TSTP Solution File: NUM924+8 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 : Tue Apr 30 14:38:35 EDT 2024
% Result : Theorem 23.08s 4.47s
% Output : Refutation 23.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of formulae : 118 ( 82 unt; 0 def)
% Number of atoms : 180 ( 78 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 105 ( 43 ~; 44 |; 9 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 18 con; 0-4 aty)
% Number of variables : 116 ( 110 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f75989,plain,
$false,
inference(resolution,[],[f75905,f18437]) ).
fof(f18437,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f5731]) ).
fof(f5731,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f75905,plain,
hBOOL(fFalse),
inference(backward_demodulation,[],[f30635,f75636]) ).
fof(f75636,plain,
fFalse = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),s)))),pls),
inference(resolution,[],[f75276,f30632]) ).
fof(f30632,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),s)))),pls)),
inference(backward_demodulation,[],[f27257,f30630]) ).
fof(f30630,plain,
hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),s))),
inference(backward_demodulation,[],[f27254,f30515]) ).
fof(f30515,plain,
! [X0] : hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),X0)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),X0),one_one(int)),
inference(backward_demodulation,[],[f27363,f26209]) ).
fof(f26209,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(cnf_transformation,[],[f10162]) ).
fof(f10162,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(rectify,[],[f265]) ).
fof(f265,axiom,
! [X0,X2,X3,X4] : hAPP(X0,X2,X3,X4) = hAPP(X0,X2,X3,ti(X0,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(f27363,plain,
! [X0] : hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),X0)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),ti(int,X0)),one_one(int)),
inference(forward_demodulation,[],[f19631,f19278]) ).
fof(f19278,plain,
! [X0] : hAPP(int,int,number_number_of(int),X0) = ti(int,X0),
inference(cnf_transformation,[],[f5766]) ).
fof(f5766,plain,
! [X0] : hAPP(int,int,number_number_of(int),X0) = ti(int,X0),
inference(rectify,[],[f295]) ).
fof(f295,axiom,
! [X14] : hAPP(int,int,number_number_of(int),X14) = ti(int,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(f19631,plain,
! [X0] : hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),X0)),one_one(int)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),X0)),
inference(cnf_transformation,[],[f6093]) ).
fof(f6093,plain,
! [X0] : hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),X0)),one_one(int)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),X0)),
inference(rectify,[],[f4003]) ).
fof(f4003,axiom,
! [X14] : hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),X14)),one_one(int)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3730_quotient__of__number_I3_J) ).
fof(f27254,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(backward_demodulation,[],[f27228,f19428]) ).
fof(f19428,plain,
! [X0] : hAPP(int,int,succ,X0) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),min_1),
inference(cnf_transformation,[],[f5894]) ).
fof(f5894,plain,
! [X0] : hAPP(int,int,succ,X0) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X0),min_1),
inference(rectify,[],[f1803]) ).
fof(f1803,axiom,
! [X14] : hAPP(int,int,succ,X14) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X14),min_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1530_diff__bin__simps_I2_J) ).
fof(f27228,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,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),min_1),
inference(forward_demodulation,[],[f27201,f18887]) ).
fof(f18887,plain,
min_1 = ti(int,min_1),
inference(cnf_transformation,[],[f105]) ).
fof(f105,axiom,
min_1 = ti(int,min_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OMin_res) ).
fof(f27201,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,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),ti(int,min_1)),
inference(backward_demodulation,[],[f27170,f19278]) ).
fof(f27170,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,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),hAPP(int,int,number_number_of(int),min_1)),
inference(backward_demodulation,[],[f27163,f27168]) ).
fof(f27168,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,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)),
inference(forward_demodulation,[],[f27167,f19219]) ).
fof(f19219,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(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/sandbox/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(f27167,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(nat,nat,suc,one_one(nat)))),one_one(int)),
inference(forward_demodulation,[],[f19225,f27131]) ).
fof(f27131,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(forward_demodulation,[],[f19161,f19015]) ).
