%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM951_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 : n001.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 12:26:16 PM UTC 2026
% Result : Theorem 1.42s 0.83s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 106 ( 85 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 98 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 61 ( 30 ~; 23 |; 3 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 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 : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 117 ( 117 !; 0 ?; 117 :)
% 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,
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,
min: int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
s: int ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(pred_def_16,type,
sP0: ( int * int ) > $o ).
tff(f7,axiom,
! [X0: int] : ( minus_minus(int,pls,bit1(X0)) = bit1(minus_minus(int,min,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_diff__bin__simps_I4_J) ).
tff(f10,axiom,
! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit0(X0)) = bit1(minus_minus(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_diff__bin__simps_I9_J) ).
tff(f27,axiom,
bit1(min) = min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Bit1__Min) ).
tff(f36,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_nat__1__add__1) ).
tff(f39,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_number__of__is__id) ).
tff(f40,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__Pls__right) ).
tff(f41,axiom,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__Pls) ).
tff(f42,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Bit0__def) ).
tff(f43,axiom,
! [X0: int] : ( minus_minus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_diff__bin__simps_I1_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(f54,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__number__of__diff1) ).
tff(f64,axiom,
! [X0: $tType] :
( ( monoid_mult(X0)
& number(X0) )
=> ! [X1: int] : ( power_power(X0,number_number_of(X0,X1),number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_power2__eq__square__number__of) ).
tff(f65,axiom,
! [X0: int] : ( times_times(int,pls,X0) = pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mult__Pls) ).
tff(f78,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__1) ).
tff(f88,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/sandbox2/benchmark/theBenchmark.p',fact_87_int__distrib_I3_J) ).
tff(f92,axiom,
! [X0: int,X1: int] :
( ( times_times(int,X1,X0) = one_one(int) )
<=> ( ( ( X1 = one_one(int) )
& ( X0 = one_one(int) ) )
| ( ( X1 = number_number_of(int,min) )
& ( X0 = number_number_of(int,min) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_zmult__eq__1__iff) ).
tff(f94,axiom,
! [X0: $tType] :
( ab_semigroup_add(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_93_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f100,axiom,
comm_monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
tff(f101,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f103,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f106,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f109,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f124,conjecture,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f125,negated_conjecture,
( ( ~ minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) ) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) ),
inference(negated_conjecture,[status(cth)],[f124]) ).
tff(f126,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) != plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(flattening,[],[f125]) ).
tff(f146,plain,
! [X0: $tType] :
( ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f54]) ).
tff(f153,plain,
! [X0: $tType] :
( ! [X1: int] : ( power_power(X0,number_number_of(X0,X1),number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X1)) )
| ~ monoid_mult(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f64]) ).
tff(f154,plain,
! [X0: $tType] :
( ! [X1: int] : ( power_power(X0,number_number_of(X0,X1),number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X1)) )
| ~ monoid_mult(X0)
| ~ number(X0) ),
inference(flattening,[],[f153]) ).
tff(f169,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f78]) ).
tff(f179,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)) )
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f94]) ).
tff(f188,plain,
! [X0: int] : ( bit1(minus_minus(int,min,X0)) = minus_minus(int,pls,bit1(X0)) ),
inference(cnf_transformation,[],[f7]) ).
tff(f191,plain,
! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit0(X0)) = bit1(minus_minus(int,X1,X0)) ),
inference(cnf_transformation,[],[f10]) ).
tff(f215,plain,
min = bit1(min),
inference(cnf_transformation,[],[f27]) ).
tff(f224,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f36]) ).
tff(f226,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f39]) ).
tff(f227,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f40]) ).
tff(f228,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f41]) ).
tff(f229,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f42]) ).
tff(f230,plain,
! [X0: int] : ( minus_minus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f43]) ).
tff(f236,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f49]) ).
tff(f241,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
inference(cnf_transformation,[],[f146]) ).
tff(f253,plain,
! [X0: $tType,X1: int] :
( ~ number(X0)
| ~ monoid_mult(X0)
| ( power_power(X0,number_number_of(X0,X1),number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X1)) ) ),
inference(cnf_transformation,[],[f154]) ).
