%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP021-1 : 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 10:12:08 AM UTC 2026
% Result : Unsatisfiable 3.76s 1.49s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 7 unt; 1 def)
% Number of atoms : 17 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 5 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f9,negated_conjecture,
multiply(a,inverse(a)) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_X_times_inverse_X_is_id) ).
fof(f10,plain,
identity != multiply(a,inverse(a)),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f12,plain,
~ sQ0_eqProxy(identity,multiply(a,inverse(a))),
inference(equality_proxy_replacement,[],[f10,f11]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( sQ0_eqProxy(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f6,f11]) ).
fof(f18,plain,
! [X0,X1] :
( ~ product(X0,X1,multiply(a,inverse(a)))
| ~ product(X0,X1,identity) ),
inference(resolution,[],[f13,f12]) ).
fof(f20,plain,
~ product(a,inverse(a),identity),
inference(resolution,[],[f18,f5]) ).
fof(f24,plain,
$false,
inference(resolution,[],[f20,f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n009.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 09:14:00 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 3.76/1.49 % (1754255)Input is clausal, will run a generic CNF schedule.
% 3.76/1.49 % (1754277)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=997369057:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.76/1.49 % (1754281)dis-21_1_sil=8000:lcm=predicate:random_seed=3587983434: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)
% 3.76/1.49 % (1754281)First to succeed.
% 3.76/1.49 % (1754275)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=2648152227:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.76/1.49 % (1754281)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1754255"
% 3.76/1.49 % (1754279)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3610296520:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.76/1.49 % (1754276)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=318259279:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.76/1.49 % (1754279)Also succeeded, but the first one will report.
% 3.76/1.49 % (1754280)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=259032159:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.76/1.49 % (1754278)lrs+10_1_sil=8000:sp=occurrence:random_seed=455597030:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.76/1.49 % (1754280)Also succeeded, but the first one will report.
% 3.76/1.49 % (1754278)Also succeeded, but the first one will report.
% 3.76/1.49 % (1754281)Refutation found. Thanks to Tanya!
% 3.76/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.76/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.76/1.49 % (1754281)------------------------------
% 3.76/1.49 % (1754281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.49 % (1754281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.49 % (1754281)CaDiCaL version: 2.1.3
% 3.76/1.49 % (1754281)Termination reason: Refutation
% 3.76/1.49 % (1754281)Time elapsed: 0.002 s
% 3.76/1.49 % (1754281)Peak memory usage: 88 MB
% 3.76/1.49 % (1754281)Instructions burned: 1 (million)
% 3.76/1.49 % (1754281)------------------------------
% 3.76/1.49 % (1754281)------------------------------
% 3.76/1.49 % (1754255)Success in time 0.445 s
% 3.76/1.49 % Vampire exiting
%------------------------------------------------------------------------------