%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW103+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 01:39:33 PM UTC 2026
% Result : Satisfiable 0.20s 0.30s
% Output : FiniteModel 0.20s
% 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_false,type,
false: $i ).
tff(false_definition,axiom,
false = 'fmb_$i_3' ).
tff(declare_true,type,
true: $i ).
tff(true_definition,axiom,
true = 'fmb_$i_1' ).
tff(declare_err,type,
err: $i ).
tff(err_definition,axiom,
err = 'fmb_$i_2' ).
tff(declare_false1,type,
false1: $i ).
tff(false1_definition,axiom,
false1 = 'fmb_$i_3' ).
tff(declare_false2,type,
false2: $i ).
tff(false2_definition,axiom,
false2 = 'fmb_$i_3' ).
tff(declare_phi,type,
phi: $i > $i ).
tff(function_phi,axiom,
( ( phi('fmb_$i_1') = 'fmb_$i_1' )
& ( phi('fmb_$i_2') = 'fmb_$i_2' )
& ( phi('fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_prop,type,
prop: $i > $i ).
tff(function_prop,axiom,
( ( prop('fmb_$i_1') = 'fmb_$i_1' )
& ( prop('fmb_$i_2') = 'fmb_$i_3' )
& ( prop('fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_impl,type,
impl: ( $i * $i ) > $i ).
tff(function_impl,axiom,
( ( impl('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( impl('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( impl('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( impl('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( impl('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( impl('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( impl('fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( impl('fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( impl('fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_lazy_impl,type,
lazy_impl: ( $i * $i ) > $i ).
tff(function_lazy_impl,axiom,
( ( lazy_impl('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( lazy_impl('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( lazy_impl('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( lazy_impl('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( lazy_impl('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( lazy_impl('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( lazy_impl('fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( lazy_impl('fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( lazy_impl('fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_and1,type,
and1: ( $i * $i ) > $i ).
tff(function_and1,axiom,
( ( and1('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( and1('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( and1('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( and1('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( and1('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( and1('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( and1('fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( and1('fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( and1('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_f1,type,
f1: ( $i * $i * $i ) > $i ).
tff(function_f1,axiom,
( ( f1('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f1('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f1('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f1('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f1('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f1('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' )
& ( f1('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_2' )
& ( f1('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_2' )
& ( f1('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f1('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f1('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_2' )
& ( f1('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_2' )
& ( f1('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f1('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( f1('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f1('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f1('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f1('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f1('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_and2,type,
and2: ( $i * $i ) > $i ).
tff(function_and2,axiom,
( ( and2('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( and2('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( and2('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( and2('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( and2('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( and2('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( and2('fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( and2('fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( and2('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_lazy_and1,type,
lazy_and1: ( $i * $i ) > $i ).
tff(function_lazy_and1,axiom,
( ( lazy_and1('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( lazy_and1('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( lazy_and1('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( lazy_and1('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( lazy_and1('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( lazy_and1('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( lazy_and1('fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( lazy_and1('fmb_$i_3','fmb_$i_2') = 'fmb_$i_3' )
& ( lazy_and1('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_f2,type,
f2: ( $i * $i * $i ) > $i ).
tff(function_f2,axiom,
( ( f2('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f2('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f2('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f2('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f2('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f2('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' )
& ( f2('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_2' )
& ( f2('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_2' )
& ( f2('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f2('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f2('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_2' )
& ( f2('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_2' )
& ( f2('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f2('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( f2('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_1' )
& ( f2('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_3' )
& ( f2('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f2('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f2('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_lazy_and2,type,
lazy_and2: ( $i * $i ) > $i ).
tff(function_lazy_and2,axiom,
( ( lazy_and2('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( lazy_and2('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( lazy_and2('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( lazy_and2('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( lazy_and2('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( lazy_and2('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( lazy_and2('fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( lazy_and2('fmb_$i_3','fmb_$i_2') = 'fmb_$i_3' )
& ( lazy_and2('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_or1,type,
or1: ( $i * $i ) > $i ).
tff(function_or1,axiom,
( ( or1('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( or1('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( or1('fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( or1('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( or1('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( or1('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( or1('fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( or1('fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( or1('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_f3,type,
f3: ( $i * $i * $i ) > $i ).
