%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP001-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 10:12:03 AM UTC 2026
% Result : Unsatisfiable 4.28s 1.58s
% Output : Refutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 11 unt; 1 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 69 ( 38 ~; 30 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f4,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/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f5,axiom,
! [X0] : product(X0,X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_element) ).
fof(f6,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f7,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,b)
| ~ product(X2,X1,c)
| ~ product(X0,a,X1) ),
inference(resolution,[],[f4,f7]) ).
fof(f20,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X5,X4,b)
| ~ product(X2,a,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,c)
| ~ product(X0,X3,X5) ),
inference(resolution,[],[f14,f3]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,a,X1)
| ~ product(X2,b,X0)
| ~ product(X3,X1,c)
| ~ product(X3,X2,identity) ),
inference(resolution,[],[f20,f1]) ).
fof(f214,definition,
( spl0_13
<=> product(c,b,a) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f215,plain,
( product(c,b,a)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( ~ product(c,b,a)
| spl0_13 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f336,plain,
! [X0,X1] :
( ~ product(X0,b,a)
| ~ product(X1,identity,c)
| ~ product(X1,X0,identity) ),
inference(resolution,[],[f66,f5]) ).
fof(f365,plain,
( ! [X2,X0,X1] :
( ~ product(X2,X1,a)
| ~ product(X0,b,X1)
| ~ product(X2,X0,c) )
| spl0_13 ),
inference(resolution,[],[f216,f4]) ).
fof(f1217,plain,
( ! [X0] :
( ~ product(a,X0,c)
| ~ product(X0,b,identity) )
| spl0_13 ),
inference(resolution,[],[f365,f2]) ).
fof(f1226,plain,
( ~ product(b,b,identity)
| spl0_13 ),
inference(resolution,[],[f1217,f6]) ).
fof(f1229,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f1226,f5]) ).
fof(f1230,plain,
spl0_13,
inference(avatar_contradiction_clause,[],[f1229]) ).
fof(f1234,plain,
( ! [X0] :
( ~ product(X0,c,identity)
| ~ product(X0,identity,c) )
| ~ spl0_13 ),
inference(resolution,[],[f215,f336]) ).
fof(f1292,plain,
( ~ product(c,identity,c)
| ~ spl0_13 ),
inference(resolution,[],[f1234,f5]) ).
fof(f1295,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1292,f2]) ).
fof(f1296,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f1295]) ).
cnf(s41,plain,
spl0_13,
inference(sat_conversion,[],[f1230]) ).
cnf(s46,plain,
~ spl0_13,
inference(sat_conversion,[],[f1296]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s41,s46]) ).
fof(f1297,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:12:59 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 4.28/1.58 % (1750949)Input is clausal, will run a generic CNF schedule.
% 4.28/1.58 % (1750977)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=973062267:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.28/1.58 % (1750972)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=2614921833:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.28/1.58 % (1750973)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1903280071:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.28/1.58 % (1750977)First to succeed.
% 4.28/1.58 % (1750977)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1750949"
% 4.28/1.58 % (1750974)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=275854040:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.28/1.58 % (1750975)lrs+10_1_sil=8000:sp=occurrence:random_seed=1617442889:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.28/1.58 % (1750975)Also succeeded, but the first one will report.
% 4.28/1.58 % (1750976)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3557990562:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.28/1.58 % (1750978)dis-21_1_sil=8000:lcm=predicate:random_seed=200118696: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)
% 4.28/1.58 % (1750976)Instruction limit reached!
% 4.28/1.58 % (1750976)------------------------------
% 4.28/1.58 % (1750976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.58 % (1750976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.58 % (1750976)CaDiCaL version: 2.1.3
% 4.28/1.58 % (1750976)Termination reason: Instruction limit
% 4.28/1.58 % (1750976)Termination phase: Saturation
% 4.28/1.58 % (1750976)Time elapsed: 0.100 s
% 4.28/1.58 % (1750976)Peak memory usage: 88 MB
% 4.28/1.58 % (1750976)Instructions burned: 114 (million)
% 4.28/1.58 % (1750978)Instruction limit reached!
% 4.28/1.58 % (1750978)------------------------------
% 4.28/1.58 % (1750978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.58 % (1750978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.58 % (1750978)CaDiCaL version: 2.1.3
% 4.28/1.58 % (1750978)Termination reason: Instruction limit
% 4.28/1.58 % (1750978)Termination phase: Saturation
% 4.28/1.58 % (1750978)Time elapsed: 0.104 s
% 4.28/1.58 % (1750978)Peak memory usage: 88 MB
% 4.28/1.58 % (1750978)Instructions burned: 118 (million)
% 4.28/1.58 % (1750977)Refutation found. Thanks to Tanya!
% 4.28/1.58 % SZS status Unsatisfiable for theBenchmark
% 4.28/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 4.28/1.58 % (1750977)------------------------------
% 4.28/1.58 % (1750977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.28/1.58 % (1750977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/1.58 % (1750977)CaDiCaL version: 2.1.3
% 4.28/1.58 % (1750977)Termination reason: Refutation
% 4.28/1.58 % (1750977)Time elapsed: 0.056 s
% 4.28/1.58 % (1750977)Peak memory usage: 90 MB
% 4.28/1.58 % (1750977)Instructions burned: 110 (million)
% 4.28/1.58 % (1750977)------------------------------
% 4.28/1.58 % (1750977)------------------------------
% 4.28/1.58 % (1750949)Success in time 0.537 s
% 4.28/1.58 % Vampire exiting
%------------------------------------------------------------------------------