%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM926+7 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:17:37 PM UTC 2026
% Result : Theorem 9.78s 2.33s
% Output : Refutation 10.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 44
% Syntax : Number of formulae : 232 ( 133 unt; 23 def)
% Number of atoms : 342 ( 236 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 206 ( 96 ~; 98 |; 5 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 25 con; 0-4 aty)
% Number of variables : 125 ( 0 sgn 113 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f89,axiom,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,ti(X0,X3)) = hAPP(X0,X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(f90,axiom,
! [X0,X1,X2,X3] : ti(X0,hAPP(X1,X0,X2,X3)) = hAPP(X1,X0,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(f97,axiom,
ti(int,t) = t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
fof(f98,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(f99,axiom,
( t = one_one(int)
=> ? [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(f100,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))
=> ? [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(f120,axiom,
! [X0,X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
& ti(int,X0) != ti(int,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).
fof(f186,axiom,
! [X0] : number_number_of(int,X0) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_number__of__is__id) ).
fof(f187,axiom,
! [X0,X1,X2] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X0),X1)),X2) = hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__assoc) ).
fof(f189,axiom,
! [X0,X1] : hAPP(int,int,plus_plus(int,X0),X1) = hAPP(int,int,plus_plus(int,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_zadd__commute) ).
fof(f223,axiom,
! [X0] : hAPP(int,int,plus_plus(int,X0),pls) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_add__Pls__right) ).
fof(f224,axiom,
! [X0] : hAPP(int,int,plus_plus(int,pls),X0) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_add__Pls) ).
fof(f226,axiom,
! [X0] : bit0(X0) = hAPP(int,int,plus_plus(int,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Bit0__def) ).
fof(f229,axiom,
! [X0,X1] : hAPP(int,int,times_times(int,number_number_of(int,X0)),number_number_of(int,X1)) = number_number_of(int,hAPP(int,int,times_times(int,X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_times__numeral__code_I5_J) ).
fof(f232,axiom,
! [X0,X1] : hAPP(int,int,plus_plus(int,number_number_of(int,X0)),number_number_of(int,X1)) = number_number_of(int,hAPP(int,int,plus_plus(int,X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_plus__numeral__code_I9_J) ).
fof(f251,axiom,
! [X0] : bit1(X0) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Bit1__def) ).
fof(f258,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_one__is__num__one) ).
fof(f302,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Pls__def) ).
fof(f305,axiom,
! [X0] : hAPP(int,int,plus_plus(int,X0),zero_zero(int)) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_zadd__0__right) ).
fof(f1248,axiom,
! [X0,X1] : ti(X0,ti(X0,X1)) = ti(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
fof(f1255,conjecture,
? [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1256,negated_conjecture,
~ ? [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
inference(negated_conjecture,[status(cth)],[f1255]) ).
fof(f1296,plain,
( ? [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
| t != one_one(int) ),
inference(ennf_transformation,[],[f99]) ).
fof(f1297,plain,
( ? [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(ennf_transformation,[],[f100]) ).
fof(f2278,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
inference(ennf_transformation,[],[f1256]) ).
fof(f2289,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,bit0(bit1(pls)))))
| t != one_one(int) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f1296]) ).
fof(f2290,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,bit0(bit1(pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f1297]) ).
fof(f2292,plain,
! [X0,X1] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
| ti(int,X0) = ti(int,X1) )
& ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
& ti(int,X0) != ti(int,X1) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f2293,plain,
! [X0,X1] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
| ti(int,X0) = ti(int,X1) )
& ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
& ti(int,X0) != ti(int,X1) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)) ) ),
inference(flattening,[],[f2292]) ).
fof(f2753,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(cnf_transformation,[],[f89]) ).
fof(f2754,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f90]) ).
fof(f2762,plain,
t = ti(int,t),
inference(cnf_transformation,[],[f97]) ).
fof(f2763,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
inference(cnf_transformation,[],[f98]) ).
fof(f2764,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,bit0(bit1(pls)))))
| t != one_one(int) ),
inference(cnf_transformation,[],[f2289]) ).
fof(f2765,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,bit0(bit1(pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(cnf_transformation,[],[f2290]) ).
fof(f2787,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1))
| ti(int,X0) = ti(int,X1) ),
inference(cnf_transformation,[],[f2293]) ).
fof(f2881,plain,
! [X0] : ti(int,X0) = number_number_of(int,X0),
inference(cnf_transformation,[],[f186]) ).
fof(f2882,plain,
! [X2,X0,X1] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X0),X1)),X2) = hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)),
inference(cnf_transformation,[],[f187]) ).
fof(f2884,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,X0),X1) = hAPP(int,int,plus_plus(int,X1),X0),
inference(cnf_transformation,[],[f189]) ).
fof(f2940,plain,
! [X0] : ti(int,X0) = hAPP(int,int,plus_plus(int,X0),pls),
inference(cnf_transformation,[],[f223]) ).
fof(f2941,plain,
! [X0] : ti(int,X0) = hAPP(int,int,plus_plus(int,pls),X0),
inference(cnf_transformation,[],[f224]) ).
fof(f2943,plain,
! [X0] : bit0(X0) = hAPP(int,int,plus_plus(int,X0),X0),
inference(cnf_transformation,[],[f226]) ).
fof(f2946,plain,
! [X0,X1] : hAPP(int,int,times_times(int,number_number_of(int,X0)),number_number_of(int,X1)) = number_number_of(int,hAPP(int,int,times_times(int,X0),X1)),
inference(cnf_transformation,[],[f229]) ).
