TSTP Solution File: NUM925+7 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 20:36:07 EDT 2024
% Result : Theorem 4.41s 0.98s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 29 unt; 0 def)
% Number of atoms : 95 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 34 ~; 29 |; 0 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [B_1_1,B_2_1,X_a] :
( cancel_semigroup_add(X_a)
=> ti(X_a,plus_plus(X_a,B_1_1,B_2_1)) = plus_plus(X_a,B_1_1,B_2_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
! [B_1_1] : ti(int,bit1(B_1_1)) = bit1(B_1_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f130,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f135,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f171,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f218,axiom,
! [K_1] : number_number_of(int,K_1) = ti(int,K_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f263,axiom,
! [X_a] :
( ring_11004092258visors(X_a)
=> ! [N,A_1] :
( ti(X_a,A_1) != zero_zero(X_a)
=> hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1104,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1111,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1251,conjecture,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1252,negated_conjecture,
~ ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f1251]) ).
fof(f1297,plain,
! [B_1_1,B_2_1,X_a] :
( ~ cancel_semigroup_add(X_a)
| ti(X_a,plus_plus(X_a,B_1_1,B_2_1)) = plus_plus(X_a,B_1_1,B_2_1) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f1298,plain,
! [X_a] :
( ~ cancel_semigroup_add(X_a)
| ! [B_1_1,B_2_1] : ti(X_a,plus_plus(X_a,B_1_1,B_2_1)) = plus_plus(X_a,B_1_1,B_2_1) ),
inference(miniscoping,[status(esa)],[f1297]) ).
fof(f1299,plain,
! [X0,X1,X2] :
( ~ cancel_semigroup_add(X0)
| ti(X0,plus_plus(X0,X1,X2)) = plus_plus(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1298]) ).
fof(f1368,plain,
! [X0] : ti(int,bit1(X0)) = bit1(X0),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f1461,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[status(esa)],[f98]) ).
fof(f1529,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(cnf_transformation,[status(esa)],[f130]) ).
fof(f1546,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[status(esa)],[f135]) ).
fof(f1657,plain,
pls = zero_zero(int),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f1754,plain,
! [X0] : number_number_of(int,X0) = ti(int,X0),
inference(cnf_transformation,[status(esa)],[f218]) ).
fof(f1895,plain,
! [X_a] :
( ~ ring_11004092258visors(X_a)
| ! [N,A_1] :
( ti(X_a,A_1) = zero_zero(X_a)
| hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
inference(pre_NNF_transformation,[status(esa)],[f263]) ).
fof(f1896,plain,
! [X_a] :
( ~ ring_11004092258visors(X_a)
| ! [A_1] :
( ti(X_a,A_1) = zero_zero(X_a)
| ! [N] : hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
inference(miniscoping,[status(esa)],[f1895]) ).
fof(f1897,plain,
! [X0,X1,X2] :
( ~ ring_11004092258visors(X0)
| ti(X0,X1) = zero_zero(X0)
| hAPP(nat,X0,power_power(X0,X1),X2) != zero_zero(X0) ),
inference(cnf_transformation,[status(esa)],[f1896]) ).
fof(f4388,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[status(esa)],[f1104]) ).
fof(f4395,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[status(esa)],[f1111]) ).
fof(f4535,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(cnf_transformation,[status(esa)],[f1252]) ).
fof(f4602,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = pls,
inference(backward_demodulation,[status(thm)],[f1657,f4535]) ).
fof(f4654,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(forward_demodulation,[status(thm)],[f1657,f1461]) ).
fof(f5044,plain,
( spl0_13
<=> pls = zero_zero(int) ),
introduced(split_symbol_definition) ).
fof(f5046,plain,
( pls != zero_zero(int)
| spl0_13 ),
inference(component_clause,[status(thm)],[f5044]) ).
fof(f5082,plain,
one_one(int) = ti(int,bit1(pls)),
inference(paramodulation,[status(thm)],[f1546,f1754]) ).
