%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN313-1.001.002 : 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 : n014.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 01:50:09 PM UTC 2026
% Result : Unsatisfiable 3.59s 1.21s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 9 unt; 1 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 35 ~; 37 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] :
( ~ p(X0,f1(X1),X2)
| ~ p(X0,f0(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
fof(f2,negated_conjecture,
! [X2,X0,X1] :
( p(h2(X2),X1,j2(X1))
| p(h1(X0),X2,j1(X1))
| p(h0,X0,j0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
fof(f3,plain,
! [X2,X0,X1] :
( p(h1(X0),X1,j1(f1(X2)))
| p(h0,X0,j0(f1(X2)))
| ~ p(h2(X1),f0(h2(X1)),X2) ),
inference(resolution,[],[f2,f1]) ).
fof(f4,plain,
! [X2,X0,X1] :
( ~ p(h2(f1(X2)),f0(h2(f1(X2))),X1)
| p(h0,X0,j0(f1(X1)))
| ~ p(h1(X0),f0(h1(X0)),X2) ),
inference(resolution,[],[f3,f1]) ).
fof(f5,plain,
! [X2,X0,X1] :
( p(h1(X2),f1(X1),j1(f0(h2(f1(X1)))))
| ~ p(h1(X0),f0(h1(X0)),X1)
| p(h0,X0,j0(f1(j2(f0(h2(f1(X1)))))))
| p(h0,X2,j0(f0(h2(f1(X1))))) ),
inference(resolution,[],[f4,f2]) ).
fof(f6,plain,
! [X2,X0,X1] :
( p(h0,X0,j0(f1(j2(f0(h2(f1(X1)))))))
| ~ p(h1(X0),f0(h1(X0)),X1)
| p(h0,X2,j0(f0(h2(f1(X1)))))
| ~ p(h1(X2),f0(h1(X2)),X1) ),
inference(resolution,[],[f5,f1]) ).
fof(f7,plain,
! [X2,X0,X1] :
( ~ p(h1(f1(X0)),f0(h1(f1(X0))),X1)
| p(h0,X2,j0(f0(h2(f1(X1)))))
| ~ p(h1(X2),f0(h1(X2)),X1)
| ~ p(h0,f0(h0),X0) ),
inference(resolution,[],[f6,f1]) ).
fof(f9,plain,
! [X0,X1] :
( ~ p(h1(f1(X0)),f0(h1(f1(X0))),X1)
| p(h0,f1(X0),j0(f0(h2(f1(X1)))))
| ~ p(h0,f0(h0),X0) ),
inference(factoring,[],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ~ p(h1(f1(X0)),f0(h1(f1(X0))),X1)
| ~ p(h0,f0(h0),X0) ),
inference(forward_subsumption_resolution,[],[f9,f1]) ).
fof(f12,plain,
! [X0,X1] :
( ~ p(h0,f0(h0),X0)
| p(h0,f1(X0),j0(f1(X1)))
| ~ p(h2(f0(h1(f1(X0)))),f0(h2(f0(h1(f1(X0))))),X1) ),
inference(resolution,[],[f10,f3]) ).
fof(f13,plain,
! [X0,X1] :
( ~ p(h2(f0(h1(f1(X0)))),f0(h2(f0(h1(f1(X0))))),X1)
| ~ p(h0,f0(h0),X0) ),
inference(forward_subsumption_resolution,[],[f12,f1]) ).
fof(f14,plain,
! [X0,X1] :
( p(h1(X1),f0(h1(f1(X0))),j1(f0(h2(f0(h1(f1(X0)))))))
| ~ p(h0,f0(h0),X0)
| p(h0,X1,j0(f0(h2(f0(h1(f1(X0))))))) ),
inference(resolution,[],[f13,f2]) ).
fof(f15,plain,
! [X0] :
( ~ p(h0,f0(h0),X0)
| p(h0,f1(X0),j0(f0(h2(f0(h1(f1(X0)))))))
| ~ p(h0,f0(h0),X0) ),
inference(resolution,[],[f14,f10]) ).
fof(f18,plain,
! [X0] :
( ~ p(h0,f0(h0),X0)
| p(h0,f1(X0),j0(f0(h2(f0(h1(f1(X0))))))) ),
inference(duplicate_literal_removal,[],[f15]) ).
fof(f20,plain,
! [X0] : ~ p(h0,f0(h0),X0),
inference(forward_subsumption_resolution,[],[f18,f1]) ).
