TSTP Solution File: HAL003+3 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : HAL003+3 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n022.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 : Sat Jul 16 12:45:24 EDT 2022
% Result : Theorem 91.88s 92.06s
% Output : CNFRefutation 91.88s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(lemma12,axiom,
! [E] :
( element(E,e)
=> ? [B1,B2] :
( element(B1,b)
& element(B2,b)
& apply(g,subtract(b,B1,B2)) = E ) ),
input ).
fof(lemma12_0,plain,
! [E] :
( ~ element(E,e)
| ? [B1,B2] :
( element(B1,b)
& element(B2,b)
& apply(g,subtract(b,B1,B2)) = E ) ),
inference(orientation,[status(thm)],[lemma12]) ).
fof(lemma8,axiom,
! [E] :
( element(E,e)
=> ? [B1,E1,A] :
( element(B1,b)
& element(E1,e)
& subtract(e,apply(g,B1),E) = E1
& element(A,a)
& apply(gamma,apply(f,A)) = E1
& apply(g,apply(alpha,A)) = E1 ) ),
input ).
fof(lemma8_0,plain,
! [E] :
( ~ element(E,e)
| ? [B1,E1,A] :
( element(B1,b)
& element(E1,e)
& subtract(e,apply(g,B1),E) = E1
& element(A,a)
& apply(gamma,apply(f,A)) = E1
& apply(g,apply(alpha,A)) = E1 ) ),
inference(orientation,[status(thm)],[lemma8]) ).
fof(lemma3,axiom,
! [E] :
( element(E,e)
=> ? [R,B1] :
( element(R,r)
& apply(delta,E) = R
& element(B1,b)
& apply(h,apply(beta,B1)) = R
& apply(delta,apply(g,B1)) = R ) ),
input ).
fof(lemma3_0,plain,
! [E] :
( ~ element(E,e)
| ? [R,B1] :
( element(R,r)
& apply(delta,E) = R
& element(B1,b)
& apply(h,apply(beta,B1)) = R
& apply(delta,apply(g,B1)) = R ) ),
inference(orientation,[status(thm)],[lemma3]) ).
fof(beta_h_g_delta_commute,axiom,
commute(beta,h,g,delta),
input ).
fof(beta_h_g_delta_commute_0,plain,
( commute(beta,h,g,delta)
| $false ),
inference(orientation,[status(thm)],[beta_h_g_delta_commute]) ).
fof(alpha_g_f_gamma_commute,axiom,
commute(alpha,g,f,gamma),
input ).
fof(alpha_g_f_gamma_commute_0,plain,
( commute(alpha,g,f,gamma)
| $false ),
inference(orientation,[status(thm)],[alpha_g_f_gamma_commute]) ).
fof(gamma_delta_exact,axiom,
exact(gammma,delta),
input ).
fof(gamma_delta_exact_0,plain,
( exact(gammma,delta)
| $false ),
inference(orientation,[status(thm)],[gamma_delta_exact]) ).
fof(alpha_beta_exact,axiom,
exact(alpha,beta),
input ).
fof(alpha_beta_exact_0,plain,
( exact(alpha,beta)
| $false ),
inference(orientation,[status(thm)],[alpha_beta_exact]) ).
fof(delta_surjection,axiom,
surjection(delta),
input ).
fof(delta_surjection_0,plain,
( surjection(delta)
| $false ),
inference(orientation,[status(thm)],[delta_surjection]) ).
fof(beta_surjection,axiom,
surjection(beta),
input ).
fof(beta_surjection_0,plain,
( surjection(beta)
| $false ),
inference(orientation,[status(thm)],[beta_surjection]) ).
fof(gamma_injection,axiom,
injection(gamma),
input ).
fof(gamma_injection_0,plain,
( injection(gamma)
| $false ),
inference(orientation,[status(thm)],[gamma_injection]) ).
fof(alpha_injection,axiom,
injection(alpha),
input ).
fof(alpha_injection_0,plain,
( injection(alpha)
| $false ),
inference(orientation,[status(thm)],[alpha_injection]) ).
fof(h_morphism,axiom,
morphism(h,c,r),
input ).
fof(h_morphism_0,plain,
( morphism(h,c,r)
| $false ),
inference(orientation,[status(thm)],[h_morphism]) ).
fof(g_morphism,axiom,
morphism(g,b,e),
input ).
fof(g_morphism_0,plain,
( morphism(g,b,e)
| $false ),
inference(orientation,[status(thm)],[g_morphism]) ).
fof(f_morphism,axiom,
morphism(f,a,d),
input ).
fof(f_morphism_0,plain,
( morphism(f,a,d)
| $false ),
inference(orientation,[status(thm)],[f_morphism]) ).
fof(delta_morphism,axiom,
morphism(delta,e,r),
input ).
fof(delta_morphism_0,plain,
( morphism(delta,e,r)
| $false ),
inference(orientation,[status(thm)],[delta_morphism]) ).
fof(gamma_morphism,axiom,
morphism(gamma,d,e),
input ).
fof(gamma_morphism_0,plain,
( morphism(gamma,d,e)
| $false ),
inference(orientation,[status(thm)],[gamma_morphism]) ).
fof(beta_morphism,axiom,
morphism(beta,b,c),
input ).
fof(beta_morphism_0,plain,
( morphism(beta,b,c)
| $false ),
inference(orientation,[status(thm)],[beta_morphism]) ).
fof(alpha_morphism,axiom,
morphism(alpha,a,b),
input ).
fof(alpha_morphism_0,plain,
( morphism(alpha,a,b)
| $false ),
inference(orientation,[status(thm)],[alpha_morphism]) ).
