%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP034-3 : 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 : n006.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 2.65s 1.34s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 11 unt; 3 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 19 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f9,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(f10,axiom,
subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).
fof(f11,negated_conjecture,
~ subgroup_member(inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_is_in_subgroup) ).
fof(f12,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ subgroup_member(identity)
| subgroup_member(inverse(X0)) ),
inference(resolution,[],[f9,f1]) ).
fof(f14,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X0)
| subgroup_member(identity) ),
inference(resolution,[],[f9,f4]) ).
fof(f15,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(identity) ),
inference(duplicate_literal_removal,[],[f14]) ).
fof(f17,definition,
( spl0_1
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f20,definition,
( spl0_2
<=> ! [X0] : ~ subgroup_member(X0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f21,plain,
( ! [X0] : ~ subgroup_member(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f22,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f15,f20,f17]) ).
fof(f29,definition,
( spl0_4
<=> ! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f30,plain,
( ! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f12,f29,f17]) ).
fof(f33,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f21,f10]) ).
fof(f34,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f33]) ).
fof(f36,plain,
( ~ subgroup_member(a)
| ~ spl0_4 ),
inference(resolution,[],[f30,f11]) ).
fof(f37,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f36,f10]) ).
fof(f38,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f37]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f34]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f38]) ).
cnf(s6,plain,
~ spl0_1,
inference(rat,[],[s3,s5]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s4,s6]) ).
fof(f39,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:15:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 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
% 2.65/1.34 % (2723933)Input is clausal, will run a generic CNF schedule.
% 2.65/1.34 % (2723942)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=159669988:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.65/1.34 % (2723942)First to succeed.
% 2.65/1.34 % (2723942)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2723933"
% 2.65/1.34 % (2723940)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3299248562:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.65/1.34 % (2723944)dis-21_1_sil=8000:lcm=predicate:random_seed=1298604238: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)
% 2.65/1.34 % (2723941)lrs+10_1_sil=8000:sp=occurrence:random_seed=3257368822:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.65/1.34 % (2723939)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1266464832:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.65/1.34 % (2723943)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1813434395:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.65/1.34 % (2723938)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=1083891586:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.65/1.34 % (2723943)Also succeeded, but the first one will report.
% 2.65/1.34 % (2723941)Also succeeded, but the first one will report.
% 2.65/1.34 % (2723944)Instruction limit reached!
% 2.65/1.34 % (2723944)------------------------------
% 2.65/1.34 % (2723944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (2723944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (2723944)CaDiCaL version: 2.1.3
% 2.65/1.34 % (2723944)Termination reason: Instruction limit
% 2.65/1.34 % (2723944)Termination phase: Saturation
% 2.65/1.34 % (2723944)Time elapsed: 0.067 s
% 2.65/1.34 % (2723944)Peak memory usage: 88 MB
% 2.65/1.34 % (2723944)Instructions burned: 117 (million)
% 2.65/1.34 % (2723942)Refutation found. Thanks to Tanya!
% 2.65/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.34 % (2723942)------------------------------
% 2.65/1.34 % (2723942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (2723942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (2723942)CaDiCaL version: 2.1.3
% 2.65/1.34 % (2723942)Termination reason: Refutation
% 2.65/1.34 % (2723942)Time elapsed: 0.001 s
% 2.65/1.34 % (2723942)Peak memory usage: 89 MB
% 2.65/1.34 % (2723942)Instructions burned: 1 (million)
% 2.65/1.34 % (2723942)------------------------------
% 2.65/1.34 % (2723942)------------------------------
% 2.65/1.34 % (2723933)Success in time 0.291 s
% 2.65/1.34 % Vampire exiting
%------------------------------------------------------------------------------