
<=> ! [X0,X1] :
( p3(X0,X0,X0)
| ~ q0(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_234])],[avatar_definition]) ).
fof(f1200,plain,
( ! [X0,X1] :
( p3(X0,X0,X0)
| ~ q0(X1,X0) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f1201,plain,
( spl0_233
| spl0_234 ),
inference(avatar_split_clause,[],[f290,f1199,f1196]) ).
fof(f1227,definition,
( spl0_242
<=> ! [X1] : ~ q0(X1,d) ),
introduced(definition,[new_symbols(definition,[spl0_242])],[avatar_definition]) ).
fof(f1228,plain,
( ! [X1] : ~ q0(X1,d)
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f1465,plain,
( $false
| ~ spl0_242 ),
inference(resolution,[],[f2,f1228]) ).
fof(f1468,plain,
~ spl0_242,
inference(avatar_contradiction_clause,[],[f1465]) ).
fof(f1826,plain,
l1(e,e),
inference(resolution,[],[f40,f3]) ).
fof(f1875,plain,
( $false
| spl0_181 ),
inference(resolution,[],[f1826,f1014]) ).
fof(f1877,plain,
spl0_181,
inference(avatar_contradiction_clause,[],[f1875]) ).
fof(f1878,plain,
( $false
| ~ spl0_182
| ~ spl0_233 ),
inference(resolution,[],[f1017,f1197]) ).
fof(f1879,plain,
( ~ spl0_182
| ~ spl0_233 ),
inference(avatar_contradiction_clause,[],[f1878]) ).
fof(f1880,plain,
( ! [X0] : ~ q0(X0,d)
| ~ spl0_234 ),
inference(resolution,[],[f1200,f369]) ).
fof(f1881,plain,
( spl0_242
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f1880,f1199,f1227]) ).
cnf(s99,plain,
( ~ spl0_181
| spl0_182 ),
inference(sat_conversion,[],[f1018]) ).
cnf(s126,plain,
( spl0_233
| spl0_234 ),
inference(sat_conversion,[],[f1201]) ).
cnf(s174,plain,
~ spl0_242,
inference(sat_conversion,[],[f1468]) ).
cnf(s246,plain,
spl0_181,
inference(sat_conversion,[],[f1877]) ).
cnf(s247,plain,
( ~ spl0_182
| ~ spl0_233 ),
inference(sat_conversion,[],[f1879]) ).
cnf(s248,plain,
( ~ spl0_234
| spl0_242 ),
inference(sat_conversion,[],[f1881]) ).
cnf(s252,plain,
~ spl0_234,
inference(rat,[],[s248,s174]) ).
cnf(s270,plain,
spl0_233,
inference(rat,[],[s126,s252]) ).
cnf(s271,plain,
~ spl0_182,
inference(rat,[],[s247,s270]) ).
cnf(s286,plain,
$false,
inference(rat,[],[s99,s271,s246]) ).
fof(f1882,plain,
$false,
inference(avatar_sat_refutation,[],[s286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN169-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n015.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 15:40:47 UTC 2026
% 0.10/0.17 % 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
% 0.10/0.21 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
% 2.82/1.17 % (2726685)Input is clausal, will run a generic CNF schedule.
% 2.82/1.17 % (2726696)dis-21_1_sil=8000:lcm=predicate:random_seed=2266277817: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)
% 2.82/1.17 % (2726696)First to succeed.
% 2.82/1.17 % (2726696)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2726685"
% 2.82/1.17 % (2726690)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=1668770708:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.82/1.17 % (2726693)lrs+10_1_sil=8000:sp=occurrence:random_seed=2949206236:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.82/1.17 % (2726695)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4002651020:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.82/1.17 % (2726691)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1849759120:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.82/1.17 % (2726694)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1410537170:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.82/1.17 % (2726692)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2579998551:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.82/1.17 % (2726693)Also succeeded, but the first one will report.
% 2.82/1.17 % (2726694)Also succeeded, but the first one will report.
% 2.82/1.17 % (2726695)Also succeeded, but the first one will report.
% 2.82/1.17 % (2726696)Refutation found. Thanks to Tanya!
% 2.82/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.82/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.17 % (2726696)------------------------------
% 2.82/1.17 % (2726696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.17 % (2726696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.17 % (2726696)CaDiCaL version: 2.1.3
% 2.82/1.17 % (2726696)Termination reason: Refutation
% 2.82/1.17 % (2726696)Time elapsed: 0.010 s
% 2.82/1.17 % (2726696)Peak memory usage: 90 MB
% 2.82/1.17 % (2726696)Instructions burned: 27 (million)
% 2.82/1.17 % (2726696)------------------------------
% 2.82/1.17 % (2726696)------------------------------
% 2.82/1.17 % (2726685)Success in time 0.314 s
% 2.82/1.17 % Vampire exiting
%------------------------------------------------------------------------------