tff(function_f3,axiom,
( ( f3('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f3('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f3('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f3('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f3('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f3('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' )
& ( f3('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_2' )
& ( f3('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_2' )
& ( f3('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f3('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f3('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_2' )
& ( f3('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_2' )
& ( f3('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f3('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f3('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( f3('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( f3('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f3('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f3('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_or2,type,
or2: ( $i * $i ) > $i ).
tff(function_or2,axiom,
( ( or2('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( or2('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( or2('fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( or2('fmb_$i_2','fmb_$i_1') = 'fmb_$i_2' )
& ( or2('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( or2('fmb_$i_2','fmb_$i_3') = 'fmb_$i_2' )
& ( or2('fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( or2('fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( or2('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_exists1,type,
exists1: $i > $i ).
tff(function_exists1,axiom,
( ( exists1('fmb_$i_1') = 'fmb_$i_3' )
& ( exists1('fmb_$i_2') = 'fmb_$i_3' )
& ( exists1('fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_apply,type,
apply: ( $i * $i ) > $i ).
tff(function_apply,axiom,
( ( apply('fmb_$i_1','fmb_$i_1') = 'fmb_$i_3' )
& ( apply('fmb_$i_1','fmb_$i_2') = 'fmb_$i_3' )
& ( apply('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( apply('fmb_$i_2','fmb_$i_1') = 'fmb_$i_3' )
& ( apply('fmb_$i_2','fmb_$i_2') = 'fmb_$i_3' )
& ( apply('fmb_$i_2','fmb_$i_3') = 'fmb_$i_3' )
& ( apply('fmb_$i_3','fmb_$i_1') = 'fmb_$i_3' )
& ( apply('fmb_$i_3','fmb_$i_2') = 'fmb_$i_3' )
& ( apply('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_f4,type,
f4: ( $i * $i * $i ) > $i ).
tff(function_f4,axiom,
( ( f4('fmb_$i_1','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_1','fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_1','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_1','fmb_$i_2','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_1','fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_1','fmb_$i_2','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_1','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_1','fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_1','fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_2','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_2','fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_2','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_2','fmb_$i_2','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_2','fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_2','fmb_$i_2','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_2','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_2','fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_2','fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_3','fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_3','fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_3','fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_3','fmb_$i_2','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_3','fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_3','fmb_$i_2','fmb_$i_3') = 'fmb_$i_1' )
& ( f4('fmb_$i_3','fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f4('fmb_$i_3','fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( f4('fmb_$i_3','fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_f5,type,
f5: ( $i * $i ) > $i ).
tff(function_f5,axiom,
( ( f5('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f5('fmb_$i_1','fmb_$i_2') = 'fmb_$i_2' )
& ( f5('fmb_$i_1','fmb_$i_3') = 'fmb_$i_1' )
& ( f5('fmb_$i_2','fmb_$i_1') = 'fmb_$i_1' )
& ( f5('fmb_$i_2','fmb_$i_2') = 'fmb_$i_2' )
& ( f5('fmb_$i_2','fmb_$i_3') = 'fmb_$i_1' )
& ( f5('fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f5('fmb_$i_3','fmb_$i_2') = 'fmb_$i_2' )
& ( f5('fmb_$i_3','fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_f6,type,
f6: ( $i * $i ) > $i ).
tff(function_f6,axiom,
( ( f6('fmb_$i_1','fmb_$i_1') = 'fmb_$i_1' )
& ( f6('fmb_$i_1','fmb_$i_2') = 'fmb_$i_1' )
& ( f6('fmb_$i_1','fmb_$i_3') = 'fmb_$i_3' )
& ( f6('fmb_$i_2','fmb_$i_1') = 'fmb_$i_1' )
& ( f6('fmb_$i_2','fmb_$i_2') = 'fmb_$i_1' )
& ( f6('fmb_$i_2','fmb_$i_3') = 'fmb_$i_3' )
& ( f6('fmb_$i_3','fmb_$i_1') = 'fmb_$i_1' )
& ( f6('fmb_$i_3','fmb_$i_2') = 'fmb_$i_1' )
& ( f6('fmb_$i_3','fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_exists2,type,
exists2: $i > $i ).
tff(function_exists2,axiom,
( ( exists2('fmb_$i_1') = 'fmb_$i_3' )
& ( exists2('fmb_$i_2') = 'fmb_$i_3' )
& ( exists2('fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_f7,type,
f7: $i > $i ).
