%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM942_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:26:15 PM UTC 2026
% Result : Theorem 4.17s 1.10s
% Output : Refutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 30
% Syntax : Number of formulae : 152 ( 112 unt; 0 typ; 10 def)
% Number of atoms : 192 ( 142 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 75 ( 35 ~; 30 |; 0 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 15 con; 0-3 aty)
% Number of variables : 196 ( 196 !; 0 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
min: int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
legendre: ( int * int ) > int ).
tff(func_def_9,type,
fFalse: bool ).
tff(func_def_10,type,
fTrue: bool ).
tff(func_def_11,type,
m: int ).
tff(func_def_12,type,
sF0: int ).
tff(func_def_13,type,
sF1: int ).
tff(func_def_14,type,
sF2: int ).
tff(func_def_15,type,
sF3: int ).
tff(func_def_16,type,
sF4: int ).
tff(func_def_17,type,
sF5: int ).
tff(func_def_18,type,
sF6: int ).
tff(func_def_19,type,
sF7: int ).
tff(func_def_20,type,
sF8: int ).
tff(func_def_21,type,
sF9: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zprime: int > $o ).
tff(pred_def_9,type,
pp: bool > $o ).
tff(f1,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_p) ).
tff(f5,axiom,
! [X0: int] :
( zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int)))
=> ( legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) = one_one(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Legendre__1mod4) ).
tff(f8,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add__Bit0__Bit1) ).
tff(f37,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_number__of__is__id) ).
tff(f38,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__Pls__right) ).
tff(f40,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Bit0__def) ).
tff(f42,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_int__distrib_I1_J) ).
tff(f43,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_int__distrib_I2_J) ).
tff(f49,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Bit1__def) ).
tff(f72,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f73,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f75,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,times_times(X0,X3,X2),X1) = times_times(X0,X3,times_times(X0,X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
tff(f79,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( times_times(X0,times_times(X0,X4,X3),times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X4,X2),times_times(X0,X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
tff(f80,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f81,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,X2,plus_plus(X0,X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f83,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
tff(f91,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
tff(f94,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
tff(f99,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f112,conjecture,
legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = one_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f113,negated_conjecture,
( ( ~ legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) = one_one(int) ),
inference(negated_conjecture,[status(cth)],[f112]) ).
tff(f114,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(flattening,[],[f113]) ).
tff(f118,plain,
! [X0: int] :
( ( legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) = one_one(int) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) ),
inference(ennf_transformation,[],[f5]) ).
tff(f150,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f72]) ).
tff(f151,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f73]) ).
tff(f153,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,times_times(X0,X3,X2),X1) = times_times(X0,X3,times_times(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f75]) ).
tff(f157,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( times_times(X0,times_times(X0,X4,X3),times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X4,X2),times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f79]) ).
tff(f158,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f80]) ).
tff(f159,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,X2,plus_plus(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f81]) ).
tff(f161,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f83]) ).
tff(f169,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f91]) ).
tff(f171,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),X1) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f94]) ).
tff(f191,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f1]) ).
tff(f195,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) ),
inference(cnf_transformation,[],[f118]) ).
tff(f198,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f235,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f37]) ).
tff(f236,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f38]) ).
tff(f238,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f240,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f42]) ).
tff(f241,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(cnf_transformation,[],[f43]) ).
tff(f247,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f49]) ).
tff(f275,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f150]) ).
tff(f276,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) ) ),
inference(cnf_transformation,[],[f151]) ).
tff(f278,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X3,X2),X1) ) ),
inference(cnf_transformation,[],[f153]) ).
tff(f282,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,times_times(X0,X4,X3),times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X4,X2),times_times(X0,X3,X1)) ) ),
inference(cnf_transformation,[],[f157]) ).
tff(f283,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f158]) ).
tff(f284,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,X2,plus_plus(X0,X3,X1)) ) ),
inference(cnf_transformation,[],[f159]) ).
tff(f286,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,plus_plus(X0,X3,X2),X1) ) ),
inference(cnf_transformation,[],[f161]) ).
tff(f298,plain,
! [X0: $tType,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,one_one(X0),X1) = X1 ) ),
inference(cnf_transformation,[],[f169]) ).
