%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:12:11 AM UTC 2026
% Result : Unsatisfiable 3.38s 1.38s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 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 : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f12,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f14,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| subgroup_member(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
fof(f20,axiom,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f22,negated_conjecture,
! [X0] :
( ~ product(j(X0),X0,j(X0))
| ~ product(X0,j(X0),j(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subgr2) ).
fof(f23,plain,
( ~ product(identity,j(identity),j(identity))
| ~ subgroup_member(identity) ),
inference(resolution,[],[f12,f22]) ).
fof(f24,plain,
~ subgroup_member(identity),
inference(forward_subsumption_resolution,[],[f23,f11]) ).
fof(f62,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X0)
| subgroup_member(identity) ),
inference(resolution,[],[f19,f14]) ).
fof(f66,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(identity) ),
inference(duplicate_literal_removal,[],[f62]) ).
fof(f67,plain,
! [X0] : ~ subgroup_member(X0),
inference(forward_subsumption_resolution,[],[f66,f24]) ).
fof(f69,plain,
$false,
inference(resolution,[],[f67,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP033-3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n026.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 09:18:26 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 3.38/1.38 % (2560748)Input is clausal, will run a generic CNF schedule.
% 3.38/1.38 % (2560755)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=990344171:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.38/1.38 % (2560753)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=3023115813:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.38/1.38 % (2560757)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2488851239:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.38/1.38 % (2560754)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2741817858:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.38/1.38 % (2560756)lrs+10_1_sil=8000:sp=occurrence:random_seed=1630074661:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.38/1.38 % (2560759)dis-21_1_sil=8000:lcm=predicate:random_seed=318517304: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)
% 3.38/1.38 % (2560758)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=75649285:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.38/1.38 % (2560757)First to succeed.
% 3.38/1.38 % (2560756)Also succeeded, but the first one will report.
% 3.38/1.38 % (2560757)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2560748"
% 3.38/1.38 % (2560758)Also succeeded, but the first one will report.
% 3.38/1.38 % (2560759)Also succeeded, but the first one will report.
% 3.38/1.38 % (2560757)Refutation found. Thanks to Tanya!
% 3.38/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.38/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.38 % (2560757)------------------------------
% 3.38/1.38 % (2560757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.38 % (2560757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.38 % (2560757)CaDiCaL version: 2.1.3
% 3.38/1.38 % (2560757)Termination reason: Refutation
% 3.38/1.38 % (2560757)Time elapsed: 0.003 s
% 3.38/1.38 % (2560757)Peak memory usage: 88 MB
% 3.38/1.38 % (2560757)Instructions burned: 2 (million)
% 3.38/1.38 % (2560757)------------------------------
% 3.38/1.38 % (2560757)------------------------------
% 3.38/1.38 % (2560748)Success in time 0.411 s
% 3.38/1.38 % Vampire exiting
%------------------------------------------------------------------------------