%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP026-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 10:16:24 AM UTC 2026
% Result : Satisfiable 0.10s 0.44s
% Output : FiniteModel 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
tff('declare_$i1',type,
'fmb_$i_1': $i ).
tff('declare_$i2',type,
'fmb_$i_2': $i ).
tff('declare_$i3',type,
'fmb_$i_3': $i ).
tff('finite_domain_$i',axiom,
! [X: $i] :
( ( X = 'fmb_$i_1' )
| ( X = 'fmb_$i_2' )
| ( X = 'fmb_$i_3' ) ) ).
tff('distinct_domain_$i',axiom,
( ( 'fmb_$i_1' != 'fmb_$i_2' )
& ( 'fmb_$i_1' != 'fmb_$i_3' )
& ( 'fmb_$i_2' != 'fmb_$i_3' ) ) ).
tff(declare_g1,type,
g1: $i ).
tff(g1_definition,axiom,
g1 = 'fmb_$i_1' ).
tff(declare_g2,type,
g2: $i ).
tff(g2_definition,axiom,
g2 = 'fmb_$i_2' ).
tff(declare_a,type,
a: $i ).
tff(a_definition,axiom,
a = 'fmb_$i_1' ).
tff(declare_b,type,
b: $i ).
tff(b_definition,axiom,
b = 'fmb_$i_2' ).
tff(declare_c,type,
c: $i ).
tff(c_definition,axiom,
c = 'fmb_$i_3' ).
tff(declare_f,type,
f: $i ).
tff(f_definition,axiom,
f = 'fmb_$i_3' ).
tff(declare_g,type,
g: $i ).
tff(g_definition,axiom,
g = 'fmb_$i_2' ).
tff(declare_h,type,
h: $i ).
tff(h_definition,axiom,
h = 'fmb_$i_1' ).
tff(declare_d1,type,
d1: $i ).
tff(d1_definition,axiom,
d1 = 'fmb_$i_3' ).
tff(declare_d2,type,
d2: $i ).
tff(d2_definition,axiom,
d2 = 'fmb_$i_3' ).
tff(declare_d3,type,
d3: $i ).
tff(d3_definition,axiom,
d3 = 'fmb_$i_2' ).
tff(declare_identity_for,type,
identity_for: $i > $i ).
tff(function_identity_for,axiom,
( ( identity_for('fmb_$i_1') = 'fmb_$i_1' )
& ( identity_for('fmb_$i_2') = 'fmb_$i_3' )
& ( identity_for('fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_inverse,type,
inverse: ( $i * $i ) > $i ).
tff(function_inverse,axiom,
( ( inverse('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( inverse('fmb_$i_1','fmb_$i_2') = 'fmb_$i_3' )
& ( inverse('fmb_$i_1','fmb_$i_3') = 'fmb_$i_2' )
& ( inverse('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( inverse('fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( inverse('fmb_$i_2','fmb_$i_3') = 'fmb_$i_3' )
& ( inverse('fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( inverse('fmb_$i_3','fmb_$i_2') = 'fmb_$i_3' )
& ( inverse('fmb_$i_3','fmb_$i_3') = 'fmb_$i_2' ) ) ).
tff(declare_multiply,type,
multiply: ( $i * $i * $i ) > $i ).
tff(function_multiply,axiom,
( ( multiply('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( multiply('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( multiply('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( multiply('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( multiply('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_3' )
& ( multiply('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_1' )
& ( multiply('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( multiply('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( multiply('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_2' )
& ( multiply('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_2' )
& ( multiply('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_3' )
& ( multiply('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( multiply('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_3' )
& ( multiply('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( multiply('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( multiply('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( multiply('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( multiply('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' )
& ( multiply('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( multiply('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( multiply('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( multiply('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( multiply('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_3' )
& ( multiply('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_1' )
& ( multiply('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( multiply('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( multiply('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_2' ) ) ).
tff(declare_isomorphism1,type,
isomorphism1: $i > $i ).
