%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN345-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:50:18 PM UTC 2026
% Result : Unsatisfiable 0.19s 1.13s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 6 unt; 7 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 118 ( 49 ~; 62 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] :
( f(a,b,X0)
| ~ f(a,a,b)
| f(a,b,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
fof(f3,negated_conjecture,
! [X0,X1] :
( f(b,X0,X1)
| f(a,a,b)
| ~ f(a,b,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
fof(f4,negated_conjecture,
! [X0,X1] :
( ~ f(X0,z(X0,X1),z(X0,X1))
| f(a,a,b)
| ~ f(a,b,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
fof(f5,negated_conjecture,
! [X0,X1] :
( f(X0,X1,z(X0,X1))
| f(a,a,b)
| f(a,b,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
fof(f6,negated_conjecture,
! [X0,X1] :
( f(X0,X1,z(X0,X1))
| ~ f(a,a,b)
| ~ f(a,b,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
fof(f7,negated_conjecture,
! [X0] :
( ~ f(b,b,X0)
| f(a,a,b)
| f(a,b,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
fof(f8,negated_conjecture,
! [X0] :
( ~ f(b,b,X0)
| ~ f(a,a,b)
| ~ f(a,b,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f10,definition,
( spl0_1
<=> f(a,b,b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f11,plain,
( ~ f(a,b,b)
| spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f13,definition,
( spl0_2
<=> f(a,a,b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f16,definition,
( spl0_3
<=> ! [X0] : ~ f(b,b,X0) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f17,plain,
( ! [X0] : ~ f(b,b,X0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f8,f16,f13,f10]) ).
fof(f21,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f7,f16,f13,f10]) ).
fof(f23,definition,
( spl0_4
<=> ! [X0,X1] : f(X0,X1,z(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f24,plain,
( ! [X0,X1] : f(X0,X1,z(X0,X1))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f25,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f6,f23,f13,f10]) ).
fof(f26,plain,
( spl0_1
| spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f5,f23,f13,f10]) ).
fof(f28,definition,
( spl0_5
<=> ! [X0,X1] : ~ f(X0,z(X0,X1),z(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f29,plain,
( ! [X0,X1] : ~ f(X0,z(X0,X1),z(X0,X1))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( ~ spl0_1
| spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f4,f28,f13,f10]) ).
fof(f32,definition,
( spl0_6
<=> ! [X0,X1] : f(b,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f33,plain,
( ! [X0,X1] : f(b,X0,X1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f34,plain,
( ~ spl0_1
| spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f3,f32,f13,f10]) ).
fof(f40,definition,
( spl0_8
<=> ! [X0] : f(a,b,X0) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f41,plain,
( ! [X0] : f(a,b,X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( spl0_1
| ~ spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f1,f40,f13,f10]) ).
fof(f43,plain,
( $false
| ~ spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f24,f17]) ).
fof(f44,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
( $false
| spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f41,f11]) ).
fof(f46,plain,
( spl0_1
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f49,plain,
( $false
| ~ spl0_5
| ~ spl0_6 ),
inference(resolution,[],[f29,f33]) ).
fof(f50,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f49]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f25]) ).
cnf(s4,plain,
( spl0_1
| spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f26]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f30]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f34]) ).
cnf(s8,plain,
( spl0_1
| ~ spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f42]) ).
cnf(s9,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s10,plain,
( spl0_1
| ~ spl0_8 ),
inference(sat_conversion,[],[f46]) ).
cnf(s12,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f50]) ).
cnf(s13,plain,
( spl0_1
| spl0_2 ),
inference(rat,[],[s9,s2,s4]) ).
cnf(s14,plain,
( spl0_1
| spl0_8 ),
inference(rat,[],[s13,s8]) ).
cnf(s15,plain,
spl0_1,
inference(rat,[],[s14,s10]) ).
cnf(s16,plain,
spl0_2,
inference(rat,[],[s12,s5,s6,s15]) ).
cnf(s17,plain,
spl0_4,
inference(rat,[],[s3,s15,s16]) ).
cnf(s18,plain,
spl0_3,
inference(rat,[],[s1,s15,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s9,s17,s18]) ).
fof(f51,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN345-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 15:47:03 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/1.13 % (4109718)Input is clausal, will run a generic CNF schedule.
% 0.19/1.13 % (4109727)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4065503428:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.13 % (4109727)First to succeed.
% 0.19/1.13 % (4109727)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4109718"
% 0.19/1.13 % (4109724)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2322182630:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.13 % (4109728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3187837699:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.13 % (4109723)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=3815619346:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.13 % (4109725)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4130185515:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.13 % (4109728)Also succeeded, but the first one will report.
% 0.19/1.13 % (4109726)lrs+10_1_sil=8000:sp=occurrence:random_seed=3668724180:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.13 % (4109726)Also succeeded, but the first one will report.
% 0.19/1.13 % (4109729)dis-21_1_sil=8000:lcm=predicate:random_seed=3538096994: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)
% 0.19/1.13 % (4109729)Also succeeded, but the first one will report.
% 0.19/1.13 % (4109727)Refutation found. Thanks to Tanya!
% 0.19/1.13 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.14 % (4109727)------------------------------
% 0.19/1.14 % (4109727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.14 % (4109727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.14 % (4109727)CaDiCaL version: 2.1.3
% 0.19/1.14 % (4109727)Termination reason: Refutation
% 0.19/1.14 % (4109727)Time elapsed: 0.001 s
% 0.19/1.14 % (4109727)Peak memory usage: 89 MB
% 0.19/1.14 % (4109727)Instructions burned: 1 (million)
% 0.19/1.14 % (4109727)------------------------------
% 0.19/1.14 % (4109727)------------------------------
% 0.19/1.14 % (4109718)Success in time 0.284 s
% 0.19/1.14 % Vampire exiting
%------------------------------------------------------------------------------