%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM954_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 : n018.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 12:26:17 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 32 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-4 aty)
% Number of variables : 47 ( 41 !; 6 ?; 47 :)
% 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,
product_prod: ( $tType * $tType ) > $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,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_9,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_10,type,
legendre: ( int * int ) > int ).
tff(func_def_11,type,
twoSqu196287499sum2sq: product_prod(int,int) > int ).
tff(func_def_12,type,
fFalse: bool ).
tff(func_def_13,type,
fTrue: bool ).
tff(func_def_14,type,
m: int ).
tff(func_def_15,type,
s1: int ).
tff(func_def_16,type,
s: int ).
tff(func_def_17,type,
t: int ).
tff(func_def_18,type,
sK0: int > int ).
tff(func_def_19,type,
sK1: int > int ).
tff(func_def_20,type,
sK2: 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,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_9,type,
zprime: int > $o ).
tff(pred_def_10,type,
quadRes: ( int * int ) > $o ).
tff(pred_def_11,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f1,axiom,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
tff(f26,axiom,
! [X0: int] : ( times_times(int,pls,X0) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_mult__Pls) ).
tff(f28,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_27_add__Bit0__Bit0) ).
tff(f32,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_number__of__is__id) ).
tff(f33,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__Pls__right) ).
tff(f35,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Bit0__def) ).
tff(f37,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_36_int__distrib_I1_J) ).
tff(f39,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_38_plus__numeral__code_I9_J) ).
tff(f44,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Bit1__def) ).
tff(f49,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_one__is__num__one) ).
tff(f59,axiom,
! [X0: int] :
( twoSqu1567020053sum2sq(X0)
<=> ? [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_is__sum2sq__def) ).
tff(f112,conjecture,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f113,negated_conjecture,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(negated_conjecture,[status(cth)],[f112]) ).
tff(f114,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(flattening,[],[f113]) ).
tff(f172,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ? [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(nnf_transformation,[],[f59]) ).
tff(f173,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ? [X3: int,X4: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X3,X4)) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(rectify,[],[f172]) ).
tff(f174,plain,
! [X0: int] :
( ( twoSqu1567020053sum2sq(X0)
| ! [X1: int,X2: int] : ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 ) )
& ( ( twoSqu196287499sum2sq(product_Pair(int,int,sK0(X0),sK1(X0))) = X0 )
| ~ twoSqu1567020053sum2sq(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0)),skolemize(X4,sK1(X0))],[f173]) ).
tff(f182,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
inference(cnf_transformation,[],[f1]) ).
tff(f212,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f214,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f28]) ).
tff(f219,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f32]) ).
tff(f220,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f33]) ).
tff(f222,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f224,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,[],[f37]) ).
tff(f226,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,[],[f39]) ).
tff(f231,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f44]) ).
tff(f236,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f49]) ).
tff(f247,plain,
! [X2: int,X0: int,X1: int] :
( ( twoSqu196287499sum2sq(product_Pair(int,int,X1,X2)) != X0 )
| twoSqu1567020053sum2sq(X0) ),
inference(cnf_transformation,[],[f174]) ).
tff(f303,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(cnf_transformation,[],[f114]) ).
tff(f304,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(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)),t),
inference(definition_unfolding,[],[f182,f222,f222,f231]) ).
tff(f327,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,[],[f214,f222,f222,f222]) ).
tff(f333,plain,
one_one(int) = number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f236,f231]) ).
tff(f369,plain,
~ twoSqu1567020053sum2sq(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)),t)),
inference(definition_unfolding,[],[f303,f222,f222,f231]) ).
tff(f376,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,times_times(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),t),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f304,f224]) ).
tff(f383,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,times_times(int,times_times(int,plus_plus(int,number_number_of(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))),number_number_of(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)))),m),t),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f376,f226]) ).
tff(f387,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(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))),m),times_times(int,number_number_of(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))),m)),t),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f383,f224]) ).
tff(f391,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,plus_plus(int,times_times(int,times_times(int,number_number_of(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))),m),t),times_times(int,times_times(int,number_number_of(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))),m),t)),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f387,f224]) ).
tff(f394,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls))),m),t),times_times(int,times_times(int,plus_plus(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls))),m),t)),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f391,f226]) ).
tff(f396,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m),times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m),times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m)),t)),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f394,f224]) ).
tff(f398,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m),t),times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m),t)),plus_plus(int,times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m),t),times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),m),t))),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f396,f224]) ).
tff(f400,plain,
twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int))) = plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t))),times_times(int,one_one(int),t)),
inference(forward_demodulation,[],[f398,f333]) ).
tff(f402,plain,
~ twoSqu1567020053sum2sq(times_times(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)),t)),
inference(superposition,[],[f369,f219]) ).
tff(f403,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,times_times(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),t),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f402,f224]) ).