tff(f254,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f65]) ).
tff(f267,plain,
! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( times_times(X0,one_one(X0),X1) = X1 ) ),
inference(cnf_transformation,[],[f169]) ).
tff(f277,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,[],[f88]) ).
tff(f284,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) != X0 )
| ( number_number_of(int,min) != X1 )
| ( one_one(int) = times_times(int,X1,X0) ) ),
inference(cnf_transformation,[],[f92]) ).
tff(f289,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ab_semigroup_add(X0)
| ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) ) ),
inference(cnf_transformation,[],[f179]) ).
tff(f295,plain,
comm_monoid_mult(int),
inference(cnf_transformation,[],[f100]) ).
tff(f296,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f298,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f103]) ).
tff(f301,plain,
number_ring(int),
inference(cnf_transformation,[],[f106]) ).
tff(f304,plain,
number(int),
inference(cnf_transformation,[],[f109]) ).
tff(f317,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) != plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(cnf_transformation,[],[f126]) ).
tff(f324,plain,
! [X0: int] : ( plus_plus(int,plus_plus(int,one_one(int),minus_minus(int,min,X0)),minus_minus(int,min,X0)) = minus_minus(int,pls,plus_plus(int,plus_plus(int,one_one(int),X0),X0)) ),
inference(definition_unfolding,[],[f188,f236,f236]) ).
tff(f327,plain,
! [X0: int,X1: int] : ( minus_minus(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,one_one(int),minus_minus(int,X1,X0)),minus_minus(int,X1,X0)) ),
inference(definition_unfolding,[],[f191,f236,f229,f236]) ).
tff(f349,plain,
min = plus_plus(int,plus_plus(int,one_one(int),min),min),
inference(definition_unfolding,[],[f215,f236]) ).
tff(f354,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,[],[f224,f229,f236]) ).
tff(f364,plain,
! [X0: $tType,X1: int] :
( ~ number(X0)
| ~ monoid_mult(X0)
| ( times_times(X0,number_number_of(X0,X1),number_number_of(X0,X1)) = power_power(X0,number_number_of(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)))) ) ),
inference(definition_unfolding,[],[f253,f229,f236]) ).
tff(f369,plain,
minus_minus(int,power_power(int,s,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)))),number_number_of(int,min)) != plus_plus(int,power_power(int,s,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)))),one_one(int)),
inference(definition_unfolding,[],[f317,f229,f236,f229,f236]) ).
tff(f379,plain,
! [X1: int] :
( ( number_number_of(int,min) != X1 )
| ( one_one(int) = times_times(int,X1,number_number_of(int,min)) ) ),
inference(equality_resolution,[],[f284]) ).
tff(f380,plain,
one_one(int) = times_times(int,number_number_of(int,min),number_number_of(int,min)),
inference(equality_resolution,[],[f379]) ).
tff(f399,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
inference(consistent_polarity_flipping,[],[f241]) ).
tff(f404,plain,
! [X0: $tType,X1: int] :
( monoid_mult(X0)
| number(X0)
| ( times_times(X0,number_number_of(X0,X1),number_number_of(X0,X1)) = power_power(X0,number_number_of(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)))) ) ),
inference(consistent_polarity_flipping,[],[f364]) ).
tff(f415,plain,
! [X0: $tType,X1: X0] :
( comm_monoid_mult(X0)
| ( times_times(X0,one_one(X0),X1) = X1 ) ),
inference(consistent_polarity_flipping,[],[f267]) ).
tff(f422,plain,
~ comm_monoid_mult(int),
inference(consistent_polarity_flipping,[],[f295]) ).
tff(f424,plain,
~ monoid_mult(int),
inference(consistent_polarity_flipping,[],[f298]) ).
tff(f426,plain,
~ number_ring(int),
inference(consistent_polarity_flipping,[],[f301]) ).
tff(f428,plain,
~ number(int),
inference(consistent_polarity_flipping,[],[f304]) ).
tff(f439,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,[],[f354,f227]) ).