fof(subtract_distribution,axiom,
! [Morphism,Dom,Cod] :
( morphism(Morphism,Dom,Cod)
=> ! [El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)) ) ),
input ).
fof(subtract_distribution_0,plain,
! [Cod,Dom,Morphism] :
( ~ morphism(Morphism,Dom,Cod)
| ! [El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)) ) ),
inference(orientation,[status(thm)],[subtract_distribution]) ).
fof(subtract_cancellation,axiom,
! [Dom,El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> subtract(Dom,El1,subtract(Dom,El1,El2)) = El2 ),
input ).
fof(subtract_cancellation_0,plain,
! [Dom,El1,El2] :
( subtract(Dom,El1,subtract(Dom,El1,El2)) = El2
| ~ ( element(El1,Dom)
& element(El2,Dom) ) ),
inference(orientation,[status(thm)],[subtract_cancellation]) ).
fof(subtract_to_0,axiom,
! [Dom,El] :
( element(El,Dom)
=> subtract(Dom,El,El) = zero(Dom) ),
input ).
fof(subtract_to_0_0,plain,
! [Dom,El] :
( ~ element(El,Dom)
| subtract(Dom,El,El) = zero(Dom) ),
inference(orientation,[status(thm)],[subtract_to_0]) ).
fof(subtract_in_domain,axiom,
! [Dom,El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> element(subtract(Dom,El1,El2),Dom) ),
input ).
fof(subtract_in_domain_0,plain,
! [Dom,El1,El2] :
( element(subtract(Dom,El1,El2),Dom)
| ~ ( element(El1,Dom)
& element(El2,Dom) ) ),
inference(orientation,[status(thm)],[subtract_in_domain]) ).
fof(properties_for_commute,axiom,
! [M1,M2,M3,M4,Dom,DomCod1,DomCod2,Cod] :
( ( morphism(M1,Dom,DomCod1)
& morphism(M2,DomCod1,Cod)
& morphism(M3,Dom,DomCod2)
& morphism(M4,DomCod2,Cod)
& ! [ElDom] :
( element(ElDom,Dom)
=> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)) ) )
=> commute(M1,M2,M3,M4) ),
input ).
fof(properties_for_commute_0,plain,
! [Cod,Dom,DomCod1,DomCod2,M1,M2,M3,M4] :
( commute(M1,M2,M3,M4)
| ~ ( morphism(M1,Dom,DomCod1)
& morphism(M2,DomCod1,Cod)
& morphism(M3,Dom,DomCod2)
& morphism(M4,DomCod2,Cod)
& ! [ElDom] :
( element(ElDom,Dom)
=> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)) ) ) ),
inference(orientation,[status(thm)],[properties_for_commute]) ).
fof(properties_for_exact,axiom,
! [Morphism1,Morphism2,Dom,CodDom,Cod] :
( ( morphism(Morphism1,Dom,CodDom)
& morphism(Morphism2,CodDom,Cod)
& ! [ElCodDom] :
( ( element(ElCodDom,CodDom)
& apply(Morphism2,ElCodDom) = zero(Cod) )
<=> ? [ElDom] :
( element(ElDom,Dom)
& apply(Morphism1,ElDom) = ElCodDom ) ) )
=> exact(Morphism1,Morphism2) ),
input ).
fof(properties_for_exact_0,plain,
! [Cod,CodDom,Dom,Morphism1,Morphism2] :
( exact(Morphism1,Morphism2)
| ~ ( morphism(Morphism1,Dom,CodDom)
& morphism(Morphism2,CodDom,Cod)
& ! [ElCodDom] :
( ( element(ElCodDom,CodDom)
& apply(Morphism2,ElCodDom) = zero(Cod) )
<=> ? [ElDom] :
( element(ElDom,Dom)
& apply(Morphism1,ElDom) = ElCodDom ) ) ) ),
inference(orientation,[status(thm)],[properties_for_exact]) ).
fof(properties_for_surjection,axiom,
! [Morphism,Dom,Cod] :
( ( morphism(Morphism,Dom,Cod)
& ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( element(ElDom,Dom)
& apply(Morphism,ElDom) = ElCod ) ) )
=> surjection(Morphism) ),
input ).
fof(properties_for_surjection_0,plain,
! [Cod,Dom,Morphism] :
( surjection(Morphism)
| ~ ( morphism(Morphism,Dom,Cod)
& ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( element(ElDom,Dom)
& apply(Morphism,ElDom) = ElCod ) ) ) ),
inference(orientation,[status(thm)],[properties_for_surjection]) ).
fof(properties_for_injection,axiom,
! [Morphism,Dom,Cod] :
( ( morphism(Morphism,Dom,Cod)
& ! [El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom)
& apply(Morphism,El1) = apply(Morphism,El2) )
=> El1 = El2 ) )
=> injection(Morphism) ),
input ).
fof(properties_for_injection_0,plain,
! [Cod,Dom,Morphism] :
( injection(Morphism)
| ~ ( morphism(Morphism,Dom,Cod)
& ! [El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom)
& apply(Morphism,El1) = apply(Morphism,El2) )
=> El1 = El2 ) ) ),
inference(orientation,[status(thm)],[properties_for_injection]) ).
fof(morphism,axiom,
! [Morphism,Dom,Cod] :
( morphism(Morphism,Dom,Cod)
=> ( ! [El] :
( element(El,Dom)
=> element(apply(Morphism,El),Cod) )
& apply(Morphism,zero(Dom)) = zero(Cod) ) ),
input ).
