TSTP Solution File: NUM924+7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 : 600s
% DateTime : Mon Jul 18 14:31:40 EDT 2022
% Result : Theorem 2.42s 2.62s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 39 RR)
% Number of literals : 39 ( 0 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(156,axiom,
equal(zero_zero(int),pls),
file('NUM924+7.p',unknown),
[] ).
cnf(160,axiom,
equal(ti(int,min),min),
file('NUM924+7.p',unknown),
[] ).
cnf(162,axiom,
equal(ti(int,m),m),
file('NUM924+7.p',unknown),
[] ).
cnf(183,axiom,
equal(ti(int,bit0(u)),bit0(u)),
file('NUM924+7.p',unknown),
[] ).
cnf(185,axiom,
equal(ti(int,bit1(u)),bit1(u)),
file('NUM924+7.p',unknown),
[] ).
cnf(192,axiom,
equal(ti(int,u),number_number_of(int,u)),
file('NUM924+7.p',unknown),
[] ).
cnf(195,axiom,
equal(number_number_of(int,bit1(pls)),one_one(int)),
file('NUM924+7.p',unknown),
[] ).
cnf(227,axiom,
equal(hAPP(int,int,times_times(int,pls),u),pls),
file('NUM924+7.p',unknown),
[] ).
cnf(270,axiom,
equal(hAPP(int,int,plus_plus(int,pls),u),ti(int,u)),
file('NUM924+7.p',unknown),
[] ).
cnf(293,axiom,
equal(hAPP(int,int,times_times(int,u),one_one(int)),ti(int,u)),
file('NUM924+7.p',unknown),
[] ).
cnf(373,axiom,
equal(hAPP(int,int,times_times(int,u),v),hAPP(int,int,times_times(int,v),u)),
file('NUM924+7.p',unknown),
[] ).
cnf(375,axiom,
equal(hAPP(int,int,plus_plus(int,u),v),hAPP(int,int,plus_plus(int,v),u)),
file('NUM924+7.p',unknown),
[] ).
cnf(449,axiom,
equal(hAPP(int,int,times_times(int,bit0(u)),v),bit0(hAPP(int,int,times_times(int,u),v))),
file('NUM924+7.p',unknown),
[] ).
cnf(486,axiom,
equal(hAPP(int,int,plus_plus(int,bit1(u)),bit0(v)),bit1(hAPP(int,int,plus_plus(int,u),v))),
file('NUM924+7.p',unknown),
[] ).
cnf(595,axiom,
equal(hAPP(u,v,combc(u,w,v,x,y),z),hAPP(w,v,hAPP(u,fun(w,v),x,z),y)),
file('NUM924+7.p',unknown),
[] ).
cnf(928,axiom,
~ 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('NUM924+7.p',unknown),
[] ).
cnf(939,axiom,
equal(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('NUM924+7.p',unknown),
[] ).
cnf(1127,axiom,
equal(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)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),
file('NUM924+7.p',unknown),
[] ).
cnf(1280,axiom,
equal(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))),skc4),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),
file('NUM924+7.p',unknown),
[] ).
cnf(1282,axiom,
equal(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('NUM924+7.p',unknown),
[] ).
cnf(1543,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('NUM924+7.p',unknown),
[] ).
cnf(1649,plain,
equal(number_number_of(int,min),min),
inference(rew,[status(thm),theory(equality)],[192,160]),
[iquote('0:Rew:192.0,160.0')] ).
cnf(1651,plain,
equal(number_number_of(int,m),m),
inference(rew,[status(thm),theory(equality)],[192,162]),
[iquote('0:Rew:192.0,162.0')] ).
cnf(1658,plain,
equal(number_number_of(int,bit1(u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[192,185]),
[iquote('0:Rew:192.0,185.0')] ).
cnf(1659,plain,
equal(one_one(int),bit1(pls)),
inference(rew,[status(thm),theory(equality)],[1658,195]),
[iquote('0:Rew:1658.0,195.0')] ).
cnf(1662,plain,
equal(number_number_of(int,bit0(u)),bit0(u)),
inference(rew,[status(thm),theory(equality)],[192,183]),
[iquote('0:Rew:192.0,183.0')] ).
cnf(1705,plain,
equal(hAPP(int,int,plus_plus(int,pls),u),number_number_of(int,u)),
inference(rew,[status(thm),theory(equality)],[192,270]),
[iquote('0:Rew:192.0,270.0')] ).
cnf(1715,plain,
equal(hAPP(int,int,times_times(int,u),bit1(pls)),number_number_of(int,u)),
inference(rew,[status(thm),theory(equality)],[1659,293,192]),
[iquote('0:Rew:1659.0,293.0,192.0,293.0')] ).
cnf(2080,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))),
inference(rew,[status(thm),theory(equality)],[595,928,375,1659,156]),
[iquote('0:Rew:595.0,928.0,375.0,928.0,1659.0,928.0,156.0,928.0')] ).
