TSTP Solution File: NUM925+8 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM925+8 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 20.45s 3.59s
% Output : CNFRefutation 21.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+8 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n013.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 : Mon Apr 29 20:54:19 EDT 2024
% 0.20/0.35 % CPUTime :
% 0.86/1.05 % Drodi V3.6.0
% 20.45/3.59 % Refutation found
% 20.45/3.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.45/3.59 % SZS output start CNFRefutation for theBenchmark
% 20.45/3.59 fof(f265,axiom,(
% 20.45/3.59 (! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f299,axiom,(
% 20.45/3.59 (! [V,W] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f305,axiom,(
% 20.45/3.59 (! [M,N] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f306,axiom,(
% 20.45/3.59 hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int) ),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f309,axiom,(
% 20.45/3.59 (! [Na] :( hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int)<=> Na = zero_zero(nat) ) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f311,axiom,(
% 20.45/3.59 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))) ),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f319,axiom,(
% 20.45/3.59 one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) ),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f327,axiom,(
% 20.45/3.59 (! [Z1,Z2,Z3] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3)) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f329,axiom,(
% 20.45/3.59 (! [Z_1,W] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f354,axiom,(
% 20.45/3.59 hAPP(int,int,bit0,pls) = pls ),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f358,axiom,(
% 20.45/3.59 pls = zero_zero(int) ),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f360,axiom,(
% 20.45/3.59 (! [K_4] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),pls) = ti(int,K_4) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f361,axiom,(
% 20.45/3.59 (! [K_4] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_4) = ti(int,K_4) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f363,axiom,(
% 20.45/3.59 (! [K_4] : hAPP(int,int,bit0,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),K_4) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f377,axiom,(
% 20.45/3.59 (! [K_4] : hAPP(int,int,bit1,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_4)),K_4) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f389,axiom,(
% 20.45/3.59 hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f439,axiom,(
% 20.45/3.59 (! [Ma,Na] :( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na) = zero_zero(nat)<=> ( Ma = zero_zero(nat)& Na = zero_zero(nat) ) ) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f441,axiom,(
% 20.45/3.59 (! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N) = N )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.45/3.59 fof(f450,axiom,(
% 20.45/3.59 (! [X_a] :( ring_11004092258visors(X_a)=> (! [N,A_1] :( ti(X_a,A_1) != zero_zero(X_a)=> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N) != zero_zero(X_a) ) )) )),
% 20.45/3.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f477,axiom,(
% 20.79/3.61 (! [Xa,Na] :( hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na) = one_one(nat)<=> ( Xa = one_one(nat)| Na = zero_zero(nat) ) ) )),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f619,axiom,(
% 20.79/3.61 (! [Ma,Na] :( hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),Na) = zero_zero(nat)<=> ( Na != zero_zero(nat)& Ma = zero_zero(nat) ) ) )),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f1049,axiom,(
% 20.79/3.61 (! [L_4] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),L_4)) )),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f2242,axiom,(
% 20.79/3.61 (! [X_a] :( ab_group_add(X_a)=> (! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),A_1) = zero_zero(X_a) )) )),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f2246,axiom,(
% 20.79/3.61 (! [X_a] :( group_add(X_a)=> (! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),zero_zero(X_a)),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1) )) )),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f2356,axiom,(
% 20.79/3.61 (! [Na,Ma] :( hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Na)) = hAPP(nat,int,semiring_1_of_nat(int),Ma)<=> ( Na = zero_zero(nat)& Ma = zero_zero(nat) ) ) )),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f5293,axiom,(
% 20.79/3.61 ring_11004092258visors(int) ),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f5318,axiom,(
% 20.79/3.61 ab_group_add(int) ),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f5328,axiom,(
% 20.79/3.61 group_add(int) ),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f5747,conjecture,(
% 20.79/3.61 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
% 20.79/3.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 20.79/3.61 fof(f5748,negated_conjecture,(
% 20.79/3.61 ~(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) )),
% 20.79/3.61 inference(negated_conjecture,[status(cth)],[f5747])).
