%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP035-3 : 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 : n005.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 10:12:12 AM UTC 2026
% Result : Unsatisfiable 3.65s 1.55s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 17 unt; 3 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 38 ~; 31 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,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(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,axiom,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f12,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f13,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
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)
| subgroup_member(inverse(X0)) ),
inference(resolution,[],[f9,f1]) ).
fof(f17,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(identity) ),
inference(duplicate_literal_removal,[],[f14]) ).
fof(f19,definition,
( spl0_1
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f27,definition,
( spl0_3
<=> ! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f15,f27,f19]) ).
fof(f31,definition,
( spl0_4
<=> ! [X0] : ~ subgroup_member(X0) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f32,plain,
( ! [X0] : ~ subgroup_member(X0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f33,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f17,f31,f19]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,X0,X3)
| ~ product(X0,identity,X1)
| product(X2,X1,X3) ),
inference(resolution,[],[f7,f2]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f7,f1]) ).
fof(f44,plain,
( $false
| ~ spl0_4 ),
inference(resolution,[],[f32,f10]) ).
fof(f47,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f60,plain,
! [X0] :
( ~ product(b,identity,X0)
| product(a,X0,c) ),
inference(resolution,[],[f34,f12]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ product(inverse(X0),X1,X2)
| product(X0,X2,X1) ),
inference(resolution,[],[f36,f4]) ).
fof(f165,plain,
! [X0] : product(X0,identity,inverse(inverse(X0))),
inference(resolution,[],[f63,f4]) ).
fof(f202,plain,
product(a,inverse(inverse(b)),c),
inference(resolution,[],[f165,f60]) ).
fof(f210,plain,
( ~ subgroup_member(inverse(b))
| ~ subgroup_member(a)
| subgroup_member(c) ),
inference(resolution,[],[f202,f9]) ).
fof(f215,plain,
( ~ subgroup_member(inverse(b))
| subgroup_member(c) ),
inference(forward_subsumption_resolution,[],[f210,f10]) ).
fof(f216,plain,
~ subgroup_member(inverse(b)),
inference(forward_subsumption_resolution,[],[f215,f13]) ).
fof(f223,plain,
( ~ subgroup_member(b)
| ~ spl0_3 ),
inference(resolution,[],[f216,f28]) ).
fof(f224,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f223,f11]) ).
fof(f225,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f224]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f29]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f47]) ).
cnf(s8,plain,
~ spl0_3,
inference(sat_conversion,[],[f225]) ).
cnf(s9,plain,
spl0_1,
inference(rat,[],[s3,s5]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s8,s9]) ).
fof(f226,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n005.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:15:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.65/1.55 % (3716575)Input is clausal, will run a generic CNF schedule.
% 3.65/1.55 % (3716614)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3385194039:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.65/1.55 % (3716612)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=2993118742:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.65/1.55 % (3716618)dis-21_1_sil=8000:lcm=predicate:random_seed=3901632848: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)
% 3.65/1.55 % (3716615)lrs+10_1_sil=8000:sp=occurrence:random_seed=2970202053:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.65/1.55 % (3716617)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2537280191:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.65/1.55 % (3716613)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1934011330:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.65/1.55 % (3716615)First to succeed.
% 3.65/1.55 % (3716615)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3716575"
% 3.65/1.55 % (3716616)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1272447458:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.65/1.55 % (3716618)Instruction limit reached!
% 3.65/1.55 % (3716618)------------------------------
% 3.65/1.55 % (3716618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.55 % (3716618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.55 % (3716618)CaDiCaL version: 2.1.3
% 3.65/1.55 % (3716618)Termination reason: Instruction limit
% 3.65/1.55 % (3716618)Termination phase: Saturation
% 3.65/1.55 % (3716618)Time elapsed: 0.066 s
% 3.65/1.55 % (3716618)Peak memory usage: 88 MB
% 3.65/1.55 % (3716618)Instructions burned: 119 (million)
% 3.65/1.55 % (3716616)Also succeeded, but the first one will report.
% 3.65/1.55 % (3716617)Instruction limit reached!
% 3.65/1.55 % (3716617)------------------------------
% 3.65/1.55 % (3716617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.55 % (3716617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.55 % (3716617)CaDiCaL version: 2.1.3
% 3.65/1.55 % (3716617)Termination reason: Instruction limit
% 3.65/1.55 % (3716617)Termination phase: Saturation
% 3.65/1.55 % (3716617)Time elapsed: 0.112 s
% 3.65/1.55 % (3716617)Peak memory usage: 88 MB
% 3.65/1.55 % (3716617)Instructions burned: 182 (million)
% 3.65/1.55 % (3716626)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2154220428:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.65/1.55 % (3716615)Refutation found. Thanks to Tanya!
% 3.65/1.55 % SZS status Unsatisfiable for theBenchmark
% 3.65/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.55 % (3716615)------------------------------
% 3.65/1.55 % (3716615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.55 % (3716615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.55 % (3716615)CaDiCaL version: 2.1.3
% 3.65/1.55 % (3716615)Termination reason: Refutation
% 3.65/1.55 % (3716615)Time elapsed: 0.006 s
% 3.65/1.55 % (3716615)Peak memory usage: 89 MB
% 3.65/1.55 % (3716615)Instructions burned: 7 (million)
% 3.65/1.55 % (3716615)------------------------------
% 3.65/1.55 % (3716615)------------------------------
% 3.65/1.55 % (3716575)Success in time 0.435 s
% 3.65/1.55 % Vampire exiting
%------------------------------------------------------------------------------