fof(f21,plain,
! [X0,X1] :
( ~ p(h1(f0(h0)),f0(h1(f0(h0))),X0)
| p(h0,X1,j0(f0(h2(f1(X0)))))
| ~ p(h1(X1),f0(h1(X1)),X0) ),
inference(resolution,[],[f20,f6]) ).
fof(f23,plain,
! [X0] :
( ~ p(h1(f0(h0)),f0(h1(f0(h0))),X0)
| p(h0,f0(h0),j0(f0(h2(f1(X0))))) ),
inference(factoring,[],[f21]) ).
fof(f24,plain,
! [X0] : ~ p(h1(f0(h0)),f0(h1(f0(h0))),X0),
inference(forward_subsumption_resolution,[],[f23,f20]) ).
fof(f26,plain,
! [X0] :
( p(h0,f0(h0),j0(f1(X0)))
| ~ p(h2(f0(h1(f0(h0)))),f0(h2(f0(h1(f0(h0))))),X0) ),
inference(resolution,[],[f24,f3]) ).
fof(f27,plain,
! [X0] : ~ p(h2(f0(h1(f0(h0)))),f0(h2(f0(h1(f0(h0))))),X0),
inference(forward_subsumption_resolution,[],[f26,f20]) ).
fof(f30,definition,
( spl0_1
<=> ! [X1] :
( p(h1(X1),f0(h1(f0(h0))),j1(f0(h2(f0(h1(f0(h0)))))))
| p(h0,X1,j0(f0(h2(f0(h1(f0(h0))))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f31,plain,
( ! [X1] :
( p(h1(X1),f0(h1(f0(h0))),j1(f0(h2(f0(h1(f0(h0)))))))
| p(h0,X1,j0(f0(h2(f0(h1(f0(h0))))))) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f36,plain,
! [X0] :
( p(h1(X0),f0(h1(f0(h0))),j1(f0(h2(f0(h1(f0(h0)))))))
| p(h0,X0,j0(f0(h2(f0(h1(f0(h0))))))) ),
inference(resolution,[],[f27,f2]) ).
fof(f37,plain,
spl0_1,
inference(avatar_split_clause,[],[f36,f30]) ).
fof(f38,plain,
( p(h0,f0(h0),j0(f0(h2(f0(h1(f0(h0)))))))
| ~ spl0_1 ),
inference(resolution,[],[f31,f24]) ).
fof(f41,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f38,f20]) ).
fof(f42,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f41]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f42]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f43,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN313-1.001.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n014.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 15:40:45 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 3.59/1.21 % (1868934)Input is clausal, will run a generic CNF schedule.
% 3.59/1.21 % (1869013)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=905647811:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.59/1.21 % (1869011)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2022387538:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.59/1.21 % (1869010)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=175055355:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.59/1.21 % (1869016)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=728864339:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.59/1.21 % (1869017)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3591284105:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.59/1.21 % (1869016)First to succeed.
% 3.59/1.21 % (1869016)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1868934"
% 3.59/1.21 % (1869017)Also succeeded, but the first one will report.
% 3.59/1.21 % (1869014)lrs+10_1_sil=8000:sp=occurrence:random_seed=2415998369:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.59/1.21 % (1869018)dis-21_1_sil=8000:lcm=predicate:random_seed=1447617528: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)
% 3.59/1.21 % (1869014)Also succeeded, but the first one will report.
% 3.59/1.21 % (1869018)Also succeeded, but the first one will report.
% 3.59/1.21 % (1869016)Refutation found. Thanks to Tanya!
% 3.59/1.21 % SZS status Unsatisfiable for theBenchmark
% 3.59/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.21 % (1869016)------------------------------
% 3.59/1.21 % (1869016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.21 % (1869016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.21 % (1869016)CaDiCaL version: 2.1.3
% 3.59/1.21 % (1869016)Termination reason: Refutation
% 3.59/1.21 % (1869016)Time elapsed: 0.003 s
% 3.59/1.21 % (1869016)Peak memory usage: 89 MB
% 3.59/1.21 % (1869016)Instructions burned: 2 (million)
% 3.59/1.21 % (1869016)------------------------------
% 3.59/1.21 % (1869016)------------------------------
% 3.59/1.21 % (1868934)Success in time 0.439 s
% 3.59/1.21 % Vampire exiting
%------------------------------------------------------------------------------