%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM924+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:26:06 PM UTC 2026
% Result : Theorem 1.11s 0.67s
% Output : Refutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 27
% Syntax : Number of formulae : 168 ( 168 unt; 0 def)
% Number of atoms : 168 ( 123 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 99 ( 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
fof(f21,axiom,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),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_3_t) ).
fof(f44,axiom,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(bit1(pls),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__special_I2_J) ).
fof(f187,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Bit0__Pls) ).
fof(f188,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Pls__def) ).
fof(f197,axiom,
! [X0,X1] : plus_plus_int(bit0(X0),bit0(X1)) = bit0(plus_plus_int(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_add__Bit0__Bit0) ).
fof(f198,axiom,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
fof(f203,axiom,
! [X0] : times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(X0)) = number_number_of_int(bit0(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_double__number__of__Bit0) ).
fof(f219,axiom,
! [X0] : power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_power2__eq__square) ).
fof(f228,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_semiring__norm_I112_J) ).
fof(f240,axiom,
! [X0,X1] : number_number_of_int(plus_plus_int(X0,X1)) = plus_plus_int(number_number_of_int(X0),number_number_of_int(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_number__of__add) ).
fof(f252,axiom,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Bit1__def) ).
fof(f264,axiom,
! [X0] : number_number_of_int(bit1(X0)) = plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(X0)),number_number_of_int(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_number__of__Bit1) ).
fof(f278,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_semiring__one__add__one__is__two) ).
fof(f281,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_one__add__one__is__two) ).
fof(f340,axiom,
! [X0,X1,X2] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(X1,times_times_int(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f343,axiom,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f346,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f349,axiom,
! [X0,X1,X2] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f355,axiom,
! [X0,X1,X2] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(f358,axiom,
! [X0,X1,X2] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(plus_plus_int(X0,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(f361,axiom,
! [X0,X1,X2,X3] : plus_plus_int(plus_plus_int(X0,X1),plus_plus_int(X2,X3)) = plus_plus_int(plus_plus_int(X0,X2),plus_plus_int(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(f380,axiom,
! [X0] : times_times_int(X0,zero_zero_int) = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f428,axiom,
! [X0] : plus_plus_int(X0,X0) = times_times_int(plus_plus_int(one_one_int,one_one_int),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(f434,axiom,
! [X0,X1] : plus_plus_int(times_times_int(X0,X1),X1) = times_times_int(plus_plus_int(X0,one_one_int),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(f456,axiom,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(f716,conjecture,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f717,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(negated_conjecture,[status(cth)],[f716]) ).
fof(f718,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(flattening,[],[f717]) ).
fof(f1346,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f20]) ).
fof(f1347,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnf_transformation,[],[f21]) ).
fof(f1382,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(bit1(pls),X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f1598,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f187]) ).
fof(f1599,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f188]) ).
fof(f1612,plain,
! [X0,X1] : plus_plus_int(bit0(X0),bit0(X1)) = bit0(plus_plus_int(X0,X1)),
inference(cnf_transformation,[],[f197]) ).
fof(f1613,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f198]) ).
fof(f1618,plain,
! [X0] : times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(X0)) = number_number_of_int(bit0(X0)),
inference(cnf_transformation,[],[f203]) ).
fof(f1634,plain,
! [X0] : power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X0,X0),
inference(cnf_transformation,[],[f219]) ).
fof(f1645,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[],[f228]) ).
fof(f1659,plain,
! [X0,X1] : plus_plus_int(number_number_of_int(X0),number_number_of_int(X1)) = number_number_of_int(plus_plus_int(X0,X1)),
inference(cnf_transformation,[],[f240]) ).
fof(f1678,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f252]) ).
fof(f1692,plain,
! [X0] : number_number_of_int(bit1(X0)) = plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(X0)),number_number_of_int(X0)),
inference(cnf_transformation,[],[f264]) ).
fof(f1711,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f278]) ).
fof(f1714,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(cnf_transformation,[],[f281]) ).
fof(f1792,plain,
! [X2,X0,X1] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(X1,times_times_int(X0,X2)),
inference(cnf_transformation,[],[f340]) ).
fof(f1795,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f343]) ).
fof(f1798,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f346]) ).
fof(f1801,plain,
! [X2,X0,X1] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)),
inference(cnf_transformation,[],[f349]) ).