tff(f301,plain,
! [X0: $tType,X1: X0] :
( ~ comm_semiring_1(X0)
| ( plus_plus(X0,X1,X1) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),X1) ) ),
inference(cnf_transformation,[],[f171]) ).
tff(f311,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f99]) ).
tff(f324,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f114]) ).
tff(f325,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f191,f238,f238,f247]) ).
tff(f329,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(definition_unfolding,[],[f195,f238,f238,f247,f238,f238,f247]) ).
tff(f332,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X1,X0)),plus_plus(int,X1,X0)) ),
inference(definition_unfolding,[],[f198,f238,f247,f247]) ).
tff(f374,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f324,f238,f238,f247]) ).
tff(f397,definition,
sF0 = one_one(int),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f398,plain,
one_one(int) = sF0,
inference(reorient_equations,[],[f397]) ).
tff(f399,definition,
sF1 = number_number_of(int,min),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f400,plain,
number_number_of(int,min) = sF1,
inference(reorient_equations,[],[f399]) ).
tff(f401,definition,
sF2 = plus_plus(int,sF0,pls),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f402,plain,
plus_plus(int,sF0,pls) = sF2,
inference(reorient_equations,[],[f401]) ).
tff(f403,definition,
sF3 = plus_plus(int,sF2,pls),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f404,plain,
plus_plus(int,sF2,pls) = sF3,
inference(reorient_equations,[],[f403]) ).
tff(f405,definition,
sF4 = plus_plus(int,sF3,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f406,plain,
plus_plus(int,sF3,sF3) = sF4,
inference(reorient_equations,[],[f405]) ).
tff(f407,definition,
sF5 = plus_plus(int,sF4,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f408,plain,
plus_plus(int,sF4,sF4) = sF5,
inference(reorient_equations,[],[f407]) ).
tff(f409,definition,
sF6 = number_number_of(int,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f410,plain,
number_number_of(int,sF5) = sF6,
inference(reorient_equations,[],[f409]) ).
tff(f411,definition,
sF7 = times_times(int,sF6,m),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
tff(f412,plain,
times_times(int,sF6,m) = sF7,
inference(reorient_equations,[],[f411]) ).
tff(f413,definition,
sF8 = plus_plus(int,sF7,sF0),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
tff(f414,plain,
plus_plus(int,sF7,sF0) = sF8,
inference(reorient_equations,[],[f413]) ).
tff(f415,definition,
sF9 = legendre(sF1,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
tff(f416,plain,
legendre(sF1,sF8) = sF9,
inference(reorient_equations,[],[f415]) ).
tff(f417,plain,
sF0 != sF9,
inference(definition_folding,[],[f374,f416,f414,f398,f412,f410,f408,f406,f404,f402,f398,f404,f402,f398,f406,f404,f402,f398,f404,f402,f398,f400,f398]) ).
tff(f419,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(forward_demodulation,[],[f329,f235]) ).
tff(f423,plain,
zprime(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),m),one_one(int))),
inference(forward_demodulation,[],[f325,f235]) ).
tff(f424,plain,
min = sF1,
inference(forward_demodulation,[],[f400,f235]) ).
tff(f425,plain,
sF0 = sF2,
inference(forward_demodulation,[],[f402,f236]) ).
tff(f426,plain,
sF2 = sF3,
inference(forward_demodulation,[],[f404,f236]) ).
tff(f427,plain,
sF5 = sF6,
inference(forward_demodulation,[],[f410,f235]) ).
tff(f429,plain,
! [X0: int] :
( ( sF0 = legendre(number_number_of(int,min),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls))),X0),sF0)) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(forward_demodulation,[],[f419,f398]) ).
tff(f433,plain,
zprime(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls))),m),sF0)),
inference(forward_demodulation,[],[f423,f398]) ).
tff(f434,plain,
sF0 = sF3,
inference(forward_demodulation,[],[f426,f425]) ).
tff(f435,plain,
! [X0: int] :
( ( sF0 = legendre(number_number_of(int,min),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),plus_plus(int,sF0,pls)),plus_plus(int,plus_plus(int,sF0,pls),plus_plus(int,sF0,pls))),X0),sF0)) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(forward_demodulation,[],[f429,f236]) ).
