%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 62 ( 19 unt; 2 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 62 ~; 68 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,X2)
| subgroup_member(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
fof(f7,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f8,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f9,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f10,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f14,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
fof(f17,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(f18,axiom,
! [X0,X1] :
( product(X0,element_in_O2(X0,X1),X1)
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f19,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f20,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f21,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f22,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
fof(f24,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ subgroup_member(X2)
| subgroup_member(X1)
| ~ product(X0,X1,X2)
| subgroup_member(X0) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f26,plain,
~ subgroup_member(identity),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subgroup_member(element_in_O2(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f28,plain,
! [X0,X1] :
( product(X0,element_in_O2(X0,X1),X1)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f29,plain,
~ subgroup_member(b),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f30,plain,
subgroup_member(d),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ product(X1,X0,d)
| subgroup_member(X0)
| subgroup_member(X1) ),
inference(resolution,[],[f25,f30]) ).
fof(f39,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference(resolution,[],[f33,f21]) ).
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(f47,plain,
( subgroup_member(c)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f39,f45,f41]) ).
fof(f49,plain,
( ! [X0,X1] :
( ~ product(X1,X0,c)
| subgroup_member(X0)
| subgroup_member(X1) )
| ~ spl0_2 ),
inference(resolution,[],[f47,f25]) ).
fof(f53,plain,
( subgroup_member(inverse(a))
| subgroup_member(b)
| ~ spl0_2 ),
inference(resolution,[],[f49,f20]) ).
fof(f54,plain,
( subgroup_member(inverse(a))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f53,f29]) ).
fof(f58,plain,
( ! [X0,X1] :
( ~ product(X1,X0,a)
| subgroup_member(X0)
| subgroup_member(X1) )
| ~ spl0_1 ),
inference(resolution,[],[f43,f25]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f11,f7]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,identity)
| ~ product(X2,X0,X3)
| product(X3,X1,X2) ),
inference(resolution,[],[f12,f8]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ product(a,X0,X2)
| ~ product(X0,X1,c)
| product(X2,X1,d) ),
inference(resolution,[],[f12,f21]) ).
fof(f120,plain,
! [X0] :
( ~ product(inverse(a),X0,c)
| product(identity,X0,d) ),
inference(resolution,[],[f100,f10]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[],[f91,f9]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| product(X2,X1,X0) ),
inference(resolution,[],[f94,f9]) ).
fof(f215,plain,
( product(identity,element_in_O2(inverse(a),c),d)
| ~ subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(resolution,[],[f120,f28]) ).
fof(f216,plain,
( product(identity,element_in_O2(inverse(a),c),d)
| ~ subgroup_member(inverse(a))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f215,f47]) ).
fof(f217,plain,
( product(identity,element_in_O2(inverse(a),c),d)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f216,f54]) ).
fof(f220,plain,
( subgroup_member(element_in_O2(inverse(a),c))
| subgroup_member(identity)
| ~ spl0_2 ),
inference(resolution,[],[f217,f33]) ).
fof(f226,plain,
( subgroup_member(element_in_O2(inverse(a),c))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f220,f26]) ).
fof(f229,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ spl0_2 ),
inference(resolution,[],[f226,f27]) ).
fof(f231,plain,
( ~ subgroup_member(inverse(a))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f229,f47]) ).
fof(f232,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f231,f54]) ).
fof(f233,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f576,plain,
product(c,a,b),
inference(resolution,[],[f189,f20]) ).
fof(f612,plain,
product(inverse(c),b,a),
inference(resolution,[],[f576,f184]) ).
fof(f619,plain,
( subgroup_member(b)
| subgroup_member(inverse(c))
| ~ spl0_1 ),
inference(resolution,[],[f612,f58]) ).
fof(f628,plain,
( subgroup_member(inverse(c))
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f619,f29]) ).
fof(f640,plain,
( subgroup_member(c)
| ~ spl0_1 ),
inference(resolution,[],[f628,f24]) ).
fof(f648,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f640,f46]) ).
fof(f649,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f648]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
~ spl0_2,
inference(sat_conversion,[],[f233]) ).
cnf(s16,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f649]) ).
cnf(s18,plain,
~ spl0_1,
inference(rat,[],[s16,s5]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s5,s18]) ).
fof(f650,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:21:46 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (3283787)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3283798)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=499957571:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (3283793)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3283792)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=804843169_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3283793)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=697288558:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3283794)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1814544973:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3283795)dis+10_1_sil=32000:sp=arity:random_seed=1147566202:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3283796)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=726916245:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3283797)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1997889891:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (3283793) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3283787-3283793"...
% 0.17/0.48 % (3283793)...printing done.
% 0.17/0.48 % (3283793)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3283793)------------------------------
% 0.17/0.48 % (3283793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3283793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3283793)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3283793)Termination reason: Refutation
% 0.17/0.48 % (3283793)Time elapsed: 0.016 s
% 0.17/0.48 % (3283793)Peak memory usage: 12 MB
% 0.17/0.48 % (3283793)Instructions burned: 21 (million)
% 0.17/0.48 % (3283787)Success in time 0.047 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------