% 20.79/3.61 fof(f6089,plain,(
% 20.79/3.61 ![X0,X1,X2,X3]: (hAPP(X0,X1,X2,ti(X0,X3))=hAPP(X0,X1,X2,X3))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f265])).
% 20.79/3.61 fof(f6149,plain,(
% 20.79/3.61 ![X0,X1]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),X0)),hAPP(int,int,number_number_of(int),X1))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),X1)))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f299])).
% 20.79/3.61 fof(f6159,plain,(
% 20.79/3.61 ![X0,X1]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X0)),hAPP(nat,int,semiring_1_of_nat(int),X1))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f305])).
% 20.79/3.61 fof(f6160,plain,(
% 20.79/3.61 hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int)),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f306])).
% 20.79/3.61 fof(f6163,plain,(
% 20.79/3.61 ![Na]: ((~hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)|Na=zero_zero(nat))&(hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)|~Na=zero_zero(nat)))),
% 20.79/3.61 inference(NNF_transformation,[status(esa)],[f309])).
% 20.79/3.61 fof(f6164,plain,(
% 20.79/3.61 (![Na]: (~hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)|Na=zero_zero(nat)))&(![Na]: (hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)|~Na=zero_zero(nat)))),
% 20.79/3.61 inference(miniscoping,[status(esa)],[f6163])).
% 20.79/3.61 fof(f6166,plain,(
% 20.79/3.61 ![X0]: (hAPP(nat,int,semiring_1_of_nat(int),X0)=zero_zero(int)|~X0=zero_zero(nat))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f6164])).
% 20.79/3.61 fof(f6168,plain,(
% 20.79/3.61 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)))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f311])).
% 20.79/3.61 fof(f6194,plain,(
% 20.79/3.61 one_one(int)=hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f319])).
% 20.79/3.61 fof(f6220,plain,(
% 20.79/3.61 ![X0,X1,X2]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),X1)),X2)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X2)))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f327])).
% 20.79/3.61 fof(f6222,plain,(
% 20.79/3.61 ![X0,X1]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),X1)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),X0))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f329])).
% 20.79/3.61 fof(f6304,plain,(
% 20.79/3.61 hAPP(int,int,bit0,pls)=pls),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f354])).
% 20.79/3.61 fof(f6313,plain,(
% 20.79/3.61 pls=zero_zero(int)),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f358])).
% 20.79/3.61 fof(f6315,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),pls)=ti(int,X0))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f360])).
% 20.79/3.61 fof(f6316,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X0)=ti(int,X0))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f361])).
% 20.79/3.61 fof(f6318,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,bit0,X0)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),X0))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f363])).
% 20.79/3.61 fof(f6345,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,bit1,X0)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),X0)),X0))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f377])).
% 20.79/3.61 fof(f6373,plain,(
% 20.79/3.61 hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f389])).
% 20.79/3.61 fof(f6517,plain,(
% 20.79/3.61 ![Ma,Na]: ((~hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na)=zero_zero(nat)|(Ma=zero_zero(nat)&Na=zero_zero(nat)))&(hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na)=zero_zero(nat)|(~Ma=zero_zero(nat)|~Na=zero_zero(nat))))),
% 20.79/3.61 inference(NNF_transformation,[status(esa)],[f439])).
% 20.79/3.61 fof(f6518,plain,(
% 20.79/3.61 (![Ma,Na]: (~hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na)=zero_zero(nat)|(Ma=zero_zero(nat)&Na=zero_zero(nat))))&(![Ma,Na]: (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na)=zero_zero(nat)|(~Ma=zero_zero(nat)|~Na=zero_zero(nat))))),
% 20.79/3.61 inference(miniscoping,[status(esa)],[f6517])).
% 20.79/3.61 fof(f6520,plain,(
% 20.79/3.61 ![X0,X1]: (~hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)=zero_zero(nat)|X1=zero_zero(nat))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f6518])).
% 20.79/3.61 fof(f6523,plain,(
% 20.79/3.61 ![X0]: (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0)=X0)),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f441])).
