%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 10:16:27 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.49s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 63 ( 27 unt; 3 def)
% Number of atoms : 118 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 107 ( 52 ~; 52 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
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/Axioms/GRP003-0.ax',associativity1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,inverse(X1),X2)
| subgroup_member(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',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,
! [X2,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| subgroup_member(X1)
| subgroup_member(X0)
| ~ subgroup_member(X2) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f15,plain,
~ subgroup_member(a),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f16,plain,
~ subgroup_member(b),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f17,plain,
subgroup_member(c),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f18,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[],[f6,f2]) ).
fof(f21,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| X0 = X1 ),
inference(resolution,[],[f6,f1]) ).
fof(f22,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| identity = X1 ),
inference(resolution,[],[f6,f3]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subgroup_member(multiply(X1,inverse(X0)))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(resolution,[],[f14,f5]) ).
fof(f30,definition,
( spl0_1
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f38,definition,
( spl0_3
<=> ! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f42,definition,
( spl0_4
<=> ! [X0] : subgroup_member(X0) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f43,plain,
( ! [X0] : subgroup_member(X0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f7,f1]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,X3)
| ~ product(X0,X1,X2)
| product(X2,inverse(X1),X3) ),
inference(resolution,[],[f8,f4]) ).
fof(f67,plain,
! [X0] : multiply(identity,X0) = X0,
inference(resolution,[],[f21,f5]) ).
fof(f79,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(resolution,[],[f22,f5]) ).
fof(f102,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(identity)
| subgroup_member(X0) ),
inference(superposition,[],[f25,f67]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ product(inverse(X0),X1,X2)
| product(X0,X2,X1) ),
inference(resolution,[],[f48,f4]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[],[f48,f3]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X2,inverse(X1),X0) ),
inference(resolution,[],[f52,f2]) ).
fof(f164,plain,
! [X0] :
( ~ subgroup_member(identity)
| subgroup_member(inverse(inverse(X0)))
| subgroup_member(X0) ),
inference(superposition,[],[f25,f79]) ).
fof(f211,plain,
! [X0] : product(X0,identity,inverse(inverse(X0))),
inference(resolution,[],[f104,f4]) ).
fof(f220,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[],[f211,f18]) ).
fof(f248,plain,
( ! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) )
| ~ spl0_3 ),
inference(superposition,[],[f39,f220]) ).
fof(f262,plain,
product(inverse(a),c,b),
inference(resolution,[],[f106,f12]) ).
fof(f297,plain,
( subgroup_member(inverse(c))
| ~ spl0_3 ),
inference(resolution,[],[f248,f17]) ).
fof(f322,plain,
product(b,inverse(c),inverse(a)),
inference(resolution,[],[f127,f262]) ).
fof(f361,plain,
product(inverse(b),inverse(a),inverse(c)),
inference(resolution,[],[f322,f106]) ).
fof(f1236,plain,
( subgroup_member(a)
| subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c)) ),
inference(resolution,[],[f361,f14]) ).
fof(f1253,plain,
( subgroup_member(inverse(b))
| ~ subgroup_member(inverse(c)) ),
inference(forward_subsumption_resolution,[],[f1236,f15]) ).
fof(f1255,plain,
( subgroup_member(inverse(b))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1253,f297]) ).
fof(f1510,plain,
( subgroup_member(inverse(inverse(b)))
| ~ spl0_3 ),
inference(resolution,[],[f1255,f248]) ).
fof(f1511,plain,
( subgroup_member(b)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f1510,f220]) ).
fof(f1514,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1511,f16]) ).
fof(f1515,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f1514]) ).
fof(f1518,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f102,f38,f30]) ).
fof(f1534,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(identity)
| subgroup_member(X0) ),
inference(forward_demodulation,[],[f164,f220]) ).
fof(f1535,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(identity) ),
inference(duplicate_literal_removal,[],[f1534]) ).
fof(f1549,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f1535,f42,f30]) ).
fof(f1553,plain,
( $false
| ~ spl0_4 ),
inference(backward_subsumption_resolution,[],[f16,f43]) ).
fof(f1555,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f1553]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f1515]) ).
cnf(s6,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f1518]) ).
cnf(s14,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s16,plain,
~ spl0_4,
inference(sat_conversion,[],[f1555]) ).
cnf(s17,plain,
~ spl0_1,
inference(rat,[],[s14,s16]) ).
cnf(s22,plain,
spl0_3,
inference(rat,[],[s6,s17]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s5,s22]) ).
fof(f1556,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:18:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.49 % (3266164)Will run a generic schedule for satisfiability detection.
% 0.15/0.49 % (3266178)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2364069456:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.49 % (3266175)% WARNING: option uhcvi not known.
% 0.15/0.49 % (3266177)dis+10_1_sil=32000:sp=arity:random_seed=4114711404:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.49 % (3266174)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1385044748_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.49 % (3266175)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=288410059:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.49 % (3266176)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2173021321:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.49 % (3266179)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1374485133:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.49 % (3266180)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1396368410:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.49 % TRYING [1]
% 0.15/0.49 % TRYING [2]
% 0.15/0.49 % TRYING [3]
% 0.15/0.49 % TRYING [4]
% 0.15/0.49 % TRYING [5]
% 0.15/0.49 % TRYING [6]
% 0.15/0.49 % (3266175) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3266164-3266175"...
% 0.15/0.49 % (3266178)Instruction limit reached!
% 0.15/0.49 % (3266178)------------------------------
% 0.15/0.49 % (3266178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (3266178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (3266178)CaDiCaL version: 2.1.3
% 0.15/0.49 % (3266178)Termination reason: Instruction limit
% 0.15/0.49 % (3266178)Termination phase: Saturation
% 0.15/0.49 % (3266178)Time elapsed: 0.036 s
% 0.15/0.49 % (3266178)Peak memory usage: 11 MB
% 0.15/0.49 % (3266178)Instructions burned: 118 (million)
% 0.15/0.49 % (3266175)...printing done.
% 0.15/0.49 % (3266177) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3266164-3266177"...
% 0.15/0.49 % (3266175)Refutation found. Thanks to Tanya!
% 0.15/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (3266175)------------------------------
% 0.15/0.49 % (3266175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (3266175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (3266175)CaDiCaL version: 2.1.3
% 0.15/0.49 % (3266175)Termination reason: Refutation
% 0.15/0.49 % (3266175)Time elapsed: 0.029 s
% 0.15/0.49 % (3266175)Peak memory usage: 12 MB
% 0.15/0.49 % (3266175)Instructions burned: 42 (million)
% 0.15/0.49 % (3266164)Success in time 0.071 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------