%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM924+2 : 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 : n011.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 02:27:15 PM UTC 2026
% Result : Theorem 7.44s 1.62s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 120 ( 113 unt; 0 def)
% Number of atoms : 134 ( 99 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 36 ( 22 ~; 10 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 113 !; 0 ?; 38 :)
% 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(f53,axiom,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
fof(f59,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_41_zmult__assoc) ).
fof(f105,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_87_nat__1__add__1) ).
fof(f148,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_130_zadd__assoc) ).
fof(f150,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
fof(f180,axiom,
! [X0] :
( is_int(X0)
=> ( plus_plus_int(X0,X0) = zero_zero_int
<=> X0 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_double__eq__0__iff) ).
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(f198,axiom,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
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(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(f332,axiom,
! [X0,X1,X2] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f333,axiom,
! [X0,X1,X2] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f341,axiom,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f342,axiom,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f344,axiom,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f345,axiom,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f350,axiom,
! [X0,X1,X2] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f351,axiom,
! [X0,X1,X2] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_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(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(f810,plain,
! [X0] :
( ~ is_int(X0)
| ( plus_plus_int(X0,X0) = zero_zero_int
<=> X0 = zero_zero_int ) ),
inference(ennf_transformation,[],[f180]) ).
fof(f1196,plain,
! [X0] :
( ~ is_int(X0)
| ( ( zero_zero_int != plus_plus_int(X0,X0)
| X0 = zero_zero_int )
& ( zero_zero_int != X0
| plus_plus_int(X0,X0) = zero_zero_int ) ) ),
inference(nnf_transformation,[],[f810]) ).
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(f1392,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f1401,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,[],[f59]) ).
fof(f1476,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f105]) ).
fof(f1545,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,[],[f148]) ).
fof(f1547,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f150]) ).
fof(f1589,plain,
! [X0] :
( ~ is_int(X0)
| zero_zero_int != X0
| zero_zero_int = plus_plus_int(X0,X0) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1598,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f187]) ).
fof(f1599,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f188]) ).
fof(f1613,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f198]) ).
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(f1678,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f252]) ).
fof(f1784,plain,
! [X2,X0,X1] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
inference(cnf_transformation,[],[f332]) ).
fof(f1785,plain,
! [X2,X0,X1] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f333]) ).
fof(f1793,plain,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(cnf_transformation,[],[f341]) ).
fof(f1794,plain,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(cnf_transformation,[],[f342]) ).
fof(f1796,plain,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(cnf_transformation,[],[f344]) ).
fof(f1797,plain,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(cnf_transformation,[],[f345]) ).
fof(f1802,plain,
! [X2,X0,X1] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2),
inference(cnf_transformation,[],[f350]) ).
fof(f1803,plain,
! [X2,X0,X1] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2),
inference(cnf_transformation,[],[f351]) ).
fof(f1836,plain,
! [X0] : zero_zero_int = times_times_int(X0,zero_zero_int),
inference(cnf_transformation,[],[f380]) ).
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(f2362,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,[],[f1476,f1613,f1678]) ).
fof(f2422,plain,
! [X0] :
( ~ is_int(X0)
| pls != X0
| pls = plus_plus_int(X0,X0) ),
inference(definition_unfolding,[],[f1589,f1599,f1599]) ).
fof(f2432,plain,
pls = plus_plus_int(pls,pls),
inference(definition_unfolding,[],[f1598,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(f2560,plain,
! [X0] : pls = times_times_int(X0,pls),
inference(definition_unfolding,[],[f1836,f1599,f1599]) ).
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(f2736,plain,
( ~ is_int(pls)
| pls = plus_plus_int(pls,pls) ),
inference(equality_resolution,[],[f2422]) ).
tcf(c_68,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(cnf_transformation,[],[f2286]) ).
tcf(c_69,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(cnf_transformation,[],[f2287]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f1392]) ).
tcf(c_123,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,[],[f1401]) ).
tcf(c_198,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,[],[f2362]) ).
tcf(c_260,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,[],[f1545]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f1547]) ).
tcf(c_303,plain,
( ( plus_plus_int(pls,pls) = pls )
| ~ is_int(pls) ),
inference(cnf_transformation,[],[f2736]) ).
tcf(c_313,plain,
plus_plus_int(pls,pls) = pls,
inference(cnf_transformation,[],[f2432]) ).
tcf(c_347,plain,
! [X0: $i] : 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(X0,X0),
inference(cnf_transformation,[],[f2462]) ).
tcf(c_496,plain,
! [X0: $i,X1: $i,X2: $i] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X1,X2)),
inference(cnf_transformation,[],[f1784]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i,X2: $i] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f1785]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(cnf_transformation,[],[f1793]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(cnf_transformation,[],[f1794]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(cnf_transformation,[],[f1796]) ).
tcf(c_509,plain,
! [X0: $i,X1: $i] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(cnf_transformation,[],[f1797]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(X0,plus_plus_real(X1,X2)),
inference(cnf_transformation,[],[f1802]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(X0,plus_plus_nat(X1,X2)),
inference(cnf_transformation,[],[f1803]) ).
tcf(c_548,plain,
! [X0: $i] : times_times_int(X0,pls) = pls,
inference(cnf_transformation,[],[f2560]) ).
tcf(c_984,negated_conjecture,
~ 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(cnf_transformation,[],[f2693]) ).
tcf(c_1467,plain,
plus_plus_int(pls,pls) = pls,
inference(global_subsumption_just,[status(thm)],[c_303,c_313]) ).