% 20.79/3.61 fof(f6551,plain,(
% 20.79/3.61 ![X_a]: (~ring_11004092258visors(X_a)|(![N,A_1]: (ti(X_a,A_1)=zero_zero(X_a)|~hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)=zero_zero(X_a))))),
% 20.79/3.61 inference(pre_NNF_transformation,[status(esa)],[f450])).
% 20.79/3.61 fof(f6552,plain,(
% 20.79/3.61 ![X_a]: (~ring_11004092258visors(X_a)|(![A_1]: (ti(X_a,A_1)=zero_zero(X_a)|(![N]: ~hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)=zero_zero(X_a)))))),
% 20.79/3.61 inference(miniscoping,[status(esa)],[f6551])).
% 20.79/3.61 fof(f6553,plain,(
% 20.79/3.61 ![X0,X1,X2]: (~ring_11004092258visors(X0)|ti(X0,X1)=zero_zero(X0)|~hAPP(nat,X0,hAPP(X0,fun(nat,X0),power_power(X0),X1),X2)=zero_zero(X0))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f6552])).
% 20.79/3.61 fof(f6623,plain,(
% 20.79/3.61 ![Xa,Na]: ((~hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na)=one_one(nat)|(Xa=one_one(nat)|Na=zero_zero(nat)))&(hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na)=one_one(nat)|(~Xa=one_one(nat)&~Na=zero_zero(nat))))),
% 20.79/3.61 inference(NNF_transformation,[status(esa)],[f477])).
% 20.79/3.61 fof(f6624,plain,(
% 20.79/3.61 (![Xa,Na]: (~hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na)=one_one(nat)|(Xa=one_one(nat)|Na=zero_zero(nat))))&(![Xa,Na]: (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na)=one_one(nat)|(~Xa=one_one(nat)&~Na=zero_zero(nat))))),
% 20.79/3.61 inference(miniscoping,[status(esa)],[f6623])).
% 20.79/3.61 fof(f6627,plain,(
% 20.79/3.61 ![X0,X1]: (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X0),X1)=one_one(nat)|~X1=zero_zero(nat))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f6624])).
% 20.79/3.61 fof(f7072,plain,(
% 20.79/3.61 ![Ma,Na]: ((~hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),Na)=zero_zero(nat)|(~Na=zero_zero(nat)&Ma=zero_zero(nat)))&(hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),Na)=zero_zero(nat)|(Na=zero_zero(nat)|~Ma=zero_zero(nat))))),
% 20.79/3.61 inference(NNF_transformation,[status(esa)],[f619])).
% 20.79/3.61 fof(f7073,plain,(
% 20.79/3.61 (![Ma,Na]: (~hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),Na)=zero_zero(nat)|(~Na=zero_zero(nat)&Ma=zero_zero(nat))))&(![Ma,Na]: (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),Na)=zero_zero(nat)|(Na=zero_zero(nat)|~Ma=zero_zero(nat))))),
% 20.79/3.61 inference(miniscoping,[status(esa)],[f7072])).
% 20.79/3.61 fof(f7074,plain,(
% 20.79/3.61 ![X0,X1]: (~hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X0),X1)=zero_zero(nat)|~X1=zero_zero(nat))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f7073])).
% 20.79/3.61 fof(f7075,plain,(
% 20.79/3.61 ![X0,X1]: (~hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X0),X1)=zero_zero(nat)|X0=zero_zero(nat))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f7073])).
% 20.79/3.61 fof(f8296,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit0,X0))=hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),X0)))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f1049])).
% 20.79/3.61 fof(f11996,plain,(
% 20.79/3.61 ![X_a]: (~ab_group_add(X_a)|(![A_1]: hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),A_1)=zero_zero(X_a)))),
% 20.79/3.61 inference(pre_NNF_transformation,[status(esa)],[f2242])).
% 20.79/3.61 fof(f11997,plain,(
% 20.79/3.61 ![X0,X1]: (~ab_group_add(X0)|hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),hAPP(X0,X0,uminus_uminus(X0),X1)),X1)=zero_zero(X0))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f11996])).