tff(function_isomorphism1,axiom,
( ( isomorphism1('fmb_$i_1') = 'fmb_$i_3' )
& ( isomorphism1('fmb_$i_2') = 'fmb_$i_2' )
& ( isomorphism1('fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_isomorphism2,type,
isomorphism2: $i > $i ).
tff(function_isomorphism2,axiom,
( ( isomorphism2('fmb_$i_1') = 'fmb_$i_3' )
& ( isomorphism2('fmb_$i_2') = 'fmb_$i_1' )
& ( isomorphism2('fmb_$i_3') = 'fmb_$i_2' ) ) ).
tff(declare_isomorphism3,type,
isomorphism3: $i > $i ).
tff(function_isomorphism3,axiom,
( ( isomorphism3('fmb_$i_1') = 'fmb_$i_2' )
& ( isomorphism3('fmb_$i_2') = 'fmb_$i_3' )
& ( isomorphism3('fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_isomorphism4,type,
isomorphism4: $i > $i ).
tff(function_isomorphism4,axiom,
( ( isomorphism4('fmb_$i_1') = 'fmb_$i_2' )
& ( isomorphism4('fmb_$i_2') = 'fmb_$i_1' )
& ( isomorphism4('fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_isomorphism5,type,
isomorphism5: $i > $i ).
tff(function_isomorphism5,axiom,
( ( isomorphism5('fmb_$i_1') = 'fmb_$i_1' )
& ( isomorphism5('fmb_$i_2') = 'fmb_$i_2' )
& ( isomorphism5('fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_isomorphism6,type,
isomorphism6: $i > $i ).
tff(function_isomorphism6,axiom,
( ( isomorphism6('fmb_$i_1') = 'fmb_$i_1' )
& ( isomorphism6('fmb_$i_2') = 'fmb_$i_3' )
& ( isomorphism6('fmb_$i_3') = 'fmb_$i_2' ) ) ).
tff(declare_group_member,type,
group_member: ( $i * $i ) > $o ).
tff(predicate_group_member,axiom,
( group_member('fmb_$i_1','fmb_$i_1')
& group_member('fmb_$i_1','fmb_$i_2')
& group_member('fmb_$i_1','fmb_$i_3')
& group_member('fmb_$i_2','fmb_$i_1')
& group_member('fmb_$i_2','fmb_$i_2')
& group_member('fmb_$i_2','fmb_$i_3')
& group_member('fmb_$i_3','fmb_$i_1')
& group_member('fmb_$i_3','fmb_$i_2')
& group_member('fmb_$i_3','fmb_$i_3') ) ).
tff(declare_product,type,
product: ( $i * $i * $i * $i ) > $o ).
tff(predicate_product,axiom,
( product('fmb_$i_1','fmb_$i_1','fmb_$i_1','fmb_$i_1')
& ~ product('fmb_$i_1','fmb_$i_1','fmb_$i_1','fmb_$i_2')
& ~ product('fmb_$i_1','fmb_$i_1','fmb_$i_1','fmb_$i_3')
& ~ product('fmb_$i_1','fmb_$i_1','fmb_$i_2','fmb_$i_1')
& product('fmb_$i_1','fmb_$i_1','fmb_$i_2','fmb_$i_2')
& ~ product('fmb_$i_1','fmb_$i_1','fmb_$i_2','fmb_$i_3')
& ~ product('fmb_$i_1','fmb_$i_1','fmb_$i_3','fmb_$i_1')
& ~ product('fmb_$i_1','fmb_$i_1','fmb_$i_3','fmb_$i_2')
& product('fmb_$i_1','fmb_$i_1','fmb_$i_3','fmb_$i_3')
& ~ product('fmb_$i_1','fmb_$i_2','fmb_$i_1','fmb_$i_1')
& product('fmb_$i_1','fmb_$i_2','fmb_$i_1','fmb_$i_2')
& ~ product('fmb_$i_1','fmb_$i_2','fmb_$i_1','fmb_$i_3')
& ~ product('fmb_$i_1','fmb_$i_2','fmb_$i_2','fmb_$i_1')
