%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM932_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 : n012.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 0.03s 0.41s
% Output : Refutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 78 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 35 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 59 ( 36 ~; 16 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 68 ( 68 !; 0 ?; 68 :)
% 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,
zero_zero:
!>[X0: $tType] : 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,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
m: int ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[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,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
zprime: int > $o ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f1,axiom,
ord_less_eq(int,m,zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096m_A_060_061_A0_096) ).
tff(f14,axiom,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
<=> ord_less_eq(int,X0,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_rel__simps_I27_J) ).
tff(f30,axiom,
! [X0: int] : ( times_times(int,pls,X0) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_mult__Pls) ).
tff(f32,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__Bit0__Bit0) ).
tff(f44,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Pls__def) ).
tff(f46,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_number__of__is__id) ).
tff(f48,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zero__is__num__zero) ).
tff(f53,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__Pls__right) ).
tff(f54,axiom,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__Pls) ).
tff(f55,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Bit0__def) ).
tff(f58,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_57_int__distrib_I1_J) ).
tff(f60,axiom,
! [X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X1),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_plus__numeral__code_I9_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(f68,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mult__numeral__1) ).
tff(f71,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_one__is__num__one) ).
tff(f89,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
<=> ord_less_eq(X0,X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__le__cancel__right) ).
tff(f97,axiom,
ordere236663937imp_le(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(f103,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f117,conjecture,
ord_less_eq(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(f118,negated_conjecture,
~ ord_less_eq(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)],[f117]) ).
tff(f119,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),
inference(flattening,[],[f118]) ).
tff(f158,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f68]) ).
tff(f176,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
<=> ord_less_eq(X0,X3,X1) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f89]) ).
tff(f181,plain,
! [X0: int] :
( ( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) )
& ( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f14]) ).
tff(f207,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
| ~ ord_less_eq(X0,X3,X1) )
& ( ord_less_eq(X0,X3,X1)
| ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f176]) ).
tff(f211,plain,
ord_less_eq(int,m,zero_zero(int)),
inference(cnf_transformation,[],[f1]) ).
tff(f228,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f181]) ).
tff(f253,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f255,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f32]) ).
tff(f271,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f44]) ).
tff(f274,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f46]) ).
tff(f276,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f48]) ).
tff(f283,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f53]) ).
tff(f284,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f54]) ).
tff(f285,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f55]) ).
tff(f289,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,[],[f58]) ).
tff(f291,plain,
! [X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X1),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f60]) ).
tff(f298,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f300,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f158]) ).
tff(f303,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f71]) ).
tff(f330,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ordere236663937imp_le(X0)
| ~ ord_less_eq(X0,X3,X1)
| ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f341,plain,
ordere236663937imp_le(int),
inference(cnf_transformation,[],[f97]) ).
tff(f347,plain,
number_ring(int),
inference(cnf_transformation,[],[f103]) ).
tff(f357,plain,
~ ord_less_eq(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,[],[f119]) ).
tff(f372,plain,
! [X0: int] :
( ord_less_eq(int,plus_plus(int,X0,X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(definition_unfolding,[],[f228,f285]) ).
tff(f394,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ),
inference(definition_unfolding,[],[f255,f285,f285,f285]) ).
tff(f405,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),X1) = X1 ) ),
inference(definition_unfolding,[],[f300,f298]) ).
tff(f408,plain,
one_one(int) = number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f303,f298]) ).
tff(f423,plain,
~ ord_less_eq(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,[],[f357,f285,f285,f298]) ).
tff(f431,plain,
! [X0: int] : ( zero_zero(int) = times_times(int,zero_zero(int),X0) ),
inference(forward_demodulation,[],[f253,f271]) ).
tff(f440,plain,
! [X0: int] :
( ord_less_eq(int,plus_plus(int,X0,X0),zero_zero(int))
| ~ ord_less_eq(int,X0,pls) ),
inference(forward_demodulation,[],[f372,f271]) ).
tff(f460,plain,
! [X0: int] :
( ~ ord_less_eq(int,X0,zero_zero(int))
| ord_less_eq(int,plus_plus(int,X0,X0),zero_zero(int)) ),
inference(forward_demodulation,[],[f440,f271]) ).
tff(f503,plain,
! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 ),
inference(superposition,[],[f283,f271]) ).
tff(f505,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(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(superposition,[],[f423,f283]) ).
tff(f506,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),number_number_of(int,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,[],[f505,f291]) ).
tff(f508,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),m),times_times(int,number_number_of(int,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,[],[f506,f289]) ).
tff(f510,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,number_number_of(int,plus_plus(int,one_one(int),pls)),number_number_of(int,plus_plus(int,one_one(int),pls))),m),times_times(int,plus_plus(int,number_number_of(int,plus_plus(int,one_one(int),pls)),number_number_of(int,plus_plus(int,one_one(int),pls))),m)),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f508,f291]) ).
tff(f512,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,one_one(int),pls)),m),times_times(int,number_number_of(int,plus_plus(int,one_one(int),pls)),m)),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,one_one(int),pls)),m),times_times(int,number_number_of(int,plus_plus(int,one_one(int),pls)),m))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f510,f289]) ).
tff(f514,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,number_number_of(int,one_one(int)),number_number_of(int,pls)),m),times_times(int,plus_plus(int,number_number_of(int,one_one(int)),number_number_of(int,pls)),m)),plus_plus(int,times_times(int,plus_plus(int,number_number_of(int,one_one(int)),number_number_of(int,pls)),m),times_times(int,plus_plus(int,number_number_of(int,one_one(int)),number_number_of(int,pls)),m))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f512,f291]) ).
