%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN960+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:06:04 PM UTC 2026
% Result : Theorem 2.21s 0.79s
% Output : Refutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 5 unt; 3 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 62 ( 29 ~; 23 |; 3 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 20 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0,X1] : a(X0,X1)
<=> ? [X1,X0] : a(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ? [X0,X1] : a(X0,X1)
<=> ? [X1,X0] : a(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0,X1] : a(X0,X1)
<=> ? [X2,X3] : a(X3,X2) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0,X1] : a(X0,X1)
<~> ? [X2,X3] : a(X3,X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X2,X3] : ~ a(X3,X2)
| ! [X0,X1] : ~ a(X0,X1) )
& ( ? [X2,X3] : a(X3,X2)
| ? [X0,X1] : a(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ! [X0,X1] : ~ a(X1,X0)
| ! [X2,X3] : ~ a(X2,X3) )
& ( ? [X4,X5] : a(X5,X4)
| ? [X6,X7] : a(X6,X7) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ! [X0,X1] : ~ a(X1,X0)
| ! [X2,X3] : ~ a(X2,X3) )
& ( a(sK1,sK0)
| a(sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f6]) ).
fof(f8,plain,
( a(sK1,sK0)
| a(sK2,sK3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( ~ a(X1,X0)
| ~ a(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,definition,
( spl4_1
<=> a(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f12,plain,
( a(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f14,definition,
( spl4_2
<=> a(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f15,plain,
( a(sK1,sK0)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f16,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f8,f14,f11]) ).
fof(f18,definition,
( spl4_3
<=> ! [X2,X3] : ~ a(X2,X3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f19,plain,
( ! [X2,X3] : ~ a(X2,X3)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f20,plain,
( spl4_3
| spl4_3 ),
inference(avatar_split_clause,[],[f9,f18,f18]) ).
fof(f21,plain,
( $false
| ~ spl4_2
| ~ spl4_3 ),
inference(resolution,[],[f19,f15]) ).
fof(f22,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f21]) ).
fof(f23,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(resolution,[],[f12,f19]) ).
fof(f24,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f23]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f16]) ).
cnf(s2,plain,
( spl4_3
| spl4_3 ),
inference(sat_conversion,[],[f20]) ).
cnf(s3,plain,
spl4_3,
inference(rat,[],[s2]) ).
cnf(s4,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f22]) ).
cnf(s5,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f24]) ).
cnf(s6,plain,
~ spl4_1,
inference(rat,[],[s5,s3]) ).
cnf(s7,plain,
~ spl4_2,
inference(rat,[],[s4,s3]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s6]) ).
fof(f25,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN960+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.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 17:19:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 2.21/0.79 % (4030305)Detected formulas, will run a generic FOF schedule.
% 2.21/0.79 % (4030316)dis-21_1_sil=8000:lcm=predicate:random_seed=342975566:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.21/0.79 % (4030316)First to succeed.
% 2.21/0.79 % (4030316)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4030305"
% 2.21/0.79 % (4030314)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1060177419:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.21/0.79 % (4030312)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1399704727:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.21/0.79 % (4030310)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=1573859813:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.21/0.79 % (4030315)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=221825881:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.21/0.79 % (4030313)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1222276434:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.21/0.79 % (4030311)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2583954540:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.21/0.79 % (4030314)Also succeeded, but the first one will report.
% 2.21/0.79 % (4030315)Also succeeded, but the first one will report.
% 2.21/0.79 % (4030313)Also succeeded, but the first one will report.
% 2.21/0.79 % (4030316)Refutation found. Thanks to Tanya!
% 2.21/0.79 % SZS status Theorem for theBenchmark
% 2.21/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.21/0.79 % (4030316)------------------------------
% 2.21/0.79 % (4030316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/0.79 % (4030316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.79 % (4030316)CaDiCaL version: 2.1.3
% 2.21/0.79 % (4030316)Termination reason: Refutation
% 2.21/0.79 % (4030316)Time elapsed: 0.001 s
% 2.21/0.79 % (4030316)Peak memory usage: 89 MB
% 2.21/0.79 % (4030316)------------------------------
% 2.21/0.79 % (4030316)------------------------------
% 2.21/0.79 % (4030305)Success in time 0.273 s
% 2.21/0.79 % Vampire exiting
%------------------------------------------------------------------------------