% 20.79/3.61 fof(f12007,plain,(
% 20.79/3.61 ![X_a]: (~group_add(X_a)|(![A_1]: hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),zero_zero(X_a)),A_1)=hAPP(X_a,X_a,uminus_uminus(X_a),A_1)))),
% 20.79/3.61 inference(pre_NNF_transformation,[status(esa)],[f2246])).
% 20.79/3.61 fof(f12008,plain,(
% 20.79/3.61 ![X0,X1]: (~group_add(X0)|hAPP(X0,X0,hAPP(X0,fun(X0,X0),minus_minus(X0),zero_zero(X0)),X1)=hAPP(X0,X0,uminus_uminus(X0),X1))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f12007])).
% 20.79/3.61 fof(f12283,plain,(
% 20.79/3.61 ![Na,Ma]: ((~hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Na))=hAPP(nat,int,semiring_1_of_nat(int),Ma)|(Na=zero_zero(nat)&Ma=zero_zero(nat)))&(hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Na))=hAPP(nat,int,semiring_1_of_nat(int),Ma)|(~Na=zero_zero(nat)|~Ma=zero_zero(nat))))),
% 20.79/3.61 inference(NNF_transformation,[status(esa)],[f2356])).
% 20.79/3.61 fof(f12284,plain,(
% 20.79/3.61 (![Na,Ma]: (~hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Na))=hAPP(nat,int,semiring_1_of_nat(int),Ma)|(Na=zero_zero(nat)&Ma=zero_zero(nat))))&(![Na,Ma]: (hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Na))=hAPP(nat,int,semiring_1_of_nat(int),Ma)|(~Na=zero_zero(nat)|~Ma=zero_zero(nat))))),
% 20.79/3.61 inference(miniscoping,[status(esa)],[f12283])).
% 20.79/3.61 fof(f12286,plain,(
% 20.79/3.61 ![X0,X1]: (~hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(nat,int,semiring_1_of_nat(int),X1)|X1=zero_zero(nat))),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f12284])).
% 20.79/3.61 fof(f20498,plain,(
% 20.79/3.61 ring_11004092258visors(int)),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f5293])).
% 20.79/3.61 fof(f20523,plain,(
% 20.79/3.61 ab_group_add(int)),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f5318])).
% 20.79/3.61 fof(f20533,plain,(
% 20.79/3.61 group_add(int)),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f5328])).
% 20.79/3.61 fof(f20963,plain,(
% 20.79/3.61 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(int)),
% 20.79/3.61 inference(cnf_transformation,[status(esa)],[f5748])).
% 20.79/3.61 fof(f21366,plain,(
% 20.79/3.61 spl0_8 <=> one_one(nat)=zero_zero(nat)),
% 20.79/3.61 introduced(split_symbol_definition)).
% 20.79/3.61 fof(f21370,plain,(
% 20.79/3.61 hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int)),
% 20.79/3.61 inference(destructive_equality_resolution,[status(esa)],[f6166])).
% 20.79/3.61 fof(f21384,plain,(
% 20.79/3.61 ![X0]: (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X0),zero_zero(nat))=one_one(nat))),
% 20.79/3.61 inference(destructive_equality_resolution,[status(esa)],[f6627])).
% 20.79/3.61 fof(f21386,plain,(
% 20.79/3.61 ![X0]: (~hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X0),zero_zero(nat))=zero_zero(nat))),
% 20.79/3.61 inference(destructive_equality_resolution,[status(esa)],[f7074])).
% 20.79/3.61 fof(f21617,plain,(
% 20.79/3.61 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=pls),
% 20.79/3.61 inference(backward_demodulation,[status(thm)],[f6313,f20963])).
% 20.79/3.61 fof(f21621,plain,(
% 20.79/3.61 hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=pls),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6313,f21370])).
% 20.79/3.61 fof(f21697,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,bit0,hAPP(int,int,number_number_of(int),X0))=hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),X0)))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f6318,f6149])).
% 20.79/3.61 fof(f21698,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,bit0,hAPP(int,int,number_number_of(int),X0))=hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,X0)))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6318,f21697])).