fof(morphism_0,plain,
! [Cod,Dom,Morphism] :
( ~ morphism(Morphism,Dom,Cod)
| ( ! [El] :
( element(El,Dom)
=> element(apply(Morphism,El),Cod) )
& apply(Morphism,zero(Dom)) = zero(Cod) ) ),
inference(orientation,[status(thm)],[morphism]) ).
fof(def_lhs_atom1,axiom,
! [Morphism,Dom,Cod] :
( lhs_atom1(Morphism,Dom,Cod)
<=> ~ morphism(Morphism,Dom,Cod) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [Cod,Dom,Morphism] :
( lhs_atom1(Morphism,Dom,Cod)
| ( ! [El] :
( element(El,Dom)
=> element(apply(Morphism,El),Cod) )
& apply(Morphism,zero(Dom)) = zero(Cod) ) ),
inference(fold_definition,[status(thm)],[morphism_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [Morphism] :
( lhs_atom2(Morphism)
<=> injection(Morphism) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [Cod,Dom,Morphism] :
( lhs_atom2(Morphism)
| ~ ( morphism(Morphism,Dom,Cod)
& ! [El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom)
& apply(Morphism,El1) = apply(Morphism,El2) )
=> El1 = El2 ) ) ),
inference(fold_definition,[status(thm)],[properties_for_injection_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [Morphism] :
( lhs_atom3(Morphism)
<=> surjection(Morphism) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [Cod,Dom,Morphism] :
( lhs_atom3(Morphism)
| ~ ( morphism(Morphism,Dom,Cod)
& ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( element(ElDom,Dom)
& apply(Morphism,ElDom) = ElCod ) ) ) ),
inference(fold_definition,[status(thm)],[properties_for_surjection_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [Morphism2,Morphism1] :
( lhs_atom4(Morphism2,Morphism1)
<=> exact(Morphism1,Morphism2) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [Cod,CodDom,Dom,Morphism1,Morphism2] :
( lhs_atom4(Morphism2,Morphism1)
| ~ ( morphism(Morphism1,Dom,CodDom)
& morphism(Morphism2,CodDom,Cod)
& ! [ElCodDom] :
( ( element(ElCodDom,CodDom)
& apply(Morphism2,ElCodDom) = zero(Cod) )
<=> ? [ElDom] :
( element(ElDom,Dom)
& apply(Morphism1,ElDom) = ElCodDom ) ) ) ),
inference(fold_definition,[status(thm)],[properties_for_exact_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [M4,M3,M2,M1] :
( lhs_atom5(M4,M3,M2,M1)
<=> commute(M1,M2,M3,M4) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [Cod,Dom,DomCod1,DomCod2,M1,M2,M3,M4] :
( lhs_atom5(M4,M3,M2,M1)
| ~ ( morphism(M1,Dom,DomCod1)
& morphism(M2,DomCod1,Cod)
& morphism(M3,Dom,DomCod2)
& morphism(M4,DomCod2,Cod)
& ! [ElDom] :
( element(ElDom,Dom)
=> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)) ) ) ),
inference(fold_definition,[status(thm)],[properties_for_commute_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [El2,El1,Dom] :
( lhs_atom6(El2,El1,Dom)
<=> element(subtract(Dom,El1,El2),Dom) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [Dom,El1,El2] :
( lhs_atom6(El2,El1,Dom)
| ~ ( element(El1,Dom)
& element(El2,Dom) ) ),
inference(fold_definition,[status(thm)],[subtract_in_domain_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [El,Dom] :
( lhs_atom7(El,Dom)
<=> ~ element(El,Dom) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [Dom,El] :
( lhs_atom7(El,Dom)
| subtract(Dom,El,El) = zero(Dom) ),
inference(fold_definition,[status(thm)],[subtract_to_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [El2,El1,Dom] :
( lhs_atom8(El2,El1,Dom)
<=> subtract(Dom,El1,subtract(Dom,El1,El2)) = El2 ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [Dom,El1,El2] :
( lhs_atom8(El2,El1,Dom)
| ~ ( element(El1,Dom)
& element(El2,Dom) ) ),
inference(fold_definition,[status(thm)],[subtract_cancellation_0,def_lhs_atom8]) ).
fof(to_be_clausified_8,plain,
! [Cod,Dom,Morphism] :
( lhs_atom1(Morphism,Dom,Cod)
| ! [El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)) ) ),
inference(fold_definition,[status(thm)],[subtract_distribution_0,def_lhs_atom1]) ).
fof(def_lhs_atom9,axiom,
( lhs_atom9
<=> morphism(alpha,a,b) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[alpha_morphism_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> morphism(beta,b,c) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[beta_morphism_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> morphism(gamma,d,e) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[gamma_morphism_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> morphism(delta,e,r) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[delta_morphism_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
( lhs_atom13
<=> morphism(f,a,d) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[f_morphism_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
( lhs_atom14
<=> morphism(g,b,e) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
( lhs_atom14
| $false ),
inference(fold_definition,[status(thm)],[g_morphism_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
( lhs_atom15
<=> morphism(h,c,r) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
( lhs_atom15
| $false ),
inference(fold_definition,[status(thm)],[h_morphism_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
( lhs_atom16
<=> injection(alpha) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[alpha_injection_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
( lhs_atom17
<=> injection(gamma) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
( lhs_atom17
| $false ),
inference(fold_definition,[status(thm)],[gamma_injection_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
( lhs_atom18
<=> surjection(beta) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
( lhs_atom18
| $false ),
inference(fold_definition,[status(thm)],[beta_surjection_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
( lhs_atom19
<=> surjection(delta) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
( lhs_atom19
| $false ),
inference(fold_definition,[status(thm)],[delta_surjection_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
( lhs_atom20
<=> exact(alpha,beta) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[alpha_beta_exact_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
( lhs_atom21
<=> exact(gammma,delta) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
( lhs_atom21
| $false ),
inference(fold_definition,[status(thm)],[gamma_delta_exact_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
( lhs_atom22
<=> commute(alpha,g,f,gamma) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
( lhs_atom22
| $false ),
inference(fold_definition,[status(thm)],[alpha_g_f_gamma_commute_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
( lhs_atom23
<=> commute(beta,h,g,delta) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
( lhs_atom23
| $false ),
inference(fold_definition,[status(thm)],[beta_h_g_delta_commute_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [E] :
( lhs_atom24(E)
<=> ~ element(E,e) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [E] :
( lhs_atom24(E)
| ? [R,B1] :
( element(R,r)
& apply(delta,E) = R
& element(B1,b)
& apply(h,apply(beta,B1)) = R
& apply(delta,apply(g,B1)) = R ) ),
inference(fold_definition,[status(thm)],[lemma3_0,def_lhs_atom24]) ).
