TSTP Solution File: NUM924+7 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM924+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:33:41 EDT 2023
% Result : Theorem 10.45s 2.20s
% Output : CNFRefutation 10.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 100 ( 100 unt; 0 def)
% Number of atoms : 100 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 19 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 8 con; 0-5 aty)
% Number of variables : 103 ( 1 sgn; 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
! [X3] : bit0(ti(int,X3)) = bit0(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(f54,axiom,
min = ti(int,min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OMin_res) ).
fof(f100,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,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(f101,axiom,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(f120,axiom,
! [X14] : number_number_of(int,X14) = ti(int,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(f121,axiom,
! [X15,X11] : hAPP(int,int,times_times(int,X15),X11) = hAPP(int,int,times_times(int,X11),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(f159,axiom,
number_number_of(nat,bit0(bit1(pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__1__add__1) ).
fof(f160,axiom,
! [X11] : pls = hAPP(int,int,times_times(int,pls),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(f165,axiom,
! [X12,X11] : hAPP(int,int,plus_plus(int,number_number_of(int,X12)),number_number_of(int,X11)) = number_number_of(int,hAPP(int,int,plus_plus(int,X12),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_plus__numeral__code_I9_J) ).
fof(f194,axiom,
! [X18,X19,X20] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X18),X19)),X20) = hAPP(int,int,plus_plus(int,X18),hAPP(int,int,plus_plus(int,X19),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_zadd__assoc) ).
fof(f195,axiom,
! [X5,X6,X15] : hAPP(int,int,plus_plus(int,X5),hAPP(int,int,plus_plus(int,X6),X15)) = hAPP(int,int,plus_plus(int,X6),hAPP(int,int,plus_plus(int,X5),X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zadd__left__commute) ).
fof(f196,axiom,
! [X15,X11] : hAPP(int,int,plus_plus(int,X11),X15) = hAPP(int,int,plus_plus(int,X15),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zadd__commute) ).
fof(f220,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Pls__def) ).
fof(f227,axiom,
! [X14] : ti(int,X14) = hAPP(int,int,plus_plus(int,X14),pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_add__Pls__right) ).
fof(f228,axiom,
! [X14] : ti(int,X14) = hAPP(int,int,plus_plus(int,pls),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_add__Pls) ).
fof(f230,axiom,
! [X14] : bit0(X14) = hAPP(int,int,plus_plus(int,X14),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Bit0__def) ).
fof(f262,axiom,
! [X14] : bit1(X14) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X14)),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Bit1__def) ).
fof(f564,axiom,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
fof(f849,axiom,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
fof(f1250,axiom,
! [X2,X1,X0,X99,X100,X101] : hAPP(X2,X1,combc(X2,X0,X1,X99,X100),X101) = hAPP(X0,X1,hAPP(X2,fun(X0,X1),X99,X101),X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
fof(f1255,conjecture,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,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(f1256,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(negated_conjecture,[],[f1255]) ).
fof(f1303,plain,
! [X0] : bit0(ti(int,X0)) = bit0(X0),
inference(rectify,[],[f50]) ).
fof(f1355,plain,
! [X0] : ti(int,X0) = number_number_of(int,X0),
inference(rectify,[],[f120]) ).
fof(f1356,plain,
! [X0,X1] : hAPP(int,int,times_times(int,X0),X1) = hAPP(int,int,times_times(int,X1),X0),
inference(rectify,[],[f121]) ).
fof(f1391,plain,
! [X0] : pls = hAPP(int,int,times_times(int,pls),X0),
inference(rectify,[],[f160]) ).
fof(f1396,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,number_number_of(int,X0)),number_number_of(int,X1)) = number_number_of(int,hAPP(int,int,plus_plus(int,X0),X1)),
inference(rectify,[],[f165]) ).
fof(f1423,plain,
! [X0,X1,X2] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X0),X1)),X2) = hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)),
inference(rectify,[],[f194]) ).
fof(f1424,plain,
! [X0,X1,X2] : hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)) = hAPP(int,int,plus_plus(int,X1),hAPP(int,int,plus_plus(int,X0),X2)),
inference(rectify,[],[f195]) ).