fof(f2949,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,number_number_of(int,X0)),number_number_of(int,X1)) = number_number_of(int,hAPP(int,int,plus_plus(int,X0),X1)),
inference(cnf_transformation,[],[f232]) ).
fof(f2968,plain,
! [X0] : bit1(X0) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X0)),X0),
inference(cnf_transformation,[],[f251]) ).
fof(f2975,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f258]) ).
fof(f3032,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f302]) ).
fof(f3035,plain,
! [X0] : ti(int,X0) = hAPP(int,int,plus_plus(int,X0),zero_zero(int)),
inference(cnf_transformation,[],[f305]) ).
fof(f4355,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(cnf_transformation,[],[f1248]) ).
fof(f4362,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),
inference(cnf_transformation,[],[f2278]) ).
fof(f4375,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))
| t != one_one(int) ),
inference(definition_unfolding,[],[f2764,f2943,f2943,f2968,f2943,f2968,f2943,f2968]) ).
fof(f4376,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(definition_unfolding,[],[f2765,f2943,f2943,f2968,f2943,f2968,f2943,f2968]) ).
fof(f4481,plain,
one_one(int) = number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),
inference(definition_unfolding,[],[f2975,f2968]) ).
fof(f4631,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),
inference(definition_unfolding,[],[f4362,f2943,f2968,f2943,f2968,f2943,f2943,f2968]) ).
fof(f4725,definition,
sF52 = one_one(int),
introduced(definition,[new_symbols(definition,[sF52])],[function_definition]) ).
fof(f4726,plain,
one_one(int) = sF52,
inference(reorient_equations,[],[f4725]) ).
fof(f4727,definition,
sF53 = plus_plus(int,sF52),
introduced(definition,[new_symbols(definition,[sF53])],[function_definition]) ).
fof(f4728,plain,
plus_plus(int,sF52) = sF53,
inference(reorient_equations,[],[f4727]) ).
fof(f4729,definition,
sF54 = hAPP(int,int,sF53,pls),
introduced(definition,[new_symbols(definition,[sF54])],[function_definition]) ).
fof(f4730,plain,
hAPP(int,int,sF53,pls) = sF54,
inference(reorient_equations,[],[f4729]) ).
fof(f4731,definition,
sF55 = plus_plus(int,sF54),
introduced(definition,[new_symbols(definition,[sF55])],[function_definition]) ).
fof(f4732,plain,
plus_plus(int,sF54) = sF55,
inference(reorient_equations,[],[f4731]) ).
fof(f4733,definition,
sF56 = hAPP(int,int,sF55,pls),
introduced(definition,[new_symbols(definition,[sF56])],[function_definition]) ).
fof(f4734,plain,
hAPP(int,int,sF55,pls) = sF56,
inference(reorient_equations,[],[f4733]) ).
fof(f4735,definition,
sF57 = plus_plus(int,sF56),
introduced(definition,[new_symbols(definition,[sF57])],[function_definition]) ).
fof(f4736,plain,
plus_plus(int,sF56) = sF57,
inference(reorient_equations,[],[f4735]) ).
fof(f4737,definition,
sF58 = hAPP(int,int,sF57,sF56),
introduced(definition,[new_symbols(definition,[sF58])],[function_definition]) ).
fof(f4738,plain,
hAPP(int,int,sF57,sF56) = sF58,
inference(reorient_equations,[],[f4737]) ).
fof(f4739,definition,
sF59 = plus_plus(int,sF58),
introduced(definition,[new_symbols(definition,[sF59])],[function_definition]) ).
fof(f4740,plain,
plus_plus(int,sF58) = sF59,
inference(reorient_equations,[],[f4739]) ).
fof(f4741,definition,
sF60 = hAPP(int,int,sF59,sF58),
introduced(definition,[new_symbols(definition,[sF60])],[function_definition]) ).
fof(f4742,plain,
hAPP(int,int,sF59,sF58) = sF60,
inference(reorient_equations,[],[f4741]) ).
fof(f4743,definition,
sF61 = number_number_of(int,sF60),
introduced(definition,[new_symbols(definition,[sF61])],[function_definition]) ).
fof(f4744,plain,
number_number_of(int,sF60) = sF61,
inference(reorient_equations,[],[f4743]) ).
fof(f4745,definition,
sF62 = times_times(int,sF61),
introduced(definition,[new_symbols(definition,[sF62])],[function_definition]) ).
fof(f4746,plain,
times_times(int,sF61) = sF62,
inference(reorient_equations,[],[f4745]) ).
fof(f4747,definition,
sF63 = hAPP(int,int,sF62,m),
introduced(definition,[new_symbols(definition,[sF63])],[function_definition]) ).
fof(f4748,plain,
hAPP(int,int,sF62,m) = sF63,
inference(reorient_equations,[],[f4747]) ).
fof(f4749,definition,
sF64 = plus_plus(int,sF63),
introduced(definition,[new_symbols(definition,[sF64])],[function_definition]) ).
fof(f4750,plain,
plus_plus(int,sF63) = sF64,
inference(reorient_equations,[],[f4749]) ).
fof(f4751,definition,
sF65 = hAPP(int,int,sF64,sF52),
introduced(definition,[new_symbols(definition,[sF65])],[function_definition]) ).
fof(f4752,plain,
hAPP(int,int,sF64,sF52) = sF65,
inference(reorient_equations,[],[f4751]) ).
