%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO632-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 02:28:28 PM UTC 2026
% Result : Unsatisfiable 2.33s 0.87s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 8 unt; 2 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 7 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : 'E'(f('AP'(s(s('0')),X0)),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2_02) ).
fof(f3,axiom,
! [X0] : 'E'(f(X0),s('0')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_03) ).
fof(f4,axiom,
! [X0,X1] :
( ~ 'E'(f(X0),'0')
| ~ 'E'(f(X1),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_04) ).
fof(f7,definition,
( spl0_1
<=> ! [X1] : ~ 'E'(f(X1),s('0')) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f8,plain,
( ! [X1] : ~ 'E'(f(X1),s('0'))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f10,definition,
( spl0_2
<=> ! [X0] : ~ 'E'(f(X0),'0') ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f11,plain,
( ! [X0] : ~ 'E'(f(X0),'0')
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f12,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f4,f10,f7]) ).
fof(f13,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f2,f11]) ).
fof(f14,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f13]) ).
fof(f15,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f8,f3]) ).
fof(f16,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f15]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f12]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f14]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f16]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f17,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO632-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 17:59:18 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
% 2.33/0.87 % (49404)Input is clausal, will run a generic CNF schedule.
% 2.33/0.87 % (49414)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4026225346:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.33/0.87 % (49414)First to succeed.
% 2.33/0.87 % (49414)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-49404"
% 2.33/0.87 % (49413)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4241903269:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.33/0.87 % (49409)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=3328263359:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.33/0.87 % (49410)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3156143120:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.33/0.87 % (49411)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1681622950:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.33/0.87 % (49415)dis-21_1_sil=8000:lcm=predicate:random_seed=577530812: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)
% 2.33/0.87 % (49413)Refutation not found, incomplete strategy
% 2.33/0.87 % (49413)------------------------------
% 2.33/0.87 % (49413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.87 % (49413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.87 % (49413)CaDiCaL version: 2.1.3
% 2.33/0.87 % (49413)Termination reason: Refutation not found, incomplete strategy
% 2.33/0.87 % (49413)Time elapsed: 0.001 s
% 2.33/0.87 % (49413)Peak memory usage: 86 MB
% 2.33/0.87 % (49415)Also succeeded, but the first one will report.
% 2.33/0.87 % (49412)lrs+10_1_sil=8000:sp=occurrence:random_seed=2063137569:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.33/0.87 % (49412)Refutation not found, incomplete strategy
% 2.33/0.87 % (49412)------------------------------
% 2.33/0.87 % (49412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.87 % (49412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.87 % (49412)CaDiCaL version: 2.1.3
% 2.33/0.87 % (49412)Termination reason: Refutation not found, incomplete strategy
% 2.33/0.87 % (49412)Time elapsed: 0.001 s
% 2.33/0.87 % (49412)Peak memory usage: 86 MB
% 2.33/0.87 % (49414)Refutation found. Thanks to Tanya!
% 2.33/0.87 % SZS status Unsatisfiable for theBenchmark
% 2.33/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.87 % (49414)------------------------------
% 2.33/0.87 % (49414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.87 % (49414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.87 % (49414)CaDiCaL version: 2.1.3
% 2.33/0.87 % (49414)Termination reason: Refutation
% 2.33/0.87 % (49414)Time elapsed: 0.001 s
% 2.33/0.87 % (49414)Peak memory usage: 89 MB
% 2.33/0.87 % (49414)------------------------------
% 2.33/0.87 % (49414)------------------------------
% 2.33/0.87 % (49404)Success in time 0.282 s
% 2.33/0.87 % Vampire exiting
%------------------------------------------------------------------------------