TSTP Solution File: NUM924+8 by Etableau---0.67
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%------------------------------------------------------------------------------
% File : Etableau---0.67
% Problem : NUM924+8 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% Computer : n016.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 09:46:45 EDT 2022
% Result : Theorem 2.20s 2.39s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 54 unt; 0 def)
% Number of atoms : 54 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-4 aty)
% Number of variables : 34 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_131_add__Pls,axiom,
! [X15] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X15) = ti(int,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add__Pls) ).
fof(help_COMBI_1_1_U,axiom,
! [X1,X228] : hAPP(X1,X1,combi(X1),X228) = ti(X1,X228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(fact_22_number__of__is__id,axiom,
! [X15] : hAPP(int,int,number_number_of(int),X15) = ti(int,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(fact_61_nat__1__add__1,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__1__add__1) ).
fof(fact_123_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Pls__def) ).
fof(fact_1525_succ__Pls,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1525_succ__Pls) ).
fof(fact_1528_succ__def,axiom,
! [X15] : hAPP(int,int,succ,X15) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X15),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1528_succ__def) ).
fof(fact_1427_semiring__norm_I115_J,axiom,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1427_semiring__norm_I115_J) ).
fof(fact_1330_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1330_One__nat__def) ).
fof(conj_0,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_99_zadd__commute,axiom,
! [X16,X12] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X16),X12) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X12),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_zadd__commute) ).
fof(fact_23_zmult__commute,axiom,
! [X16,X12] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X16),X12) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X12),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(fact_62_mult__Pls,axiom,
! [X12] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X12) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(fact_3_t,axiom,
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)) = 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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(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,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/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(c_0_15,plain,
! [X631] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X631) = ti(int,X631),
inference(variable_rename,[status(thm)],[fact_131_add__Pls]) ).
fof(c_0_16,plain,
! [X13971,X13972] : hAPP(X13971,X13971,combi(X13971),X13972) = ti(X13971,X13972),
inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).
fof(c_0_17,plain,
! [X417] : hAPP(int,int,number_number_of(int),X417) = ti(int,X417),
inference(variable_rename,[status(thm)],[fact_22_number__of__is__id]) ).
cnf(c_0_18,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_61_nat__1__add__1]) ).
cnf(c_0_19,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_123_Pls__def]) ).
cnf(c_0_20,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_1525_succ__Pls]) ).
fof(c_0_21,plain,
! [X4168] : hAPP(int,int,succ,X4168) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X4168),one_one(int)),
inference(variable_rename,[status(thm)],[fact_1528_succ__def]) ).
cnf(c_0_22,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_1427_semiring__norm_I115_J]) ).
cnf(c_0_26,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,zero_zero(int)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_1330_One__nat__def]) ).
cnf(c_0_28,plain,
hAPP(int,int,succ,zero_zero(int)) = hAPP(int,int,bit1,zero_zero(int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19]),c_0_19]) ).
cnf(c_0_29,plain,
hAPP(int,int,succ,X1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X1) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_24,c_0_23]) ).
fof(c_0_32,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(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_33,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)) = hAPP(nat,nat,suc,one_one(nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_19]),c_0_26]),c_0_27]) ).
cnf(c_0_34,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),one_one(int)) = hAPP(int,int,bit1,zero_zero(int)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),X1) = hAPP(int,int,number_number_of(int),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_19]) ).
fof(c_0_36,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(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X576,X577] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X576),X577) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X577),X576),
inference(variable_rename,[status(thm)],[fact_99_zadd__commute]) ).
fof(c_0_38,plain,
! [X418,X419] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X418),X419) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X419),X418),
inference(variable_rename,[status(thm)],[fact_23_zmult__commute]) ).
cnf(c_0_39,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,zero_zero(int)))) = hAPP(nat,nat,suc,one_one(nat)),
inference(rw,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_40,plain,
hAPP(int,int,bit1,zero_zero(int)) = hAPP(int,int,number_number_of(int),one_one(int)),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_41,plain,
! [X497] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X497) = pls,
inference(variable_rename,[status(thm)],[fact_62_mult__Pls]) ).
cnf(c_0_42,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(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
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)) = 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),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
cnf(c_0_44,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,number_number_of(int),one_one(int)))) = hAPP(nat,nat,suc,one_one(nat)),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,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(nat,nat,suc,one_one(nat)))),one_one(int))),zero_zero(int))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_19]),c_0_26]),c_0_33]) ).
cnf(c_0_49,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(split_conjunct,[status(thm)],[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]) ).
cnf(c_0_50,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(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,number_number_of(int),one_one(int)))))),m))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_19]),c_0_40]),c_0_44]),c_0_45]),c_0_19]),c_0_40]),c_0_46]),c_0_44]) ).
cnf(c_0_51,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),X1) = zero_zero(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_19]),c_0_19]) ).
cnf(c_0_52,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),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int))),
inference(rw,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_53,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_19]),c_0_40]),c_0_44]),c_0_45]),c_0_50]),c_0_19]),c_0_40]),c_0_44]),c_0_45]),c_0_51]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM924+8 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 08:50:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.20/2.39 # No SInE strategy applied
% 2.20/2.39 # Auto-Mode selected heuristic C07_19_nc_SAT001_MinMin_rr
% 2.20/2.39 # and selection function SelectMaxLComplexAvoidPosPred.
% 2.20/2.39 #
% 2.20/2.39 # Presaturation interreduction done
% 2.20/2.39
% 2.20/2.39 # Proof found!
% 2.20/2.39 # SZS status Theorem
% 2.20/2.39 # SZS output start CNFRefutation
% See solution above
% 2.20/2.40 # Training examples: 0 positive, 0 negative
%------------------------------------------------------------------------------