fof(f4753,definition,
! [X0] : sF66(X0) = power_power(int,X0),
introduced(definition,[new_symbols(definition,[sF66])],[function_definition]) ).
fof(f4754,plain,
! [X0] : power_power(int,X0) = sF66(X0),
inference(reorient_equations,[],[f4753]) ).
fof(f4755,definition,
sF67 = number_number_of(nat,sF58),
introduced(definition,[new_symbols(definition,[sF67])],[function_definition]) ).
fof(f4756,plain,
number_number_of(nat,sF58) = sF67,
inference(reorient_equations,[],[f4755]) ).
fof(f4757,definition,
! [X0] : sF68(X0) = hAPP(nat,int,sF66(X0),sF67),
introduced(definition,[new_symbols(definition,[sF68])],[function_definition]) ).
fof(f4758,plain,
! [X0] : hAPP(nat,int,sF66(X0),sF67) = sF68(X0),
inference(reorient_equations,[],[f4757]) ).
fof(f4759,definition,
! [X0] : sF69(X0) = plus_plus(int,sF68(X0)),
introduced(definition,[new_symbols(definition,[sF69])],[function_definition]) ).
fof(f4760,plain,
! [X0] : plus_plus(int,sF68(X0)) = sF69(X0),
inference(reorient_equations,[],[f4759]) ).
fof(f4761,definition,
! [X0,X1] : sF70(X0,X1) = hAPP(int,int,sF69(X0),sF68(X1)),
introduced(definition,[new_symbols(definition,[sF70])],[function_definition]) ).
fof(f4762,plain,
! [X0,X1] : hAPP(int,int,sF69(X0),sF68(X1)) = sF70(X0,X1),
inference(reorient_equations,[],[f4761]) ).
fof(f4763,plain,
! [X0,X1] : sF65 != sF70(X0,X1),
inference(definition_folding,[],[f4631,f4762,f4758,f4756,f4738,f4734,f4732,f4730,f4728,f4726,f4736,f4734,f4732,f4730,f4728,f4726,f4754,f4760,f4758,f4756,f4738,f4734,f4732,f4730,f4728,f4726,f4736,f4734,f4732,f4730,f4728,f4726,f4754,f4752,f4726,f4750,f4748,f4746,f4744,f4742,f4738,f4734,f4732,f4730,f4728,f4726,f4736,f4734,f4732,f4730,f4728,f4726,f4740,f4738,f4734,f4732,f4730,f4728,f4726,f4736,f4734,f4732,f4730,f4728,f4726]) ).
fof(f4868,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f4376,f2882]) ).
fof(f4869,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f4375,f2882]) ).
fof(f4873,plain,
sF61 = ti(int,sF60),
inference(forward_demodulation,[],[f4744,f2881]) ).
fof(f4940,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f4868,f2882]) ).
fof(f4941,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f4869,f2882]) ).
fof(f5005,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f4940,f2941]) ).
fof(f5006,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f4941,f2941]) ).
fof(f5048,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5005,f2753]) ).
fof(f5049,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5006,f2753]) ).
fof(f5084,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5048,f2941]) ).
fof(f5085,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5049,f2941]) ).
fof(f5110,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5084,f2753]) ).
fof(f5111,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5085,f2753]) ).
fof(f5135,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls)))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls)))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5110,f2882]) ).
fof(f5136,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls)))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls)))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,pls),pls))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5111,f2882]) ).
fof(f5160,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls)))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls)))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5135,f2940]) ).
fof(f5161,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls)))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls)))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,pls))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5136,f2940]) ).
fof(f5184,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5160,f2753]) ).
fof(f5185,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),pls)))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5161,f2753]) ).
fof(f5208,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int)))),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int)))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5184,f2940]) ).
fof(f5209,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int)))),hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int)))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int)))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),ti(int,one_one(int))))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5185,f2940]) ).
fof(f5231,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),one_one(int))),hAPP(int,int,plus_plus(int,one_one(int)),one_one(int))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),one_one(int))))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),one_one(int)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5208,f2753]) ).
fof(f5232,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),one_one(int))),hAPP(int,int,plus_plus(int,one_one(int)),one_one(int))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),one_one(int))))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),one_one(int)))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5209,f2753]) ).
fof(f5254,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,sF52),sF52)),hAPP(int,int,plus_plus(int,sF52),sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,plus_plus(int,sF52),sF52)))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,plus_plus(int,sF52),sF52))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5231,f4726]) ).
fof(f5255,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,sF52),sF52)),hAPP(int,int,plus_plus(int,sF52),sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,plus_plus(int,sF52),sF52)))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,plus_plus(int,sF52),sF52))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5232,f4726]) ).
fof(f5277,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,power_power(int,sK8),number_number_of(nat,hAPP(int,int,sF53,sF52))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5254,f4728]) ).
fof(f5278,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,power_power(int,sK6),number_number_of(nat,hAPP(int,int,sF53,sF52))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5255,f4728]) ).
fof(f5290,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5277,f4754]) ).
fof(f5291,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5278,f4754]) ).
fof(f5302,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5290,f4754]) ).
fof(f5303,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52))))
| t != one_one(int) ),
inference(forward_demodulation,[],[f5291,f4754]) ).
fof(f5311,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5302,f2881]) ).
fof(f5312,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,ti(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52)))),m)),sF52)
| t != one_one(int) ),
inference(forward_demodulation,[],[f5303,f2881]) ).