fof(to_be_clausified_25,plain,
! [E] :
( lhs_atom24(E)
| ? [B1,E1,A] :
( element(B1,b)
& element(E1,e)
& subtract(e,apply(g,B1),E) = E1
& element(A,a)
& apply(gamma,apply(f,A)) = E1
& apply(g,apply(alpha,A)) = E1 ) ),
inference(fold_definition,[status(thm)],[lemma8_0,def_lhs_atom24]) ).
fof(to_be_clausified_26,plain,
! [E] :
( lhs_atom24(E)
| ? [B1,B2] :
( element(B1,b)
& element(B2,b)
& apply(g,subtract(b,B1,B2)) = E ) ),
inference(fold_definition,[status(thm)],[lemma12_0,def_lhs_atom24]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X13,X14,X15,X16,X17,X18,X2,X3] :
( lhs_atom5(X13,X14,X15,X16)
| ~ ( morphism(X16,X2,X18)
& morphism(X15,X18,X3)
& morphism(X14,X2,X17)
& morphism(X13,X17,X3)
& ! [X8] :
( element(X8,X2)
=> apply(X15,apply(X16,X8)) = apply(X13,apply(X14,X8)) ) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_1,axiom,
! [X9,X10,X2,X11,X3] :
( lhs_atom4(X9,X10)
| ~ ( morphism(X10,X2,X11)
& morphism(X9,X11,X3)
& ! [X12] :
( ( element(X12,X11)
& apply(X9,X12) = zero(X3) )
<=> ? [X8] :
( element(X8,X2)
& apply(X10,X8) = X12 ) ) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_2,axiom,
! [X1,X2,X3] :
( lhs_atom1(X1,X2,X3)
| ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_3,axiom,
! [X1,X2,X3] :
( lhs_atom3(X1)
| ~ ( morphism(X1,X2,X3)
& ! [X7] :
( element(X7,X3)
=> ? [X8] :
( element(X8,X2)
& apply(X1,X8) = X7 ) ) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_4,axiom,
! [X1,X2,X3] :
( lhs_atom2(X1)
| ~ ( morphism(X1,X2,X3)
& ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2)
& apply(X1,X5) = apply(X1,X6) )
=> X5 = X6 ) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_5,axiom,
! [X19] :
( lhs_atom24(X19)
| ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_6,axiom,
! [X1,X2,X3] :
( lhs_atom1(X1,X2,X3)
| ( ! [X4] :
( element(X4,X2)
=> element(apply(X1,X4),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_7,axiom,
! [X6,X5,X2] :
( lhs_atom8(X6,X5,X2)
| ~ ( element(X5,X2)
& element(X6,X2) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_8,axiom,
! [X6,X5,X2] :
( lhs_atom6(X6,X5,X2)
| ~ ( element(X5,X2)
& element(X6,X2) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_9,axiom,
! [X19] :
( lhs_atom24(X19)
| ? [X21,X22,X23] :
( element(X21,b)
& element(X22,e)
& subtract(e,apply(g,X21),X19) = X22
& element(X23,a)
& apply(gamma,apply(f,X23)) = X22
& apply(g,apply(alpha,X23)) = X22 ) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_10,axiom,
! [X4,X2] :
( lhs_atom7(X4,X2)
| subtract(X2,X4,X4) = zero(X2) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_11,axiom,
! [X19] :
( lhs_atom24(X19)
| ? [X20,X21] :
( element(X20,r)
& apply(delta,X19) = X20
& element(X21,b)
& apply(h,apply(beta,X21)) = X20
& apply(delta,apply(g,X21)) = X20 ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_12,axiom,
( lhs_atom23
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_13,axiom,
( lhs_atom22
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_14,axiom,
( lhs_atom21
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_15,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_16,axiom,
( lhs_atom19
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_17,axiom,
( lhs_atom18
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_18,axiom,
( lhs_atom17
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_19,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_20,axiom,
( lhs_atom15
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_21,axiom,
( lhs_atom14
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_22,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_23,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_24,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_25,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_26,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_27,axiom,
! [X13,X14,X15,X16,X17,X18,X2,X3] :
( lhs_atom5(X13,X14,X15,X16)
| ~ ( morphism(X16,X2,X18)
& morphism(X15,X18,X3)
& morphism(X14,X2,X17)
& morphism(X13,X17,X3)
& ! [X8] :
( element(X8,X2)
=> apply(X15,apply(X16,X8)) = apply(X13,apply(X14,X8)) ) ) ),
c_0_0 ).