fof(f1807,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f355]) ).
fof(f1810,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(plus_plus_int(X0,X2),X1),
inference(cnf_transformation,[],[f358]) ).
fof(f1813,plain,
! [X2,X3,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),plus_plus_int(X2,X3)) = plus_plus_int(plus_plus_int(X0,X2),plus_plus_int(X1,X3)),
inference(cnf_transformation,[],[f361]) ).
fof(f1836,plain,
! [X0] : zero_zero_int = times_times_int(X0,zero_zero_int),
inference(cnf_transformation,[],[f380]) ).
fof(f1899,plain,
! [X0] : plus_plus_int(X0,X0) = times_times_int(plus_plus_int(one_one_int,one_one_int),X0),
inference(cnf_transformation,[],[f428]) ).
fof(f1905,plain,
! [X0,X1] : plus_plus_int(times_times_int(X0,X1),X1) = times_times_int(plus_plus_int(X0,one_one_int),X1),
inference(cnf_transformation,[],[f434]) ).
fof(f1936,plain,
! [X0] : power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(X0,X0),
inference(cnf_transformation,[],[f456]) ).
fof(f2281,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(cnf_transformation,[],[f718]) ).
fof(f2286,plain,
ord_less_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),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),pls)),
inference(definition_unfolding,[],[f1346,f1613,f1613,f1678,f1613,f1613,f1678,f1599]) ).
fof(f2287,plain,
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) = plus_plus_int(power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),one_one_int),
inference(definition_unfolding,[],[f1347,f1613,f1613,f1678,f1613,f1678]) ).
fof(f2321,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),X0)),
inference(definition_unfolding,[],[f1382,f1678]) ).
fof(f2432,plain,
pls = plus_plus_int(pls,pls),
inference(definition_unfolding,[],[f1598,f1613]) ).
fof(f2442,plain,
! [X0,X1] : plus_plus_int(plus_plus_int(X0,X0),plus_plus_int(X1,X1)) = plus_plus_int(plus_plus_int(X0,X1),plus_plus_int(X0,X1)),
inference(definition_unfolding,[],[f1612,f1613,f1613,f1613]) ).
fof(f2446,plain,
! [X0] : times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(X0)) = number_number_of_int(plus_plus_int(X0,X0)),
inference(definition_unfolding,[],[f1618,f1613]) ).
fof(f2462,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),
inference(definition_unfolding,[],[f1634,f1613,f1678]) ).
fof(f2467,plain,
pls = number_number_of_int(pls),
inference(definition_unfolding,[],[f1645,f1599]) ).
fof(f2496,plain,
! [X0] : plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(X0)),number_number_of_int(X0)) = number_number_of_int(plus_plus_int(plus_plus_int(one_one_int,X0),X0)),
inference(definition_unfolding,[],[f1692,f1678]) ).
fof(f2511,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))),
inference(definition_unfolding,[],[f1711,f1613,f1678]) ).
fof(f2514,plain,
plus_plus_int(one_one_int,one_one_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))),
inference(definition_unfolding,[],[f1714,f1613,f1678]) ).
fof(f2560,plain,
! [X0] : pls = times_times_int(X0,pls),
inference(definition_unfolding,[],[f1836,f1599,f1599]) ).
fof(f2589,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),
inference(definition_unfolding,[],[f1936,f1613,f1678]) ).
fof(f2693,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),one_one_int),pls),
inference(definition_unfolding,[],[f2281,f1613,f1678,f1599]) ).
fof(f2891,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),
inference(forward_demodulation,[],[f2514,f1807]) ).
fof(f2894,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls)))),
inference(forward_demodulation,[],[f2511,f1807]) ).
fof(f2905,plain,
! [X0] : plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(X0)),number_number_of_int(X0)) = number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(X0,X0))),
inference(forward_demodulation,[],[f2496,f1807]) ).
fof(f2926,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f2462,f1807]) ).
fof(f2942,plain,
! [X0,X1] : plus_plus_int(plus_plus_int(X0,X0),plus_plus_int(X1,X1)) = plus_plus_int(X0,plus_plus_int(X1,plus_plus_int(X0,X1))),
inference(forward_demodulation,[],[f2442,f1807]) ).
fof(f3022,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(pls,X0))),
inference(forward_demodulation,[],[f2321,f1807]) ).