fof(f5320,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
inference(forward_demodulation,[],[f5311,f2754]) ).
fof(f5321,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52)
| t != one_one(int) ),
inference(forward_demodulation,[],[f5312,f2754]) ).
fof(f5329,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sF52),t))
| hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52) ),
inference(forward_demodulation,[],[f5320,f4726]) ).
fof(f5330,plain,
( t != sF52
| hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52) ),
inference(forward_demodulation,[],[f5321,f4726]) ).
fof(f5339,definition,
( spl71_3
<=> hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52) ),
introduced(definition,[new_symbols(definition,[spl71_3])],[avatar_definition]) ).
fof(f5341,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52)
| ~ spl71_3 ),
inference(avatar_component_clause,[],[f5339]) ).
fof(f5343,definition,
( spl71_4
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sF52),t)) ),
introduced(definition,[new_symbols(definition,[spl71_4])],[avatar_definition]) ).
fof(f5345,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sF52),t))
| spl71_4 ),
inference(avatar_component_clause,[],[f5343]) ).
fof(f5346,plain,
( spl71_3
| ~ spl71_4 ),
inference(avatar_split_clause,[],[f5329,f5343,f5339]) ).
fof(f5348,definition,
( spl71_5
<=> hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52) ),
introduced(definition,[new_symbols(definition,[spl71_5])],[avatar_definition]) ).
fof(f5350,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m)),sF52)
| ~ spl71_5 ),
inference(avatar_component_clause,[],[f5348]) ).
fof(f5352,definition,
( spl71_6
<=> t = sF52 ),
introduced(definition,[new_symbols(definition,[spl71_6])],[avatar_definition]) ).
fof(f5354,plain,
( t != sF52
| spl71_6 ),
inference(avatar_component_clause,[],[f5352]) ).
fof(f5355,plain,
( spl71_5
| ~ spl71_6 ),
inference(avatar_split_clause,[],[f5330,f5352,f5348]) ).
fof(f5504,plain,
! [X0] : hAPP(int,int,sF53,X0) = hAPP(int,int,plus_plus(int,X0),sF52),
inference(superposition,[],[f2884,f4728]) ).
fof(f5507,plain,
! [X0] : hAPP(int,int,plus_plus(int,X0),sF58) = hAPP(int,int,sF59,X0),
inference(superposition,[],[f2884,f4740]) ).
fof(f5508,plain,
! [X0] : hAPP(int,int,plus_plus(int,X0),sF63) = hAPP(int,int,sF64,X0),
inference(superposition,[],[f2884,f4750]) ).
fof(f5509,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,X1),sF68(X0)) = hAPP(int,int,sF69(X0),X1),
inference(superposition,[],[f2884,f4760]) ).
fof(f5519,plain,
ti(int,sF52) = hAPP(int,int,sF53,zero_zero(int)),
inference(superposition,[],[f3035,f4728]) ).
fof(f5520,plain,
ti(int,sF54) = hAPP(int,int,sF55,zero_zero(int)),
inference(superposition,[],[f3035,f4732]) ).
fof(f5533,plain,
hAPP(int,int,sF55,pls) = ti(int,sF54),
inference(forward_demodulation,[],[f5520,f3032]) ).
fof(f5534,plain,
hAPP(int,int,sF53,pls) = ti(int,sF52),
inference(forward_demodulation,[],[f5519,f3032]) ).
fof(f5535,plain,
sF56 = ti(int,sF54),
inference(forward_demodulation,[],[f5533,f4734]) ).
fof(f5536,plain,
sF54 = ti(int,sF52),
inference(forward_demodulation,[],[f5534,f4730]) ).
fof(f5560,plain,
! [X0,X1] : number_number_of(int,hAPP(int,int,times_times(int,X1),X0)) = hAPP(int,int,times_times(int,number_number_of(int,X1)),ti(int,X0)),
inference(superposition,[],[f2946,f2881]) ).
fof(f5569,plain,
! [X0,X1] : number_number_of(int,hAPP(int,int,times_times(int,X1),X0)) = hAPP(int,int,times_times(int,number_number_of(int,X1)),X0),
inference(forward_demodulation,[],[f5560,f2753]) ).
fof(f5575,plain,
! [X0,X1] : number_number_of(int,hAPP(int,int,times_times(int,X1),X0)) = hAPP(int,int,times_times(int,ti(int,X1)),X0),
inference(forward_demodulation,[],[f5569,f2881]) ).
fof(f5581,plain,
! [X0,X1] : ti(int,hAPP(int,int,times_times(int,X1),X0)) = hAPP(int,int,times_times(int,ti(int,X1)),X0),
inference(forward_demodulation,[],[f5575,f2881]) ).
fof(f5587,plain,
! [X0,X1] : hAPP(int,int,times_times(int,X1),X0) = hAPP(int,int,times_times(int,ti(int,X1)),X0),
inference(forward_demodulation,[],[f5581,f2754]) ).
fof(f5608,plain,
hAPP(int,int,sF64,sF52) = hAPP(int,int,sF53,sF63),
inference(superposition,[],[f5508,f4728]) ).
fof(f5619,plain,
sF65 = hAPP(int,int,sF53,sF63),
inference(forward_demodulation,[],[f5608,f4752]) ).
fof(f5672,plain,
! [X0] : hAPP(int,int,times_times(int,sF61),X0) = hAPP(int,int,times_times(int,sF60),X0),
inference(superposition,[],[f5587,f4873]) ).
