%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM962_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:26:18 PM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 36 ( 23 ~; 11 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 58 ( 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $tType ).
tff(func_def_0,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > 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,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
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,
s: int ).
tff(func_def_13,type,
t: int ).
tff(func_def_14,type,
sK0: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
zprime: int > $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f42,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nat__1__add__1) ).
tff(f49,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_number__of__is__id) ).
tff(f51,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__Pls__right) ).
tff(f53,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Bit0__def) ).
tff(f56,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/sandbox/benchmark/theBenchmark.p',fact_55_int__distrib_I1_J) ).
tff(f57,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/sandbox/benchmark/theBenchmark.p',fact_56_int__distrib_I2_J) ).
tff(f59,axiom,
! [X0: int,X1: int,X2: int] : ( times_times(int,minus_minus(int,X2,X1),X0) = minus_minus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_int__distrib_I3_J) ).
tff(f66,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Bit1__def) ).
tff(f74,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) = number_number_of(X0,bit0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_double__number__of__Bit0) ).
tff(f82,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,X1,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_power2__eq__square) ).
tff(f102,axiom,
monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f105,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f127,conjecture,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) = minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f128,negated_conjecture,
( ( ~ power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) ) = minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,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)],[f127]) ).
tff(f129,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))),
inference(flattening,[],[f128]) ).
tff(f168,plain,
! [X0: $tType] :
( ! [X1: int] : ( times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) = number_number_of(X0,bit0(X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f74]) ).
tff(f175,plain,
! [X0: $tType] :
( ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,X1,X1) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f82]) ).
tff(f238,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f42]) ).
tff(f245,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f49]) ).
tff(f247,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f51]) ).
tff(f249,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f252,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,[],[f56]) ).
tff(f253,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,[],[f57]) ).
tff(f255,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,minus_minus(int,X2,X1),X0) = minus_minus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f59]) ).
tff(f262,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f270,plain,
! [X0: $tType,X1: int] :
( ( times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) = number_number_of(X0,bit0(X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f168]) ).
tff(f278,plain,
! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,X1,X1) )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f175]) ).
tff(f300,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f102]) ).
tff(f303,plain,
number_ring(int),
inference(cnf_transformation,[],[f105]) ).
tff(f325,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),number_number_of(nat,bit0(bit1(pls)))) != minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,one_one(int),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))),
inference(cnf_transformation,[],[f129]) ).
tff(f360,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,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))),
inference(definition_unfolding,[],[f238,f249,f262]) ).
tff(f371,plain,
! [X0: $tType,X1: int] :
( ~ number_ring(X0)
| ( times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) ) ),
inference(definition_unfolding,[],[f270,f249]) ).
tff(f379,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,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)))) )
| ~ monoid_mult(X0) ),
inference(definition_unfolding,[],[f278,f249,f262]) ).
tff(f394,plain,
power_power(int,minus_minus(int,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)),one_one(int)),number_number_of(nat,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)))) != minus_minus(int,times_times(int,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)),minus_minus(int,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)),one_one(int))),times_times(int,one_one(int),minus_minus(int,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)),one_one(int)))),
inference(definition_unfolding,[],[f325,f249,f249,f262,f249,f262,f249,f249,f262,f249,f249,f262,f249,f249,f262]) ).
tff(f604,plain,
! [X0: int,X1: int] : ( times_times(int,plus_plus(int,X0,X0),X1) = times_times(int,X0,plus_plus(int,X1,X1)) ),
inference(superposition,[],[f253,f252]) ).
tff(f702,plain,
! [X0: int] : ( times_times(int,plus_plus(int,one_one(int),one_one(int)),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X0,X0)) ),
inference(resolution,[],[f371,f303]) ).
tff(f704,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,plus_plus(int,one_one(int),one_one(int)),number_number_of(int,X0)) ),
inference(forward_demodulation,[],[f702,f245]) ).
tff(f705,plain,
! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,plus_plus(int,one_one(int),one_one(int)),X0) ),
inference(forward_demodulation,[],[f704,f245]) ).
