%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP032-3 : 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 : n002.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 0.15s 0.43s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| subgroup_member(X2)
| ~ product(X0,inverse(X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
fof(f10,axiom,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f11,negated_conjecture,
~ subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_is_in_subgroup) ).
fof(f30,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,inverse(X1),identity) ),
inference(resolution,[],[f9,f11]) ).
fof(f33,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ product(a,inverse(X0),identity) ),
inference(resolution,[],[f30,f10]) ).
fof(f61,plain,
~ product(a,inverse(a),identity),
inference(resolution,[],[f33,f10]) ).
fof(f63,plain,
$false,
inference(forward_subsumption_resolution,[],[f61,f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP032-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 09:18:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 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
% 0.15/0.43 % (3265465)Will run a generic schedule for satisfiability detection.
% 0.15/0.43 % (3265474)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3859132124:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.43 % (3265474) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3265465-3265474"...
% 0.15/0.43 % (3265474)...printing done.
% 0.15/0.43 % (3265474)Refutation found. Thanks to Tanya!
% 0.15/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.43 % (3265474)------------------------------
% 0.15/0.43 % (3265474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.43 % (3265474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.43 % (3265474)CaDiCaL version: 2.1.3
% 0.15/0.43 % (3265474)Termination reason: Refutation
% 0.15/0.43 % (3265474)Time elapsed: 0.001 s
% 0.15/0.43 % (3265474)Peak memory usage: 11 MB
% 0.15/0.43 % (3265474)Instructions burned: 3 (million)
% 0.15/0.43 % (3265465)Success in time 0.026 s
% 0.15/0.44 % Vampire exiting
%------------------------------------------------------------------------------