%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 10:12:13 AM UTC 2026
% Result : Unsatisfiable 3.35s 1.35s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 21 unt; 3 def)
% Number of atoms : 117 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 93 ( 37 ~; 53 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| multiply(X0,X1) != X2
| subgroup_member(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f14,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f15,axiom,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| multiply(X0,element_in_O2(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f16,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
fof(f17,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f18,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f19,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f20,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(equality_resolution,[],[f6]) ).
fof(f39,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[],[f20,f17]) ).
fof(f40,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[],[f20,f18]) ).
fof(f41,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f40,f19]) ).
fof(f42,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_subsumption_resolution,[],[f39,f16]) ).
fof(f44,definition,
( spl0_1
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f45,plain,
( subgroup_member(a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl0_2
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f50,plain,
( ~ subgroup_member(c)
| spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f41,f48,f44]) ).
fof(f53,definition,
( spl0_3
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f55,plain,
( ~ subgroup_member(inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f42,f48,f53]) ).
fof(f61,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f62,plain,
! [X0] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[],[f4,f17]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f61,f1]) ).
fof(f73,plain,
! [X0] :
( subgroup_member(X0)
| d = multiply(X0,element_in_O2(X0,d)) ),
inference(resolution,[],[f15,f19]) ).
fof(f80,plain,
( ~ subgroup_member(a)
| spl0_3 ),
inference(resolution,[],[f55,f5]) ).
fof(f105,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[],[f62,f3]) ).
fof(f114,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f105,f7]) ).
fof(f130,plain,
c = multiply(inverse(a),d),
inference(superposition,[],[f69,f18]) ).
fof(f133,plain,
a = multiply(inverse(c),b),
inference(superposition,[],[f69,f114]) ).
fof(f180,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f20,f133]) ).
fof(f181,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f180,f46]) ).
fof(f183,plain,
( ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f181,f16]) ).
fof(f265,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(resolution,[],[f183,f5]) ).
fof(f271,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f265,f44,f48]) ).
fof(f338,plain,
( $false
| ~ spl0_1
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f80,f45]) ).
fof(f339,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f352,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_1 ),
inference(resolution,[],[f46,f73]) ).
fof(f451,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_1 ),
inference(superposition,[],[f69,f352]) ).
fof(f454,plain,
( c = element_in_O2(a,d)
| spl0_1 ),
inference(forward_demodulation,[],[f451,f130]) ).
fof(f503,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a)
| spl0_1 ),
inference(superposition,[],[f14,f454]) ).
fof(f504,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f503,f50]) ).
fof(f507,plain,
( subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f504,f19]) ).
fof(f508,plain,
( $false
| spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f507,f46]) ).
fof(f509,plain,
( spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f508]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f271]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f339]) ).
cnf(s16,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f509]) ).
cnf(s17,plain,
spl0_1,
inference(rat,[],[s3,s16]) ).
cnf(s18,plain,
spl0_3,
inference(rat,[],[s6,s17]) ).
cnf(s19,plain,
~ spl0_2,
inference(rat,[],[s1,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s2,s18,s19]) ).
fof(f510,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n002.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 09:18:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.35/1.35 % (3266400)Input is clausal, will run a generic CNF schedule.
% 3.35/1.35 % (3266454)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3888290339:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.35/1.35 % (3266455)lrs+10_1_sil=8000:sp=occurrence:random_seed=3213813599:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.35/1.35 % (3266453)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3979782935:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.35/1.35 % (3266456)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3504448313:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.35/1.35 % (3266452)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=3944470643:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.35/1.35 % (3266457)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3859366575:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.35/1.35 % (3266458)dis-21_1_sil=8000:lcm=predicate:random_seed=605236109: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)
% 3.35/1.35 % (3266458)Refutation not found, incomplete strategy
% 3.35/1.35 % (3266458)------------------------------
% 3.35/1.35 % (3266458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.35 % (3266458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.35 % (3266458)CaDiCaL version: 2.1.3
% 3.35/1.35 % (3266458)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.35 % (3266458)Time elapsed: 0.001 s
% 3.35/1.35 % (3266458)Peak memory usage: 88 MB
% 3.35/1.35 % (3266455)First to succeed.
% 3.35/1.35 % (3266455)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3266400"
% 3.35/1.35 % (3266457)Also succeeded, but the first one will report.
% 3.35/1.35 % (3266456)Instruction limit reached!
% 3.35/1.35 % (3266456)------------------------------
% 3.35/1.35 % (3266456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.35 % (3266456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.35 % (3266456)CaDiCaL version: 2.1.3
% 3.35/1.35 % (3266456)Termination reason: Instruction limit
% 3.35/1.35 % (3266456)Termination phase: Saturation
% 3.35/1.35 % (3266456)Time elapsed: 0.073 s
% 3.35/1.35 % (3266456)Peak memory usage: 89 MB
% 3.35/1.35 % (3266456)Instructions burned: 115 (million)
% 3.35/1.35 % (3266466)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=1397392417:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.35/1.35 % (3266458)------------------------------
% 3.35/1.35 % (3266458)------------------------------
% 3.35/1.35 % (3266455)Refutation found. Thanks to Tanya!
% 3.35/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.35/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.35 % (3266455)------------------------------
% 3.35/1.35 % (3266455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.35 % (3266455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.35 % (3266455)CaDiCaL version: 2.1.3
% 3.35/1.35 % (3266455)Termination reason: Refutation
% 3.35/1.35 % (3266455)Time elapsed: 0.013 s
% 3.35/1.35 % (3266455)Peak memory usage: 89 MB
% 3.35/1.35 % (3266455)Instructions burned: 16 (million)
% 3.35/1.35 % (3266455)------------------------------
% 3.35/1.35 % (3266455)------------------------------
% 3.35/1.35 % (3266400)Success in time 0.397 s
% 3.35/1.35 % Vampire exiting
%------------------------------------------------------------------------------