fof(c_0_28,axiom,
! [X9,X10,X2,X11,X3] :
( lhs_atom4(X9,X10)
| ~ ( morphism(X10,X2,X11)
& morphism(X9,X11,X3)
& ! [X12] :
( ( element(X12,X11)
& apply(X9,X12) = zero(X3) )
<=> ? [X8] :
( element(X8,X2)
& apply(X10,X8) = X12 ) ) ) ),
c_0_1 ).
fof(c_0_29,axiom,
! [X1,X2,X3] :
( lhs_atom1(X1,X2,X3)
| ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
c_0_2 ).
fof(c_0_30,axiom,
! [X1,X2,X3] :
( lhs_atom3(X1)
| ~ ( morphism(X1,X2,X3)
& ! [X7] :
( element(X7,X3)
=> ? [X8] :
( element(X8,X2)
& apply(X1,X8) = X7 ) ) ) ),
c_0_3 ).
fof(c_0_31,axiom,
! [X1,X2,X3] :
( lhs_atom2(X1)
| ~ ( morphism(X1,X2,X3)
& ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2)
& apply(X1,X5) = apply(X1,X6) )
=> X5 = X6 ) ) ),
c_0_4 ).
fof(c_0_32,axiom,
! [X19] :
( lhs_atom24(X19)
| ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
c_0_5 ).
fof(c_0_33,axiom,
! [X1,X2,X3] :
( lhs_atom1(X1,X2,X3)
| ( ! [X4] :
( element(X4,X2)
=> element(apply(X1,X4),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
c_0_6 ).
fof(c_0_34,axiom,
! [X6,X5,X2] :
( lhs_atom8(X6,X5,X2)
| ~ ( element(X5,X2)
& element(X6,X2) ) ),
c_0_7 ).
fof(c_0_35,axiom,
! [X6,X5,X2] :
( lhs_atom6(X6,X5,X2)
| ~ ( element(X5,X2)
& element(X6,X2) ) ),
c_0_8 ).
fof(c_0_36,axiom,
! [X19] :
( lhs_atom24(X19)
| ? [X21,X22,X23] :
( element(X21,b)
& element(X22,e)
& subtract(e,apply(g,X21),X19) = X22
& element(X23,a)
& apply(gamma,apply(f,X23)) = X22
& apply(g,apply(alpha,X23)) = X22 ) ),
c_0_9 ).
fof(c_0_37,axiom,
! [X4,X2] :
( lhs_atom7(X4,X2)
| subtract(X2,X4,X4) = zero(X2) ),
c_0_10 ).
fof(c_0_38,axiom,
! [X19] :
( lhs_atom24(X19)
| ? [X20,X21] :
( element(X20,r)
& apply(delta,X19) = X20
& element(X21,b)
& apply(h,apply(beta,X21)) = X20
& apply(delta,apply(g,X21)) = X20 ) ),
c_0_11 ).
fof(c_0_39,plain,
lhs_atom23,
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_40,plain,
lhs_atom22,
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_41,plain,
lhs_atom21,
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_42,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_43,plain,
lhs_atom19,
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_44,plain,
lhs_atom18,
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_45,plain,
lhs_atom17,
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_46,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_47,plain,
lhs_atom15,
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_48,plain,
lhs_atom14,
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_49,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_50,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_51,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_52,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_53,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_54,plain,
! [X19,X20,X21,X22,X23,X24,X25,X26] :
( ( element(esk6_8(X19,X20,X21,X22,X23,X24,X25,X26),X25)
| ~ morphism(X19,X23,X26)
| ~ morphism(X20,X25,X23)
| ~ morphism(X21,X24,X26)
| ~ morphism(X22,X25,X24)
| lhs_atom5(X19,X20,X21,X22) )
& ( apply(X21,apply(X22,esk6_8(X19,X20,X21,X22,X23,X24,X25,X26))) != apply(X19,apply(X20,esk6_8(X19,X20,X21,X22,X23,X24,X25,X26)))
| ~ morphism(X19,X23,X26)
| ~ morphism(X20,X25,X23)
| ~ morphism(X21,X24,X26)
| ~ morphism(X22,X25,X24)
| lhs_atom5(X19,X20,X21,X22) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])])]) ).
fof(c_0_55,plain,
! [X13,X14,X15,X16,X17,X19] :
( ( ~ element(esk4_5(X13,X14,X15,X16,X17),X16)
| apply(X13,esk4_5(X13,X14,X15,X16,X17)) != zero(X17)
| ~ element(X19,X15)
| apply(X14,X19) != esk4_5(X13,X14,X15,X16,X17)
| ~ morphism(X13,X16,X17)
| ~ morphism(X14,X15,X16)
| lhs_atom4(X13,X14) )
& ( element(esk5_5(X13,X14,X15,X16,X17),X15)
| element(esk4_5(X13,X14,X15,X16,X17),X16)
| ~ morphism(X13,X16,X17)
| ~ morphism(X14,X15,X16)
| lhs_atom4(X13,X14) )
& ( apply(X14,esk5_5(X13,X14,X15,X16,X17)) = esk4_5(X13,X14,X15,X16,X17)
| element(esk4_5(X13,X14,X15,X16,X17),X16)
| ~ morphism(X13,X16,X17)
| ~ morphism(X14,X15,X16)
| lhs_atom4(X13,X14) )
& ( element(esk5_5(X13,X14,X15,X16,X17),X15)
| apply(X13,esk4_5(X13,X14,X15,X16,X17)) = zero(X17)
| ~ morphism(X13,X16,X17)
| ~ morphism(X14,X15,X16)
| lhs_atom4(X13,X14) )
& ( apply(X14,esk5_5(X13,X14,X15,X16,X17)) = esk4_5(X13,X14,X15,X16,X17)
| apply(X13,esk4_5(X13,X14,X15,X16,X17)) = zero(X17)
| ~ morphism(X13,X16,X17)
| ~ morphism(X14,X15,X16)
| lhs_atom4(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])])]) ).
