%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM925+7 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 : Fri Sep 25 02:27:19 PM UTC 2026
% Result : Theorem 49.81s 12.90s
% Output : CNFRefutation 49.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 33
% Syntax : Number of formulae : 178 ( 134 unt; 0 def)
% Number of atoms : 241 ( 195 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 120 ( 57 ~; 51 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 5 con; 0-4 aty)
% Number of variables : 214 ( 0 sgn 214 !; 0 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
fof(f48,axiom,
! [X0] : ti(int,bit0(X0)) = bit0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
fof(f53,axiom,
! [X0] : nat_1(ti(int,X0)) = nat_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onat_arg1) ).
fof(f98,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(f100,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X1,X2] :
( plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X0,power_power(X0,X2),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X0)
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
fof(f105,axiom,
! [X0] :
( number_ring(X0)
=> ! [X1] : plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_add__special_I3_J) ).
fof(f106,axiom,
! [X0] :
( number_ring(X0)
=> plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
fof(f115,axiom,
! [X0,X1] : plus_plus(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,plus_plus(int,X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_plus__numeral__code_I9_J) ).
fof(f117,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
fof(f127,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_29_nat__1__add__1) ).
fof(f130,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
fof(f135,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(f143,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_45_zadd__assoc) ).
fof(f144,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_46_zadd__left__commute) ).
fof(f145,axiom,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
fof(f171,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(f173,axiom,
! [X0] : plus_plus(int,X0,pls) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
fof(f174,axiom,
! [X0] : plus_plus(int,pls,X0) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__Pls) ).
fof(f176,axiom,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
fof(f190,axiom,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
fof(f202,axiom,
number_number_of(int,bit0(bit1(pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_transfer__int__nat__numerals_I3_J) ).
fof(f218,axiom,
! [X0] : number_number_of(int,X0) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_number__of__is__id) ).
fof(f350,axiom,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_zmult__commute) ).
fof(f352,axiom,
! [X0,X1,X2] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_zmult__assoc) ).
fof(f444,axiom,
! [X0] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_nat__int) ).
fof(f468,axiom,
! [X0] : times_times(int,pls,X0) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_mult__Pls) ).
fof(f525,axiom,
! [X0] : number_number_of(nat,X0) = nat_1(number_number_of(int,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_nat__number__of__def) ).
fof(f635,axiom,
! [X0] :
( number_ring(X0)
=> ! [X1] : times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) = plus_plus(X0,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_mult__2) ).
fof(f688,axiom,
! [X0] : minus_minus(int,X0,pls) = ti(int,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_diff__bin__simps_I1_J) ).
fof(f801,axiom,
! [X0,X1] : hAPP(nat,int,power_power(int,minus_minus(int,X0,X1)),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,minus_minus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X0),X1)),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_zdiff__power2) ).
fof(f1122,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(f1141,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(f1247,axiom,
! [X0,X1] : ti(X0,ti(X0,X1)) = ti(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
fof(f1251,conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1252,negated_conjecture,
~ ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f1251]) ).
fof(f1253,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))),
inference(flattening,[],[f1252]) ).
fof(f1711,plain,
! [X0] :
( ~ linordered_idom(X0)
| ! [X1,X2] :
( plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X0,power_power(X0,X2),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X0)
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) ) ),
inference(ennf_transformation,[],[f100]) ).
fof(f1713,plain,
! [X0] :
( ~ number_ring(X0)
| ! [X1] : times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) = plus_plus(X0,X1,X1) ),
inference(ennf_transformation,[],[f635]) ).
fof(f1735,plain,
! [X0] :
( ~ number_ring(X0)
| plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f1736,plain,
! [X0] :
( ~ number_ring(X0)
| ! [X1] : plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f2049,plain,
! [X0] :
( ~ linordered_idom(X0)
| ! [X1,X2] :
( ( zero_zero(X0) != plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X0,power_power(X0,X2),number_number_of(nat,bit0(bit1(pls)))))
| ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
& ( zero_zero(X0) != ti(X0,X2)
| zero_zero(X0) != ti(X0,X1)
| plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X0,power_power(X0,X2),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X0) ) ) ),
inference(nnf_transformation,[],[f1711]) ).
