%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP008-1 : 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 : n003.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 10:12:05 AM UTC 2026
% Result : Unsatisfiable 0.16s 1.30s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 7 unt; 2 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 41 ~; 44 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f10,axiom,
! [X0] :
( q(X0)
| product(X0,j(X0),h(X0))
| product(j(X0),X0,h(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown_meaning3) ).
fof(f11,axiom,
! [X0] :
( q(X0)
| ~ product(X0,j(X0),h(X0))
| ~ product(j(X0),X0,h(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown_meaning4) ).
fof(f12,negated_conjecture,
~ q(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_identity_is_q) ).
fof(f13,plain,
( product(identity,j(identity),h(identity))
| product(j(identity),identity,h(identity)) ),
inference(resolution,[],[f10,f12]) ).
fof(f16,definition,
( spl0_1
<=> product(j(identity),identity,h(identity)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f17,plain,
( product(j(identity),identity,h(identity))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f19,definition,
( spl0_2
<=> product(identity,j(identity),h(identity)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f20,plain,
( product(identity,j(identity),h(identity))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f21,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f13,f19,f16]) ).
fof(f22,plain,
( ~ product(identity,j(identity),h(identity))
| ~ product(j(identity),identity,h(identity)) ),
inference(resolution,[],[f11,f12]) ).
fof(f24,plain,
( ~ product(j(identity),identity,h(identity))
| spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f25,plain,
( ~ product(identity,j(identity),h(identity))
| spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f26,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f22,f19,f16]) ).
fof(f27,plain,
( ! [X2,X0,X1] :
( ~ product(X0,X1,identity)
| ~ product(X2,X1,h(identity))
| ~ product(j(identity),X0,X2) )
| spl0_1 ),
inference(resolution,[],[f7,f24]) ).
fof(f31,plain,
( ! [X0] :
( ~ product(X0,j(identity),identity)
| ~ product(j(identity),X0,identity) )
| spl0_1
| ~ spl0_2 ),
inference(resolution,[],[f27,f20]) ).
fof(f44,plain,
( ~ product(j(identity),inverse(j(identity)),identity)
| spl0_1
| ~ spl0_2 ),
inference(resolution,[],[f31,f3]) ).
fof(f51,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(resolution,[],[f44,f4]) ).
fof(f53,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f51]) ).
fof(f55,plain,
( ! [X2,X0,X1] :
( ~ product(X0,j(identity),X1)
| ~ product(X2,X1,h(identity))
| ~ product(X2,X0,identity) )
| spl0_2 ),
inference(resolution,[],[f25,f8]) ).
fof(f61,plain,
( ! [X0] :
( ~ product(X0,j(identity),identity)
| ~ product(j(identity),X0,identity) )
| ~ spl0_1
| spl0_2 ),
inference(resolution,[],[f55,f17]) ).
fof(f85,plain,
( ~ product(j(identity),inverse(j(identity)),identity)
| ~ spl0_1
| spl0_2 ),
inference(resolution,[],[f61,f3]) ).
fof(f93,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(resolution,[],[f85,f4]) ).
fof(f96,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f93]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f96]) ).
cnf(s6,plain,
spl0_1,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
spl0_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
fof(f97,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:15:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.16/1.30 % (234040)Input is clausal, will run a generic CNF schedule.
% 0.16/1.30 % (234051)dis-21_1_sil=8000:lcm=predicate:random_seed=4059292518: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)
% 0.16/1.30 % (234051)First to succeed.
% 0.16/1.30 % (234051)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-234040"
% 0.16/1.30 % (234050)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4042632410:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.16/1.30 % (234046)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4024612534:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.16/1.30 % (234048)lrs+10_1_sil=8000:sp=occurrence:random_seed=1194729444:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.16/1.30 % (234049)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1659822412:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.16/1.30 % (234045)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=3157014272:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.16/1.30 % (234047)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=955066800:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.16/1.30 % (234049)Refutation not found, incomplete strategy
% 0.16/1.30 % (234049)------------------------------
% 0.16/1.30 % (234049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.30 % (234049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.30 % (234049)CaDiCaL version: 2.1.3
% 0.16/1.30 % (234049)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.30 % (234049)Time elapsed: 0.001 s
% 0.16/1.30 % (234049)Peak memory usage: 87 MB
% 0.16/1.30 % (234050)Also succeeded, but the first one will report.
% 0.16/1.30 % (234048)Also succeeded, but the first one will report.
% 0.16/1.30 % (234051)Refutation found. Thanks to Tanya!
% 0.16/1.30 % SZS status Unsatisfiable for theBenchmark
% 0.16/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.30 % (234051)------------------------------
% 0.16/1.30 % (234051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.30 % (234051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.30 % (234051)CaDiCaL version: 2.1.3
% 0.16/1.30 % (234051)Termination reason: Refutation
% 0.16/1.30 % (234051)Time elapsed: 0.002 s
% 0.16/1.30 % (234051)Peak memory usage: 89 MB
% 0.16/1.30 % (234051)Instructions burned: 3 (million)
% 0.16/1.30 % (234051)------------------------------
% 0.16/1.30 % (234051)------------------------------
% 0.16/1.30 % (234040)Success in time 0.279 s
% 0.16/1.30 % Vampire exiting
%------------------------------------------------------------------------------