%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 10:16:28 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 21 unt; 3 def)
% Number of atoms : 110 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 87 ( 36 ~; 48 |; 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/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',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/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f16,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).
fof(f17,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f18,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f19,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/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(f36,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(superposition,[],[f20,f17]) ).
fof(f37,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(superposition,[],[f20,f18]) ).
fof(f38,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[],[f37,f19]) ).
fof(f39,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_subsumption_resolution,[],[f36,f16]) ).
fof(f41,definition,
( spl0_1
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f43,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl0_2
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f46,plain,
( subgroup_member(c)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f38,f45,f41]) ).
fof(f50,definition,
( spl0_3
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f52,plain,
( ~ subgroup_member(inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f39,f45,f50]) ).
fof(f58,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f59,plain,
! [X0] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[],[f4,f17]) ).
fof(f66,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f58,f1]) ).
fof(f70,plain,
( ~ subgroup_member(a)
| spl0_3 ),
inference(resolution,[],[f52,f5]) ).
fof(f71,plain,
! [X0] :
( subgroup_member(X0)
| d = multiply(X0,element_in_O2(X0,d)) ),
inference(resolution,[],[f15,f19]) ).
fof(f87,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_1 ),
inference(resolution,[],[f71,f43]) ).
fof(f94,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[],[f59,f3]) ).
fof(f103,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f94,f7]) ).
fof(f123,plain,
c = multiply(inverse(a),d),
inference(superposition,[],[f66,f18]) ).
fof(f224,plain,
a = multiply(inverse(c),b),
inference(superposition,[],[f66,f103]) ).
fof(f255,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_1 ),
inference(superposition,[],[f66,f87]) ).
fof(f258,plain,
( c = element_in_O2(a,d)
| spl0_1 ),
inference(forward_demodulation,[],[f255,f123]) ).
fof(f260,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a)
| spl0_1 ),
inference(superposition,[],[f14,f258]) ).
fof(f261,plain,
( subgroup_member(c)
| subgroup_member(a)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f260,f19]) ).
fof(f262,plain,
( subgroup_member(c)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f261,f43]) ).
fof(f263,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f262,f41,f45]) ).
fof(f264,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f70,f50,f41]) ).
fof(f280,plain,
( subgroup_member(a)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f20,f224]) ).
fof(f281,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f280,f43]) ).
fof(f284,plain,
( ~ subgroup_member(inverse(c))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f281,f16]) ).
fof(f286,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(resolution,[],[f284,f5]) ).
fof(f292,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f286,f46]) ).
fof(f293,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f292]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f263]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f264]) ).
cnf(s7,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f293]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s3,s7]) ).
cnf(s10,plain,
spl0_3,
inference(rat,[],[s4,s8]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s1,s8]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s10,s11]) ).
fof(f294,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n004.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:16:22 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.50 % (3237929)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (3237946)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1822002429:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (3237942)% WARNING: option uhcvi not known.
% 0.17/0.50 % (3237940)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=558830844_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % (3237943)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1086560489:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (3237942)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2071797:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (3237944)dis+10_1_sil=32000:sp=arity:random_seed=1162349303:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (3237947)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2335201581:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % (3237945)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3082110302:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % TRYING [4]
% 0.17/0.50 % (3237942) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3237929-3237942"...
% 0.17/0.50 % TRYING [5]
% 0.17/0.50 % (3237942)...printing done.
% 0.17/0.50 % (3237942)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (3237942)------------------------------
% 0.17/0.50 % (3237942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (3237942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (3237942)CaDiCaL version: 2.1.3
% 0.17/0.50 % (3237942)Termination reason: Refutation
% 0.17/0.50 % (3237942)Time elapsed: 0.008 s
% 0.17/0.50 % (3237942)Peak memory usage: 12 MB
% 0.17/0.50 % (3237942)Instructions burned: 11 (million)
% 0.17/0.50 % (3237929)Success in time 0.054 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------