fof(f1425,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,X0),X1) = hAPP(int,int,plus_plus(int,X1),X0),
inference(rectify,[],[f196]) ).
fof(f1450,plain,
! [X0] : ti(int,X0) = hAPP(int,int,plus_plus(int,X0),pls),
inference(rectify,[],[f227]) ).
fof(f1451,plain,
! [X0] : ti(int,X0) = hAPP(int,int,plus_plus(int,pls),X0),
inference(rectify,[],[f228]) ).
fof(f1453,plain,
! [X0] : bit0(X0) = hAPP(int,int,plus_plus(int,X0),X0),
inference(rectify,[],[f230]) ).
fof(f1483,plain,
! [X0] : bit1(X0) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X0)),X0),
inference(rectify,[],[f262]) ).
fof(f2287,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(X0,X1,combc(X0,X2,X1,X3,X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),X4),
inference(rectify,[],[f1250]) ).
fof(f2292,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(flattening,[],[f1256]) ).
fof(f3777,plain,
! [X0] : bit0(ti(int,X0)) = bit0(X0),
inference(cnf_transformation,[],[f1303]) ).
fof(f3781,plain,
min = ti(int,min),
inference(cnf_transformation,[],[f54]) ).
fof(f3828,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))),
inference(cnf_transformation,[],[f100]) ).
fof(f3829,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
inference(cnf_transformation,[],[f101]) ).
fof(f3854,plain,
! [X0] : ti(int,X0) = number_number_of(int,X0),
inference(cnf_transformation,[],[f1355]) ).
fof(f3855,plain,
! [X0,X1] : hAPP(int,int,times_times(int,X0),X1) = hAPP(int,int,times_times(int,X1),X0),
inference(cnf_transformation,[],[f1356]) ).
fof(f3916,plain,
number_number_of(nat,bit0(bit1(pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
inference(cnf_transformation,[],[f159]) ).
fof(f3917,plain,
! [X0] : pls = hAPP(int,int,times_times(int,pls),X0),
inference(cnf_transformation,[],[f1391]) ).
fof(f3923,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,number_number_of(int,X0)),number_number_of(int,X1)) = number_number_of(int,hAPP(int,int,plus_plus(int,X0),X1)),
inference(cnf_transformation,[],[f1396]) ).
fof(f3973,plain,
! [X2,X0,X1] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X0),X1)),X2) = hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)),
inference(cnf_transformation,[],[f1423]) ).
fof(f3974,plain,
! [X2,X0,X1] : hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)) = hAPP(int,int,plus_plus(int,X1),hAPP(int,int,plus_plus(int,X0),X2)),
inference(cnf_transformation,[],[f1424]) ).
fof(f3975,plain,
! [X0,X1] : hAPP(int,int,plus_plus(int,X0),X1) = hAPP(int,int,plus_plus(int,X1),X0),
inference(cnf_transformation,[],[f1425]) ).
fof(f4008,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f220]) ).
fof(f4019,plain,
! [X0] : ti(int,X0) = hAPP(int,int,plus_plus(int,X0),pls),
inference(cnf_transformation,[],[f1450]) ).
fof(f4020,plain,
! [X0] : ti(int,X0) = hAPP(int,int,plus_plus(int,pls),X0),
inference(cnf_transformation,[],[f1451]) ).
fof(f4022,plain,
! [X0] : bit0(X0) = hAPP(int,int,plus_plus(int,X0),X0),
inference(cnf_transformation,[],[f1453]) ).
fof(f4063,plain,
! [X0] : bit1(X0) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X0)),X0),
inference(cnf_transformation,[],[f1483]) ).
fof(f4465,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),
inference(cnf_transformation,[],[f564]) ).
fof(f4923,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(cnf_transformation,[],[f849]) ).
fof(f5419,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(X0,X1,combc(X0,X2,X1,X3,X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),X4),
inference(cnf_transformation,[],[f2287]) ).
