%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 10:16:26 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 29 ( 15 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f5,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f6,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f7,negated_conjecture,
! [X0] : ~ product(X0,a,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_has_a_left_inverse) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X3,X0,X1)
| product(X3,X2,identity) ),
inference(resolution,[],[f3,f5]) ).
fof(f12,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,X3)
| ~ product(X0,X1,X2)
| product(X2,inverse(X1),X3) ),
inference(resolution,[],[f4,f5]) ).
fof(f28,plain,
! [X2,X0,X1] :
( product(X2,inverse(X1),X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f12,f6]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X2,X1)
| ~ product(X0,X1,X2)
| product(X3,X0,identity) ),
inference(resolution,[],[f28,f9]) ).
fof(f560,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X1,X0,identity) ),
inference(resolution,[],[f66,f6]) ).
fof(f598,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(resolution,[],[f560,f5]) ).
fof(f650,plain,
$false,
inference(resolution,[],[f598,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n020.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 09:16:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 % (3121331)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (3121336)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3683986721_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % TRYING [4]
% 0.09/0.45 % TRYING [5]
% 0.09/0.45 % (3121337)% WARNING: option uhcvi not known.
% 0.09/0.45 % (3121339)dis+10_1_sil=32000:sp=arity:random_seed=1739389533:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (3121338)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=250991858:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (3121340)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3830763430:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (3121341)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3417645822:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (3121342)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1560778900:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % (3121337)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=588204003:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.45 % TRYING [6]
% 0.09/0.45 % (3121339) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3121331-3121339"...
% 0.09/0.45 % (3121339)...printing done.
% 0.09/0.45 % (3121339)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (3121339)------------------------------
% 0.09/0.45 % (3121339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (3121339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (3121339)CaDiCaL version: 2.1.3
% 0.09/0.45 % (3121339)Termination reason: Refutation
% 0.09/0.45 % (3121339)Time elapsed: 0.013 s
% 0.09/0.45 % (3121339)Peak memory usage: 11 MB
% 0.09/0.45 % (3121339)Instructions burned: 20 (million)
% 0.09/0.45 % (3121331)Success in time 0.049 s
% 0.09/0.46 % Vampire exiting
%------------------------------------------------------------------------------