tff(function_f7,axiom,
( ( f7('fmb_$i_1') = 'fmb_$i_1' )
& ( f7('fmb_$i_2') = 'fmb_$i_1' )
& ( f7('fmb_$i_3') = 'fmb_$i_3' ) ) ).
tff(declare_not1,type,
not1: $i > $i ).
tff(function_not1,axiom,
( ( not1('fmb_$i_1') = 'fmb_$i_3' )
& ( not1('fmb_$i_2') = 'fmb_$i_2' )
& ( not1('fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_not2,type,
not2: $i > $i ).
tff(function_not2,axiom,
( ( not2('fmb_$i_1') = 'fmb_$i_3' )
& ( not2('fmb_$i_2') = 'fmb_$i_2' )
& ( not2('fmb_$i_3') = 'fmb_$i_1' ) ) ).
tff(declare_bool,type,
bool: $i > $o ).
tff(predicate_bool,axiom,
( bool('fmb_$i_1')
& ~ bool('fmb_$i_2')
& bool('fmb_$i_3') ) ).
tff(declare_d,type,
d: $i > $o ).
tff(predicate_d,axiom,
( d('fmb_$i_1')
& d('fmb_$i_2')
& d('fmb_$i_3') ) ).
tff(declare_forallprefers,type,
forallprefers: ( $i * $i ) > $o ).
tff(predicate_forallprefers,axiom,
( ~ forallprefers('fmb_$i_1','fmb_$i_1')
& ~ forallprefers('fmb_$i_1','fmb_$i_2')
& ~ forallprefers('fmb_$i_1','fmb_$i_3')
& forallprefers('fmb_$i_2','fmb_$i_1')
& ~ forallprefers('fmb_$i_2','fmb_$i_2')
& forallprefers('fmb_$i_2','fmb_$i_3')
& forallprefers('fmb_$i_3','fmb_$i_1')
& ~ forallprefers('fmb_$i_3','fmb_$i_2')
& ~ forallprefers('fmb_$i_3','fmb_$i_3') ) ).
tff(declare_existsprefers,type,
existsprefers: ( $i * $i ) > $o ).
tff(predicate_existsprefers,axiom,
( ~ existsprefers('fmb_$i_1','fmb_$i_1')
& ~ existsprefers('fmb_$i_1','fmb_$i_2')
& existsprefers('fmb_$i_1','fmb_$i_3')
& existsprefers('fmb_$i_2','fmb_$i_1')
& ~ existsprefers('fmb_$i_2','fmb_$i_2')
& existsprefers('fmb_$i_2','fmb_$i_3')
& ~ existsprefers('fmb_$i_3','fmb_$i_1')
& ~ existsprefers('fmb_$i_3','fmb_$i_2')
& ~ existsprefers('fmb_$i_3','fmb_$i_3') ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW103+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n003.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 13:13:42 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.30 % (1572684)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (1572691)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1708927049:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (1572690)% WARNING: option uhcvi not known.
% 0.20/0.30 % (1572689)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1602596949_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (1572690)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=816501250:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (1572692)dis+10_1_sil=32000:sp=arity:random_seed=3239817849:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (1572693)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2065873490:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (1572694)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3196753655:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (1572695)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1629254207:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % Detected minimum model sizes of [3]
% 0.20/0.30 % Detected maximum model sizes of [max]
% 0.20/0.30 % TRYING [3]
% 0.20/0.30 % Finite Model Found!
% 0.20/0.30 % SZS status Satisfiable for theBenchmark
% 0.20/0.30 % (1572689) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1572684-1572689"...
% 0.20/0.30 % (1572689)...printing done.
% 0.20/0.30 % SZS output start FiniteModel for theBenchmark
% See solution above
% 0.20/0.30 % (1572689)------------------------------
% 0.20/0.30 % (1572689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1572689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1572689)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1572689)Termination reason: Satisfiable
% 0.20/0.30 % (1572689)Time elapsed: 0.019 s
% 0.20/0.30 % (1572689)Peak memory usage: 13 MB
% 0.20/0.30 % (1572689)Instructions burned: 42 (million)
% 0.20/0.30 % (1572684)Success in time 0.055 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------