fof(c_0_56,plain,
! [X7,X8,X9,X10,X11] :
( lhs_atom1(X7,X8,X9)
| ~ element(X10,X8)
| ~ element(X11,X8)
| apply(X7,subtract(X8,X10,X11)) = subtract(X9,apply(X7,X10),apply(X7,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
fof(c_0_57,plain,
! [X9,X10,X11,X13] :
( ( element(esk3_3(X9,X10,X11),X11)
| ~ morphism(X9,X10,X11)
| lhs_atom3(X9) )
& ( ~ element(X13,X10)
| apply(X9,X13) != esk3_3(X9,X10,X11)
| ~ morphism(X9,X10,X11)
| lhs_atom3(X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])])])]) ).
fof(c_0_58,plain,
! [X7,X8,X9] :
( ( element(esk1_2(X7,X8),X8)
| ~ morphism(X7,X8,X9)
| lhs_atom2(X7) )
& ( element(esk2_2(X7,X8),X8)
| ~ morphism(X7,X8,X9)
| lhs_atom2(X7) )
& ( apply(X7,esk1_2(X7,X8)) = apply(X7,esk2_2(X7,X8))
| ~ morphism(X7,X8,X9)
| lhs_atom2(X7) )
& ( esk1_2(X7,X8) != esk2_2(X7,X8)
| ~ morphism(X7,X8,X9)
| lhs_atom2(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])])]) ).
fof(c_0_59,plain,
! [X25] :
( ( element(esk12_1(X25),b)
| lhs_atom24(X25) )
& ( element(esk13_1(X25),b)
| lhs_atom24(X25) )
& ( apply(g,subtract(b,esk12_1(X25),esk13_1(X25))) = X25
| lhs_atom24(X25) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_32])])])]) ).
fof(c_0_60,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,X6)
| element(apply(X5,X8),X7)
| lhs_atom1(X5,X6,X7) )
& ( apply(X5,zero(X6)) = zero(X7)
| lhs_atom1(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
fof(c_0_61,plain,
! [X7,X8,X9] :
( lhs_atom8(X7,X8,X9)
| ~ element(X8,X9)
| ~ element(X7,X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])]) ).
fof(c_0_62,plain,
! [X7,X8,X9] :
( lhs_atom6(X7,X8,X9)
| ~ element(X8,X9)
| ~ element(X7,X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
fof(c_0_63,plain,
! [X24] :
( ( element(esk9_1(X24),b)
| lhs_atom24(X24) )
& ( element(esk10_1(X24),e)
| lhs_atom24(X24) )
& ( subtract(e,apply(g,esk9_1(X24)),X24) = esk10_1(X24)
| lhs_atom24(X24) )
& ( element(esk11_1(X24),a)
| lhs_atom24(X24) )
& ( apply(gamma,apply(f,esk11_1(X24))) = esk10_1(X24)
| lhs_atom24(X24) )
& ( apply(g,apply(alpha,esk11_1(X24))) = esk10_1(X24)
| lhs_atom24(X24) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_36])])])]) ).
fof(c_0_64,plain,
! [X5,X6] :
( lhs_atom7(X5,X6)
| subtract(X6,X5,X5) = zero(X6) ),
inference(variable_rename,[status(thm)],[c_0_37]) ).
fof(c_0_65,plain,
! [X22] :
( ( element(esk7_1(X22),r)
| lhs_atom24(X22) )
& ( apply(delta,X22) = esk7_1(X22)
| lhs_atom24(X22) )
& ( element(esk8_1(X22),b)
| lhs_atom24(X22) )
& ( apply(h,apply(beta,esk8_1(X22))) = esk7_1(X22)
| lhs_atom24(X22) )
& ( apply(delta,apply(g,esk8_1(X22))) = esk7_1(X22)
| lhs_atom24(X22) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_38])])])]) ).
fof(c_0_66,plain,
lhs_atom23,
c_0_39 ).
fof(c_0_67,plain,
lhs_atom22,
c_0_40 ).
fof(c_0_68,plain,
lhs_atom21,
c_0_41 ).
fof(c_0_69,plain,
lhs_atom20,
c_0_42 ).
fof(c_0_70,plain,
lhs_atom19,
c_0_43 ).
fof(c_0_71,plain,
lhs_atom18,
c_0_44 ).
fof(c_0_72,plain,
lhs_atom17,
c_0_45 ).
fof(c_0_73,plain,
lhs_atom16,
c_0_46 ).
fof(c_0_74,plain,
lhs_atom15,
c_0_47 ).
fof(c_0_75,plain,
lhs_atom14,
c_0_48 ).
fof(c_0_76,plain,
lhs_atom13,
c_0_49 ).
fof(c_0_77,plain,
lhs_atom12,
c_0_50 ).
fof(c_0_78,plain,
lhs_atom11,
c_0_51 ).
fof(c_0_79,plain,
lhs_atom10,
c_0_52 ).
fof(c_0_80,plain,
lhs_atom9,
c_0_53 ).