fof(f5689,plain,
! [X0] : hAPP(int,int,sF62,X0) = hAPP(int,int,times_times(int,sF60),X0),
inference(forward_demodulation,[],[f5672,f4746]) ).
fof(f5756,plain,
! [X0,X1] : number_number_of(int,hAPP(int,int,plus_plus(int,X1),X0)) = hAPP(int,int,plus_plus(int,number_number_of(int,X1)),ti(int,X0)),
inference(superposition,[],[f2949,f2881]) ).
fof(f5765,plain,
! [X0,X1] : number_number_of(int,hAPP(int,int,plus_plus(int,X1),X0)) = hAPP(int,int,plus_plus(int,number_number_of(int,X1)),X0),
inference(forward_demodulation,[],[f5756,f2753]) ).
fof(f5771,plain,
! [X0,X1] : number_number_of(int,hAPP(int,int,plus_plus(int,X1),X0)) = hAPP(int,int,plus_plus(int,ti(int,X1)),X0),
inference(forward_demodulation,[],[f5765,f2881]) ).
fof(f5777,plain,
! [X0,X1] : ti(int,hAPP(int,int,plus_plus(int,X1),X0)) = hAPP(int,int,plus_plus(int,ti(int,X1)),X0),
inference(forward_demodulation,[],[f5771,f2881]) ).
fof(f5783,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,X1),X0) = hAPP(int,int,plus_plus(int,ti(int,X1)),X0),
inference(forward_demodulation,[],[f5777,f2754]) ).
fof(f5789,plain,
! [X0] : hAPP(int,int,plus_plus(int,sF52),X0) = hAPP(int,int,plus_plus(int,sF54),X0),
inference(superposition,[],[f5783,f5536]) ).
fof(f5790,plain,
! [X0] : hAPP(int,int,plus_plus(int,sF54),X0) = hAPP(int,int,plus_plus(int,sF56),X0),
inference(superposition,[],[f5783,f5535]) ).
fof(f5828,plain,
! [X0] : hAPP(int,int,plus_plus(int,sF54),X0) = hAPP(int,int,sF57,X0),
inference(forward_demodulation,[],[f5790,f4736]) ).
fof(f5829,plain,
! [X0] : hAPP(int,int,plus_plus(int,sF52),X0) = hAPP(int,int,sF55,X0),
inference(forward_demodulation,[],[f5789,f4732]) ).
fof(f5830,plain,
! [X0] : hAPP(int,int,sF55,X0) = hAPP(int,int,sF57,X0),
inference(forward_demodulation,[],[f5828,f4732]) ).
fof(f5831,plain,
! [X0] : hAPP(int,int,sF53,X0) = hAPP(int,int,sF55,X0),
inference(forward_demodulation,[],[f5829,f4728]) ).
fof(f5833,plain,
sF58 = hAPP(int,int,sF55,sF56),
inference(superposition,[],[f4738,f5830]) ).
fof(f5834,plain,
sF58 = hAPP(int,int,sF53,sF56),
inference(forward_demodulation,[],[f5833,f5831]) ).
fof(f5837,plain,
hAPP(int,int,sF53,pls) = sF56,
inference(superposition,[],[f4734,f5831]) ).
fof(f5838,plain,
sF54 = sF56,
inference(forward_demodulation,[],[f5837,f4730]) ).
fof(f5857,plain,
! [X0,X1] : hAPP(int,X0,X1,sF52) = hAPP(int,X0,X1,sF54),
inference(superposition,[],[f2753,f5536]) ).
fof(f5908,plain,
! [X0,X1] : hAPP(int,X0,X1,sF52) = hAPP(int,X0,X1,sF56),
inference(forward_demodulation,[],[f5857,f5838]) ).
fof(f5991,plain,
sF58 = hAPP(int,int,sF53,sF52),
inference(superposition,[],[f5834,f5908]) ).
fof(f11949,plain,
one_one(int) = number_number_of(int,ti(int,hAPP(int,int,plus_plus(int,one_one(int)),pls))),
inference(superposition,[],[f4481,f2940]) ).
fof(f11966,plain,
one_one(int) = ti(int,ti(int,hAPP(int,int,plus_plus(int,one_one(int)),pls))),
inference(forward_demodulation,[],[f11949,f2881]) ).
fof(f11979,plain,
one_one(int) = ti(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),
inference(forward_demodulation,[],[f11966,f4355]) ).
fof(f11992,plain,
one_one(int) = hAPP(int,int,plus_plus(int,one_one(int)),pls),
inference(forward_demodulation,[],[f11979,f2754]) ).
fof(f12005,plain,
one_one(int) = ti(int,one_one(int)),
inference(forward_demodulation,[],[f11992,f2940]) ).
fof(f12018,plain,
sF52 = ti(int,sF52),
inference(forward_demodulation,[],[f12005,f4726]) ).
fof(f12031,plain,
sF52 = sF54,
inference(forward_demodulation,[],[f12018,f5536]) ).
fof(f12044,plain,
sF52 = sF56,
inference(forward_demodulation,[],[f12031,f5838]) ).
fof(f13800,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t))
| ti(int,t) = ti(int,one_one(int)) ),
inference(resolution,[],[f2763,f2787]) ).
fof(f13802,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sF52),t))
| ti(int,t) = ti(int,one_one(int)) ),
inference(forward_demodulation,[],[f13800,f4726]) ).
fof(f13804,plain,
( ti(int,t) = ti(int,one_one(int))
| spl71_4 ),
inference(forward_subsumption_resolution,[],[f13802,f5345]) ).