fof(f5125,plain,
one_one(int) = bit1(pls),
inference(paramodulation,[status(thm)],[f1368,f5082]) ).
fof(f5158,plain,
hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(one_one(int)))) = pls,
inference(backward_demodulation,[status(thm)],[f5125,f4602]) ).
fof(f5684,plain,
( spl0_95
<=> cancel_semigroup_add(int) ),
introduced(split_symbol_definition) ).
fof(f5686,plain,
( ~ cancel_semigroup_add(int)
| spl0_95 ),
inference(component_clause,[status(thm)],[f5684]) ).
fof(f6165,plain,
( spl0_159
<=> ring_11004092258visors(int) ),
introduced(split_symbol_definition) ).
fof(f6167,plain,
( ~ ring_11004092258visors(int)
| spl0_159 ),
inference(component_clause,[status(thm)],[f6165]) ).
fof(f6632,plain,
( spl0_235
<=> ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) ),
introduced(split_symbol_definition) ).
fof(f6633,plain,
( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int)
| ~ spl0_235 ),
inference(component_clause,[status(thm)],[f6632]) ).
fof(f6635,plain,
( ~ ring_11004092258visors(int)
| ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int)
| pls != zero_zero(int) ),
inference(paramodulation,[status(thm)],[f5158,f1897]) ).
fof(f6636,plain,
( ~ spl0_159
| spl0_235
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f6635,f6165,f6632,f5044]) ).
fof(f8163,plain,
( pls != pls
| spl0_13 ),
inference(forward_demodulation,[status(thm)],[f1657,f5046]) ).
fof(f8164,plain,
( $false
| spl0_13 ),
inference(trivial_equality_resolution,[status(esa)],[f8163]) ).
fof(f8165,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f8164]) ).
fof(f8218,plain,
( $false
| spl0_159 ),
inference(forward_subsumption_resolution,[status(thm)],[f4388,f6167]) ).
fof(f8219,plain,
spl0_159,
inference(contradiction_clause,[status(thm)],[f8218]) ).
fof(f8221,plain,
( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = pls
| ~ spl0_235 ),
inference(forward_demodulation,[status(thm)],[f1657,f6633]) ).
fof(f8230,plain,
( $false
| spl0_95 ),
inference(forward_subsumption_resolution,[status(thm)],[f4395,f5686]) ).
fof(f8231,plain,
spl0_95,
inference(contradiction_clause,[status(thm)],[f8230]) ).
fof(f8719,plain,
( spl0_407
<=> pls = plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)) ),
introduced(split_symbol_definition) ).
fof(f8720,plain,
( pls = plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ spl0_407 ),
inference(component_clause,[status(thm)],[f8719]) ).
fof(f8722,plain,
( ~ cancel_semigroup_add(int)
| pls = plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ spl0_235 ),
inference(paramodulation,[status(thm)],[f8221,f1299]) ).
fof(f8723,plain,
( ~ spl0_95
| spl0_407
| ~ spl0_235 ),
inference(split_clause,[status(thm)],[f8722,f5684,f8719,f6632]) ).
fof(f8790,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls))
| ~ spl0_407 ),
inference(backward_demodulation,[status(thm)],[f8720,f4654]) ).
fof(f8791,plain,
( $false
| ~ spl0_407 ),
inference(forward_subsumption_resolution,[status(thm)],[f8790,f1529]) ).
fof(f8792,plain,
~ spl0_407,
inference(contradiction_clause,[status(thm)],[f8791]) ).
fof(f8793,plain,
$false,
inference(sat_refutation,[status(thm)],[f6636,f8165,f8219,f8231,f8723,f8792]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Apr 29 20:58:50 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 4.41/0.98 % Refutation found
% 4.41/0.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.41/0.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.95/1.02 % Elapsed time: 0.741093 seconds
% 4.95/1.02 % CPU time: 5.099512 seconds
% 4.95/1.02 % Total memory used: 253.052 MB
% 4.95/1.02 % Net memory used: 250.518 MB
%------------------------------------------------------------------------------