fof(f5424,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(cnf_transformation,[],[f2292]) ).
fof(f5426,plain,
! [X0] : hAPP(int,int,plus_plus(int,X0),X0) = hAPP(int,int,plus_plus(int,ti(int,X0)),ti(int,X0)),
inference(definition_unfolding,[],[f3777,f4022,f4022]) ).
fof(f5437,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),zero_zero(int)))),
inference(definition_unfolding,[],[f3828,f4022,f4022,f4063,f4022,f4022,f4063]) ).
fof(f5438,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),t) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int)),
inference(definition_unfolding,[],[f3829,f4022,f4022,f4063,f4022,f4063]) ).
fof(f5483,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),
inference(definition_unfolding,[],[f3916,f4022,f4063]) ).
fof(f5631,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),number_number_of(int,min)),
inference(definition_unfolding,[],[f4465,f4022,f4063,f4022,f4063]) ).
fof(f5656,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),t),
inference(definition_unfolding,[],[f4923,f4022,f4022,f4063]) ).
fof(f5690,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int))),zero_zero(int))),
inference(definition_unfolding,[],[f5424,f4022,f4063]) ).
cnf(c_98,plain,
hAPP(int,int,plus_plus(int,ti(int,X0)),ti(int,X0)) = hAPP(int,int,plus_plus(int,X0),X0),
inference(cnf_transformation,[],[f5426]) ).
cnf(c_102,plain,
ti(int,min) = min,
inference(cnf_transformation,[],[f3781]) ).
cnf(c_149,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),zero_zero(int)))),
inference(cnf_transformation,[],[f5437]) ).
cnf(c_150,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),t) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int)),
inference(cnf_transformation,[],[f5438]) ).
cnf(c_175,plain,
ti(int,X0) = number_number_of(int,X0),
inference(cnf_transformation,[],[f3854]) ).
cnf(c_176,plain,
hAPP(int,int,times_times(int,X0),X1) = hAPP(int,int,times_times(int,X1),X0),
inference(cnf_transformation,[],[f3855]) ).
cnf(c_237,plain,
number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
inference(cnf_transformation,[],[f5483]) ).
cnf(c_238,plain,
hAPP(int,int,times_times(int,pls),X0) = pls,
inference(cnf_transformation,[],[f3917]) ).
cnf(c_244,plain,
hAPP(int,int,plus_plus(int,number_number_of(int,X0)),number_number_of(int,X1)) = number_number_of(int,hAPP(int,int,plus_plus(int,X0),X1)),
inference(cnf_transformation,[],[f3923]) ).
cnf(c_290,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X0),X1)),X2) = hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)),
inference(cnf_transformation,[],[f3973]) ).
cnf(c_291,plain,
hAPP(int,int,plus_plus(int,X0),hAPP(int,int,plus_plus(int,X1),X2)) = hAPP(int,int,plus_plus(int,X1),hAPP(int,int,plus_plus(int,X0),X2)),
inference(cnf_transformation,[],[f3974]) ).
cnf(c_292,plain,
hAPP(int,int,plus_plus(int,X0),X1) = hAPP(int,int,plus_plus(int,X1),X0),
inference(cnf_transformation,[],[f3975]) ).
cnf(c_325,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f4008]) ).
cnf(c_336,plain,
hAPP(int,int,plus_plus(int,X0),pls) = ti(int,X0),
inference(cnf_transformation,[],[f4019]) ).
cnf(c_337,plain,
hAPP(int,int,plus_plus(int,pls),X0) = ti(int,X0),
inference(cnf_transformation,[],[f4020]) ).
cnf(c_779,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int)),
inference(cnf_transformation,[],[f5631]) ).
cnf(c_1193,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(cnf_transformation,[],[f5656]) ).
cnf(c_1671,plain,
hAPP(X0,X1,hAPP(X2,fun(X0,X1),X3,X4),X5) = hAPP(X2,X1,combc(X2,X0,X1,X3,X5),X4),
inference(cnf_transformation,[],[f5419]) ).