fof(f13806,plain,
( ti(int,t) = ti(int,sF52)
| spl71_4 ),
inference(forward_demodulation,[],[f13804,f4726]) ).
fof(f13808,plain,
( ti(int,t) = sF54
| spl71_4 ),
inference(forward_demodulation,[],[f13806,f5536]) ).
fof(f13810,plain,
( ti(int,t) = sF56
| spl71_4 ),
inference(forward_demodulation,[],[f13808,f5838]) ).
fof(f13812,plain,
( ti(int,t) = sF52
| spl71_4 ),
inference(forward_demodulation,[],[f13810,f12044]) ).
fof(f13814,plain,
( t = sF52
| spl71_4 ),
inference(forward_demodulation,[],[f13812,f2762]) ).
fof(f13816,plain,
( $false
| spl71_4
| spl71_6 ),
inference(forward_subsumption_resolution,[],[f13814,f5354]) ).
fof(f13817,plain,
( spl71_4
| spl71_6 ),
inference(avatar_contradiction_clause,[],[f13816]) ).
fof(f13818,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK6),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m))
| ~ spl71_5 ),
inference(forward_demodulation,[],[f5350,f5504]) ).
fof(f13870,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),number_number_of(nat,sF58))),hAPP(nat,int,sF66(sK6),number_number_of(nat,sF58)))
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13818,f5991]) ).
fof(f13887,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),sF67)),hAPP(nat,int,sF66(sK6),sF67))
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13870,f4756]) ).
fof(f13902,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK5),sF67)),sF68(sK6))
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13887,f4758]) ).
fof(f13908,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,sF69(sK6),hAPP(nat,int,sF66(sK5),sF67))
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13902,f5509]) ).
fof(f13912,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,sF69(sK6),sF68(sK5))
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13908,f4758]) ).
fof(f13916,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = sF70(sK6,sK5)
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13912,f4762]) ).
fof(f13919,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,sF59,sF58)),m)) = sF70(sK6,sK5)
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13916,f5507]) ).
fof(f13938,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,sF60),m)) = sF70(sK6,sK5)
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13919,f4742]) ).
fof(f13940,plain,
( hAPP(int,int,sF53,hAPP(int,int,sF62,m)) = sF70(sK6,sK5)
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13938,f5689]) ).
fof(f13942,plain,
( hAPP(int,int,sF53,sF63) = sF70(sK6,sK5)
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13940,f4748]) ).
fof(f13952,plain,
( sF65 = sF70(sK6,sK5)
| ~ spl71_5 ),
inference(forward_demodulation,[],[f13942,f5619]) ).
fof(f13953,plain,
( $false
| ~ spl71_5 ),
inference(forward_subsumption_resolution,[],[f13952,f4763]) ).
fof(f13954,plain,
~ spl71_5,
inference(avatar_contradiction_clause,[],[f13953]) ).
fof(f13955,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,hAPP(int,int,sF53,sF52)))),hAPP(nat,int,sF66(sK8),number_number_of(nat,hAPP(int,int,sF53,sF52)))) = hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,sF53,sF52)),hAPP(int,int,sF53,sF52))),m))
| ~ spl71_3 ),
inference(forward_demodulation,[],[f5341,f5504]) ).
fof(f13970,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),number_number_of(nat,sF58))),hAPP(nat,int,sF66(sK8),number_number_of(nat,sF58)))
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13955,f5991]) ).
fof(f13976,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),sF67)),hAPP(nat,int,sF66(sK8),sF67))
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13970,f4756]) ).
fof(f13981,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,sF66(sK7),sF67)),sF68(sK8))
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13976,f4758]) ).
fof(f13986,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,sF69(sK8),hAPP(nat,int,sF66(sK7),sF67))
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13981,f5509]) ).
fof(f13990,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = hAPP(int,int,sF69(sK8),sF68(sK7))
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13986,f4758]) ).
fof(f13994,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,sF58),sF58)),m)) = sF70(sK8,sK7)
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13990,f4762]) ).
fof(f13998,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,hAPP(int,int,sF59,sF58)),m)) = sF70(sK8,sK7)
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13994,f5507]) ).
fof(f14002,plain,
( hAPP(int,int,sF53,hAPP(int,int,times_times(int,sF60),m)) = sF70(sK8,sK7)
| ~ spl71_3 ),
inference(forward_demodulation,[],[f13998,f4742]) ).
fof(f14014,plain,
( hAPP(int,int,sF53,hAPP(int,int,sF62,m)) = sF70(sK8,sK7)
| ~ spl71_3 ),
inference(forward_demodulation,[],[f14002,f5689]) ).
fof(f14017,plain,
( hAPP(int,int,sF53,sF63) = sF70(sK8,sK7)
| ~ spl71_3 ),
inference(forward_demodulation,[],[f14014,f4748]) ).
fof(f14020,plain,
( sF65 = sF70(sK8,sK7)
| ~ spl71_3 ),
inference(forward_demodulation,[],[f14017,f5619]) ).
fof(f14023,plain,
( $false
| ~ spl71_3 ),
inference(forward_subsumption_resolution,[],[f14020,f4763]) ).
fof(f14024,plain,
~ spl71_3,
inference(avatar_contradiction_clause,[],[f14023]) ).
cnf(s4,plain,
( spl71_3
| ~ spl71_4 ),
inference(sat_conversion,[],[f5346]) ).
cnf(s5,plain,
( spl71_5
| ~ spl71_6 ),
inference(sat_conversion,[],[f5355]) ).
cnf(s29,plain,
( spl71_4
| spl71_6 ),
inference(sat_conversion,[],[f13817]) ).
cnf(s35,plain,
~ spl71_5,
inference(sat_conversion,[],[f13954]) ).
cnf(s39,plain,
~ spl71_3,
inference(sat_conversion,[],[f14024]) ).
cnf(s41,plain,
~ spl71_6,
inference(rat,[],[s5,s35]) ).
cnf(s43,plain,
spl71_4,
inference(rat,[],[s29,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s4,s43,s39]) ).
fof(f14049,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 21:47:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.78/2.33 % (2757599)Detected formulas, will run a generic FOF schedule.