& ~ product('fmb_$i_1','fmb_$i_2','fmb_$i_2','fmb_$i_2')
& product('fmb_$i_1','fmb_$i_2','fmb_$i_2','fmb_$i_3')
& product('fmb_$i_1','fmb_$i_2','fmb_$i_3','fmb_$i_1')
& ~ product('fmb_$i_1','fmb_$i_2','fmb_$i_3','fmb_$i_2')
& ~ product('fmb_$i_1','fmb_$i_2','fmb_$i_3','fmb_$i_3')
& ~ product('fmb_$i_1','fmb_$i_3','fmb_$i_1','fmb_$i_1')
& ~ product('fmb_$i_1','fmb_$i_3','fmb_$i_1','fmb_$i_2')
& product('fmb_$i_1','fmb_$i_3','fmb_$i_1','fmb_$i_3')
& product('fmb_$i_1','fmb_$i_3','fmb_$i_2','fmb_$i_1')
& ~ product('fmb_$i_1','fmb_$i_3','fmb_$i_2','fmb_$i_2')
& ~ product('fmb_$i_1','fmb_$i_3','fmb_$i_2','fmb_$i_3')
& ~ product('fmb_$i_1','fmb_$i_3','fmb_$i_3','fmb_$i_1')
& product('fmb_$i_1','fmb_$i_3','fmb_$i_3','fmb_$i_2')
& ~ product('fmb_$i_1','fmb_$i_3','fmb_$i_3','fmb_$i_3')
& ~ product('fmb_$i_2','fmb_$i_1','fmb_$i_1','fmb_$i_1')
& product('fmb_$i_2','fmb_$i_1','fmb_$i_1','fmb_$i_2')
& ~ product('fmb_$i_2','fmb_$i_1','fmb_$i_1','fmb_$i_3')
& ~ product('fmb_$i_2','fmb_$i_1','fmb_$i_2','fmb_$i_1')
& ~ product('fmb_$i_2','fmb_$i_1','fmb_$i_2','fmb_$i_2')
& product('fmb_$i_2','fmb_$i_1','fmb_$i_2','fmb_$i_3')
& product('fmb_$i_2','fmb_$i_1','fmb_$i_3','fmb_$i_1')
& ~ product('fmb_$i_2','fmb_$i_1','fmb_$i_3','fmb_$i_2')
& ~ product('fmb_$i_2','fmb_$i_1','fmb_$i_3','fmb_$i_3')
& ~ product('fmb_$i_2','fmb_$i_2','fmb_$i_1','fmb_$i_1')
& ~ product('fmb_$i_2','fmb_$i_2','fmb_$i_1','fmb_$i_2')
& product('fmb_$i_2','fmb_$i_2','fmb_$i_1','fmb_$i_3')
& product('fmb_$i_2','fmb_$i_2','fmb_$i_2','fmb_$i_1')
& ~ product('fmb_$i_2','fmb_$i_2','fmb_$i_2','fmb_$i_2')
& ~ product('fmb_$i_2','fmb_$i_2','fmb_$i_2','fmb_$i_3')
& ~ product('fmb_$i_2','fmb_$i_2','fmb_$i_3','fmb_$i_1')
& product('fmb_$i_2','fmb_$i_2','fmb_$i_3','fmb_$i_2')
& ~ product('fmb_$i_2','fmb_$i_2','fmb_$i_3','fmb_$i_3')
& product('fmb_$i_2','fmb_$i_3','fmb_$i_1','fmb_$i_1')
& ~ product('fmb_$i_2','fmb_$i_3','fmb_$i_1','fmb_$i_2')
& ~ product('fmb_$i_2','fmb_$i_3','fmb_$i_1','fmb_$i_3')
& ~ product('fmb_$i_2','fmb_$i_3','fmb_$i_2','fmb_$i_1')
& product('fmb_$i_2','fmb_$i_3','fmb_$i_2','fmb_$i_2')
& ~ product('fmb_$i_2','fmb_$i_3','fmb_$i_2','fmb_$i_3')
& ~ product('fmb_$i_2','fmb_$i_3','fmb_$i_3','fmb_$i_1')
& ~ product('fmb_$i_2','fmb_$i_3','fmb_$i_3','fmb_$i_2')
& product('fmb_$i_2','fmb_$i_3','fmb_$i_3','fmb_$i_3')
& product('fmb_$i_3','fmb_$i_1','fmb_$i_1','fmb_$i_1')
& ~ product('fmb_$i_3','fmb_$i_1','fmb_$i_1','fmb_$i_2')
& ~ product('fmb_$i_3','fmb_$i_1','fmb_$i_1','fmb_$i_3')
& ~ product('fmb_$i_3','fmb_$i_1','fmb_$i_2','fmb_$i_1')
& product('fmb_$i_3','fmb_$i_1','fmb_$i_2','fmb_$i_2')