fof(f2050,plain,
! [X0] :
( ~ linordered_idom(X0)
| ! [X1,X2] :
( ( zero_zero(X0) != plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X0,power_power(X0,X2),number_number_of(nat,bit0(bit1(pls)))))
| ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
& ( zero_zero(X0) != ti(X0,X2)
| zero_zero(X0) != ti(X0,X1)
| plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X0,power_power(X0,X2),number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X0) ) ) ),
inference(flattening,[],[f2049]) ).
fof(f2052,plain,
! [X0] : bit0(X0) = ti(int,bit0(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f2057,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1253]) ).
fof(f2058,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(cnf_transformation,[],[f1247]) ).
fof(f2070,plain,
! [X0] : ti(int,X0) = number_number_of(int,X0),
inference(cnf_transformation,[],[f218]) ).
fof(f2073,plain,
! [X0] : ti(int,X0) = plus_plus(int,pls,X0),
inference(cnf_transformation,[],[f174]) ).
fof(f2074,plain,
! [X0] : ti(int,X0) = plus_plus(int,X0,pls),
inference(cnf_transformation,[],[f173]) ).
fof(f2100,plain,
! [X2,X0,X1] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)),
inference(cnf_transformation,[],[f352]) ).
fof(f2102,plain,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(cnf_transformation,[],[f350]) ).
fof(f2107,plain,
! [X0,X1] : hAPP(nat,int,power_power(int,minus_minus(int,X0,X1)),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,minus_minus(int,hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),X0),X1)),hAPP(nat,int,power_power(int,X1),number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f801]) ).
fof(f2148,plain,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
inference(cnf_transformation,[],[f176]) ).
fof(f2173,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f127]) ).
fof(f2186,plain,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(cnf_transformation,[],[f190]) ).
fof(f2195,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f135]) ).
fof(f2208,plain,
! [X0] : ti(int,X0) = minus_minus(int,X0,pls),
inference(cnf_transformation,[],[f688]) ).
fof(f2214,plain,
! [X0] : pls = times_times(int,pls,X0),
inference(cnf_transformation,[],[f468]) ).
fof(f2221,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f171]) ).
fof(f2226,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(cnf_transformation,[],[f130]) ).
fof(f2229,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f117]) ).
fof(f2248,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[],[f98]) ).
fof(f2350,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(cnf_transformation,[],[f145]) ).
fof(f2351,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,[],[f144]) ).
fof(f2352,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,[],[f143]) ).
fof(f2396,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,[],[f115]) ).
fof(f2446,plain,
number_number_of(int,bit0(bit1(pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f202]) ).
fof(f2934,plain,
! [X0] : number_number_of(nat,X0) = nat_1(number_number_of(int,X0)),
inference(cnf_transformation,[],[f525]) ).
fof(f2963,plain,
! [X0] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X0)) = X0,
inference(cnf_transformation,[],[f444]) ).
fof(f2984,plain,
! [X0] : nat_1(ti(int,X0)) = nat_1(X0),
inference(cnf_transformation,[],[f53]) ).
fof(f2986,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f1122]) ).
fof(f3042,plain,
! [X2,X0,X1] :
( ~ linordered_idom(X0)
| zero_zero(X0) != plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,bit0(bit1(pls)))),hAPP(nat,X0,power_power(X0,X2),number_number_of(nat,bit0(bit1(pls)))))
| zero_zero(X0) = ti(X0,X2) ),
inference(cnf_transformation,[],[f2050]) ).
fof(f3046,plain,
number_ring(int),
inference(cnf_transformation,[],[f1141]) ).
fof(f3049,plain,
! [X0,X1] :
( ~ number_ring(X0)
| plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) ),
inference(cnf_transformation,[],[f1713]) ).
fof(f3071,plain,
! [X0] :
( ~ number_ring(X0)
| plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ),
inference(cnf_transformation,[],[f1735]) ).
fof(f3072,plain,
! [X0,X1] :
( ~ number_ring(X0)
| plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ),
inference(cnf_transformation,[],[f1736]) ).
