%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP003-2 : 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 : n004.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 2.82s 1.07s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 31 ( 19 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f5,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(f6,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(f8,negated_conjecture,
~ product(a,identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_identity) ).
fof(f11,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,a)
| ~ product(X0,identity,X1)
| ~ product(X2,X0,a) ),
inference(resolution,[],[f6,f8]) ).
fof(f21,plain,
! [X0,X1] :
( ~ product(X1,identity,X1)
| ~ product(X0,X1,a) ),
inference(factoring,[],[f11]) ).
fof(f38,plain,
! [X0] : ~ product(X0,identity,a),
inference(resolution,[],[f21,f1]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,X1,a)
| ~ product(X0,X1,identity)
| ~ product(X3,X0,X2) ),
inference(resolution,[],[f38,f5]) ).
fof(f276,plain,
! [X0,X1] :
( ~ product(X0,a,identity)
| ~ product(X1,X0,identity) ),
inference(resolution,[],[f44,f1]) ).
fof(f284,plain,
! [X0] : ~ product(X0,inverse(a),identity),
inference(resolution,[],[f276,f2]) ).
fof(f296,plain,
$false,
inference(resolution,[],[f284,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 09:13:07 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 2.82/1.07 % (3232059)Input is clausal, will run a generic CNF schedule.
% 2.82/1.07 % (3232064)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=3264478287:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.82/1.07 % (3232070)dis-21_1_sil=8000:lcm=predicate:random_seed=4165277612: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)
% 2.82/1.07 % (3232065)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1625270365:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.82/1.07 % (3232066)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3997083794:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.82/1.07 % (3232067)lrs+10_1_sil=8000:sp=occurrence:random_seed=116621814:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.82/1.07 % (3232069)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1800164118:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.82/1.07 % (3232068)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3443843295:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.82/1.07 % (3232069)First to succeed.
% 2.82/1.07 % (3232069)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3232059"
% 2.82/1.07 % (3232070)Instruction limit reached!
% 2.82/1.07 % (3232070)------------------------------
% 2.82/1.07 % (3232070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.07 % (3232070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.07 % (3232070)CaDiCaL version: 2.1.3
% 2.82/1.07 % (3232070)Termination reason: Instruction limit
% 2.82/1.07 % (3232070)Termination phase: Saturation
% 2.82/1.07 % (3232070)Time elapsed: 0.060 s
% 2.82/1.07 % (3232070)Peak memory usage: 87 MB
% 2.82/1.07 % (3232070)Instructions burned: 117 (million)
% 2.82/1.07 % (3232068)Instruction limit reached!
% 2.82/1.07 % (3232068)------------------------------
% 2.82/1.07 % (3232068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.07 % (3232068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.07 % (3232068)CaDiCaL version: 2.1.3
% 2.82/1.07 % (3232068)Termination reason: Instruction limit
% 2.82/1.07 % (3232068)Termination phase: Saturation
% 2.82/1.07 % (3232068)Time elapsed: 0.063 s
% 2.82/1.07 % (3232068)Peak memory usage: 87 MB
% 2.82/1.07 % (3232068)Instructions burned: 116 (million)
% 2.82/1.07 % (3232067)Instruction limit reached!
% 2.82/1.07 % (3232067)------------------------------
% 2.82/1.07 % (3232067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.07 % (3232067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.07 % (3232067)CaDiCaL version: 2.1.3
% 2.82/1.07 % (3232067)Termination reason: Instruction limit
% 2.82/1.07 % (3232067)Termination phase: Saturation
% 2.82/1.07 % (3232067)Time elapsed: 0.070 s
% 2.82/1.07 % (3232067)Peak memory usage: 88 MB
% 2.82/1.07 % (3232067)Instructions burned: 108 (million)
% 2.82/1.07 % (3232069)Refutation found. Thanks to Tanya!
% 2.82/1.07 % SZS status Unsatisfiable for theBenchmark
% 2.82/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.07 % (3232069)------------------------------
% 2.82/1.07 % (3232069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.07 % (3232069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.07 % (3232069)CaDiCaL version: 2.1.3
% 2.82/1.07 % (3232069)Termination reason: Refutation
% 2.82/1.07 % (3232069)Time elapsed: 0.013 s
% 2.82/1.07 % (3232069)Peak memory usage: 88 MB
% 2.82/1.07 % (3232069)Instructions burned: 20 (million)
% 2.82/1.07 % (3232069)------------------------------
% 2.82/1.07 % (3232069)------------------------------
% 2.82/1.07 % (3232059)Success in time 0.349 s
% 2.82/1.07 % Vampire exiting
%------------------------------------------------------------------------------