TSTP Solution File: NUM924+8 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 131.34s 20.33s
% Output : CNFRefutation 131.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 81 unt; 0 def)
% Number of atoms : 81 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 13 con; 0-4 aty)
% Number of variables : 64 ( 1 sgn; 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f275,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),
file('/export/starexec/sandbox2/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(f276,axiom,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
fof(f295,axiom,
! [X14] : hAPP(int,int,number_number_of(int),X14) = ti(int,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(f296,axiom,
! [X15,X11] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X15),X11) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X11),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(f335,axiom,
! [X11] : pls = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(f396,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Pls__def) ).
fof(f752,axiom,
! [X14] : ti(int,X14) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X14),pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_diff__bin__simps_I1_J) ).
fof(f1009,axiom,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),s),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
fof(f1385,axiom,
! [X12] : hAPP(int,nat,number_number_of(nat),X12) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_nat__number__of__def) ).
fof(f1603,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1330_One__nat__def) ).
fof(f1699,axiom,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1426_numeral__2__eq__2) ).
fof(f1801,axiom,
! [X14] : hAPP(int,int,succ,X14) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X14),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1528_succ__def) ).
fof(f4531,axiom,
! [X79] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X79)) = hAPP(int,nat,nat_1,X79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4258_card__atLeastZeroLessThan__int) ).
fof(f4532,axiom,
! [X17,X79] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X17),X79)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X79),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4259_card__atLeastLessThan__int) ).
fof(f5060,axiom,
! [X0,X7] : ti(X0,X7) = hAPP(fun(X0,bool),X0,hilbert_Eps(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4787_some__eq__trivial) ).
fof(f5720,axiom,
! [X0,X227] : hAPP(X0,X0,combi(X0),X227) = ti(X0,X227),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(f5738,conjecture,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5739,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(negated_conjecture,[],[f5738]) ).
fof(f5761,plain,
! [X0] : hAPP(int,int,number_number_of(int),X0) = ti(int,X0),
inference(rectify,[],[f295]) ).
fof(f5762,plain,
! [X0,X1] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X0),X1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X0),
inference(rectify,[],[f296]) ).
fof(f5797,plain,
! [X0] : pls = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X0),
inference(rectify,[],[f335]) ).
fof(f6162,plain,
! [X0] : ti(int,X0) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),pls),
inference(rectify,[],[f752]) ).
fof(f6790,plain,
! [X0] : hAPP(int,nat,number_number_of(nat),X0) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X0)),
inference(rectify,[],[f1385]) ).
fof(f7175,plain,
! [X0] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),one_one(int)) = hAPP(int,int,succ,X0),
inference(rectify,[],[f1801]) ).
fof(f9728,plain,
! [X0] : hAPP(int,nat,nat_1,X0) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X0)),
inference(rectify,[],[f4531]) ).
fof(f9729,plain,
! [X0,X1] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X0),X1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X0)),
inference(rectify,[],[f4532]) ).
fof(f10249,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,hilbert_Eps(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(rectify,[],[f5060]) ).
fof(f10469,plain,
! [X0,X1] : ti(X0,X1) = hAPP(X0,X0,combi(X0),X1),
inference(rectify,[],[f5720]) ).
fof(f10485,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(flattening,[],[f5739]) ).
fof(f18306,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),
inference(cnf_transformation,[],[f275]) ).
fof(f18307,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),
inference(cnf_transformation,[],[f276]) ).
fof(f18332,plain,
! [X0] : hAPP(int,int,number_number_of(int),X0) = ti(int,X0),
inference(cnf_transformation,[],[f5761]) ).
fof(f18333,plain,
! [X0,X1] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X0),X1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X0),
inference(cnf_transformation,[],[f5762]) ).
fof(f18395,plain,
! [X0] : pls = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X0),
inference(cnf_transformation,[],[f5797]) ).
fof(f18487,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f396]) ).
fof(f18961,plain,
! [X0] : ti(int,X0) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),pls),
inference(cnf_transformation,[],[f6162]) ).
fof(f19372,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),s),one_one(int))),
inference(cnf_transformation,[],[f1009]) ).
fof(f19911,plain,
! [X0] : hAPP(int,nat,number_number_of(nat),X0) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X0)),
inference(cnf_transformation,[],[f6790]) ).
fof(f20246,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(cnf_transformation,[],[f1603]) ).
fof(f20390,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
inference(cnf_transformation,[],[f1699]) ).
fof(f20558,plain,
! [X0] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),one_one(int)) = hAPP(int,int,succ,X0),
inference(cnf_transformation,[],[f7175]) ).
fof(f24494,plain,
! [X0] : hAPP(int,nat,nat_1,X0) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X0)),
inference(cnf_transformation,[],[f9728]) ).
fof(f24495,plain,
! [X0,X1] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X0),X1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X0)),
inference(cnf_transformation,[],[f9729]) ).
fof(f25371,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,hilbert_Eps(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(cnf_transformation,[],[f10249]) ).
fof(f26167,plain,
! [X0,X1] : ti(X0,X1) = hAPP(X0,X0,combi(X0),X1),
inference(cnf_transformation,[],[f10469]) ).
fof(f26185,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(cnf_transformation,[],[f10485]) ).
fof(f26469,plain,
! [X0] : hAPP(int,int,number_number_of(int),X0) = hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),X0)),
inference(definition_unfolding,[],[f18332,f25371]) ).
fof(f26584,plain,
! [X0] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),pls) = hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),X0)),
inference(definition_unfolding,[],[f18961,f25371]) ).