tff(f443,plain,
! [X0: int] : ( minus_minus(int,pls,plus_plus(int,plus_plus(int,one_one(int),X0),X0)) = minus_minus(int,plus_plus(int,plus_plus(int,one_one(int),min),min),plus_plus(int,X0,X0)) ),
inference(forward_demodulation,[],[f324,f327]) ).
tff(f452,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,[],[f439,f227]) ).
tff(f454,plain,
! [X0: int] : ( minus_minus(int,min,plus_plus(int,X0,X0)) = minus_minus(int,pls,plus_plus(int,plus_plus(int,one_one(int),X0),X0)) ),
inference(forward_demodulation,[],[f443,f349]) ).
tff(f462,plain,
plus_plus(int,power_power(int,s,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)))),one_one(int)) != minus_minus(int,power_power(int,s,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)))),min),
inference(superposition,[],[f369,f226]) ).
tff(f463,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),one_one(int)) != minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),min),
inference(forward_demodulation,[],[f462,f227]) ).
tff(f464,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),one_one(int)) != minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),min),
inference(forward_demodulation,[],[f463,f227]) ).
tff(f465,plain,
plus_plus(int,power_power(int,s,plus_plus(nat,one_one(nat),one_one(nat))),one_one(int)) != minus_minus(int,power_power(int,s,plus_plus(nat,one_one(nat),one_one(nat))),min),
inference(forward_demodulation,[],[f464,f452]) ).
tff(f484,plain,
! [X0: int] : ( times_times(int,one_one(int),X0) = X0 ),
inference(resolution,[],[f415,f422]) ).
tff(f500,plain,
one_one(int) = times_times(int,min,min),
inference(superposition,[],[f380,f226]) ).
tff(f805,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)) ),
inference(resolution,[],[f289,f296]) ).
tff(f1076,plain,
! [X0: int,X1: int] : ( times_times(int,minus_minus(int,pls,X0),X1) = minus_minus(int,pls,times_times(int,X0,X1)) ),
inference(superposition,[],[f277,f254]) ).
tff(f1436,plain,
! [X0: int] :
( number(int)
| ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),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(resolution,[],[f404,f424]) ).
tff(f1439,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),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(forward_subsumption_resolution,[],[f1436,f428]) ).
tff(f1441,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,pls,plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) ),
inference(forward_demodulation,[],[f1439,f805]) ).
tff(f1443,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))) ),
inference(forward_demodulation,[],[f1441,f805]) ).
tff(f1445,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,pls,plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) ),
inference(forward_demodulation,[],[f1443,f228]) ).
tff(f1447,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) ),
inference(forward_demodulation,[],[f1445,f228]) ).
tff(f1449,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,pls,pls))))) ),
inference(forward_demodulation,[],[f1447,f805]) ).
tff(f1451,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,one_one(int),pls)))) ),
inference(forward_demodulation,[],[f1449,f228]) ).
tff(f1453,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) ),
inference(forward_demodulation,[],[f1451,f227]) ).
tff(f1455,plain,
! [X0: int] : ( times_times(int,number_number_of(int,X0),number_number_of(int,X0)) = power_power(int,number_number_of(int,X0),plus_plus(nat,one_one(nat),one_one(nat))) ),
inference(forward_demodulation,[],[f1453,f452]) ).
tff(f1456,plain,
! [X0: int] : ( times_times(int,X0,X0) = power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) ),
inference(forward_demodulation,[],[f1455,f226]) ).
tff(f1495,plain,
plus_plus(int,times_times(int,s,s),one_one(int)) != minus_minus(int,times_times(int,s,s),min),
inference(superposition,[],[f465,f1456]) ).
tff(f1687,plain,
minus_minus(int,min,plus_plus(int,pls,pls)) = minus_minus(int,pls,plus_plus(int,one_one(int),pls)),
inference(superposition,[],[f454,f227]) ).
tff(f1690,plain,
minus_minus(int,min,plus_plus(int,pls,pls)) = minus_minus(int,pls,one_one(int)),
inference(forward_demodulation,[],[f1687,f227]) ).
tff(f1694,plain,
minus_minus(int,pls,one_one(int)) = minus_minus(int,min,pls),
inference(forward_demodulation,[],[f1690,f228]) ).