fof(f19015,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(cnf_transformation,[],[f1603]) ).
fof(f1603,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1330_One__nat__def) ).
fof(f19161,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,[],[f1700]) ).
fof(f1700,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/sandbox/benchmark/theBenchmark.p',fact_1427_semiring__norm_I115_J) ).
fof(f19225,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(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/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(f27163,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(nat,nat,suc,one_one(nat)))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),hAPP(int,int,number_number_of(int),min_1)),
inference(forward_demodulation,[],[f19220,f27131]) ).
fof(f19220,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),minus_minus(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))))),hAPP(int,int,number_number_of(int),min_1)),
inference(cnf_transformation,[],[f740]) ).
fof(f740,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),minus_minus(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))))),hAPP(int,int,number_number_of(int),min_1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
fof(f27257,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(backward_demodulation,[],[f27171,f27254]) ).
fof(f27171,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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)))),pls)),
inference(backward_demodulation,[],[f27134,f27168]) ).
fof(f27134,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(nat,nat,suc,one_one(nat)))),one_one(int))),pls)),
inference(backward_demodulation,[],[f27091,f27131]) ).
fof(f27091,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(backward_demodulation,[],[f18430,f18877]) ).
fof(f18877,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f396]) ).
fof(f396,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Pls__def) ).
fof(f18430,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,[],[f5740]) ).
fof(f5740,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(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(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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f75276,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,X2))
| fFalse = hAPP(X0,bool,X1,X2) ),
inference(superposition,[],[f75209,f26208]) ).
fof(f26208,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f10161]) ).
fof(f10161,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(rectify,[],[f266]) ).
fof(f266,axiom,
! [X2,X0,X3,X4] : hAPP(X0,X2,X3,X4) = ti(X2,hAPP(X0,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(f75209,plain,
! [X0] :
( hBOOL(ti(bool,X0))
| fFalse = ti(bool,X0) ),
inference(forward_demodulation,[],[f75205,f26211]) ).
fof(f26211,plain,
! [X2,X3,X0,X1] : ti(X1,X2) = hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3),
inference(cnf_transformation,[],[f10164]) ).
fof(f10164,plain,
! [X0,X1,X2,X3] : ti(X1,X2) = hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3),
inference(rectify,[],[f5721]) ).
fof(f5721,axiom,
! [X1,X0,X227,X228] : ti(X0,X227) = hAPP(X1,X0,hAPP(X0,fun(X1,X0),combk(X0,X1),X227),X228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(f75205,plain,
! [X0] :
( hBOOL(ti(bool,X0))
| fFalse = hAPP(int,bool,hAPP(bool,fun(int,bool),combk(bool,int),X0),sK430(hAPP(bool,fun(int,bool),combk(bool,int),X0))) ),
inference(superposition,[],[f72952,f26211]) ).
fof(f72952,plain,
! [X0] :
( hBOOL(hAPP(int,bool,X0,pls))
| fFalse = hAPP(int,bool,X0,sK430(X0)) ),
inference(forward_demodulation,[],[f72902,f26208]) ).
fof(f72902,plain,
! [X0] :
( hBOOL(hAPP(int,bool,X0,pls))
| fFalse = ti(bool,hAPP(int,bool,X0,sK430(X0))) ),
inference(resolution,[],[f72477,f36517]) ).
fof(f36517,plain,
! [X0] :
( hBOOL(X0)
| fFalse = ti(bool,X0) ),
inference(resolution,[],[f36510,f18437]) ).
fof(f36510,plain,
! [X0] :
( hBOOL(fFalse)
| hBOOL(X0)
| fFalse = ti(bool,X0) ),
inference(superposition,[],[f19830,f36498]) ).
fof(f36498,plain,
! [X0] :
( fFalse = hAPP(bool,bool,fNot,X0)
| fFalse = ti(bool,X0) ),
inference(resolution,[],[f32022,f18870]) ).
fof(f18870,plain,
hBOOL(fTrue),
inference(cnf_transformation,[],[f5723]) ).