fof(f3075,plain,
! [X0] : plus_plus(int,X0,X0) = ti(int,plus_plus(int,X0,X0)),
inference(definition_unfolding,[],[f2052,f2148,f2148]) ).
fof(f3078,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),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,[],[f2057,f2148,f2186]) ).
fof(f3084,plain,
! [X0,X1] : hAPP(nat,int,power_power(int,minus_minus(int,X0,X1)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) = plus_plus(int,minus_minus(int,hAPP(nat,int,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)))),times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),X0),X1)),hAPP(nat,int,power_power(int,X1),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),
inference(definition_unfolding,[],[f2107,f2148,f2186,f2148,f2186,f2148,f2186,f2148,f2186]) ).
fof(f3149,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,[],[f2173,f2148,f2186]) ).
fof(f3170,plain,
one_one(int) = number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f2195,f2186]) ).
fof(f3177,plain,
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))) = hAPP(nat,int,semiring_1_of_nat(int),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,[],[f2446,f2148,f2186,f2148,f2186]) ).
fof(f3258,plain,
! [X2,X0,X1] :
( ~ linordered_idom(X0)
| zero_zero(X0) != plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),hAPP(nat,X0,power_power(X0,X2),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)))))
| zero_zero(X0) = ti(X0,X2) ),
inference(definition_unfolding,[],[f3042,f2148,f2186,f2148,f2186]) ).
fof(f3259,plain,
! [X0,X1] :
( ~ number_ring(X0)
| plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,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))),X1) ),
inference(definition_unfolding,[],[f3049,f2148,f2186]) ).
fof(f3269,plain,
! [X0] :
( ~ number_ring(X0)
| plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,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,[],[f3071,f2148,f2186]) ).
fof(f3270,plain,
! [X0,X1] :
( ~ number_ring(X0)
| plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))) ),
inference(definition_unfolding,[],[f3072,f2186]) ).
tcf(c_50,plain,
! [X0: $i] : ti(int,plus_plus(int,X0,X0)) = plus_plus(int,X0,X0),
inference(cnf_transformation,[],[f3075]) ).
tcf(c_55,negated_conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),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)))) = zero_zero(int),
inference(cnf_transformation,[],[f3078]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : ti(X0,ti(X0,X1)) = ti(X0,X1),
inference(cnf_transformation,[],[f2058]) ).
tcf(c_68,plain,
! [X0: $i] : ti(int,X0) = number_number_of(int,X0),
inference(cnf_transformation,[],[f2070]) ).
tcf(c_71,plain,
! [X0: $i] : plus_plus(int,pls,X0) = ti(int,X0),
inference(cnf_transformation,[],[f2073]) ).
tcf(c_72,plain,
! [X0: $i] : plus_plus(int,X0,pls) = ti(int,X0),
inference(cnf_transformation,[],[f2074]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)),
inference(cnf_transformation,[],[f2100]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(cnf_transformation,[],[f2102]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] : plus_plus(int,minus_minus(int,hAPP(nat,int,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)))),times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),X0),X1)),hAPP(nat,int,power_power(int,X1),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) = hAPP(nat,int,power_power(int,minus_minus(int,X0,X1)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),
inference(cnf_transformation,[],[f3084]) ).
tcf(c_166,plain,
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))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f3149]) ).
tcf(c_187,plain,
number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)) = one_one(int),
inference(cnf_transformation,[],[f3170]) ).
tcf(c_200,plain,
! [X0: $i] : minus_minus(int,X0,pls) = ti(int,X0),
inference(cnf_transformation,[],[f2208]) ).
tcf(c_206,plain,
! [X0: $i] : times_times(int,pls,X0) = pls,
inference(cnf_transformation,[],[f2214]) ).
tcf(c_212,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f2221]) ).
tcf(c_217,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(cnf_transformation,[],[f2226]) ).
tcf(c_220,plain,
number_number_of(int,pls) = zero_zero(int),
inference(cnf_transformation,[],[f2229]) ).
tcf(c_236,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[],[f2248]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(cnf_transformation,[],[f2350]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
inference(cnf_transformation,[],[f2351]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)),
inference(cnf_transformation,[],[f2352]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] : 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,[],[f2396]) ).