% 9.78/2.33 % (2757610)dis-21_1_sil=8000:lcm=predicate:random_seed=4086069610:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 9.78/2.33 % (2757610)Instruction limit reached!
% 9.78/2.33 % (2757610)------------------------------
% 9.78/2.33 % (2757610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757610)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757610)Termination reason: Instruction limit
% 9.78/2.33 % (2757610)Termination phase: Property scanning
% 9.78/2.33 % (2757610)Time elapsed: 0.031 s
% 9.78/2.33 % (2757610)Peak memory usage: 88 MB
% 9.78/2.33 % (2757610)Instructions burned: 133 (million)
% 9.78/2.33 % (2757607)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2041287660:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.78/2.33 % (2757608)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3089996399:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.78/2.33 % (2757606)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2271126224:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.78/2.33 % (2757604)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1637152471:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.78/2.33 % (2757605)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2738558282:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.78/2.33 % (2757609)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2091759938:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.78/2.33 % (2757607)Instruction limit reached!
% 9.78/2.33 % (2757607)------------------------------
% 9.78/2.33 % (2757607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757607)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757607)Termination reason: Instruction limit
% 9.78/2.33 % (2757607)Termination phase: Saturation
% 9.78/2.33 % (2757607)Time elapsed: 0.055 s
% 9.78/2.33 % (2757607)Peak memory usage: 90 MB
% 9.78/2.33 % (2757607)Instructions burned: 110 (million)
% 9.78/2.33 % (2757608)Instruction limit reached!
% 9.78/2.33 % (2757608)------------------------------
% 9.78/2.33 % (2757608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757608)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757608)Termination reason: Instruction limit
% 9.78/2.33 % (2757608)Termination phase: Saturation
% 9.78/2.33 % (2757608)Time elapsed: 0.057 s
% 9.78/2.33 % (2757608)Peak memory usage: 89 MB
% 9.78/2.33 % (2757608)Instructions burned: 120 (million)
% 9.78/2.33 % (2757609)Instruction limit reached!
% 9.78/2.33 % (2757609)------------------------------
% 9.78/2.33 % (2757609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757609)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757609)Termination reason: Instruction limit
% 9.78/2.33 % (2757609)Termination phase: Property scanning
% 9.78/2.33 % (2757609)Time elapsed: 0.059 s
% 9.78/2.33 % (2757609)Peak memory usage: 88 MB
% 9.78/2.33 % (2757609)Instructions burned: 139 (million)
% 9.78/2.33 % (2757618)lrs+10_1_sil=8000:sp=occurrence:random_seed=2727574003:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.78/2.33 % (2757618)Instruction limit reached!
% 9.78/2.33 % (2757618)------------------------------
% 9.78/2.33 % (2757618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757618)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757618)Termination reason: Instruction limit
% 9.78/2.33 % (2757618)Termination phase: Saturation
% 9.78/2.33 % (2757618)Time elapsed: 0.084 s
% 9.78/2.33 % (2757618)Peak memory usage: 92 MB
% 9.78/2.33 % (2757618)Instructions burned: 287 (million)
% 9.78/2.33 % (2757621)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1668078517:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.78/2.33 % (2757619)lrs+10_1_sil=32000:urr=on:br=off:random_seed=23338411:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.78/2.33 % (2757620)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2996322665:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.78/2.33 % (2757619)Instruction limit reached!
% 9.78/2.33 % (2757619)------------------------------
% 9.78/2.33 % (2757619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757619)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757619)Termination reason: Instruction limit
% 9.78/2.33 % (2757619)Termination phase: Saturation
% 9.78/2.33 % (2757619)Time elapsed: 0.077 s
% 9.78/2.33 % (2757619)Peak memory usage: 90 MB
% 9.78/2.33 % (2757619)Instructions burned: 158 (million)
% 9.78/2.33 % (2757623)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3525795266:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.78/2.33 % (2757621)Instruction limit reached!
% 9.78/2.33 % (2757621)------------------------------
% 9.78/2.33 % (2757621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757621)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757621)Termination reason: Instruction limit
% 9.78/2.33 % (2757621)Termination phase: Saturation
% 9.78/2.33 % (2757621)Time elapsed: 0.128 s
% 9.78/2.33 % (2757621)Peak memory usage: 91 MB
% 9.78/2.33 % (2757621)Instructions burned: 249 (million)
% 9.78/2.33 % (2757623)Instruction limit reached!
% 9.78/2.33 % (2757623)------------------------------
% 9.78/2.33 % (2757623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757623)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757623)Termination reason: Instruction limit
% 9.78/2.33 % (2757623)Termination phase: Saturation
% 9.78/2.33 % (2757623)Time elapsed: 0.077 s
% 9.78/2.33 % (2757623)Peak memory usage: 92 MB
% 9.78/2.33 % (2757623)Instructions burned: 296 (million)
% 9.78/2.33 % (2757620)Instruction limit reached!