fof(f5723,axiom,
hBOOL(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
fof(f32022,plain,
! [X0] :
( ~ hBOOL(fTrue)
| fFalse = hAPP(bool,bool,fNot,X0)
| fFalse = ti(bool,X0) ),
inference(duplicate_literal_removal,[],[f31999]) ).
fof(f31999,plain,
! [X0] :
( ~ hBOOL(fTrue)
| fFalse = hAPP(bool,bool,fNot,X0)
| ~ hBOOL(fTrue)
| fFalse = ti(bool,X0) ),
inference(resolution,[],[f31472,f31427]) ).
fof(f31427,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(fTrue)
| fFalse = ti(bool,X0) ),
inference(superposition,[],[f18435,f19831]) ).
fof(f19831,plain,
! [X0] :
( fTrue = ti(bool,X0)
| fFalse = ti(bool,X0) ),
inference(cnf_transformation,[],[f6256]) ).
fof(f6256,plain,
! [X0] :
( fFalse = ti(bool,X0)
| fTrue = ti(bool,X0) ),
inference(rectify,[],[f5724]) ).
fof(f5724,axiom,
! [X227] :
( fFalse = ti(bool,X227)
| fTrue = ti(bool,X227) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
fof(f18435,plain,
! [X0] :
( ~ hBOOL(ti(bool,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f15560]) ).
fof(f15560,plain,
! [X0] :
( ( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) )
& ( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ) ),
inference(nnf_transformation,[],[f5741]) ).
fof(f5741,plain,
! [X0] :
( hBOOL(ti(bool,X0))
<=> hBOOL(X0) ),
inference(rectify,[],[f267]) ).
fof(f267,axiom,
! [X3] :
( hBOOL(ti(bool,X3))
<=> hBOOL(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(f31472,plain,
! [X0] :
( ~ hBOOL(fTrue)
| ~ hBOOL(X0)
| fFalse = hAPP(bool,bool,fNot,X0) ),
inference(forward_demodulation,[],[f31455,f26208]) ).
fof(f31455,plain,
! [X0] :
( ~ hBOOL(fTrue)
| fFalse = ti(bool,hAPP(bool,bool,fNot,X0))
| ~ hBOOL(X0) ),
inference(resolution,[],[f31427,f19834]) ).
fof(f19834,plain,
! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f6259]) ).
fof(f6259,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(rectify,[],[f5716]) ).
fof(f5716,axiom,
! [X227] :
( ~ hBOOL(X227)
| ~ hBOOL(hAPP(bool,bool,fNot,X227)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(f19830,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f6255]) ).
fof(f6255,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f5717]) ).
fof(f5717,axiom,
! [X227] :
( hBOOL(hAPP(bool,bool,fNot,X227))
| hBOOL(X227) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(f72477,plain,
! [X0] :
( ~ hBOOL(hAPP(int,bool,X0,sK430(X0)))
| hBOOL(hAPP(int,bool,X0,pls)) ),
inference(superposition,[],[f22914,f27104]) ).
fof(f27104,plain,
pls = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
inference(forward_demodulation,[],[f19052,f18877]) ).
fof(f19052,plain,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
inference(cnf_transformation,[],[f1564]) ).
fof(f1564,axiom,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1291_transfer__int__nat__numerals_I1_J) ).
fof(f22914,plain,
! [X3,X0] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ~ hBOOL(hAPP(int,bool,X0,sK430(X0))) ),
inference(cnf_transformation,[],[f16694]) ).
fof(f16694,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),sK429(X0)))) )
& ( ! [X3] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ( ~ hBOOL(hAPP(int,bool,X0,sK430(X0)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK430(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK429,sK430])],[f16691,f16693,f16692]) ).
fof(f16692,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2)))
=> ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),sK429(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f16693,plain,
! [X0] :
( ? [X4] :
( ~ hBOOL(hAPP(int,bool,X0,X4))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) )
=> ( ~ hBOOL(hAPP(int,bool,X0,sK430(X0)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK430(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f16691,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ? [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) )
& ( ! [X3] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ? [X4] :
( ~ hBOOL(hAPP(int,bool,X0,X4))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) ) ) ),
inference(rectify,[],[f16690]) ).