tff(f516,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,pls),m)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,pls),m))),plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,pls),m)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,pls),m)))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f514,f289]) ).
tff(f518,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,times_times(int,number_number_of(int,pls),m),times_times(int,number_number_of(int,pls),m))),plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,times_times(int,number_number_of(int,pls),m),times_times(int,number_number_of(int,pls),m)))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f516,f394]) ).
tff(f520,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m))),plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,pls),m),times_times(int,number_number_of(int,pls),m)),plus_plus(int,times_times(int,number_number_of(int,pls),m),times_times(int,number_number_of(int,pls),m)))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f518,f394]) ).
tff(f522,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m))),plus_plus(int,plus_plus(int,times_times(int,zero_zero(int),m),times_times(int,zero_zero(int),m)),plus_plus(int,times_times(int,zero_zero(int),m),times_times(int,zero_zero(int),m)))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f520,f276]) ).
tff(f524,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m))),plus_plus(int,plus_plus(int,zero_zero(int),zero_zero(int)),plus_plus(int,zero_zero(int),zero_zero(int)))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f522,f431]) ).
tff(f526,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,zero_zero(int),zero_zero(int))),plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,zero_zero(int),zero_zero(int)))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f524,f394]) ).
tff(f528,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),zero_zero(int)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),zero_zero(int))),plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),zero_zero(int)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),zero_zero(int)))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f526,f394]) ).
tff(f530,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m)),plus_plus(int,times_times(int,number_number_of(int,one_one(int)),m),times_times(int,number_number_of(int,one_one(int)),m))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f528,f503]) ).
tff(f532,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,one_one(int),m),times_times(int,one_one(int),m)),plus_plus(int,times_times(int,one_one(int),m),times_times(int,one_one(int),m))),one_one(int)),one_one(int)),
inference(forward_demodulation,[],[f530,f274]) ).
tff(f534,plain,
! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 ),
inference(superposition,[],[f284,f271]) ).
tff(f672,plain,
ord_less_eq(int,plus_plus(int,m,m),zero_zero(int)),
inference(resolution,[],[f460,f211]) ).
tff(f676,plain,
ord_less_eq(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),zero_zero(int)),
inference(resolution,[],[f672,f460]) ).
tff(f935,plain,
! [X2: int,X0: int,X1: int] :
( ~ ord_less_eq(int,X0,X1)
| ord_less_eq(int,plus_plus(int,X0,X2),plus_plus(int,X1,X2)) ),
inference(resolution,[],[f330,f341]) ).
tff(f1091,plain,
! [X0: int] : ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),X0),plus_plus(int,zero_zero(int),X0)),
inference(resolution,[],[f935,f676]) ).
tff(f1098,plain,
! [X0: int] : ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),X0),X0),
inference(forward_demodulation,[],[f1091,f534]) ).
tff(f1101,plain,
! [X0: int] : ( times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),X0) = X0 ),
inference(resolution,[],[f405,f347]) ).
tff(f1102,plain,
! [X0: int] : ( times_times(int,one_one(int),X0) = X0 ),
inference(forward_demodulation,[],[f1101,f408]) ).
tff(f1123,plain,
~ ord_less_eq(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),
inference(superposition,[],[f532,f1102]) ).
tff(f1126,plain,
$false,
inference(forward_subsumption_resolution,[],[f1123,f1098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM932_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.34 % Computer : n012.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.03/0.34 % CPULimit : 300
% 0.03/0.34 % WCLimit : 300
% 0.03/0.34 % DateTime : Sun Sep 27 21:45:05 UTC 2026
% 0.03/0.34 % CPUTime :
% 0.03/0.34 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.36 Running first-order model finding
% 0.03/0.36 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
% 0.03/0.41 % (2778359)Will run a generic schedule for satisfiability detection.
% 0.03/0.41 % (2778364)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3467230313_2999 on theBenchmark for (2999ds/0Mi)
% 0.03/0.41 % Exception at run slice level
% 0.03/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.03/0.41 % (2778365)% WARNING: option uhcvi not known.
% 0.03/0.41 % (2778367)dis+10_1_sil=32000:sp=arity:random_seed=3632187052:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.03/0.41 % (2778370)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2770907355:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.03/0.41 % (2778368)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4104619305:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.03/0.41 % (2778369)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=945935322:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.03/0.41 % (2778366)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1331357173:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.03/0.41 % (2778365)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1035507868:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.03/0.41 % (2778372)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1848310160:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.03/0.41 % Exception at run slice level
% 0.03/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.03/0.41 % (2778369) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2778359-2778369"...
% 0.03/0.41 % (2778369)...printing done.
% 0.03/0.41 % (2778369)Refutation found. Thanks to Tanya!
% 0.03/0.41 % SZS status Theorem for theBenchmark
% 0.03/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.03/0.41 % (2778369)------------------------------
% 0.03/0.41 % (2778369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.03/0.41 % (2778369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.03/0.41 % (2778369)CaDiCaL version: 2.1.3
% 0.03/0.41 % (2778369)Termination reason: Refutation
% 0.03/0.41 % (2778369)Time elapsed: 0.018 s
% 0.03/0.41 % (2778369)Peak memory usage: 12 MB
% 0.03/0.41 % (2778369)Instructions burned: 33 (million)
% 0.03/0.41 % (2778359)Success in time 0.043 s
% 0.03/0.41 % Vampire exiting
%------------------------------------------------------------------------------