cnf(c_1676,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int))),zero_zero(int))),
inference(cnf_transformation,[],[f5690]) ).
cnf(c_12634,plain,
number_number_of(int,min) = min,
inference(demodulation,[status(thm)],[c_102,c_175]) ).
cnf(c_12703,plain,
hAPP(int,int,plus_plus(int,pls),X0) = number_number_of(int,X0),
inference(light_normalisation,[status(thm)],[c_337,c_175]) ).
cnf(c_12705,plain,
hAPP(int,int,plus_plus(int,X0),pls) = number_number_of(int,X0),
inference(light_normalisation,[status(thm)],[c_336,c_175]) ).
cnf(c_13200,plain,
hAPP(int,int,plus_plus(int,number_number_of(int,X0)),number_number_of(int,X0)) = hAPP(int,int,plus_plus(int,X0),X0),
inference(light_normalisation,[status(thm)],[c_98,c_175]) ).
cnf(c_13333,plain,
number_number_of(int,hAPP(int,int,plus_plus(int,X0),X0)) = hAPP(int,int,plus_plus(int,X0),X0),
inference(demodulation,[status(thm)],[c_13200,c_244]) ).
cnf(c_16462,plain,
number_number_of(nat,number_number_of(int,number_number_of(int,hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,number_number_of(int,one_one(int))))))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
inference(demodulation,[status(thm)],[c_237,c_290,c_291,c_12703,c_12705]) ).
cnf(c_18137,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int))),pls)),
inference(light_normalisation,[status(thm)],[c_1676,c_325]) ).
cnf(c_18138,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))))),
inference(demodulation,[status(thm)],[c_18137,c_290,c_291,c_292,c_1671,c_12703,c_12705,c_16462]) ).
cnf(c_19121,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),one_one(int)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),min),
inference(light_normalisation,[status(thm)],[c_779,c_12634]) ).
cnf(c_19122,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min),
inference(demodulation,[status(thm)],[c_19121,c_290,c_291,c_292,c_12703,c_12705,c_16462]) ).
cnf(c_19123,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min))),
inference(demodulation,[status(thm)],[c_18138,c_19122]) ).
cnf(c_19136,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,number_number_of(int,hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,number_number_of(int,hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,number_number_of(int,hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,number_number_of(int,one_one(int))))))))))))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(demodulation,[status(thm)],[c_1193,c_176,c_290,c_291,c_292,c_12703,c_12705,c_13333]) ).
cnf(c_19386,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),min) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(demodulation,[status(thm)],[c_150,c_176,c_290,c_291,c_292,c_12703,c_12705,c_13333,c_16462,c_19122,c_19136]) ).
cnf(c_19388,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))),
inference(demodulation,[status(thm)],[c_19123,c_19386]) ).
cnf(c_19467,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls)),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),pls)),pls))))),m)),one_one(int))),pls))),
inference(light_normalisation,[status(thm)],[c_149,c_325]) ).
cnf(c_19468,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))),
inference(demodulation,[status(thm)],[c_19467,c_176,c_238,c_290,c_291,c_292,c_1671,c_12703,c_12705,c_13333,c_19136]) ).
cnf(c_19469,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_19468,c_19388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM924+7 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 09:29:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.45/2.20 % SZS status Started for theBenchmark.p
% 10.45/2.20 % SZS status Theorem for theBenchmark.p
% 10.45/2.20
% 10.45/2.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.45/2.20
% 10.45/2.20 ------ iProver source info
% 10.45/2.20
% 10.45/2.20 git: date: 2023-05-31 18:12:56 +0000
% 10.45/2.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.45/2.20 git: non_committed_changes: false
% 10.45/2.20 git: last_make_outside_of_git: false
% 10.45/2.20
% 10.45/2.20 ------ Parsing...
% 10.45/2.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.45/2.20
% 10.45/2.20 ------ Preprocessing...
% 10.45/2.20
% 10.45/2.20 % SZS status Theorem for theBenchmark.p
% 10.45/2.20
% 10.45/2.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.45/2.20
% 10.45/2.20
%------------------------------------------------------------------------------