% 20.79/3.61 fof(f21741,plain,(
% 20.79/3.61 ~one_one(nat)=zero_zero(nat)),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f21384,f21386])).
% 20.79/3.61 fof(f21755,plain,(
% 20.79/3.61 spl0_21 <=> X0=zero_zero(nat)),
% 20.79/3.61 introduced(split_symbol_definition)).
% 20.79/3.61 fof(f21756,plain,(
% 20.79/3.61 ![X0]: (X0=zero_zero(nat)|~spl0_21)),
% 20.79/3.61 inference(component_clause,[status(thm)],[f21755])).
% 20.79/3.61 fof(f21758,plain,(
% 20.79/3.61 ![X0]: (~one_one(nat)=zero_zero(nat)|X0=zero_zero(nat))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f21384,f7075])).
% 20.79/3.61 fof(f21759,plain,(
% 20.79/3.61 ~spl0_8|spl0_21),
% 20.79/3.61 inference(split_clause,[status(thm)],[f21758,f21366,f21755])).
% 20.79/3.61 fof(f21787,plain,(
% 20.79/3.61 $false|~spl0_21),
% 20.79/3.61 inference(backward_subsumption_resolution,[status(thm)],[f21741,f21756])).
% 20.79/3.61 fof(f21788,plain,(
% 20.79/3.61 ~spl0_21),
% 20.79/3.61 inference(contradiction_clause,[status(thm)],[f21787])).
% 20.79/3.61 fof(f21809,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,bit0,hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X0)))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f6318,f6159])).
% 20.79/3.61 fof(f21810,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0)))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f21621,f6159])).
% 20.79/3.61 fof(f21811,plain,(
% 20.79/3.61 ![X0]: (ti(int,hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0)))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6316,f21810])).
% 20.79/3.61 fof(f21812,plain,(
% 20.79/3.61 ![X0]: (ti(int,hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(nat,int,semiring_1_of_nat(int),X0))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6523,f21811])).
% 20.79/3.61 fof(f22019,plain,(
% 20.79/3.61 ti(int,one_one(int))=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f6160,f21812])).
% 20.79/3.61 fof(f22020,plain,(
% 20.79/3.61 ti(int,one_one(int))=one_one(int)),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6160,f22019])).
% 20.79/3.61 fof(f22088,plain,(
% 20.79/3.61 spl0_31 <=> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))=zero_zero(nat)),
% 20.79/3.61 introduced(split_symbol_definition)).
% 20.79/3.61 fof(f22090,plain,(
% 20.79/3.61 ~hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))=zero_zero(nat)|spl0_31),
% 20.79/3.61 inference(component_clause,[status(thm)],[f22088])).
% 20.79/3.61 fof(f22091,plain,(
% 20.79/3.61 ~hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))=zero_zero(nat)|one_one(nat)=zero_zero(nat)),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f6168,f6520])).
% 20.79/3.61 fof(f22092,plain,(
% 20.79/3.61 ~spl0_31|spl0_8),
% 20.79/3.61 inference(split_clause,[status(thm)],[f22091,f22088,f21366])).
% 20.79/3.61 fof(f22751,plain,(
% 20.79/3.61 ![X0,X1]: (ti(int,X0)=zero_zero(int)|~hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X0),X1)=zero_zero(int))),
% 20.79/3.61 inference(resolution,[status(thm)],[f20498,f6553])).
% 20.79/3.61 fof(f22752,plain,(
% 20.79/3.61 ![X0,X1]: (ti(int,X0)=pls|~hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X0),X1)=zero_zero(int))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6313,f22751])).
% 20.79/3.61 fof(f22753,plain,(
% 20.79/3.61 ![X0,X1]: (ti(int,X0)=pls|~hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X0),X1)=pls)),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6313,f22752])).
% 20.79/3.61 fof(f22790,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),X0)),X0)=zero_zero(int))),
% 20.79/3.61 inference(resolution,[status(thm)],[f20523,f11997])).