% 9.78/2.33 % (2757620)------------------------------
% 9.78/2.33 % (2757620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757620)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757620)Termination reason: Instruction limit
% 9.78/2.33 % (2757620)Termination phase: Saturation
% 9.78/2.33 % (2757620)Time elapsed: 0.172 s
% 9.78/2.33 % (2757620)Peak memory usage: 92 MB
% 9.78/2.33 % (2757620)Instructions burned: 326 (million)
% 9.78/2.33 % (2757628)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1851674259:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.78/2.33 % (2757630)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3185219677:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 9.78/2.33 % (2757629)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=502136273:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.78/2.33 % (2757630)Instruction limit reached!
% 9.78/2.33 % (2757630)------------------------------
% 9.78/2.33 % (2757630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757630)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757630)Termination reason: Instruction limit
% 9.78/2.33 % (2757630)Termination phase: Property scanning
% 9.78/2.33 % (2757630)Time elapsed: 0.028 s
% 9.78/2.33 % (2757630)Peak memory usage: 88 MB
% 9.78/2.33 % (2757630)Instructions burned: 129 (million)
% 9.78/2.33 % (2757629)Instruction limit reached!
% 9.78/2.33 % (2757629)------------------------------
% 9.78/2.33 % (2757629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757629)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757629)Termination reason: Instruction limit
% 9.78/2.33 % (2757629)Termination phase: Property scanning
% 9.78/2.33 % (2757629)Time elapsed: 0.050 s
% 9.78/2.33 % (2757629)Peak memory usage: 88 MB
% 9.78/2.33 % (2757629)Instructions burned: 115 (million)
% 9.78/2.33 % (2757631)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1211877336:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 9.78/2.33 % (2757631)Instruction limit reached!
% 9.78/2.33 % (2757631)------------------------------
% 9.78/2.33 % (2757631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757631)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757631)Termination reason: Instruction limit
% 9.78/2.33 % (2757631)Termination phase: Saturation
% 9.78/2.33 % (2757631)Time elapsed: 0.048 s
% 9.78/2.33 % (2757631)Peak memory usage: 89 MB
% 9.78/2.33 % (2757631)Instructions burned: 114 (million)
% 9.78/2.33 % (2757635)lrs+10_1_sil=8000:sp=occurrence:random_seed=2858653581:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 9.78/2.33 % (2757637)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=761430820:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 9.78/2.33 % (2757638)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2248865106:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 9.78/2.33 % (2757637)Instruction limit reached!
% 9.78/2.33 % (2757637)------------------------------
% 9.78/2.33 % (2757637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757637)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757637)Termination reason: Instruction limit
% 9.78/2.33 % (2757637)Termination phase: Saturation
% 9.78/2.33 % (2757637)Time elapsed: 0.221 s
% 9.78/2.33 % (2757637)Peak memory usage: 94 MB
% 9.78/2.33 % (2757637)Instructions burned: 438 (million)
% 9.78/2.33 % (2757642)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2687183730:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 9.78/2.33 % (2757642)Instruction limit reached!
% 9.78/2.33 % (2757642)------------------------------
% 9.78/2.33 % (2757642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757642)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757642)Termination reason: Instruction limit
% 9.78/2.33 % (2757642)Termination phase: Property scanning
% 9.78/2.33 % (2757642)Time elapsed: 0.057 s
% 9.78/2.33 % (2757642)Peak memory usage: 88 MB
% 9.78/2.33 % (2757642)Instructions burned: 136 (million)
% 9.78/2.33 % (2757604)First to succeed.
% 9.78/2.33 % (2757604)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2757599"
% 9.78/2.33 % (2757635)Instruction limit reached!
% 9.78/2.33 % (2757635)------------------------------
% 9.78/2.33 % (2757635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.78/2.33 % (2757635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.78/2.33 % (2757635)CaDiCaL version: 2.1.3
% 9.78/2.33 % (2757635)Termination reason: Instruction limit
% 9.78/2.33 % (2757635)Termination phase: Saturation
% 9.78/2.33 % (2757635)Time elapsed: 0.492 s
% 9.78/2.33 % (2757635)Peak memory usage: 96 MB
% 9.78/2.33 % (2757635)Instructions burned: 908 (million)
% 9.78/2.33 % (2757644)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2849300945:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 9.78/2.33 % (2757645)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4080906864:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 9.78/2.33 % (2757604)Refutation found. Thanks to Tanya!
% 9.78/2.33 % SZS status Theorem for theBenchmark
% 9.78/2.33 % SZS output start Proof for theBenchmark
% See solution above
% 10.52/2.55 % (2757604)------------------------------
% 10.52/2.55 % (2757604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.55 % (2757604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.55 % (2757604)CaDiCaL version: 2.1.3
% 10.52/2.55 % (2757604)Termination reason: Refutation
% 10.52/2.55 % (2757604)Time elapsed: 1.071 s
% 10.52/2.55 % (2757604)Peak memory usage: 152 MB
% 10.52/2.55 % (2757604)Instructions burned: 2541 (million)
% 10.52/2.55 % (2757604)------------------------------
% 10.52/2.55 % (2757604)------------------------------
% 10.52/2.55 % (2757599)Success in time 1.478 s
% 10.52/2.55 % Vampire exiting
%------------------------------------------------------------------------------