fof(f27359,plain,
! [X0,X1] : hAPP(fun(X0,bool),X0,hilbert_Eps(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) = hAPP(X0,X0,combi(X0),X1),
inference(definition_unfolding,[],[f26167,f25371]) ).
cnf(c_324,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),
inference(cnf_transformation,[],[f18306]) ).
cnf(c_325,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),
inference(cnf_transformation,[],[f18307]) ).
cnf(c_350,plain,
hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),X0)) = hAPP(int,int,number_number_of(int),X0),
inference(cnf_transformation,[],[f26469]) ).
cnf(c_351,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X0),X1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X0),
inference(cnf_transformation,[],[f18333]) ).
cnf(c_413,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X0) = pls,
inference(cnf_transformation,[],[f18395]) ).
cnf(c_502,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f18487]) ).
cnf(c_975,plain,
hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),X0)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),pls),
inference(cnf_transformation,[],[f26584]) ).
cnf(c_1344,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),s),one_one(int))),
inference(cnf_transformation,[],[f19372]) ).
cnf(c_1865,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X0)) = hAPP(int,nat,number_number_of(nat),X0),
inference(cnf_transformation,[],[f19911]) ).
cnf(c_2189,plain,
hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat),
inference(cnf_transformation,[],[f20246]) ).
cnf(c_2331,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
inference(cnf_transformation,[],[f20390]) ).
cnf(c_2495,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),one_one(int)) = hAPP(int,int,succ,X0),
inference(cnf_transformation,[],[f20558]) ).
cnf(c_6379,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X0)) = hAPP(int,nat,nat_1,X0),
inference(cnf_transformation,[],[f24494]) ).
cnf(c_6380,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X0),X1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),X0)),
inference(cnf_transformation,[],[f24495]) ).
cnf(c_8050,plain,
hAPP(fun(X0,bool),X0,hilbert_Eps(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) = hAPP(X0,X0,combi(X0),X1),
inference(cnf_transformation,[],[f27359]) ).
cnf(c_8068,negated_conjecture,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(cnf_transformation,[],[f26185]) ).
cnf(c_68541,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)),
inference(light_normalisation,[status(thm)],[c_2331,c_2189]) ).
cnf(c_69794,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),pls),X0)) = hAPP(int,nat,nat_1,X0),
inference(light_normalisation,[status(thm)],[c_6379,c_502]) ).
cnf(c_72932,plain,
hAPP(int,int,combi(int),X0) = hAPP(int,int,number_number_of(int),X0),
inference(demodulation,[status(thm)],[c_350,c_8050]) ).
cnf(c_74010,plain,
hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),pls)) = hAPP(int,nat,nat_1,X0),
inference(demodulation,[status(thm)],[c_69794,c_6380]) ).
cnf(c_75786,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),pls) = hAPP(int,int,number_number_of(int),X0),
inference(demodulation,[status(thm)],[c_975,c_8050,c_72932]) ).
cnf(c_75787,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X0)) = hAPP(int,nat,nat_1,X0),
inference(demodulation,[status(thm)],[c_74010,c_75786]) ).
cnf(c_75788,plain,
hAPP(int,nat,number_number_of(nat),X0) = hAPP(int,nat,nat_1,X0),
inference(light_normalisation,[status(thm)],[c_75787,c_1865]) ).
cnf(c_75838,plain,
hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)),
inference(demodulation,[status(thm)],[c_68541,c_75788]) ).
cnf(c_78767,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),pls)),
inference(light_normalisation,[status(thm)],[c_8068,c_502]) ).
cnf(c_78768,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)),
inference(demodulation,[status(thm)],[c_78767,c_2495,c_75788,c_75838]) ).
cnf(c_89227,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),s),one_one(int))),
inference(demodulation,[status(thm)],[c_1344,c_351,c_2495]) ).
cnf(c_92357,plain,
hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),s),one_one(int))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),
inference(demodulation,[status(thm)],[c_325,c_351,c_2495,c_75788,c_75838,c_89227]) ).
cnf(c_92359,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),
inference(demodulation,[status(thm)],[c_89227,c_92357]) ).
cnf(c_95615,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),pls))),
inference(light_normalisation,[status(thm)],[c_324,c_502]) ).
cnf(c_95616,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)),
inference(demodulation,[status(thm)],[c_95615,c_351,c_413,c_2495,c_92359]) ).
cnf(c_95617,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_95616,c_78768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n020.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 15:24:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 131.34/20.33 % SZS status Started for theBenchmark.p
% 131.34/20.33 % SZS status Theorem for theBenchmark.p
% 131.34/20.33
% 131.34/20.33 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 131.34/20.33
% 131.34/20.33 ------ iProver source info
% 131.34/20.33
% 131.34/20.33 git: date: 2023-05-31 18:12:56 +0000
% 131.34/20.33 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 131.34/20.33 git: non_committed_changes: false
% 131.34/20.33 git: last_make_outside_of_git: false
% 131.34/20.33
% 131.34/20.33 ------ Parsing...
% 131.34/20.33 ------ Clausification by vclausify_rel & Parsing by iProver...
% 131.34/20.33
% 131.34/20.33 ------ Preprocessing...
% 131.34/20.33
% 131.34/20.33 % SZS status Theorem for theBenchmark.p
% 131.34/20.33
% 131.34/20.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 131.34/20.33
% 131.34/20.34
%------------------------------------------------------------------------------