% 20.79/3.61 fof(f22791,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),hAPP(int,int,uminus_uminus(int),X0))=zero_zero(int))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6222,f22790])).
% 20.79/3.61 fof(f22792,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),hAPP(int,int,uminus_uminus(int),X0))=pls)),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6313,f22791])).
% 20.79/3.61 fof(f22800,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),zero_zero(int)),X0)=hAPP(int,int,uminus_uminus(int),X0))),
% 20.79/3.61 inference(resolution,[status(thm)],[f20533,f12008])).
% 20.79/3.61 fof(f22801,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),X0)=hAPP(int,int,uminus_uminus(int),X0))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6313,f22800])).
% 20.79/3.61 fof(f22854,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit0,X0))=hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),X0)))),
% 20.79/3.61 inference(backward_demodulation,[status(thm)],[f22801,f8296])).
% 20.79/3.61 fof(f22855,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit0,X0))=hAPP(int,int,bit0,hAPP(int,int,uminus_uminus(int),X0)))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f22801,f22854])).
% 20.79/3.61 fof(f22904,plain,(
% 20.79/3.61 ti(int,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))=pls),
% 20.79/3.61 inference(resolution,[status(thm)],[f22753,f21617])).
% 20.79/3.61 fof(f22949,plain,(
% 20.79/3.61 ![X0,X1]: (hAPP(int,X0,X1,pls)=hAPP(int,X0,X1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f22904,f6089])).
% 20.79/3.61 fof(f22981,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),pls)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),X0))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f6222,f22949])).
% 20.79/3.61 fof(f22982,plain,(
% 20.79/3.61 ![X0]: (ti(int,X0)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),X0))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6315,f22981])).
% 20.79/3.61 fof(f22983,plain,(
% 20.79/3.61 ![X0]: (ti(int,X0)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),n)),X0)))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6220,f22982])).
% 20.79/3.61 fof(f23355,plain,(
% 20.79/3.61 ti(int,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),n)))=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),pls)),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f22792,f22983])).
% 20.79/3.61 fof(f23356,plain,(
% 20.79/3.61 ti(int,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),n)))=ti(int,one_one(int))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6315,f23355])).
% 20.79/3.61 fof(f23357,plain,(
% 20.79/3.61 ti(int,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),n)))=one_one(int)),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f22020,f23356])).
% 20.79/3.61 fof(f23405,plain,(
% 20.79/3.61 ![X0,X1]: (hAPP(int,X0,X1,one_one(int))=hAPP(int,X0,X1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),n))))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f23357,f6089])).
% 20.79/3.61 fof(f24202,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,bit1,X0)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X0),X0)))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6220,f6345])).
% 20.79/3.61 fof(f24203,plain,(
% 20.79/3.61 ![X0]: (hAPP(int,int,bit1,X0)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,bit0,X0)))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6318,f24202])).
% 20.79/3.61 fof(f24211,plain,(
% 20.79/3.61 hAPP(int,int,bit1,pls)=hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),pls)),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f6304,f24203])).
% 20.79/3.61 fof(f24212,plain,(
% 20.79/3.61 hAPP(int,int,bit1,pls)=ti(int,one_one(int))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f6315,f24211])).
% 20.79/3.61 fof(f24213,plain,(
% 20.79/3.61 hAPP(int,int,bit1,pls)=one_one(int)),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f22020,f24212])).
% 20.79/3.61 fof(f24689,plain,(
% 20.79/3.61 ~hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,one_one(int)))=zero_zero(nat)|spl0_31),
% 20.79/3.61 inference(backward_demodulation,[status(thm)],[f24213,f22090])).
% 20.79/3.61 fof(f24697,plain,(
% 20.79/3.61 one_one(int)=hAPP(int,int,number_number_of(int),one_one(int))),
% 20.79/3.61 inference(backward_demodulation,[status(thm)],[f24213,f6194])).
% 20.79/3.61 fof(f24964,plain,(
% 20.79/3.61 hAPP(int,int,bit0,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f21698,f6373])).