cnf(c_0_81,plain,
( lhs_atom5(X1,X2,X3,X4)
| ~ morphism(X4,X5,X6)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X5,X8)
| ~ morphism(X1,X8,X7)
| apply(X3,apply(X4,esk6_8(X1,X2,X3,X4,X8,X6,X5,X7))) != apply(X1,apply(X2,esk6_8(X1,X2,X3,X4,X8,X6,X5,X7))) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_82,plain,
( lhs_atom5(X1,X2,X3,X4)
| element(esk6_8(X1,X2,X3,X4,X8,X6,X5,X7),X5)
| ~ morphism(X4,X5,X6)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X5,X8)
| ~ morphism(X1,X8,X7) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_83,plain,
( lhs_atom4(X1,X2)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5)
| apply(X2,X6) != esk4_5(X1,X2,X3,X4,X5)
| ~ element(X6,X3)
| apply(X1,esk4_5(X1,X2,X3,X4,X5)) != zero(X5)
| ~ element(esk4_5(X1,X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_84,plain,
( lhs_atom4(X1,X2)
| apply(X1,esk4_5(X1,X2,X3,X4,X5)) = zero(X5)
| apply(X2,esk5_5(X1,X2,X3,X4,X5)) = esk4_5(X1,X2,X3,X4,X5)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_85,plain,
( lhs_atom4(X1,X2)
| element(esk4_5(X1,X2,X3,X4,X5),X4)
| apply(X2,esk5_5(X1,X2,X3,X4,X5)) = esk4_5(X1,X2,X3,X4,X5)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_86,plain,
( lhs_atom4(X1,X2)
| apply(X1,esk4_5(X1,X2,X3,X4,X5)) = zero(X5)
| element(esk5_5(X1,X2,X3,X4,X5),X3)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_87,plain,
( lhs_atom4(X1,X2)
| element(esk4_5(X1,X2,X3,X4,X5),X4)
| element(esk5_5(X1,X2,X3,X4,X5),X3)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_88,plain,
( apply(X1,subtract(X2,X3,X4)) = subtract(X5,apply(X1,X3),apply(X1,X4))
| lhs_atom1(X1,X2,X5)
| ~ element(X4,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_89,plain,
( lhs_atom3(X1)
| ~ morphism(X1,X2,X3)
| apply(X1,X4) != esk3_3(X1,X2,X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_90,plain,
( lhs_atom3(X1)
| element(esk3_3(X1,X2,X3),X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_91,plain,
( lhs_atom2(X1)
| apply(X1,esk1_2(X1,X2)) = apply(X1,esk2_2(X1,X2))
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_92,plain,
( lhs_atom24(X1)
| apply(g,subtract(b,esk12_1(X1),esk13_1(X1))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_93,plain,
( lhs_atom2(X1)
| ~ morphism(X1,X2,X3)
| esk1_2(X1,X2) != esk2_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_94,plain,
( lhs_atom2(X1)
| element(esk1_2(X1,X2),X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_95,plain,
( lhs_atom2(X1)
| element(esk2_2(X1,X2),X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_96,plain,
( lhs_atom1(X1,X2,X3)
| element(apply(X1,X4),X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_97,plain,
( lhs_atom8(X1,X3,X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_98,plain,
( lhs_atom6(X1,X3,X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_99,plain,
( lhs_atom24(X1)
| subtract(e,apply(g,esk9_1(X1)),X1) = esk10_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_100,plain,
( lhs_atom1(X1,X2,X3)
| apply(X1,zero(X2)) = zero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_101,plain,
( subtract(X1,X2,X2) = zero(X1)
| lhs_atom7(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_102,plain,
( lhs_atom24(X1)
| apply(gamma,apply(f,esk11_1(X1))) = esk10_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_103,plain,
( lhs_atom24(X1)
| apply(g,apply(alpha,esk11_1(X1))) = esk10_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_104,plain,
( lhs_atom24(X1)
| apply(h,apply(beta,esk8_1(X1))) = esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_105,plain,
( lhs_atom24(X1)
| apply(delta,apply(g,esk8_1(X1))) = esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_106,plain,
( lhs_atom24(X1)
| element(esk12_1(X1),b) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_107,plain,
( lhs_atom24(X1)
| element(esk13_1(X1),b) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_108,plain,
( lhs_atom24(X1)
| element(esk9_1(X1),b) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_109,plain,
( lhs_atom24(X1)
| element(esk10_1(X1),e) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_110,plain,
( lhs_atom24(X1)
| element(esk11_1(X1),a) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_111,plain,
( lhs_atom24(X1)
| element(esk7_1(X1),r) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_112,plain,
( lhs_atom24(X1)
| element(esk8_1(X1),b) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_113,plain,
( lhs_atom24(X1)
| apply(delta,X1) = esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_114,plain,
lhs_atom23,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_115,plain,
lhs_atom22,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_116,plain,
lhs_atom21,
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_117,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_118,plain,
lhs_atom19,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_119,plain,
lhs_atom18,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_120,plain,
lhs_atom17,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_121,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_122,plain,
lhs_atom15,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_123,plain,
lhs_atom14,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_124,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_125,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_126,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_127,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_128,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_129,plain,
( lhs_atom5(X1,X2,X3,X4)
| ~ morphism(X4,X5,X6)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X5,X8)
| ~ morphism(X1,X8,X7)
| apply(X3,apply(X4,esk6_8(X1,X2,X3,X4,X8,X6,X5,X7))) != apply(X1,apply(X2,esk6_8(X1,X2,X3,X4,X8,X6,X5,X7))) ),
c_0_81,
[final] ).
cnf(c_0_130,plain,
( lhs_atom5(X1,X2,X3,X4)
| element(esk6_8(X1,X2,X3,X4,X8,X6,X5,X7),X5)
| ~ morphism(X4,X5,X6)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X5,X8)
| ~ morphism(X1,X8,X7) ),
c_0_82,
[final] ).