tff(f439,plain,
zprime(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),plus_plus(int,sF0,pls)),plus_plus(int,plus_plus(int,sF0,pls),plus_plus(int,sF0,pls))),m),sF0)),
inference(forward_demodulation,[],[f433,f236]) ).
tff(f440,plain,
! [X0: int] :
( ( sF0 = legendre(number_number_of(int,min),plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),X0),sF0)) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(forward_demodulation,[],[f435,f236]) ).
tff(f441,plain,
zprime(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),m),sF0)),
inference(forward_demodulation,[],[f439,f236]) ).
tff(f442,plain,
! [X0: int] :
( ( sF0 = legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),X0),sF0)) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(forward_demodulation,[],[f440,f235]) ).
tff(f443,plain,
! [X0: int] :
( ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls)))),X0),sF0))
| ( sF0 = legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),X0),sF0)) ) ),
inference(forward_demodulation,[],[f442,f398]) ).
tff(f444,plain,
! [X0: int] :
( ~ zprime(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),pls),plus_plus(int,plus_plus(int,sF0,pls),pls))),X0),sF0))
| ( sF0 = legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),X0),sF0)) ) ),
inference(forward_demodulation,[],[f443,f235]) ).
tff(f445,plain,
! [X0: int] :
( ~ zprime(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,sF0,pls),plus_plus(int,sF0,pls)),plus_plus(int,plus_plus(int,sF0,pls),plus_plus(int,sF0,pls))),X0),sF0))
| ( sF0 = legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),X0),sF0)) ) ),
inference(forward_demodulation,[],[f444,f236]) ).
tff(f446,plain,
! [X0: int] :
( ~ zprime(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),X0),sF0))
| ( sF0 = legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),X0),sF0)) ) ),
inference(forward_demodulation,[],[f445,f236]) ).
tff(f447,plain,
sF9 = legendre(min,sF8),
inference(superposition,[],[f416,f424]) ).
tff(f450,plain,
sF4 = plus_plus(int,sF0,sF0),
inference(superposition,[],[f406,f434]) ).
tff(f453,plain,
sF7 = times_times(int,sF5,m),
inference(superposition,[],[f412,f427]) ).
tff(f457,plain,
! [X0: int] : ( times_times(int,one_one(int),X0) = X0 ),
inference(resolution,[],[f298,f311]) ).
tff(f459,plain,
! [X0: int] : ( times_times(int,sF0,X0) = X0 ),
inference(forward_demodulation,[],[f457,f398]) ).
tff(f481,plain,
! [X0: int,X1: int] : ( times_times(int,X1,X0) = times_times(int,X0,X1) ),
inference(resolution,[],[f275,f311]) ).
tff(f488,plain,
! [X0: int,X1: int] : ( plus_plus(int,X1,X0) = plus_plus(int,X0,X1) ),
inference(resolution,[],[f283,f311]) ).
tff(f511,plain,
sF7 = times_times(int,m,sF5),
inference(superposition,[],[f453,f481]) ).
tff(f747,plain,
sF8 = plus_plus(int,sF0,sF7),
inference(superposition,[],[f414,f488]) ).
tff(f933,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,plus_plus(int,one_one(int),one_one(int)),X0) ),
inference(resolution,[],[f301,f311]) ).
tff(f935,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,plus_plus(int,sF0,sF0),X0) ),
inference(forward_demodulation,[],[f933,f398]) ).
tff(f936,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,sF4,X0) ),
inference(forward_demodulation,[],[f935,f450]) ).
tff(f964,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,X0,sF4) ),
inference(superposition,[],[f481,f936]) ).
tff(f1003,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X0,times_times(int,X1,X2)) = times_times(int,X1,times_times(int,X0,X2)) ),
inference(resolution,[],[f276,f311]) ).
tff(f1010,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X0,times_times(int,X1,X2)) = times_times(int,times_times(int,X0,X1),X2) ),
inference(resolution,[],[f278,f311]) ).
tff(f1030,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)) ),
inference(resolution,[],[f284,f311]) ).
tff(f1040,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2) ),
inference(resolution,[],[f286,f311]) ).