tcf(c_430,plain,
hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) = number_number_of(int,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(cnf_transformation,[],[f3177]) ).
tcf(c_882,plain,
! [X0: $i] : nat_1(number_number_of(int,X0)) = number_number_of(nat,X0),
inference(cnf_transformation,[],[f2934]) ).
tcf(c_909,plain,
! [X0: $i] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X0)) = X0,
inference(cnf_transformation,[],[f2963]) ).
tcf(c_930,plain,
! [X0: $i] : nat_1(ti(int,X0)) = nat_1(X0),
inference(cnf_transformation,[],[f2984]) ).
tcf(c_932,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f2986]) ).
tcf(c_990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ti(X0,X2) = zero_zero(X0) )
| ~ linordered_idom(X0)
| ( plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),hAPP(nat,X0,power_power(X0,X2),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))))) != zero_zero(X0) ) ),
inference(cnf_transformation,[],[f3258]) ).
tcf(c_992,plain,
number_ring(int),
inference(cnf_transformation,[],[f3046]) ).
tcf(c_995,plain,
! [X0: $i,X1: $i] :
( ( times_times(X0,number_number_of(X0,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))),X1) = plus_plus(X0,X1,X1) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f3259]) ).
tcf(c_1017,plain,
! [X0: $i] :
( ( number_number_of(X0,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(X0,one_one(X0),one_one(X0)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f3269]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i] :
( ( number_number_of(X0,plus_plus(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))) = plus_plus(X0,number_number_of(X0,X1),one_one(X0)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f3270]) ).
tcf(c_2257,plain,
! [X0: $i,X1: $i] :
( ( times_times(X0,number_number_of(X0,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))),X1) = plus_plus(X0,X1,X1) )
| ~ number_ring(X0) ),
inference(prop_impl_just,[status(thm)],[c_995]) ).
tcf(c_2293,plain,
! [X0: $i] :
( ( number_number_of(X0,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(X0,one_one(X0),one_one(X0)) )
| ~ number_ring(X0) ),
inference(prop_impl_just,[status(thm)],[c_1017]) ).
tcf(c_2295,plain,
! [X0: $i,X1: $i] :
( ( number_number_of(X0,plus_plus(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))) = plus_plus(X0,number_number_of(X0,X1),one_one(X0)) )
| ~ number_ring(X0) ),
inference(prop_impl_just,[status(thm)],[c_1018]) ).
tcf(c_7348,plain,
number_number_of(int,pls) = pls,
inference(light_normalisation,[status(thm)],[c_220,c_212]) ).
tcf(c_7367,plain,
! [X0: $i] : nat_1(number_number_of(int,X0)) = nat_1(X0),
inference(demodulation,[status(thm)],[c_930,c_68]) ).
tcf(c_7371,plain,
! [X0: $i] : number_number_of(nat,X0) = nat_1(X0),
inference(light_normalisation,[status(thm)],[c_882,c_7367]) ).
tcf(c_7375,plain,
! [X0: $i] : minus_minus(int,X0,pls) = number_number_of(int,X0),
inference(light_normalisation,[status(thm)],[c_200,c_68]) ).
tcf(c_7376,plain,
! [X0: $i] : plus_plus(int,X0,pls) = number_number_of(int,X0),
inference(light_normalisation,[status(thm)],[c_72,c_68]) ).
tcf(c_7378,plain,
! [X0: $i] : plus_plus(int,pls,X0) = number_number_of(int,X0),
inference(light_normalisation,[status(thm)],[c_71,c_68]) ).
tcf(c_7410,plain,
! [X0: $i] : number_number_of(int,plus_plus(int,X0,X0)) = plus_plus(int,X0,X0),
inference(demodulation,[status(thm)],[c_50,c_68]) ).
tcf(c_7443,plain,
number_number_of(int,number_number_of(int,number_number_of(int,one_one(int)))) = one_one(int),
inference(demodulation,[status(thm)],[c_187,c_7376]) ).
tcf(c_7862,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(light_normalisation,[status(thm)],[c_236,c_212]) ).