cnf(2089,plain,
equal(hAPP(int,int,times_times(int,t),bit1(bit0(m))),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))),
inference(rew,[status(thm),theory(equality)],[373,939,1662,1705,486,375,1651,1715,449,1659]),
[iquote('0:Rew:373.0,939.0,1662.0,939.0,1705.0,939.0,486.0,939.0,375.0,939.0,1651.0,939.0,1715.0,939.0,373.0,939.0,449.0,939.0,449.0,939.0,1662.0,939.0,1659.0,939.0')] ).
cnf(2231,plain,
equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)),
inference(rew,[status(thm),theory(equality)],[1649,1127,375,1659]),
[iquote('0:Rew:1649.0,1127.0,375.0,1127.0,1659.0,1127.0')] ).
cnf(2233,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),number_number_of(nat,bit0(bit1(pls))))),min))),
inference(rew,[status(thm),theory(equality)],[2231,2080]),
[iquote('0:Rew:2231.0,2080.0')] ).
cnf(2371,plain,
equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),hAPP(int,int,times_times(int,skc4),bit1(bit0(m)))),
inference(rew,[status(thm),theory(equality)],[373,1280,1662,1705,486,375,1651,1715,449,2231,1659]),
[iquote('0:Rew:373.0,1280.0,1662.0,1280.0,1705.0,1280.0,486.0,1280.0,375.0,1280.0,1651.0,1280.0,1715.0,1280.0,373.0,1280.0,449.0,1280.0,449.0,1280.0,1662.0,1280.0,2231.0,1280.0,375.0,1280.0,1659.0,1280.0')] ).
cnf(2372,plain,
equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,skc4),bit1(bit0(m)))),
inference(rew,[status(thm),theory(equality)],[2371,2231]),
[iquote('0:Rew:2371.0,2231.0')] ).
cnf(2374,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,skc4),bit1(bit0(m))))),
inference(rew,[status(thm),theory(equality)],[2371,2233]),
[iquote('0:Rew:2371.0,2233.0')] ).
cnf(2376,plain,
equal(hAPP(int,int,times_times(int,skc4),bit1(bit0(m))),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))),
inference(rew,[status(thm),theory(equality)],[2089,1282,373,1662,1705,486,375,1651,1715,449,2372,1659]),
[iquote('0:Rew:2089.0,1282.0,373.0,1282.0,1662.0,1282.0,1705.0,1282.0,486.0,1282.0,375.0,1282.0,1651.0,1282.0,1715.0,1282.0,373.0,1282.0,449.0,1282.0,449.0,1282.0,1662.0,1282.0,2372.0,1282.0,375.0,1282.0,1659.0,1282.0')] ).
cnf(2379,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))),
inference(rew,[status(thm),theory(equality)],[2376,2374]),
[iquote('0:Rew:2376.0,2374.0')] ).
cnf(2623,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))),
inference(rew,[status(thm),theory(equality)],[595,1543,2089,373,227,1662,1705,486,375,1651,1715,449,1659,156]),
[iquote('0:Rew:595.0,1543.0,2089.0,1543.0,373.0,1543.0,227.0,1543.0,373.0,1543.0,1662.0,1543.0,1705.0,1543.0,486.0,1543.0,375.0,1543.0,1651.0,1543.0,1715.0,1543.0,373.0,1543.0,449.0,1543.0,449.0,1543.0,1662.0,1543.0,1659.0,1543.0,156.0,1543.0')] ).
cnf(2624,plain,
$false,
inference(mrr,[status(thm)],[2623,2379]),
[iquote('0:MRR:2623.0,2379.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jul 5 15:18:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.42/2.62
% 2.42/2.62 SPASS V 3.9
% 2.42/2.62 SPASS beiseite: Proof found.
% 2.42/2.62 % SZS status Theorem
% 2.42/2.62 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.42/2.62 SPASS derived 96 clauses, backtracked 0 clauses, performed 0 splits and kept 1386 clauses.
% 2.42/2.62 SPASS allocated 110516 KBytes.
% 2.42/2.62 SPASS spent 0:00:02.21 on the problem.
% 2.42/2.62 0:00:00.07 for the input.
% 2.42/2.62 0:00:00.95 for the FLOTTER CNF translation.
% 2.42/2.62 0:00:00.00 for inferences.
% 2.42/2.62 0:00:00.00 for the backtracking.
% 2.42/2.62 0:00:00.79 for the reduction.
% 2.42/2.62
% 2.42/2.62
% 2.42/2.62 Here is a proof with depth 0, length 39 :
% 2.42/2.62 % SZS output start Refutation
% See solution above
% 2.42/2.62 Formulae used in the proof : fact_122_Pls__def tsy_c_Int_OMin_res tsy_v_m_res tsy_c_Int_OBit0_res tsy_c_Int_OBit1_res fact_22_number__of__is__id fact_111_one__is__num__one fact_62_mult__Pls fact_130_add__Pls fact_65_zmult__1__right fact_23_zmult__commute fact_98_zadd__commute fact_63_mult__Bit0 fact_161_add__Bit1__Bit0 help_COMBC_1_1_U conj_0 fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096 fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096 fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_ fact_3_t 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
% 2.42/2.62
%------------------------------------------------------------------------------