tff(f1110,plain,
! [X0: int,X1: int] : ( times_times(int,plus_plus(int,sF4,X1),X0) = plus_plus(int,plus_plus(int,X0,X0),times_times(int,X1,X0)) ),
inference(superposition,[],[f240,f936]) ).
tff(f1138,plain,
! [X0: int,X1: int] : ( times_times(int,sF4,times_times(int,X0,X1)) = times_times(int,plus_plus(int,X0,X0),X1) ),
inference(superposition,[],[f936,f240]) ).
tff(f1163,plain,
! [X0: int,X1: int] : ( times_times(int,plus_plus(int,sF4,X1),X0) = plus_plus(int,X0,plus_plus(int,X0,times_times(int,X1,X0))) ),
inference(forward_demodulation,[],[f1110,f1040]) ).
tff(f1224,plain,
! [X0: int,X1: int] : ( times_times(int,plus_plus(int,X0,X1),sF4) = plus_plus(int,plus_plus(int,X0,X0),times_times(int,X1,sF4)) ),
inference(superposition,[],[f240,f964]) ).
tff(f1240,plain,
! [X0: int,X1: int] : ( times_times(int,plus_plus(int,X0,X1),sF4) = plus_plus(int,X0,plus_plus(int,X0,times_times(int,X1,sF4))) ),
inference(forward_demodulation,[],[f1224,f1040]) ).
tff(f1251,plain,
! [X0: int,X1: int] : ( plus_plus(int,X0,plus_plus(int,X0,times_times(int,X1,sF4))) = times_times(int,sF4,plus_plus(int,X0,X1)) ),
inference(forward_demodulation,[],[f1240,f481]) ).
tff(f2107,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( times_times(int,times_times(int,X0,X1),times_times(int,X2,X3)) = times_times(int,times_times(int,X0,X2),times_times(int,X1,X3)) ),
inference(resolution,[],[f282,f311]) ).
tff(f2110,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( times_times(int,times_times(int,X0,X1),times_times(int,X2,X3)) = times_times(int,X0,times_times(int,X2,times_times(int,X1,X3))) ),
inference(forward_demodulation,[],[f2107,f1010]) ).
tff(f2112,plain,
! [X2: int,X3: int,X0: int,X1: int] : ( times_times(int,X0,times_times(int,X1,times_times(int,X2,X3))) = times_times(int,X0,times_times(int,X2,times_times(int,X1,X3))) ),
inference(forward_demodulation,[],[f2110,f1010]) ).
tff(f3011,plain,
! [X0: int] : ( plus_plus(int,times_times(int,X0,sF4),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,plus_plus(int,one_one(int),times_times(int,X0,sF4)),times_times(int,X0,sF4)) ),
inference(superposition,[],[f332,f964]) ).
tff(f3012,plain,
! [X0: int] : ( plus_plus(int,times_times(int,sF4,X0),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,plus_plus(int,one_one(int),times_times(int,sF4,X0)),times_times(int,sF4,X0)) ),
inference(superposition,[],[f332,f936]) ).
tff(f3069,plain,
! [X0: int] : ( plus_plus(int,times_times(int,sF4,X0),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,one_one(int),plus_plus(int,times_times(int,sF4,X0),times_times(int,sF4,X0))) ),
inference(forward_demodulation,[],[f3012,f1040]) ).
tff(f3070,plain,
! [X0: int] : ( plus_plus(int,times_times(int,X0,sF4),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,one_one(int),plus_plus(int,times_times(int,X0,sF4),times_times(int,X0,sF4))) ),
inference(forward_demodulation,[],[f3011,f1040]) ).
tff(f3121,plain,
! [X0: int] : ( plus_plus(int,times_times(int,sF4,X0),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,one_one(int),times_times(int,sF4,plus_plus(int,X0,X0))) ),
inference(forward_demodulation,[],[f3069,f241]) ).
tff(f3122,plain,
! [X0: int] : ( plus_plus(int,times_times(int,X0,sF4),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,one_one(int),times_times(int,X0,plus_plus(int,sF4,sF4))) ),
inference(forward_demodulation,[],[f3070,f241]) ).