tcf(c_7971,plain,
! [X0: $i,X1: $i] :
( ( number_number_of(X0,plus_plus(int,X1,number_number_of(int,number_number_of(int,one_one(int))))) = plus_plus(X0,number_number_of(X0,X1),one_one(X0)) )
| ~ number_ring(X0) ),
inference(demodulation,[status(thm)],[c_2295,c_337,c_338,c_7376,c_7378]) ).
tcf(c_8292,plain,
nat_1(plus_plus(int,one_one(int),number_number_of(int,number_number_of(int,one_one(int))))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(demodulation,[status(thm)],[c_166,c_337,c_338,c_7367,c_7371,c_7376,c_7378]) ).
tcf(c_8612,plain,
! [X0: $i] :
( ( number_number_of(X0,number_number_of(int,number_number_of(int,plus_plus(int,one_one(int),number_number_of(int,number_number_of(int,one_one(int))))))) = plus_plus(X0,one_one(X0),one_one(X0)) )
| ~ number_ring(X0) ),
inference(demodulation,[status(thm)],[c_2293,c_337,c_338,c_7376,c_7378]) ).
tcf(c_8761,plain,
! [X0: $i,X1: $i] :
( ( times_times(X0,number_number_of(X0,number_number_of(int,number_number_of(int,plus_plus(int,one_one(int),number_number_of(int,number_number_of(int,one_one(int))))))),X1) = plus_plus(X0,X1,X1) )
| ~ number_ring(X0) ),
inference(demodulation,[status(thm)],[c_2257,c_337,c_338,c_7376,c_7378]) ).
tcf(c_9709,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),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)))) = pls,
inference(light_normalisation,[status(thm)],[c_55,c_212]) ).
tcf(c_9710,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),plus_plus(nat,one_one(nat),one_one(nat))) = pls,
inference(demodulation,[status(thm)],[c_9709,c_337,c_338,c_7367,c_7371,c_7376,c_7378,c_8292]) ).
tcf(c_10322,plain,
number_number_of(int,number_number_of(int,plus_plus(int,one_one(int),number_number_of(int,number_number_of(int,one_one(int)))))) = hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat))),
inference(demodulation,[status(thm)],[c_430,c_337,c_338,c_7367,c_7371,c_7376,c_7378,c_7410,c_8292]) ).
tcf(c_10327,plain,
! [X0: $i,X1: $i] :
( ( times_times(X0,number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat)))),X1) = plus_plus(X0,X1,X1) )
| ~ number_ring(X0) ),
inference(demodulation,[status(thm)],[c_8761,c_10322]) ).
tcf(c_10329,plain,
! [X0: $i] :
( ( number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat)))) = plus_plus(X0,one_one(X0),one_one(X0)) )
| ~ number_ring(X0) ),
inference(demodulation,[status(thm)],[c_8612,c_10322]) ).
tcf(c_11140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ti(X0,X2) = zero_zero(X0) )
| ~ linordered_idom(X0)
| ( plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,X0,power_power(X0,X2),plus_plus(nat,one_one(nat),one_one(nat)))) != zero_zero(X0) ) ),
inference(demodulation,[status(thm)],[c_990,c_337,c_338,c_909,c_7371,c_7376,c_7378,c_10322]) ).
tcf(c_11467,plain,
! [X0: $i,X1: $i] : plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),minus_minus(int,hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat))),times_times(int,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat))),times_times(int,X1,X0)))) = hAPP(nat,int,power_power(int,minus_minus(int,X1,X0)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(demodulation,[status(thm)],[c_101,c_94,c_336,c_337,c_338,c_909,c_7371,c_7376,c_7378,c_7410,c_10322]) ).
tcf(c_12085,plain,
! [X0: $i] :
( ( number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat)))) = plus_plus(X0,one_one(X0),one_one(X0)) )
| ( X0 != int ) ),
inference(resolution_lifted,[status(thm)],[c_10329,c_992]) ).
tcf(c_12086,plain,
number_number_of(int,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat)))) = plus_plus(int,one_one(int),one_one(int)),
inference(unflattening,[status(thm)],[c_12085]) ).
tcf(c_12096,plain,
! [X0: $i,X1: $i] :
( ( times_times(X0,number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat)))),X1) = plus_plus(X0,X1,X1) )
| ( X0 != int ) ),
inference(resolution_lifted,[status(thm)],[c_10327,c_992]) ).