tff(f1696,plain,
min = minus_minus(int,pls,one_one(int)),
inference(forward_demodulation,[],[f1694,f230]) ).
tff(f1698,plain,
! [X0: int] : ( times_times(int,min,X0) = minus_minus(int,pls,times_times(int,one_one(int),X0)) ),
inference(superposition,[],[f1076,f1696]) ).
tff(f1699,plain,
! [X0: int] : ( minus_minus(int,pls,X0) = times_times(int,min,X0) ),
inference(forward_demodulation,[],[f1698,f484]) ).
tff(f1712,plain,
one_one(int) = minus_minus(int,pls,min),
inference(superposition,[],[f500,f1699]) ).
tff(f7599,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X0),minus_minus(int,number_number_of(int,X1),X2)) = minus_minus(int,number_number_of(int,plus_plus(int,X0,X1)),X2) ),
inference(resolution,[],[f399,f426]) ).
tff(f7600,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X0),minus_minus(int,number_number_of(int,X1),X2)) = minus_minus(int,plus_plus(int,X0,X1),X2) ),
inference(forward_demodulation,[],[f7599,f226]) ).
tff(f7601,plain,
! [X2: int,X0: int,X1: int] : ( minus_minus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,number_number_of(int,X0),minus_minus(int,X1,X2)) ),
inference(forward_demodulation,[],[f7600,f226]) ).
tff(f7602,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus(int,X0,minus_minus(int,X1,X2)) = minus_minus(int,plus_plus(int,X0,X1),X2) ),
inference(forward_demodulation,[],[f7601,f226]) ).
tff(f12344,plain,
! [X0: int] : ( plus_plus(int,X0,one_one(int)) = minus_minus(int,plus_plus(int,X0,pls),min) ),
inference(superposition,[],[f7602,f1712]) ).
tff(f12571,plain,
! [X0: int] : ( plus_plus(int,X0,one_one(int)) = minus_minus(int,X0,min) ),
inference(forward_demodulation,[],[f12344,f227]) ).
tff(f12640,plain,
$false,
inference(backward_subsumption_resolution,[],[f1495,f12571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM951_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 % Computer : n001.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 21:53:32 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.45 Running first-order model finding
% 0.14/0.45 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
% 1.42/0.83 % (3992802)Will run a generic schedule for satisfiability detection.
% 1.42/0.83 % (3992807)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1553032122_2999 on theBenchmark for (2999ds/0Mi)
% 1.42/0.83 % Exception at run slice level
% 1.42/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.42/0.83 % (3992808)% WARNING: option uhcvi not known.
% 1.42/0.83 % (3992808)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=74717128:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.42/0.83 % (3992813)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=831996300:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.42/0.83 % (3992811)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1317580501:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.42/0.83 % (3992810)dis+10_1_sil=32000:sp=arity:random_seed=3536839400:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.42/0.83 % (3992816)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4133952469:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.42/0.83 % (3992812)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=160848235:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.42/0.83 % (3992809)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3578149125:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.42/0.83 % Exception at run slice level
% 1.42/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.42/0.83 % (3992824)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1398076738:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.42/0.83 % (3992810)Instruction limit reached!
% 1.42/0.83 % (3992810)------------------------------
% 1.42/0.83 % (3992810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.83 % (3992810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.83 % (3992810)CaDiCaL version: 2.1.3
% 1.42/0.83 % (3992810)Termination reason: Instruction limit
% 1.42/0.83 % (3992810)Termination phase: Saturation
% 1.42/0.83 % (3992810)Time elapsed: 0.056 s
% 1.42/0.83 % (3992810)Peak memory usage: 12 MB
% 1.42/0.83 % (3992810)Instructions burned: 103 (million)
% 1.42/0.83 % (3992824)Instruction limit reached!
% 1.42/0.83 % (3992824)------------------------------
% 1.42/0.83 % (3992824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.83 % (3992824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.83 % (3992824)CaDiCaL version: 2.1.3
% 1.42/0.83 % (3992824)Termination reason: Instruction limit
% 1.42/0.83 % (3992824)Termination phase: Saturation
% 1.42/0.83 % (3992824)Time elapsed: 0.043 s
% 1.42/0.83 % (3992824)Peak memory usage: 13 MB
% 1.42/0.83 % (3992824)Instructions burned: 135 (million)
% 1.42/0.83 % (3992811)Instruction limit reached!