tff(f3172,plain,
! [X0: int] : ( plus_plus(int,times_times(int,sF4,X0),plus_plus(int,plus_plus(int,sF0,X0),X0)) = plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,X0,X0))) ),
inference(forward_demodulation,[],[f3121,f398]) ).
tff(f3173,plain,
! [X0: int] : ( plus_plus(int,times_times(int,X0,sF4),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = plus_plus(int,one_one(int),times_times(int,X0,sF5)) ),
inference(forward_demodulation,[],[f3122,f408]) ).
tff(f3220,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,X0,X0))) = plus_plus(int,plus_plus(int,sF0,X0),plus_plus(int,times_times(int,sF4,X0),X0)) ),
inference(forward_demodulation,[],[f3172,f1030]) ).
tff(f3221,plain,
! [X0: int] : ( plus_plus(int,times_times(int,X0,sF4),plus_plus(int,plus_plus(int,sF0,X0),X0)) = plus_plus(int,sF0,times_times(int,X0,sF5)) ),
inference(forward_demodulation,[],[f3173,f398]) ).
tff(f3262,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,X0,X0))) = plus_plus(int,sF0,plus_plus(int,X0,plus_plus(int,times_times(int,sF4,X0),X0))) ),
inference(forward_demodulation,[],[f3220,f1040]) ).
tff(f3263,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,X0,sF5)) = plus_plus(int,plus_plus(int,sF0,X0),plus_plus(int,times_times(int,X0,sF4),X0)) ),
inference(forward_demodulation,[],[f3221,f1030]) ).
tff(f3304,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,X0,X0))) = plus_plus(int,sF0,plus_plus(int,X0,plus_plus(int,X0,times_times(int,sF4,X0)))) ),
inference(forward_demodulation,[],[f3262,f488]) ).
tff(f3305,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,X0,sF5)) = plus_plus(int,sF0,plus_plus(int,X0,plus_plus(int,times_times(int,X0,sF4),X0))) ),
inference(forward_demodulation,[],[f3263,f1040]) ).
tff(f3342,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,X0,X0))) = plus_plus(int,sF0,times_times(int,plus_plus(int,sF4,sF4),X0)) ),
inference(forward_demodulation,[],[f3304,f1163]) ).
tff(f3343,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,X0,sF5)) = plus_plus(int,sF0,plus_plus(int,X0,plus_plus(int,X0,times_times(int,X0,sF4)))) ),
inference(forward_demodulation,[],[f3305,f488]) ).
tff(f3374,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,X0,X0))) = plus_plus(int,sF0,times_times(int,sF4,times_times(int,sF4,X0))) ),
inference(forward_demodulation,[],[f3342,f1138]) ).
tff(f3375,plain,
! [X0: int] : ( plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,X0,X0))) = plus_plus(int,sF0,times_times(int,X0,sF5)) ),
inference(forward_demodulation,[],[f3343,f1251]) ).
tff(f4068,plain,
sF0 = legendre(min,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),m),sF0)),
inference(resolution,[],[f446,f441]) ).
tff(f4087,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,plus_plus(int,plus_plus(int,sF0,sF0),plus_plus(int,sF0,sF0)),m))),
inference(forward_demodulation,[],[f4068,f488]) ).
tff(f4097,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,sF4,times_times(int,plus_plus(int,sF0,sF0),m)))),
inference(forward_demodulation,[],[f4087,f1138]) ).
tff(f4106,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,sF4,times_times(int,sF4,times_times(int,sF0,m))))),
inference(forward_demodulation,[],[f4097,f1138]) ).
tff(f4115,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,sF4,times_times(int,sF0,times_times(int,sF4,m))))),
inference(forward_demodulation,[],[f4106,f2112]) ).
tff(f4123,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,sF0,times_times(int,sF4,times_times(int,sF4,m))))),
inference(forward_demodulation,[],[f4115,f1003]) ).
tff(f4131,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,sF4,times_times(int,sF4,m)))),
inference(forward_demodulation,[],[f4123,f459]) ).
tff(f4137,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,sF4,plus_plus(int,m,m)))),
inference(forward_demodulation,[],[f4131,f3374]) ).
tff(f4143,plain,
sF0 = legendre(min,plus_plus(int,sF0,times_times(int,m,sF5))),
inference(forward_demodulation,[],[f4137,f3375]) ).