tcf(c_12097,plain,
! [X0: $i] : times_times(int,number_number_of(int,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat)))),X0) = plus_plus(int,X0,X0),
inference(unflattening,[status(thm)],[c_12096]) ).
tcf(c_12171,plain,
! [X0: $i,X1: $i] :
( ( number_number_of(X0,plus_plus(int,X1,number_number_of(int,number_number_of(int,one_one(int))))) = plus_plus(X0,number_number_of(X0,X1),one_one(X0)) )
| ( X0 != int ) ),
inference(resolution_lifted,[status(thm)],[c_7971,c_992]) ).
tcf(c_12172,plain,
! [X0: $i] : number_number_of(int,plus_plus(int,X0,number_number_of(int,number_number_of(int,one_one(int))))) = plus_plus(int,number_number_of(int,X0),one_one(int)),
inference(unflattening,[status(thm)],[c_12171]) ).
tcf(c_13093,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ti(X0,X2) = zero_zero(X0) )
| ( X0 != int )
| ( plus_plus(X0,hAPP(nat,X0,power_power(X0,X1),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,X0,power_power(X0,X2),plus_plus(nat,one_one(nat),one_one(nat)))) != zero_zero(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_11140,c_932]) ).
tcf(c_13094,plain,
! [X0: $i,X1: $i] :
( ( ti(int,X1) = zero_zero(int) )
| ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat)))) != zero_zero(int) ) ),
inference(unflattening,[status(thm)],[c_13093]) ).
tcf(c_14223,plain,
! [X0: $i,X1: $i] :
( ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat)))) != zero_zero(int) )
| ( ti(int,X1) = zero_zero(int) ) ),
inference(prop_impl_just,[status(thm)],[c_13094]) ).
tcf(c_14224,plain,
! [X0: $i,X1: $i] :
( ( ti(int,X1) = zero_zero(int) )
| ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat)))) != zero_zero(int) ) ),
inference(renaming,[status(thm)],[c_14223]) ).
tcf(c_19103,plain,
! [X0: $i] : number_number_of(int,plus_plus(int,X0,number_number_of(int,number_number_of(int,one_one(int))))) = plus_plus(int,one_one(int),number_number_of(int,X0)),
inference(demodulation,[status(thm)],[c_12172,c_336]) ).
tcf(c_19186,plain,
! [X0: $i] : times_times(int,plus_plus(int,one_one(int),one_one(int)),X0) = plus_plus(int,X0,X0),
inference(light_normalisation,[status(thm)],[c_12097,c_12086]) ).
tcf(c_19431,plain,
hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat))) = number_number_of(int,plus_plus(int,one_one(int),number_number_of(int,one_one(int)))),
inference(demodulation,[status(thm)],[c_10322,c_19103]) ).
tcf(c_20706,plain,
! [X0: $i,X1: $i] :
( ( ti(int,X1) = pls )
| ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat)))) != pls ) ),
inference(light_normalisation,[status(thm)],[c_14224,c_212]) ).
tcf(c_20707,plain,
! [X0: $i,X1: $i] :
( ( number_number_of(int,X1) = pls )
| ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat)))) != pls ) ),
inference(demodulation,[status(thm)],[c_20706,c_68]) ).
tcf(c_21639,plain,
! [X0: $i,X1: $i] : plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),minus_minus(int,hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat))),times_times(int,number_number_of(int,plus_plus(int,one_one(int),number_number_of(int,one_one(int)))),times_times(int,X1,X0)))) = hAPP(nat,int,power_power(int,minus_minus(int,X1,X0)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(light_normalisation,[status(thm)],[c_11467,c_19431]) ).
tcf(c_31180,plain,
! [X0: $i,X1: $i] :
( ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat)))) != pls )
| ( number_number_of(int,X1) = pls ) ),
inference(prop_impl_just,[status(thm)],[c_20707]) ).
tcf(c_31181,plain,
! [X0: $i,X1: $i] :
( ( number_number_of(int,X1) = pls )
| ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat)))) != pls ) ),
inference(renaming,[status(thm)],[c_31180]) ).