& ~ product('fmb_$i_3','fmb_$i_1','fmb_$i_2','fmb_$i_3')
& ~ product('fmb_$i_3','fmb_$i_1','fmb_$i_3','fmb_$i_1')
& ~ product('fmb_$i_3','fmb_$i_1','fmb_$i_3','fmb_$i_2')
& product('fmb_$i_3','fmb_$i_1','fmb_$i_3','fmb_$i_3')
& ~ product('fmb_$i_3','fmb_$i_2','fmb_$i_1','fmb_$i_1')
& product('fmb_$i_3','fmb_$i_2','fmb_$i_1','fmb_$i_2')
& ~ product('fmb_$i_3','fmb_$i_2','fmb_$i_1','fmb_$i_3')
& ~ product('fmb_$i_3','fmb_$i_2','fmb_$i_2','fmb_$i_1')
& ~ product('fmb_$i_3','fmb_$i_2','fmb_$i_2','fmb_$i_2')
& product('fmb_$i_3','fmb_$i_2','fmb_$i_2','fmb_$i_3')
& product('fmb_$i_3','fmb_$i_2','fmb_$i_3','fmb_$i_1')
& ~ product('fmb_$i_3','fmb_$i_2','fmb_$i_3','fmb_$i_2')
& ~ product('fmb_$i_3','fmb_$i_2','fmb_$i_3','fmb_$i_3')
& ~ product('fmb_$i_3','fmb_$i_3','fmb_$i_1','fmb_$i_1')
& ~ product('fmb_$i_3','fmb_$i_3','fmb_$i_1','fmb_$i_2')
& product('fmb_$i_3','fmb_$i_3','fmb_$i_1','fmb_$i_3')
& product('fmb_$i_3','fmb_$i_3','fmb_$i_2','fmb_$i_1')
& ~ product('fmb_$i_3','fmb_$i_3','fmb_$i_2','fmb_$i_2')
& ~ product('fmb_$i_3','fmb_$i_3','fmb_$i_2','fmb_$i_3')
& ~ product('fmb_$i_3','fmb_$i_3','fmb_$i_3','fmb_$i_1')
& product('fmb_$i_3','fmb_$i_3','fmb_$i_3','fmb_$i_2')
& ~ product('fmb_$i_3','fmb_$i_3','fmb_$i_3','fmb_$i_3') ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP026-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:14:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.44 % (2722659)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (2722664)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2673518219_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.44 % Detected minimum model sizes of [3]
% 0.10/0.44 % Detected maximum model sizes of [max]
% 0.10/0.44 % TRYING [3]
% 0.10/0.44 % Finite Model Found!
% 0.10/0.44 % SZS status Satisfiable for theBenchmark
% 0.10/0.44 % (2722664) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2722659-2722664"...
% 0.10/0.44 % (2722665)% WARNING: option uhcvi not known.
% 0.10/0.44 % (2722664)...printing done.
% 0.10/0.44 % SZS output start FiniteModel for theBenchmark
% See solution above
% 0.10/0.44 % (2722664)------------------------------
% 0.10/0.44 % (2722664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (2722664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (2722664)CaDiCaL version: 2.1.3
% 0.10/0.44 % (2722664)Termination reason: Satisfiable
% 0.10/0.44 % (2722664)Time elapsed: 0.006 s
% 0.10/0.44 % (2722664)Peak memory usage: 12 MB
% 0.10/0.44 % (2722664)Instructions burned: 22 (million)
% 0.10/0.44 % (2722659)Success in time 0.021 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------