%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN034-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 01:49:01 PM UTC 2026
% Result : Unsatisfiable 2.24s 0.88s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 7 unt; 3 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 52 ( 25 ~; 24 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( p(X0,f(X0))
| p(X0,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
fof(f2,axiom,
! [X0] :
( p(f(X0),X0)
| p(X0,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
fof(f3,negated_conjecture,
! [X0,X1] :
( ~ p(X0,X1)
| ~ p(X1,X0)
| ~ p(X1,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem) ).
fof(f5,plain,
( ~ p(a,a)
| ~ p(a,a) ),
inference(factoring,[],[f3]) ).
fof(f7,plain,
~ p(a,a),
inference(duplicate_literal_removal,[],[f5]) ).
fof(f10,plain,
! [X0] :
( p(a,a)
| ~ p(X0,f(a))
| ~ p(f(a),X0) ),
inference(resolution,[],[f2,f3]) ).
fof(f12,definition,
( spl0_1
<=> ! [X0] :
( ~ p(X0,f(a))
| ~ p(f(a),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f13,plain,
( ! [X0] :
( ~ p(X0,f(a))
| ~ p(f(a),X0) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f15,definition,
( spl0_2
<=> p(a,a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f16,plain,
( p(a,a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f10,f15,f12]) ).
fof(f18,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f16,f7]) ).
fof(f20,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f18]) ).
fof(f22,plain,
( ~ p(a,f(a))
| p(a,a)
| ~ spl0_1 ),
inference(resolution,[],[f13,f2]) ).
fof(f25,definition,
( spl0_3
<=> p(a,f(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f26,plain,
( ~ p(a,f(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f22,f12,f25,f15]) ).
fof(f35,plain,
( p(a,a)
| spl0_3 ),
inference(resolution,[],[f26,f1]) ).
fof(f36,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f35,f25,f15]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f20]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s5,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f36]) ).
cnf(s6,plain,
spl0_3,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
~ spl0_1,
inference(rat,[],[s3,s6,s2]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s2,s7]) ).
fof(f37,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN034-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:23:27 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.24/0.88 % (3937311)Input is clausal, will run a generic CNF schedule.
% 2.24/0.88 % (3937322)dis-21_1_sil=8000:lcm=predicate:random_seed=2473761036: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)
% 2.24/0.88 % (3937322)First to succeed.
% 2.24/0.88 % (3937322)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3937311"
% 2.24/0.88 % (3937319)lrs+10_1_sil=8000:sp=occurrence:random_seed=3105952600:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.24/0.88 % (3937321)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1430443705:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.24/0.88 % (3937317)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3275970235:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.24/0.88 % (3937316)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=2823589462:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.24/0.88 % (3937320)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3801801524:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.24/0.88 % (3937318)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3922303663:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.24/0.88 % (3937320)Also succeeded, but the first one will report.
% 2.24/0.88 % (3937321)Also succeeded, but the first one will report.
% 2.24/0.88 % (3937319)Also succeeded, but the first one will report.
% 2.24/0.88 % (3937322)Refutation found. Thanks to Tanya!
% 2.24/0.88 % SZS status Unsatisfiable for theBenchmark
% 2.24/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.24/0.88 % (3937322)------------------------------
% 2.24/0.88 % (3937322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/0.88 % (3937322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.88 % (3937322)CaDiCaL version: 2.1.3
% 2.24/0.88 % (3937322)Termination reason: Refutation
% 2.24/0.88 % (3937322)Time elapsed: 0.001 s
% 2.24/0.88 % (3937322)Peak memory usage: 89 MB
% 2.24/0.88 % (3937322)Instructions burned: 1 (million)
% 2.24/0.88 % (3937322)------------------------------
% 2.24/0.88 % (3937322)------------------------------
% 2.24/0.88 % (3937311)Success in time 0.259 s
% 2.24/0.88 % Vampire exiting
%------------------------------------------------------------------------------