tff(f404,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,times_times(int,plus_plus(int,times_times(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)),m),times_times(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)),m)),t),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f403,f224]) ).
tff(f405,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,times_times(int,times_times(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)),m),t),times_times(int,times_times(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)),m),t)),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f404,f224]) ).
tff(f406,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m),times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m)),t),times_times(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m),times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m)),t)),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f405,f224]) ).
tff(f407,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m),t),times_times(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m),t)),plus_plus(int,times_times(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m),t),times_times(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),m),t))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f406,f224]) ).
tff(f408,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),pls),m),times_times(int,pls,m)),t),times_times(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),pls),m),times_times(int,pls,m)),t)),plus_plus(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),pls),m),times_times(int,pls,m)),t),times_times(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),pls),m),times_times(int,pls,m)),t))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f407,f224]) ).
tff(f409,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,times_times(int,pls,m),t)),plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,times_times(int,pls,m),t))),plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,times_times(int,pls,m),t)),plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,times_times(int,pls,m),t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f408,f224]) ).
tff(f410,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,pls,t)),plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,pls,t))),plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,pls,t)),plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,pls,t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f409,f212]) ).
tff(f411,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),pls),plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),pls)),plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),pls),plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),pls))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f410,f212]) ).
tff(f412,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t)),plus_plus(int,times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t),times_times(int,times_times(int,plus_plus(int,one_one(int),pls),m),t))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f411,f220]) ).
tff(f413,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,one_one(int),m),times_times(int,pls,m)),t),times_times(int,plus_plus(int,times_times(int,one_one(int),m),times_times(int,pls,m)),t)),plus_plus(int,times_times(int,plus_plus(int,times_times(int,one_one(int),m),times_times(int,pls,m)),t),times_times(int,plus_plus(int,times_times(int,one_one(int),m),times_times(int,pls,m)),t))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f412,f224]) ).
tff(f414,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,pls,m),t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,pls,m),t))),plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,pls,m),t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,pls,m),t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f413,f224]) ).
tff(f415,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,times_times(int,pls,m),t),times_times(int,times_times(int,pls,m),t))),plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,times_times(int,pls,m),t),times_times(int,times_times(int,pls,m),t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f414,f327]) ).
tff(f416,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t))),plus_plus(int,plus_plus(int,times_times(int,times_times(int,pls,m),t),times_times(int,times_times(int,pls,m),t)),plus_plus(int,times_times(int,times_times(int,pls,m),t),times_times(int,times_times(int,pls,m),t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f415,f327]) ).
tff(f417,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t))),plus_plus(int,plus_plus(int,times_times(int,pls,t),times_times(int,pls,t)),plus_plus(int,times_times(int,pls,t),times_times(int,pls,t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f416,f212]) ).
tff(f418,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,pls,t),times_times(int,pls,t))),plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,pls,t),times_times(int,pls,t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f417,f327]) ).
tff(f419,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,pls,t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,pls,t))),plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,pls,t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,pls,t)))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f418,f327]) ).
tff(f420,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),pls),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),pls)),plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),pls),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),pls))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f419,f212]) ).
tff(f421,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,plus_plus(int,plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t)),plus_plus(int,times_times(int,times_times(int,one_one(int),m),t),times_times(int,times_times(int,one_one(int),m),t))),times_times(int,one_one(int),t))),
inference(forward_demodulation,[],[f420,f220]) ).
tff(f422,plain,
~ twoSqu1567020053sum2sq(twoSqu196287499sum2sq(product_Pair(int,int,s,one_one(int)))),
inference(forward_demodulation,[],[f421,f400]) ).
tff(f474,plain,
! [X0: int,X1: int] : twoSqu1567020053sum2sq(twoSqu196287499sum2sq(product_Pair(int,int,X0,X1))),
inference(equality_resolution,[],[f247]) ).
tff(f479,plain,
$false,
inference(resolution,[],[f474,f422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM954_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 21:50:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.45 % (2761002)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (2761012)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2539393238:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (2761012) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2761002-2761012"...
% 0.09/0.45 % (2761007)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2531237317_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (2761009)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=78146734:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (2761010)dis+10_1_sil=32000:sp=arity:random_seed=4286934645:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (2761012)...printing done.
% 0.09/0.45 % (2761011)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3538757187:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (2761013)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3128136766:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % (2761012)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (2761012)------------------------------
% 0.09/0.45 % (2761012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (2761012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (2761012)CaDiCaL version: 2.1.3
% 0.09/0.45 % (2761012)Termination reason: Refutation
% 0.09/0.45 % (2761012)Time elapsed: 0.006 s
% 0.09/0.45 % (2761012)Peak memory usage: 12 MB
% 0.09/0.45 % (2761012)Instructions burned: 20 (million)
% 0.09/0.45 % (2761002)Success in time 0.038 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------