fof(f3056,plain,
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) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f2287,f1798]) ).
fof(f3057,plain,
ord_less_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),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),pls),pls)),
inference(forward_demodulation,[],[f2286,f1905]) ).
fof(f3109,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f2891,f1807]) ).
fof(f3112,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f2894,f1807]) ).
fof(f3121,plain,
! [X0] : number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(X0,X0))) = plus_plus_int(one_one_int,plus_plus_int(number_number_of_int(X0),number_number_of_int(X0))),
inference(forward_demodulation,[],[f2905,f1807]) ).
fof(f3133,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls)))))),
inference(forward_demodulation,[],[f2926,f1807]) ).
fof(f3149,plain,
! [X0,X1] : plus_plus_int(X0,plus_plus_int(X1,plus_plus_int(X0,X1))) = plus_plus_int(X0,plus_plus_int(X0,plus_plus_int(X1,X1))),
inference(forward_demodulation,[],[f2942,f1807]) ).
fof(f3203,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,X0)))),
inference(forward_demodulation,[],[f3022,f1807]) ).
fof(f3228,plain,
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) = plus_plus_int(one_one_int,times_times_int(s,s)),
inference(forward_demodulation,[],[f3056,f2589]) ).
fof(f3229,plain,
ord_less_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),plus_plus_int(pls,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),pls))),
inference(forward_demodulation,[],[f3057,f1798]) ).
fof(f3273,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f3109,f1801]) ).
fof(f3276,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f3112,f1801]) ).
fof(f3285,plain,
! [X0] : number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(X0,X0))) = plus_plus_int(one_one_int,number_number_of_int(plus_plus_int(X0,X0))),
inference(forward_demodulation,[],[f3121,f1659]) ).
fof(f3296,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(plus_plus_int(one_one_int,pls),pls)))))),
inference(forward_demodulation,[],[f3133,f1801]) ).
fof(f3353,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,X0)))),
inference(forward_demodulation,[],[f3203,f1801]) ).
fof(f3375,plain,
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),t) = plus_plus_int(one_one_int,times_times_int(s,s)),
inference(forward_demodulation,[],[f3228,f1905]) ).
fof(f3376,plain,
ord_less_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),plus_plus_int(pls,pls)),
inference(forward_demodulation,[],[f3229,f2560]) ).
fof(f3410,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f3273,f1801]) ).
fof(f3413,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(forward_demodulation,[],[f3276,f1801]) ).
fof(f3424,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(one_one_int,pls),pls)))))),
inference(forward_demodulation,[],[f3296,f1801]) ).
fof(f3470,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,X0)))),
inference(forward_demodulation,[],[f3353,f1801]) ).
fof(f3492,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,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)),
inference(forward_demodulation,[],[f3375,f1798]) ).
fof(f3493,plain,
ord_less_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),pls),
inference(forward_demodulation,[],[f3376,f2432]) ).
fof(f3521,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))),
inference(forward_demodulation,[],[f3410,f1807]) ).
fof(f3524,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))),
inference(forward_demodulation,[],[f3413,f1807]) ).
fof(f3533,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))))),
inference(forward_demodulation,[],[f3424,f1807]) ).
fof(f3591,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(t,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))),
inference(forward_demodulation,[],[f3492,f1795]) ).
fof(f3592,plain,
ord_less_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),t),pls),
inference(forward_demodulation,[],[f3493,f1905]) ).
fof(f3620,plain,
plus_plus_int(one_one_int,one_one_int) = plus_plus_int(one_one_int,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(pls,pls)))),
inference(forward_demodulation,[],[f3521,f3470]) ).
fof(f3623,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(one_one_int,pls)))))),
inference(forward_demodulation,[],[f3524,f3149]) ).
fof(f3631,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(one_one_int,pls))))))),
inference(forward_demodulation,[],[f3533,f3149]) ).
fof(f3686,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(t,times_times_int(m,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))))))),
inference(forward_demodulation,[],[f3591,f1795]) ).
fof(f3687,plain,
ord_less_int(plus_plus_int(t,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)),pls),
inference(forward_demodulation,[],[f3592,f1798]) ).
fof(f3715,plain,
plus_plus_int(one_one_int,one_one_int) = plus_plus_int(one_one_int,plus_plus_int(one_one_int,number_number_of_int(plus_plus_int(pls,pls)))),
inference(forward_demodulation,[],[f3620,f3285]) ).