fof(f16690,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ? [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) )
& ( ! [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ? [X1] :
( ~ hBOOL(hAPP(int,bool,X0,X1))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) ) ),
inference(nnf_transformation,[],[f12904]) ).
fof(f12904,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
<=> ! [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(ennf_transformation,[],[f8146]) ).
fof(f8146,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
=> hBOOL(hAPP(int,bool,X0,X1)) )
<=> ! [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(rectify,[],[f1570]) ).
fof(f1570,axiom,
! [X36] :
( ! [X34] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X34))
=> hBOOL(hAPP(int,bool,X36,X34)) )
<=> ! [X34] : hBOOL(hAPP(int,bool,X36,hAPP(nat,int,semiring_1_of_nat(int),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1297_transfer__int__nat__quantifiers_I1_J) ).
fof(f30635,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),s)))),pls)),
inference(backward_demodulation,[],[f30455,f30630]) ).
fof(f30455,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(forward_demodulation,[],[f30454,f19325]) ).
fof(f19325,plain,
! [X0] : pls = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X0),
inference(cnf_transformation,[],[f5801]) ).
fof(f5801,plain,
! [X0] : pls = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X0),
inference(rectify,[],[f335]) ).
fof(f335,axiom,
! [X11] : pls = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(f30454,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))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),m))))),
inference(forward_demodulation,[],[f30365,f23017]) ).
fof(f23017,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,[],[f8219]) ).
fof(f8219,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(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/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(f30365,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))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),m))),pls))),
inference(backward_demodulation,[],[f27281,f26208]) ).
fof(f27281,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))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m))),pls))),
inference(backward_demodulation,[],[f27260,f19458]) ).
fof(f19458,plain,
! [X0] : hAPP(int,int,succ,X0) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),one_one(int)),
inference(cnf_transformation,[],[f5923]) ).
fof(f5923,plain,
! [X0] : hAPP(int,int,succ,X0) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),one_one(int)),
inference(rectify,[],[f1801]) ).
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/sandbox/benchmark/theBenchmark.p',fact_1528_succ__def) ).
fof(f27260,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))))),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),ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),pls))),
inference(backward_demodulation,[],[f27217,f27254]) ).
fof(f27217,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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,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),ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),pls))),
inference(backward_demodulation,[],[f27176,f19278]) ).
fof(f27176,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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,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(forward_demodulation,[],[f27175,f19219]) ).
fof(f27175,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(forward_demodulation,[],[f19229,f18877]) ).
fof(f19229,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(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/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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 00:13:04 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (28708)Running in auto input_syntax mode. Trying TPTP
% 1.07/1.30 % (28784)WARNING: value z3 for option sas not known
% 1.07/1.30 % (28785)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 1.07/1.30 % (28782)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.07/1.31 % (28786)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 1.07/1.31 % (28784)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 1.07/1.31 % (28783)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 1.07/1.31 % (28787)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 1.07/1.31 % (28788)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 23.08/4.46 % (28787)First to succeed.
% 23.08/4.47 % (28787)Refutation found. Thanks to Tanya!
% 23.08/4.47 % SZS status Theorem for theBenchmark
% 23.08/4.47 % SZS output start Proof for theBenchmark
% See solution above
% 23.08/4.47 % (28787)------------------------------
% 23.08/4.47 % (28787)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 23.08/4.47 % (28787)Termination reason: Refutation
% 23.08/4.47
% 23.08/4.47 % (28787)Memory used [KB]: 48055
% 23.08/4.47 % (28787)Time elapsed: 3.160 s
% 23.08/4.47 % (28787)Instructions burned: 8900 (million)
% 23.08/4.47 % (28787)------------------------------
% 23.08/4.47 % (28787)------------------------------
% 23.08/4.47 % (28708)Success in time 4.071 s
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