%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 3.79s 1.51s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 27 unt; 3 def)
% Number of atoms : 103 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 30 ~; 41 |; 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 : 26 ( 0 sgn 26 !; 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(f8,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f9,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f8]) ).
fof(f10,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(f11,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(f12,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
fof(f13,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f14,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f15,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f16,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(equality_resolution,[],[f6]) ).
fof(f28,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[],[f16,f13]) ).
fof(f29,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[],[f16,f14]) ).
fof(f30,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f29,f15]) ).
fof(f31,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_subsumption_resolution,[],[f28,f12]) ).
fof(f35,definition,
( spl0_1
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f37,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl0_2
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f42,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f30,f39,f35]) ).
fof(f44,definition,
( spl0_3
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f46,plain,
( ~ subgroup_member(inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f31,f39,f44]) ).
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,f13]) ).
fof(f63,plain,
! [X0] : multiply(a,multiply(c,X0)) = multiply(d,X0),
inference(superposition,[],[f4,f14]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f61,f1]) ).
fof(f73,plain,
( ~ subgroup_member(a)
| spl0_3 ),
inference(resolution,[],[f46,f5]) ).
fof(f77,plain,
! [X0] :
( subgroup_member(X0)
| multiply(d,element_in_O2(d,X0)) = X0 ),
inference(resolution,[],[f11,f15]) ).
fof(f102,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f73,f44,f35]) ).
fof(f106,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(superposition,[],[f63,f9]) ).
fof(f110,plain,
a = multiply(d,inverse(c)),
inference(forward_demodulation,[],[f106,f7]) ).
fof(f120,plain,
( a = multiply(d,element_in_O2(d,a))
| spl0_1 ),
inference(resolution,[],[f77,f37]) ).
fof(f125,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[],[f62,f3]) ).
fof(f134,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f125,f7]) ).
fof(f154,plain,
a = multiply(inverse(c),b),
inference(superposition,[],[f69,f134]) ).
fof(f156,plain,
inverse(c) = multiply(inverse(d),a),
inference(superposition,[],[f69,f110]) ).
fof(f192,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f16,f154]) ).
fof(f193,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f192,f37]) ).
fof(f195,plain,
( ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f193,f12]) ).
fof(f366,plain,
( element_in_O2(d,a) = multiply(inverse(d),a)
| spl0_1 ),
inference(superposition,[],[f69,f120]) ).
fof(f369,plain,
( inverse(c) = element_in_O2(d,a)
| spl0_1 ),
inference(forward_demodulation,[],[f366,f156]) ).
fof(f471,plain,
( subgroup_member(inverse(c))
| subgroup_member(a)
| subgroup_member(d)
| spl0_1 ),
inference(superposition,[],[f10,f369]) ).
fof(f472,plain,
( subgroup_member(a)
| subgroup_member(d)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f471,f195]) ).
fof(f473,plain,
( subgroup_member(d)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f472,f37]) ).
fof(f474,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f473,f15]) ).
fof(f475,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f474]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f102]) ).
cnf(s16,plain,
spl0_1,
inference(sat_conversion,[],[f475]) ).
cnf(s17,plain,
spl0_3,
inference(rat,[],[s6,s16]) ).
cnf(s19,plain,
spl0_2,
inference(rat,[],[s2,s17]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s19,s16]) ).
fof(f476,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n009.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 09:16:00 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.79/1.51 % (1759789)Input is clausal, will run a generic CNF schedule.
% 3.79/1.51 % (1759798)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2907396271:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.79/1.51 % (1759798)Instruction limit reached!
% 3.79/1.51 % (1759798)------------------------------
% 3.79/1.51 % (1759798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.51 % (1759798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.51 % (1759798)CaDiCaL version: 2.1.3
% 3.79/1.51 % (1759798)Termination reason: Instruction limit
% 3.79/1.51 % (1759798)Termination phase: Saturation
% 3.79/1.51 % (1759798)Time elapsed: 0.040 s
% 3.79/1.51 % (1759798)Peak memory usage: 89 MB
% 3.79/1.51 % (1759798)Instructions burned: 117 (million)
% 3.79/1.51 % (1759795)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=746739573:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.79/1.51 % (1759797)lrs+10_1_sil=8000:sp=occurrence:random_seed=2991134871:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.79/1.51 % (1759799)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=835148858:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.79/1.51 % (1759800)dis-21_1_sil=8000:lcm=predicate:random_seed=1864034615: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)
% 3.79/1.51 % (1759794)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=4164980418:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.79/1.51 % (1759796)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2481974210:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.79/1.51 % (1759800)Refutation not found, incomplete strategy
% 3.79/1.51 % (1759800)------------------------------
% 3.79/1.51 % (1759800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.51 % (1759800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.51 % (1759800)CaDiCaL version: 2.1.3
% 3.79/1.51 % (1759800)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.51 % (1759800)Time elapsed: 0.001 s
% 3.79/1.51 % (1759800)Peak memory usage: 88 MB
% 3.79/1.51 % (1759797)First to succeed.
% 3.79/1.51 % (1759797)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1759789"
% 3.79/1.51 % (1759799)Also succeeded, but the first one will report.
% 3.79/1.51 % (1759808)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=1568110724:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.79/1.51 % (1759808)Instruction limit reached!
% 3.79/1.51 % (1759808)------------------------------
% 3.79/1.51 % (1759808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.51 % (1759808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.51 % (1759808)CaDiCaL version: 2.1.3
% 3.79/1.51 % (1759808)Termination reason: Instruction limit
% 3.79/1.51 % (1759808)Termination phase: Saturation
% 3.79/1.51 % (1759808)Time elapsed: 0.050 s
% 3.79/1.51 % (1759808)Peak memory usage: 89 MB
% 3.79/1.51 % (1759808)Instructions burned: 144 (million)
% 3.79/1.51 % (1759800)------------------------------
% 3.79/1.51 % (1759800)------------------------------
% 3.79/1.51 % (1759797)Refutation found. Thanks to Tanya!
% 3.79/1.51 % SZS status Unsatisfiable for theBenchmark
% 3.79/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.51 % (1759797)------------------------------
% 3.79/1.51 % (1759797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.51 % (1759797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.51 % (1759797)CaDiCaL version: 2.1.3
% 3.79/1.51 % (1759797)Termination reason: Refutation
% 3.79/1.51 % (1759797)Time elapsed: 0.012 s
% 3.79/1.51 % (1759797)Peak memory usage: 89 MB
% 3.79/1.51 % (1759797)Instructions burned: 15 (million)
% 3.79/1.51 % (1759797)------------------------------
% 3.79/1.51 % (1759797)------------------------------
% 3.79/1.51 % (1759789)Success in time 0.438 s
% 3.79/1.51 % Vampire exiting
%------------------------------------------------------------------------------