fof(f3718,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))),
inference(forward_demodulation,[],[f3623,f1801]) ).
fof(f3726,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))))),
inference(forward_demodulation,[],[f3631,f1801]) ).
fof(f3781,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,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))))))),
inference(forward_demodulation,[],[f3686,f1792]) ).
fof(f3782,plain,
ord_less_int(plus_plus_int(t,times_times_int(t,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))),pls),
inference(forward_demodulation,[],[f3687,f1795]) ).
fof(f3810,plain,
plus_plus_int(one_one_int,one_one_int) = plus_plus_int(one_one_int,plus_plus_int(one_one_int,number_number_of_int(pls))),
inference(forward_demodulation,[],[f3715,f2432]) ).
fof(f3813,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int)))))),
inference(forward_demodulation,[],[f3718,f1798]) ).
fof(f3821,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int))))))),
inference(forward_demodulation,[],[f3726,f1798]) ).
fof(f3876,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_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))))))),
inference(forward_demodulation,[],[f3781,f2446]) ).
fof(f3877,plain,
ord_less_int(plus_plus_int(t,times_times_int(t,times_times_int(m,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))))))),pls),
inference(forward_demodulation,[],[f3782,f1795]) ).
fof(f3905,plain,
plus_plus_int(one_one_int,one_one_int) = plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)),
inference(forward_demodulation,[],[f3810,f2467]) ).
fof(f3907,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))),
inference(forward_demodulation,[],[f3813,f3149]) ).
fof(f3914,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),
inference(forward_demodulation,[],[f3821,f3149]) ).
fof(f3969,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls))))))),
inference(forward_demodulation,[],[f3876,f2446]) ).
fof(f3970,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,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))))))),pls),
inference(forward_demodulation,[],[f3877,f1792]) ).
fof(f3997,plain,
plus_plus_int(one_one_int,one_one_int) = plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int)),
inference(forward_demodulation,[],[f3905,f1798]) ).
fof(f4005,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f3914,f3907]) ).
fof(f4055,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))))),
inference(forward_demodulation,[],[f3969,f1807]) ).
fof(f4056,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_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))))))),pls),
inference(forward_demodulation,[],[f3970,f2446]) ).
fof(f4083,plain,
plus_plus_int(one_one_int,one_one_int) = plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)),
inference(forward_demodulation,[],[f3997,f1801]) ).
fof(f4102,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,number_number_of_int(plus_plus_int(pls,pls)))))))),
inference(forward_demodulation,[],[f4055,f3285]) ).
fof(f4103,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls))))))),pls),
inference(forward_demodulation,[],[f4056,f2446]) ).
fof(f4136,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,number_number_of_int(pls))))))),
inference(forward_demodulation,[],[f4102,f2432]) ).
fof(f4137,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))))),pls),
inference(forward_demodulation,[],[f4103,f1807]) ).
fof(f4166,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,pls)))))),
inference(forward_demodulation,[],[f4136,f2467]) ).
fof(f4167,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,number_number_of_int(plus_plus_int(pls,pls)))))))),pls),
inference(forward_demodulation,[],[f4137,f3285]) ).
fof(f4196,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(one_one_int,pls)))))),
inference(forward_demodulation,[],[f4166,f1899]) ).
fof(f4197,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,number_number_of_int(pls))))))),pls),
inference(forward_demodulation,[],[f4167,f2432]) ).
fof(f4223,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(one_one_int,pls))))))),
inference(forward_demodulation,[],[f4196,f1807]) ).
fof(f4224,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,pls)))))),pls),
inference(forward_demodulation,[],[f4197,f2467]) ).
fof(f4249,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))))),
inference(forward_demodulation,[],[f4223,f1801]) ).
fof(f4250,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(plus_plus_int(one_one_int,pls),plus_plus_int(one_one_int,pls)))))),pls),
inference(forward_demodulation,[],[f4224,f1899]) ).
fof(f4275,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int))))))),
inference(forward_demodulation,[],[f4249,f1798]) ).
fof(f4276,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(one_one_int,pls))))))),pls),
inference(forward_demodulation,[],[f4250,f1807]) ).
fof(f4287,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),
inference(forward_demodulation,[],[f4275,f3149]) ).
