%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN223-1 : 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 : 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 01:49:57 PM UTC 2026
% Result : Unsatisfiable 3.58s 1.28s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 11 unt; 4 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 36 ~; 29 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
fof(f28,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
fof(f128,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_090) ).
fof(f183,axiom,
! [X0,X1] :
( p2(e,X0,X1)
| ~ r0(e)
| ~ p1(X0,X1,e) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_145) ).
fof(f253,axiom,
! [X0,X1] :
( l3(X0,X1)
| ~ r0(X0)
| ~ p2(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_215) ).
fof(f369,negated_conjecture,
! [X0] : ~ l3(X0,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f790,definition,
( spl0_107
<=> r0(e) ),
introduced(definition,[new_symbols(definition,[spl0_107])],[avatar_definition]) ).
fof(f791,plain,
( r0(e)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f790]) ).
fof(f1055,definition,
( spl0_173
<=> ! [X0,X1] :
( p2(e,X0,X1)
| ~ p1(X0,X1,e) ) ),
introduced(definition,[new_symbols(definition,[spl0_173])],[avatar_definition]) ).
fof(f1056,plain,
( ! [X0,X1] :
( p2(e,X0,X1)
| ~ p1(X0,X1,e) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1057,plain,
( ~ spl0_107
| spl0_173 ),
inference(avatar_split_clause,[],[f183,f1055,f790]) ).
fof(f1186,definition,
( spl0_205
<=> k0(e) ),
introduced(definition,[new_symbols(definition,[spl0_205])],[avatar_definition]) ).
fof(f1263,definition,
( spl0_224
<=> p1(e,e,e) ),
introduced(definition,[new_symbols(definition,[spl0_224])],[avatar_definition]) ).
fof(f1265,plain,
( p1(e,e,e)
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f1266,plain,
( ~ spl0_205
| ~ spl0_107
| spl0_224 ),
inference(avatar_split_clause,[],[f128,f1263,f790,f1186]) ).
fof(f1556,plain,
spl0_205,
inference(avatar_split_clause,[],[f28,f1186]) ).
fof(f1562,plain,
spl0_107,
inference(avatar_split_clause,[],[f13,f790]) ).
fof(f1577,plain,
! [X0] :
( ~ p2(X0,e,X0)
| ~ r0(X0) ),
inference(resolution,[],[f253,f369]) ).
fof(f1578,plain,
( ~ r0(e)
| ~ p1(e,e,e)
| ~ spl0_173 ),
inference(resolution,[],[f1577,f1056]) ).
fof(f1579,plain,
( ~ p1(e,e,e)
| ~ spl0_107
| ~ spl0_173 ),
inference(forward_subsumption_resolution,[],[f1578,f791]) ).
fof(f1580,plain,
( $false
| ~ spl0_107
| ~ spl0_173
| ~ spl0_224 ),
inference(forward_subsumption_resolution,[],[f1579,f1265]) ).
fof(f1581,plain,
( ~ spl0_107
| ~ spl0_173
| ~ spl0_224 ),
inference(avatar_contradiction_clause,[],[f1580]) ).
cnf(s80,plain,
( ~ spl0_107
| spl0_173 ),
inference(sat_conversion,[],[f1057]) ).
cnf(s109,plain,
( ~ spl0_107
| ~ spl0_205
| spl0_224 ),
inference(sat_conversion,[],[f1266]) ).
cnf(s156,plain,
spl0_205,
inference(sat_conversion,[],[f1556]) ).
cnf(s162,plain,
spl0_107,
inference(sat_conversion,[],[f1562]) ).
cnf(s173,plain,
( ~ spl0_107
| ~ spl0_173
| ~ spl0_224 ),
inference(sat_conversion,[],[f1581]) ).
cnf(s199,plain,
spl0_224,
inference(rat,[],[s109,s156,s162]) ).
cnf(s200,plain,
~ spl0_173,
inference(rat,[],[s173,s162,s199]) ).
cnf(s216,plain,
$false,
inference(rat,[],[s80,s200,s162]) ).
fof(f1582,plain,
$false,
inference(avatar_sat_refutation,[],[s216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN223-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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
% 0.09/0.19 % DateTime : Mon Sep 28 15:38:49 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 3.58/1.28 % (4102522)Input is clausal, will run a generic CNF schedule.
% 3.58/1.28 % (4102552)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=227584108:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.58/1.28 % (4102550)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=3543335575:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.58/1.28 % (4102554)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=720291212:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.58/1.28 % (4102553)lrs+10_1_sil=8000:sp=occurrence:random_seed=1150467874:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.58/1.28 % (4102551)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=631323075:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.58/1.28 % (4102556)dis-21_1_sil=8000:lcm=predicate:random_seed=3246636613: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)
% 3.58/1.28 % (4102555)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3601482103:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.58/1.28 % (4102555)First to succeed.
% 3.58/1.28 % (4102555)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4102522"
% 3.58/1.28 % (4102553)Also succeeded, but the first one will report.
% 3.58/1.28 % (4102554)Also succeeded, but the first one will report.
% 3.58/1.28 % (4102556)Also succeeded, but the first one will report.
% 3.58/1.28 % (4102555)Refutation found. Thanks to Tanya!
% 3.58/1.28 % SZS status Unsatisfiable for theBenchmark
% 3.58/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.28 % (4102555)------------------------------
% 3.58/1.28 % (4102555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.28 % (4102555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.28 % (4102555)CaDiCaL version: 2.1.3
% 3.58/1.28 % (4102555)Termination reason: Refutation
% 3.58/1.28 % (4102555)Time elapsed: 0.010 s
% 3.58/1.28 % (4102555)Peak memory usage: 90 MB
% 3.58/1.28 % (4102555)Instructions burned: 14 (million)
% 3.58/1.28 % (4102555)------------------------------
% 3.58/1.28 % (4102555)------------------------------
% 3.58/1.28 % (4102522)Success in time 0.422 s
% 3.58/1.28 % Vampire exiting
%------------------------------------------------------------------------------