tff(f4149,plain,
sF0 = legendre(min,plus_plus(int,sF0,sF7)),
inference(forward_demodulation,[],[f4143,f511]) ).
tff(f4155,plain,
sF0 = legendre(min,sF8),
inference(forward_demodulation,[],[f4149,f747]) ).
tff(f4161,plain,
sF0 = sF9,
inference(superposition,[],[f447,f4155]) ).
tff(f4162,plain,
$false,
inference(forward_subsumption_resolution,[],[f4161,f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM942_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:51:03 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 4.17/1.10 % (3020802)Will run a generic schedule for satisfiability detection.
% 4.17/1.10 % (3020807)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2429636491_2999 on theBenchmark for (2999ds/0Mi)
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020808)% WARNING: option uhcvi not known.
% 4.17/1.10 % (3020808)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2176814351:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.17/1.10 % (3020809)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3029705761:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.17/1.10 % (3020812)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1591041377:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.17/1.10 % (3020810)dis+10_1_sil=32000:sp=arity:random_seed=4073892728:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.17/1.10 % (3020811)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1594785788:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.17/1.10 % (3020813)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1859095609:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.17/1.10 % (3020815)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3288673646:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020823)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=553779699:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.17/1.10 % (3020810)Instruction limit reached!
% 4.17/1.10 % (3020810)------------------------------
% 4.17/1.10 % (3020810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020810)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020810)Termination reason: Instruction limit
% 4.17/1.10 % (3020810)Termination phase: Saturation
% 4.17/1.10 % (3020810)Time elapsed: 0.056 s
% 4.17/1.10 % (3020810)Peak memory usage: 12 MB
% 4.17/1.10 % (3020810)Instructions burned: 104 (million)
% 4.17/1.10 % (3020823)Instruction limit reached!
% 4.17/1.10 % (3020823)------------------------------
% 4.17/1.10 % (3020823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020823)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020823)Termination reason: Instruction limit
% 4.17/1.10 % (3020823)Termination phase: Saturation
% 4.17/1.10 % (3020823)Time elapsed: 0.043 s
% 4.17/1.10 % (3020823)Peak memory usage: 13 MB
% 4.17/1.10 % (3020823)Instructions burned: 132 (million)
% 4.17/1.10 % (3020811)Instruction limit reached!
% 4.17/1.10 % (3020811)------------------------------
% 4.17/1.10 % (3020811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020811)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020811)Termination reason: Instruction limit
% 4.17/1.10 % (3020811)Termination phase: Saturation
% 4.17/1.10 % (3020811)Time elapsed: 0.064 s
% 4.17/1.10 % (3020811)Peak memory usage: 13 MB
% 4.17/1.10 % (3020811)Instructions burned: 116 (million)
% 4.17/1.10 % (3020812)Instruction limit reached!
% 4.17/1.10 % (3020812)------------------------------
% 4.17/1.10 % (3020812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020812)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020812)Termination reason: Instruction limit
% 4.17/1.10 % (3020812)Termination phase: Saturation
% 4.17/1.10 % (3020812)Time elapsed: 0.071 s
% 4.17/1.10 % (3020812)Peak memory usage: 12 MB
% 4.17/1.10 % (3020812)Instructions burned: 137 (million)
% 4.17/1.10 % (3020826)ott-21_1_sil=16000:fs=off:random_seed=2300868784:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.17/1.10 % (3020825)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1063691761:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.17/1.10 % (3020813)Instruction limit reached!
% 4.17/1.10 % (3020813)------------------------------
% 4.17/1.10 % (3020813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020813)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020813)Termination reason: Instruction limit
% 4.17/1.10 % (3020813)Termination phase: Saturation
% 4.17/1.10 % (3020813)Time elapsed: 0.084 s
% 4.17/1.10 % (3020813)Peak memory usage: 13 MB
% 4.17/1.10 % (3020813)Instructions burned: 161 (million)
% 4.17/1.10 % (3020827)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2849412145:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 4.17/1.10 % (3020829)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3546823695:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020831)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4012722465:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 4.17/1.10 % (3020834)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2171425712:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020826)Instruction limit reached!