fof(f4288,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))))),pls),
inference(forward_demodulation,[],[f4276,f1801]) ).
fof(f4297,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))),
inference(forward_demodulation,[],[f4287,f4083]) ).
fof(f4298,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int))))))),pls),
inference(forward_demodulation,[],[f4288,f1798]) ).
fof(f4306,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,one_one_int))))),
inference(forward_demodulation,[],[f4297,f4083]) ).
fof(f4307,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))))),pls),
inference(forward_demodulation,[],[f4298,f3149]) ).
fof(f4311,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,plus_plus_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,one_one_int))))),
inference(forward_demodulation,[],[f4306,f1899]) ).
fof(f4312,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))),pls),
inference(forward_demodulation,[],[f4307,f4083]) ).
fof(f4315,plain,
plus_plus_int(one_one_int,times_times_int(s,s)) = plus_plus_int(t,times_times_int(m,times_times_int(t,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))),
inference(forward_demodulation,[],[f4311,f1807]) ).
fof(f4316,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,times_times_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,one_one_int))))),pls),
inference(forward_demodulation,[],[f4312,f4083]) ).
fof(f4319,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,plus_plus_int(plus_plus_int(one_one_int,one_one_int),plus_plus_int(one_one_int,one_one_int))))),pls),
inference(forward_demodulation,[],[f4316,f1899]) ).
fof(f4322,plain,
ord_less_int(plus_plus_int(t,times_times_int(m,times_times_int(t,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))),pls),
inference(forward_demodulation,[],[f4319,f1807]) ).
fof(f4325,plain,
ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(forward_demodulation,[],[f4322,f4315]) ).
fof(f4800,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(pls,one_one_int),pls),plus_plus_int(plus_plus_int(pls,one_one_int),pls)))),one_one_int),pls),
inference(superposition,[],[f2693,f1798]) ).
fof(f4809,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(plus_plus_int(pls,one_one_int),pls),plus_plus_int(plus_plus_int(pls,one_one_int),pls))))),pls),
inference(forward_demodulation,[],[f4800,f1798]) ).
fof(f4814,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(pls,one_one_int),plus_plus_int(pls,plus_plus_int(plus_plus_int(pls,one_one_int),pls)))))),pls),
inference(forward_demodulation,[],[f4809,f1807]) ).
fof(f4818,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(plus_plus_int(pls,pls),plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(pls,one_one_int),pls)))))),pls),
inference(forward_demodulation,[],[f4814,f1813]) ).
fof(f4822,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(pls,one_one_int),pls))))))),pls),
inference(forward_demodulation,[],[f4818,f1807]) ).
fof(f4826,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(plus_plus_int(pls,pls),one_one_int))))))),pls),
inference(forward_demodulation,[],[f4822,f1810]) ).
fof(f4830,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,one_one_int)))))))),pls),
inference(forward_demodulation,[],[f4826,f1807]) ).
fof(f4834,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(pls,one_one_int)))))))),pls),
inference(forward_demodulation,[],[f4830,f1801]) ).
fof(f4838,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))))))),pls),
inference(forward_demodulation,[],[f4834,f3149]) ).
fof(f4842,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls),
inference(forward_demodulation,[],[f4838,f3907]) ).
fof(f4844,plain,
~ ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(forward_demodulation,[],[f4842,f4005]) ).
fof(f5480,plain,
$false,
inference(resolution,[],[f4325,f4844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 21:43:57 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 1.11/0.67 % (3234516)Will run a generic schedule for satisfiability detection.
% 1.11/0.67 % (3234525)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1059516591:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.11/0.67 % (3234522)% WARNING: option uhcvi not known.
% 1.11/0.67 % (3234521)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=787569296_2999 on theBenchmark for (2999ds/0Mi)
% 1.11/0.67 % (3234522)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1400881888:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.11/0.67 % (3234523)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2463274453:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.11/0.67 % (3234524)dis+10_1_sil=32000:sp=arity:random_seed=2948878388:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.11/0.67 % (3234526)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=728467265:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.11/0.67 % (3234527)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3471273409:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.11/0.67 % (3234525)Instruction limit reached!