tcf(c_1515,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int))))))))))))))),times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))))))))))),
inference(theory_normalisation,[status(thm)],[c_68,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
tcf(c_1516,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_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)))))))),
inference(theory_normalisation,[status(thm)],[c_69,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
tcf(c_1566,plain,
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)))))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(theory_normalisation,[status(thm)],[c_198,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
tcf(c_1616,plain,
! [X0: $i] : 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))))))) = times_times_int(X0,X0),
inference(theory_normalisation,[status(thm)],[c_347,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
tcf(c_1721,negated_conjecture,
~ 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(theory_normalisation,[status(thm)],[c_984,c_497,c_506,c_496,c_505,c_515,c_509,c_514,c_508,c_123,c_114,c_260,c_262]) ).
tcf(c_7805,plain,
number_number_of_nat(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(ac_demodulation,[status(thm)],[c_1566,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_7806,plain,
number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(ac_demodulation,[status(thm)],[c_7805,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_7807,plain,
number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(ac_demodulation,[status(thm)],[c_7806,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_7808,plain,
number_number_of_nat(plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(theory_normalisation,[status(thm)],[c_7807,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8039,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(one_one_int,pls))))))),pls),
inference(ac_demodulation,[status(thm)],[c_1721,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8040,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))),pls),
inference(ac_demodulation,[status(thm)],[c_8039,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8041,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))),pls),
inference(ac_demodulation,[status(thm)],[c_8040,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8042,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(one_one_int,one_one_int))))),pls),
inference(theory_normalisation,[status(thm)],[c_8041,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8043,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(light_normalisation,[status(thm)],[c_8042,c_7808]) ).
tcf(c_8056,plain,
! [X0: $i] : 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,pls)))))) = times_times_int(X0,X0),
inference(ac_demodulation,[status(thm)],[c_1616,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8057,plain,
! [X0: $i] : power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))) = times_times_int(X0,X0),
inference(ac_demodulation,[status(thm)],[c_8056,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8058,plain,
! [X0: $i] : power_power_int(X0,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))) = times_times_int(X0,X0),
inference(ac_demodulation,[status(thm)],[c_8057,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8059,plain,
! [X0: $i] : power_power_int(X0,number_number_of_nat(plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int)))) = times_times_int(X0,X0),
inference(theory_normalisation,[status(thm)],[c_8058,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_8060,plain,
! [X0: $i] : power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)) = times_times_int(X0,X0),
inference(light_normalisation,[status(thm)],[c_8059,c_7808]) ).
tcf(c_8062,plain,
~ ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(demodulation,[status(thm)],[c_8043,c_8060]) ).
tcf(c_9234,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))))))))))) = 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(one_one_int,pls))))))),
inference(ac_demodulation,[status(thm)],[c_1516,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9235,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))))),
inference(ac_demodulation,[status(thm)],[c_9234,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9236,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,pls)))))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))),
inference(ac_demodulation,[status(thm)],[c_9235,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9237,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,pls))))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))),
inference(ac_demodulation,[status(thm)],[c_9236,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9238,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,pls)))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))),
inference(ac_demodulation,[status(thm)],[c_9237,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9239,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))),
inference(ac_demodulation,[status(thm)],[c_9238,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9240,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))),
inference(ac_demodulation,[status(thm)],[c_9239,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9241,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(plus_plus_int(pls,plus_plus_int(one_one_int,one_one_int))))),
inference(theory_normalisation,[status(thm)],[c_9240,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9242,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),
inference(light_normalisation,[status(thm)],[c_9241,c_7808]) ).
tcf(c_9243,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))) = plus_plus_int(one_one_int,times_times_int(s,s)),
inference(demodulation,[status(thm)],[c_9242,c_8060]) ).
tcf(c_9289,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_1515,c_548,c_1467,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9290,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9289,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9291,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,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(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,pls)))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9290,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9292,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,pls))))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9291,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9293,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,pls)))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9292,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9294,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,pls))))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9293,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9295,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls)))))))),pls),
inference(ac_demodulation,[status(thm)],[c_9294,c_1467,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9296,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(plus_plus_int(pls,plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int)))))))),pls),
inference(theory_normalisation,[status(thm)],[c_9295,c_260,c_262,c_123,c_114,c_514,c_508,c_515,c_509,c_496,c_505,c_497,c_506]) ).
tcf(c_9297,plain,
ord_less_int(plus_plus_int(one_one_int,times_times_int(s,s)),pls),
inference(light_normalisation,[status(thm)],[c_9296,c_9243]) ).
tcf(c_9298,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9297,c_8062]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 05:41:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 7.44/1.62 % SZS status Started for theBenchmark.p
% 7.44/1.62 % SZS status Theorem for theBenchmark.p
% 7.44/1.62
% 7.44/1.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.44/1.62
% 7.44/1.62 % ------ iProver source info
% 7.44/1.62
% 7.44/1.62 % git: date: 2026-07-19 20:42:38 +0200
% 7.44/1.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.44/1.62 % git: non_committed_changes: false
% 7.44/1.62
% 7.44/1.62 % ------ Parsing...
% 7.44/1.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.44/1.62
% 7.44/1.62 % ------ Preprocessing...%
% 7.44/1.62
% 7.44/1.62 % SZS status Theorem for theBenchmark.p
% 7.44/1.62
% 7.44/1.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.44/1.62
% 7.44/1.62
%------------------------------------------------------------------------------