tcf(c_49617,plain,
! [X0: $i] : number_number_of(int,ti(int,X0)) = ti(int,X0),
inference(superposition,[status(thm)],[c_56,c_68]) ).
tcf(c_49620,plain,
! [X0: $i] : number_number_of(int,number_number_of(int,X0)) = number_number_of(int,X0),
inference(light_normalisation,[status(thm)],[c_49617,c_68]) ).
tcf(c_49623,plain,
! [X0: $i] : times_times(int,X0,pls) = pls,
inference(superposition,[status(thm)],[c_206,c_96]) ).
tcf(c_49819,plain,
number_number_of(int,one_one(int)) = one_one(int),
inference(demodulation,[status(thm)],[c_7443,c_49620]) ).
tcf(c_51036,plain,
! [X0: $i,X1: $i] : plus_plus(int,pls,plus_plus(int,X0,X1)) = plus_plus(int,X0,number_number_of(int,X1)),
inference(superposition,[status(thm)],[c_7378,c_337]) ).
tcf(c_51037,plain,
! [X0: $i,X1: $i] : plus_plus(int,X0,plus_plus(int,X1,pls)) = plus_plus(int,X1,number_number_of(int,X0)),
inference(superposition,[status(thm)],[c_7376,c_337]) ).
tcf(c_51144,plain,
! [X0: $i,X1: $i] : plus_plus(int,pls,plus_plus(int,X0,X1)) = plus_plus(int,number_number_of(int,X0),X1),
inference(superposition,[status(thm)],[c_7378,c_338]) ).
tcf(c_51155,plain,
! [X0: $i,X1: $i] : plus_plus(int,X0,plus_plus(int,X1,pls)) = number_number_of(int,plus_plus(int,X0,X1)),
inference(superposition,[status(thm)],[c_338,c_7376]) ).
tcf(c_51180,plain,
! [X0: $i,X1: $i] : plus_plus(int,X0,number_number_of(int,X1)) = number_number_of(int,plus_plus(int,X1,X0)),
inference(light_normalisation,[status(thm)],[c_51155,c_51037]) ).
tcf(c_51181,plain,
! [X0: $i,X1: $i] : plus_plus(int,number_number_of(int,X0),X1) = plus_plus(int,X0,number_number_of(int,X1)),
inference(light_normalisation,[status(thm)],[c_51144,c_51036]) ).
tcf(c_51544,plain,
! [X0: $i,X1: $i] : plus_plus(int,X0,number_number_of(int,X1)) = plus_plus(int,X1,number_number_of(int,X0)),
inference(demodulation,[status(thm)],[c_381,c_49620,c_51180,c_51181]) ).
tcf(c_51563,plain,
! [X0: $i] : plus_plus(int,one_one(int),number_number_of(int,X0)) = plus_plus(int,X0,one_one(int)),
inference(superposition,[status(thm)],[c_49819,c_51544]) ).
tcf(c_51865,plain,
! [X0: $i,X1: $i] : plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),minus_minus(int,hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat))),times_times(int,number_number_of(int,plus_plus(int,one_one(int),one_one(int))),times_times(int,X1,X0)))) = hAPP(nat,int,power_power(int,minus_minus(int,X1,X0)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(light_normalisation,[status(thm)],[c_21639,c_49819]) ).
tcf(c_51866,plain,
! [X0: $i,X1: $i] : plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),minus_minus(int,hAPP(nat,int,power_power(int,X1),plus_plus(nat,one_one(nat),one_one(nat))),times_times(int,plus_plus(int,one_one(int),one_one(int)),times_times(int,X1,X0)))) = hAPP(nat,int,power_power(int,minus_minus(int,X1,X0)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(demodulation,[status(thm)],[c_51865,c_51180,c_51563]) ).
tcf(c_51870,plain,
! [X0: $i] : plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),minus_minus(int,pls,times_times(int,plus_plus(int,one_one(int),one_one(int)),times_times(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)),X0)))) = hAPP(nat,int,power_power(int,minus_minus(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)),X0)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(superposition,[status(thm)],[c_9710,c_51866]) ).