% 1.11/0.67 % (3234525)------------------------------
% 1.11/0.67 % (3234525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.11/0.67 % (3234525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.11/0.67 % (3234525)CaDiCaL version: 2.1.3
% 1.11/0.67 % (3234525)Termination reason: Instruction limit
% 1.11/0.67 % (3234525)Termination phase: Saturation
% 1.11/0.67 % (3234525)Time elapsed: 0.033 s
% 1.11/0.67 % (3234525)Peak memory usage: 14 MB
% 1.11/0.67 % (3234525)Instructions burned: 117 (million)
% 1.11/0.67 % (3234535)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1350729693:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.11/0.67 % (3234524)Instruction limit reached!
% 1.11/0.67 % (3234524)------------------------------
% 1.11/0.67 % (3234524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.11/0.67 % (3234524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.11/0.67 % (3234524)CaDiCaL version: 2.1.3
% 1.11/0.67 % (3234524)Termination reason: Instruction limit
% 1.11/0.67 % (3234524)Termination phase: Saturation
% 1.11/0.67 % (3234524)Time elapsed: 0.061 s
% 1.11/0.67 % (3234524)Peak memory usage: 14 MB
% 1.11/0.67 % (3234524)Instructions burned: 104 (million)
% 1.11/0.67 % (3234526)Instruction limit reached!
% 1.11/0.67 % (3234526)------------------------------
% 1.11/0.67 % (3234526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.11/0.67 % (3234526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.11/0.67 % (3234526)CaDiCaL version: 2.1.3
% 1.11/0.67 % (3234526)Termination reason: Instruction limit
% 1.11/0.67 % (3234526)Termination phase: Saturation
% 1.11/0.67 % (3234526)Time elapsed: 0.068 s
% 1.11/0.67 % (3234526)Peak memory usage: 14 MB
% 1.11/0.67 % (3234526)Instructions burned: 133 (million)
% 1.11/0.67 % (3234537)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2214019999:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.11/0.67 % (3234538)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3430295945:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.11/0.67 % (3234527)Instruction limit reached!
% 1.11/0.67 % (3234527)------------------------------
% 1.11/0.67 % (3234527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.11/0.67 % (3234527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.11/0.67 % (3234527)CaDiCaL version: 2.1.3
% 1.11/0.67 % (3234527)Termination reason: Instruction limit
% 1.11/0.67 % (3234527)Termination phase: Saturation
% 1.11/0.67 % (3234527)Time elapsed: 0.101 s
% 1.11/0.67 % (3234527)Peak memory usage: 15 MB
% 1.11/0.67 % (3234527)Instructions burned: 160 (million)
% 1.11/0.67 % (3234541)ott-21_1_sil=16000:fs=off:random_seed=1377541542:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.11/0.67 % TRYING [1]
% 1.11/0.67 % TRYING [2]
% 1.11/0.67 % (3234537)Instruction limit reached!
% 1.11/0.67 % (3234537)------------------------------
% 1.11/0.67 % (3234537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.11/0.67 % (3234537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.11/0.67 % (3234537)CaDiCaL version: 2.1.3
% 1.11/0.67 % (3234537)Termination reason: Instruction limit
% 1.11/0.67 % (3234537)Termination phase: Saturation
% 1.11/0.67 % (3234537)Time elapsed: 0.074 s
% 1.11/0.67 % (3234537)Peak memory usage: 14 MB
% 1.11/0.67 % (3234537)Instructions burned: 132 (million)
% 1.11/0.67 % (3234543)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=984836484:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.11/0.67 % (3234541) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3234516-3234541"...
% 1.11/0.67 % (3234541)...printing done.
% 1.11/0.67 % TRYING [3]
% 1.11/0.67 % (3234541)Refutation found. Thanks to Tanya!
% 1.11/0.67 % SZS status Theorem for theBenchmark
% 1.11/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 1.11/0.67 % (3234541)------------------------------
% 1.11/0.67 % (3234541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.11/0.67 % (3234541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.11/0.67 % (3234541)CaDiCaL version: 2.1.3
% 1.11/0.67 % (3234541)Termination reason: Refutation
% 1.11/0.67 % (3234541)Time elapsed: 0.061 s
% 1.11/0.67 % (3234541)Peak memory usage: 14 MB
% 1.11/0.67 % (3234541)Instructions burned: 122 (million)
% 1.11/0.67 % (3234516)Success in time 0.239 s
% 1.11/0.67 % Vampire exiting
%------------------------------------------------------------------------------