% 1.42/0.83 % (3992811)------------------------------
% 1.42/0.83 % (3992811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.83 % (3992811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.83 % (3992811)CaDiCaL version: 2.1.3
% 1.42/0.83 % (3992811)Termination reason: Instruction limit
% 1.42/0.83 % (3992811)Termination phase: Saturation
% 1.42/0.83 % (3992811)Time elapsed: 0.063 s
% 1.42/0.83 % (3992811)Peak memory usage: 12 MB
% 1.42/0.83 % (3992811)Instructions burned: 116 (million)
% 1.42/0.83 % (3992812)Instruction limit reached!
% 1.42/0.83 % (3992812)------------------------------
% 1.42/0.83 % (3992812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.83 % (3992812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.83 % (3992812)CaDiCaL version: 2.1.3
% 1.42/0.83 % (3992812)Termination reason: Instruction limit
% 1.42/0.83 % (3992812)Termination phase: Saturation
% 1.42/0.83 % (3992812)Time elapsed: 0.065 s
% 1.42/0.83 % (3992812)Peak memory usage: 12 MB
% 1.42/0.83 % (3992812)Instructions burned: 133 (million)
% 1.42/0.83 % (3992827)ott-21_1_sil=16000:fs=off:random_seed=838891120:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.42/0.83 % (3992826)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=612870980:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.42/0.83 % (3992828)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=254458693:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 1.42/0.83 % (3992813)Instruction limit reached!
% 1.42/0.83 % (3992813)------------------------------
% 1.42/0.83 % (3992813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.83 % (3992813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.83 % (3992813)CaDiCaL version: 2.1.3
% 1.42/0.83 % (3992813)Termination reason: Instruction limit
% 1.42/0.83 % (3992813)Termination phase: Saturation
% 1.42/0.83 % (3992813)Time elapsed: 0.091 s
% 1.42/0.83 % (3992813)Peak memory usage: 13 MB
% 1.42/0.83 % (3992813)Instructions burned: 160 (million)
% 1.42/0.83 % (3992829)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3776414657:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 1.42/0.83 % Exception at run slice level
% 1.42/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.42/0.83 % (3992833)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2965825607:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.42/0.83 % (3992827)Instruction limit reached!
% 1.42/0.83 % (3992827)------------------------------
% 1.42/0.83 % (3992827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.83 % (3992827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.83 % (3992827)CaDiCaL version: 2.1.3
% 1.42/0.83 % (3992827)Termination reason: Instruction limit
% 1.42/0.83 % (3992827)Termination phase: Saturation
% 1.42/0.83 % (3992827)Time elapsed: 0.049 s
% 1.42/0.83 % (3992827)Peak memory usage: 12 MB
% 1.42/0.83 % (3992827)Instructions burned: 182 (million)
% 1.42/0.83 % (3992835)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=974683144:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.42/0.83 % Exception at run slice level
% 1.42/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.42/0.83 % (3992837)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=2202346336: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)
% 1.42/0.83 % (3992839)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1885962832:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.42/0.83 % (3992837) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3992802-3992837"...
% 1.42/0.83 % (3992837)...printing done.
% 1.42/0.83 % (3992837)Refutation found. Thanks to Tanya!
% 1.42/0.83 % SZS status Theorem for theBenchmark
% 1.42/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.83 % (3992837)------------------------------
% 1.42/0.83 % (3992837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.83 % (3992837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.83 % (3992837)CaDiCaL version: 2.1.3
% 1.42/0.83 % (3992837)Termination reason: Refutation
% 1.42/0.83 % (3992837)Time elapsed: 0.201 s
% 1.42/0.83 % (3992837)Peak memory usage: 18 MB
% 1.42/0.83 % (3992837)Instructions burned: 646 (million)
% 1.42/0.83 % (3992802)Success in time 0.372 s
% 1.42/0.83 % Vampire exiting
%------------------------------------------------------------------------------