tff(f919,plain,
power_power(int,minus_minus(int,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)),one_one(int)),number_number_of(nat,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)))) != times_times(int,minus_minus(int,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)),one_one(int)),minus_minus(int,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)),one_one(int))),
inference(forward_demodulation,[],[f394,f255]) ).
tff(f920,plain,
power_power(int,minus_minus(int,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)),one_one(int)),number_number_of(nat,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)))) != times_times(int,minus_minus(int,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)),one_one(int)),minus_minus(int,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)),one_one(int))),
inference(forward_demodulation,[],[f919,f245]) ).
tff(f921,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),m),one_one(int)),one_one(int)),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))) != times_times(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),m),one_one(int)),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),m),one_one(int)),one_one(int))),
inference(forward_demodulation,[],[f920,f247]) ).
tff(f922,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),one_one(int)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) != times_times(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),one_one(int))),
inference(forward_demodulation,[],[f921,f247]) ).
tff(f988,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),
inference(forward_demodulation,[],[f360,f247]) ).
tff(f989,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f988,f247]) ).
tff(f1380,plain,
power_power(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)),one_one(int)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) != times_times(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)),one_one(int))),
inference(superposition,[],[f922,f604]) ).
tff(f1408,plain,
power_power(int,minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) != times_times(int,minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int))),
inference(forward_demodulation,[],[f1380,f705]) ).
tff(f1413,plain,
times_times(int,minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int))) != power_power(int,minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(forward_demodulation,[],[f1408,f989]) ).
tff(f1614,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) )
| ~ monoid_mult(X0) ),
inference(forward_demodulation,[],[f379,f705]) ).
tff(f1615,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),pls)))) )
| ~ monoid_mult(X0) ),
inference(forward_demodulation,[],[f1614,f247]) ).
tff(f1616,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))) )
| ~ monoid_mult(X0) ),
inference(forward_demodulation,[],[f1615,f705]) ).
tff(f1617,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) )
| ~ monoid_mult(X0) ),
inference(forward_demodulation,[],[f1616,f247]) ).
tff(f1618,plain,
! [X0: $tType,X1: X0] :
( ~ monoid_mult(X0)
| ( times_times(X0,X1,X1) = power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))) ) ),
inference(forward_demodulation,[],[f1617,f989]) ).
tff(f1631,plain,
! [X0: int] : ( times_times(int,X0,X0) = power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) ),
inference(resolution,[],[f1618,f300]) ).
tff(f1696,plain,
power_power(int,minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),plus_plus(nat,one_one(nat),one_one(nat))) != power_power(int,minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(superposition,[],[f1413,f1631]) ).
tff(f1711,plain,
$false,
inference(trivial_inequality_removal,[],[f1696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM962_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 21:53:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.19/0.47 % (3023358)Will run a generic schedule for satisfiability detection.
% 0.19/0.47 % (3023366)dis+10_1_sil=32000:sp=arity:random_seed=3217048287:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.47 % (3023364)% WARNING: option uhcvi not known.
% 0.19/0.47 % (3023364)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3582242814:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.47 % (3023363)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1472209933_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.47 % (3023365)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1951713626:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.47 % (3023367)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2679625370:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.47 % Exception at run slice level
% 0.19/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.47 % (3023368)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=912916959:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.47 % (3023369)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2757802593:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.47 % (3023366) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3023358-3023366"...
% 0.19/0.47 % (3023366)...printing done.
% 0.19/0.47 % (3023366)Refutation found. Thanks to Tanya!
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (3023366)------------------------------
% 0.19/0.48 % (3023366)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.48 % (3023366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.48 % (3023366)CaDiCaL version: 2.1.3
% 0.19/0.48 % (3023366)Termination reason: Refutation
% 0.19/0.48 % (3023366)Time elapsed: 0.027 s
% 0.19/0.48 % (3023366)Peak memory usage: 12 MB
% 0.19/0.48 % (3023366)Instructions burned: 86 (million)
% 0.19/0.48 % (3023358)Success in time 0.065 s
% 0.19/0.48 % Vampire exiting
%------------------------------------------------------------------------------