% 4.17/1.10 % (3020826)------------------------------
% 4.17/1.10 % (3020826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020826)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020826)Termination reason: Instruction limit
% 4.17/1.10 % (3020826)Termination phase: Saturation
% 4.17/1.10 % (3020826)Time elapsed: 0.049 s
% 4.17/1.10 % (3020826)Peak memory usage: 12 MB
% 4.17/1.10 % (3020826)Instructions burned: 184 (million)
% 4.17/1.10 % (3020838)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1769796219:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 4.17/1.10 % (3020837)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=977332809:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 4.17/1.10 % (3020827)Instruction limit reached!
% 4.17/1.10 % (3020827)------------------------------
% 4.17/1.10 % (3020827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020827)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020827)Termination reason: Instruction limit
% 4.17/1.10 % (3020827)Termination phase: Saturation
% 4.17/1.10 % (3020827)Time elapsed: 0.263 s
% 4.17/1.10 % (3020827)Peak memory usage: 15 MB
% 4.17/1.10 % (3020827)Instructions burned: 479 (million)
% 4.17/1.10 % (3020841)fmb+10_1_sil=64000:random_seed=1130900864:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 4.17/1.10 % (3020841)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020838)Instruction limit reached!
% 4.17/1.10 % (3020838)------------------------------
% 4.17/1.10 % (3020838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020838)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020838)Termination reason: Instruction limit
% 4.17/1.10 % (3020838)Termination phase: Saturation
% 4.17/1.10 % (3020838)Time elapsed: 0.241 s
% 4.17/1.10 % (3020838)Peak memory usage: 17 MB
% 4.17/1.10 % (3020838)Instructions burned: 881 (million)
% 4.17/1.10 % (3020843)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3023693328:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 4.17/1.10 % (3020844)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=894815960:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020847)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4217642523:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 4.17/1.10 % (3020848)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3343830924:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 4.17/1.10 % (3020825)Instruction limit reached!
% 4.17/1.10 % (3020825)------------------------------
% 4.17/1.10 % (3020825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020825)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020825)Termination reason: Instruction limit
% 4.17/1.10 % (3020825)Termination phase: Saturation
% 4.17/1.10 % (3020825)Time elapsed: 0.338 s
% 4.17/1.10 % (3020825)Peak memory usage: 16 MB
% 4.17/1.10 % (3020825)Instructions burned: 684 (million)
% 4.17/1.10 % (3020848)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.17/1.10 % (3020851)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2820365448:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020853)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1411041348:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 4.17/1.10 % Exception at run slice level
% 4.17/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.10 % (3020855)ott-2_1_sil=16000:newcnf=on:random_seed=1991300426:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 4.17/1.10 % (3020837)Instruction limit reached!
% 4.17/1.10 % (3020837)------------------------------
% 4.17/1.10 % (3020837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020837)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020837)Termination reason: Instruction limit
% 4.17/1.10 % (3020837)Termination phase: Saturation
% 4.17/1.10 % (3020837)Time elapsed: 0.375 s
% 4.17/1.10 % (3020837)Peak memory usage: 16 MB
% 4.17/1.10 % (3020837)Instructions burned: 693 (million)
% 4.17/1.10 % (3020857)ott+10_1_sil=32000:tgt=ground:random_seed=2738482541:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 4.17/1.10 % (3020857) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3020802-3020857"...
% 4.17/1.10 % (3020857)...printing done.
% 4.17/1.10 % (3020857)Refutation found. Thanks to Tanya!
% 4.17/1.10 % SZS status Theorem for theBenchmark
% 4.17/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 4.17/1.10 % (3020857)------------------------------
% 4.17/1.10 % (3020857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.10 % (3020857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.10 % (3020857)CaDiCaL version: 2.1.3
% 4.17/1.10 % (3020857)Termination reason: Refutation
% 4.17/1.10 % (3020857)Time elapsed: 0.091 s
% 4.17/1.10 % (3020857)Peak memory usage: 13 MB
% 4.17/1.10 % (3020857)Instructions burned: 174 (million)
% 4.17/1.10 % (3020802)Success in time 0.662 s
% 4.17/1.10 % Vampire exiting
%------------------------------------------------------------------------------