tcf(c_52245,plain,
plus_plus(int,hAPP(nat,int,power_power(int,pls),plus_plus(nat,one_one(nat),one_one(nat))),minus_minus(int,pls,times_times(int,plus_plus(int,one_one(int),one_one(int)),pls))) = hAPP(nat,int,power_power(int,minus_minus(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)),pls)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(superposition,[status(thm)],[c_49623,c_51870]) ).
tcf(c_52339,plain,
number_number_of(int,hAPP(nat,int,power_power(int,pls),plus_plus(nat,one_one(nat),one_one(nat)))) = pls,
inference(demodulation,[status(thm)],[c_52245,c_336,c_7348,c_7375,c_7376,c_7378,c_9710,c_19186,c_51180,c_51544,c_51563]) ).
tcf(c_61197,plain,
! [X0: $i] :
( ( number_number_of(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = pls )
| ( plus_plus(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat))),pls) != pls ) ),
inference(superposition,[status(thm)],[c_9710,c_31181]) ).
tcf(c_61620,plain,
! [X0: $i] :
( ( plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)) = pls )
| ( number_number_of(int,hAPP(nat,int,power_power(int,X0),plus_plus(nat,one_one(nat),one_one(nat)))) != pls ) ),
inference(demodulation,[status(thm)],[c_61197,c_336,c_7376,c_51180,c_51544,c_51563]) ).
tcf(c_61627,plain,
plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)) = pls,
inference(superposition,[status(thm)],[c_52339,c_61620]) ).
tcf(c_62569,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(light_normalisation,[status(thm)],[c_7862,c_61627]) ).
tcf(c_62570,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_62569,c_217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n014.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 05:44:08 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 49.81/12.90 % SZS status Started for theBenchmark.p
% 49.81/12.90 ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 49.81/12.90 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 49.81/12.90 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_98iccq_h/8g2g8obg 2>> /export/starexec/sandbox/tmp/iprover_out_98iccq_h/8g2g8obg_error
% 49.81/12.90 % SZS status Theorem for theBenchmark.p
% 49.81/12.90
% 49.81/12.90 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 49.81/12.90
% 49.81/12.90 % ------ iProver source info
% 49.81/12.90
% 49.81/12.90 % git: date: 2026-07-19 20:42:38 +0200
% 49.81/12.90 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 49.81/12.90 % git: non_committed_changes: false
% 49.81/12.90
% 49.81/12.90 % ------ Parsing...
% 49.81/12.90 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 49.81/12.90
% 49.81/12.90 % ------ Preprocessing... sup_sim: 366 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 111 sf_s rm: 3 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 49.81/12.90
% 49.81/12.90 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 49.81/12.90
% 49.81/12.90 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 49.81/12.90 % ------ Proving...
% 49.81/12.90 % ------ Problem Properties
% 49.81/12.90
% 49.81/12.90 %
% 49.81/12.90 % clauses 775
% 49.81/12.90 % conjectures 0
% 49.81/12.90 % EPR 1
% 49.81/12.90 % Horn 674
% 49.81/12.90 % unary 225
% 49.81/12.90 % binary 325
% 49.81/12.90 % lits 1627
% 49.81/12.90 % lits eq 401
% 49.81/12.90 % fd_pure 0
% 49.81/12.90 % fd_pseudo 0
% 49.81/12.90 % fd_cond 34
% 49.81/12.90 % fd_pseudo_cond 20
% 49.81/12.90 % AC symbols 0
% 49.81/12.90
% 49.81/12.90 % ------ Schedule dynamic 5 is on
% 49.81/12.90
% 49.81/12.90 % ------ no conjectures: strip conj schedule
% 49.81/12.90
% 49.81/12.90 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 49.81/12.90
% 49.81/12.90
% 49.81/12.90 % ------
% 49.81/12.90 % Current options:
% 49.81/12.90 % ------
% 49.81/12.90
% 49.81/12.90
% 49.81/12.90 %
% 49.81/12.90
% 49.81/12.90 % ------ Proving...
% 49.81/12.90 %
% 49.81/12.90
% 49.81/12.90 % SZS status Theorem for theBenchmark.p
% 49.81/12.90
% 49.81/12.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.81/12.91
% 49.81/12.91
%------------------------------------------------------------------------------