% 20.79/3.61 fof(f24965,plain,(
% 20.79/3.61 hAPP(int,int,bit0,hAPP(int,int,number_number_of(int),one_one(int)))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f24213,f24964])).
% 20.79/3.61 fof(f24966,plain,(
% 20.79/3.61 hAPP(int,int,bit0,one_one(int))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f24697,f24965])).
% 20.79/3.61 fof(f24967,plain,(
% 20.79/3.61 hAPP(int,int,bit0,one_one(int))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,one_one(int))))),
% 20.79/3.61 inference(forward_demodulation,[status(thm)],[f24213,f24966])).
% 20.79/3.61 fof(f24990,plain,(
% 20.79/3.61 spl0_150 <=> ~hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(int,int,bit0,one_one(int))),
% 20.79/3.61 introduced(split_symbol_definition)).
% 20.79/3.61 fof(f24991,plain,(
% 20.79/3.61 ![X0]: (~hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(int,int,bit0,one_one(int))|~spl0_150)),
% 20.79/3.61 inference(component_clause,[status(thm)],[f24990])).
% 20.79/3.61 fof(f24993,plain,(
% 20.79/3.61 spl0_151 <=> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,one_one(int)))=zero_zero(nat)),
% 20.79/3.61 introduced(split_symbol_definition)).
% 20.79/3.61 fof(f24994,plain,(
% 20.79/3.61 hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,one_one(int)))=zero_zero(nat)|~spl0_151),
% 20.79/3.61 inference(component_clause,[status(thm)],[f24993])).
% 20.79/3.61 fof(f24996,plain,(
% 20.79/3.61 ![X0]: (~hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),X0))=hAPP(int,int,bit0,one_one(int))|hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,one_one(int)))=zero_zero(nat))),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f24967,f12286])).
% 20.79/3.61 fof(f24997,plain,(
% 20.79/3.61 spl0_150|spl0_151),
% 20.79/3.61 inference(split_clause,[status(thm)],[f24996,f24990,f24993])).
% 20.79/3.61 fof(f25032,plain,(
% 20.79/3.61 $false|spl0_31|~spl0_151),
% 20.79/3.61 inference(forward_subsumption_resolution,[status(thm)],[f24994,f24689])).
% 20.79/3.61 fof(f25033,plain,(
% 20.79/3.61 spl0_31|~spl0_151),
% 20.79/3.61 inference(contradiction_clause,[status(thm)],[f25032])).
% 20.79/3.61 fof(f25860,plain,(
% 20.79/3.61 ![X0]: (~hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit0,hAPP(nat,int,semiring_1_of_nat(int),X0)))=hAPP(int,int,bit0,one_one(int))|~spl0_150)),
% 20.79/3.61 inference(paramodulation,[status(thm)],[f21809,f24991])).
% 20.79/3.61 fof(f25861,plain,(
% 20.79/3.61 ![X0]: (~hAPP(int,int,bit0,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),X0)))=hAPP(int,int,bit0,one_one(int))|~spl0_150)),
% 21.12/3.71 inference(forward_demodulation,[status(thm)],[f22855,f25860])).
% 21.12/3.71 fof(f28234,plain,(
% 21.12/3.71 $false|~spl0_150),
% 21.12/3.71 inference(resolution,[status(thm)],[f25861,f23405])).
% 21.12/3.71 fof(f28235,plain,(
% 21.12/3.71 ~spl0_150),
% 21.12/3.71 inference(contradiction_clause,[status(thm)],[f28234])).
% 21.12/3.71 fof(f28236,plain,(
% 21.12/3.71 $false),
% 21.12/3.71 inference(sat_refutation,[status(thm)],[f21759,f21788,f22092,f24997,f25033,f28235])).
% 21.12/3.71 % SZS output end CNFRefutation for theBenchmark.p
% 22.29/3.80 % Elapsed time: 3.429791 seconds
% 22.29/3.80 % CPU time: 21.364483 seconds
% 22.29/3.80 % Total memory used: 1.153 GB
% 22.29/3.80 % Net memory used: 1.151 GB
%------------------------------------------------------------------------------