cnf(c_0_131,plain,
( lhs_atom4(X1,X2)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5)
| apply(X2,X6) != esk4_5(X1,X2,X3,X4,X5)
| ~ element(X6,X3)
| apply(X1,esk4_5(X1,X2,X3,X4,X5)) != zero(X5)
| ~ element(esk4_5(X1,X2,X3,X4,X5),X4) ),
c_0_83,
[final] ).
cnf(c_0_132,plain,
( lhs_atom4(X1,X2)
| apply(X1,esk4_5(X1,X2,X3,X4,X5)) = zero(X5)
| apply(X2,esk5_5(X1,X2,X3,X4,X5)) = esk4_5(X1,X2,X3,X4,X5)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
c_0_84,
[final] ).
cnf(c_0_133,plain,
( lhs_atom4(X1,X2)
| element(esk4_5(X1,X2,X3,X4,X5),X4)
| apply(X2,esk5_5(X1,X2,X3,X4,X5)) = esk4_5(X1,X2,X3,X4,X5)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
c_0_85,
[final] ).
cnf(c_0_134,plain,
( lhs_atom4(X1,X2)
| apply(X1,esk4_5(X1,X2,X3,X4,X5)) = zero(X5)
| element(esk5_5(X1,X2,X3,X4,X5),X3)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
c_0_86,
[final] ).
cnf(c_0_135,plain,
( lhs_atom4(X1,X2)
| element(esk4_5(X1,X2,X3,X4,X5),X4)
| element(esk5_5(X1,X2,X3,X4,X5),X3)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
c_0_87,
[final] ).
cnf(c_0_136,plain,
( apply(X1,subtract(X2,X3,X4)) = subtract(X5,apply(X1,X3),apply(X1,X4))
| lhs_atom1(X1,X2,X5)
| ~ element(X4,X2)
| ~ element(X3,X2) ),
c_0_88,
[final] ).
cnf(c_0_137,plain,
( lhs_atom3(X1)
| ~ morphism(X1,X2,X3)
| apply(X1,X4) != esk3_3(X1,X2,X3)
| ~ element(X4,X2) ),
c_0_89,
[final] ).
cnf(c_0_138,plain,
( lhs_atom3(X1)
| element(esk3_3(X1,X2,X3),X3)
| ~ morphism(X1,X2,X3) ),
c_0_90,
[final] ).
cnf(c_0_139,plain,
( lhs_atom2(X1)
| apply(X1,esk2_2(X1,X2)) = apply(X1,esk1_2(X1,X2))
| ~ morphism(X1,X2,X3) ),
c_0_91,
[final] ).
cnf(c_0_140,plain,
( lhs_atom24(X1)
| apply(g,subtract(b,esk12_1(X1),esk13_1(X1))) = X1 ),
c_0_92,
[final] ).
cnf(c_0_141,plain,
( lhs_atom2(X1)
| ~ morphism(X1,X2,X3)
| esk2_2(X1,X2) != esk1_2(X1,X2) ),
c_0_93,
[final] ).
cnf(c_0_142,plain,
( lhs_atom2(X1)
| element(esk1_2(X1,X2),X2)
| ~ morphism(X1,X2,X3) ),
c_0_94,
[final] ).
cnf(c_0_143,plain,
( lhs_atom2(X1)
| element(esk2_2(X1,X2),X2)
| ~ morphism(X1,X2,X3) ),
c_0_95,
[final] ).
cnf(c_0_144,plain,
( lhs_atom1(X1,X2,X3)
| element(apply(X1,X4),X3)
| ~ element(X4,X2) ),
c_0_96,
[final] ).
cnf(c_0_145,plain,
( lhs_atom8(X1,X3,X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
c_0_97,
[final] ).
cnf(c_0_146,plain,
( lhs_atom6(X1,X3,X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
c_0_98,
[final] ).
cnf(c_0_147,plain,
( lhs_atom24(X1)
| subtract(e,apply(g,esk9_1(X1)),X1) = esk10_1(X1) ),
c_0_99,
[final] ).
cnf(c_0_148,plain,
( lhs_atom1(X1,X2,X3)
| apply(X1,zero(X2)) = zero(X3) ),
c_0_100,
[final] ).
cnf(c_0_149,plain,
( subtract(X1,X2,X2) = zero(X1)
| lhs_atom7(X2,X1) ),
c_0_101,
[final] ).
cnf(c_0_150,plain,
( lhs_atom24(X1)
| apply(gamma,apply(f,esk11_1(X1))) = esk10_1(X1) ),
c_0_102,
[final] ).
cnf(c_0_151,plain,
( lhs_atom24(X1)
| apply(g,apply(alpha,esk11_1(X1))) = esk10_1(X1) ),
c_0_103,
[final] ).
cnf(c_0_152,plain,
( lhs_atom24(X1)
| apply(h,apply(beta,esk8_1(X1))) = esk7_1(X1) ),
c_0_104,
[final] ).
cnf(c_0_153,plain,
( lhs_atom24(X1)
| apply(delta,apply(g,esk8_1(X1))) = esk7_1(X1) ),
c_0_105,
[final] ).
cnf(c_0_154,plain,
( lhs_atom24(X1)
| element(esk12_1(X1),b) ),
c_0_106,
[final] ).
cnf(c_0_155,plain,
( lhs_atom24(X1)
| element(esk13_1(X1),b) ),
c_0_107,
[final] ).
cnf(c_0_156,plain,
( lhs_atom24(X1)
| element(esk9_1(X1),b) ),
c_0_108,
[final] ).
cnf(c_0_157,plain,
( lhs_atom24(X1)
| element(esk10_1(X1),e) ),
c_0_109,
[final] ).
cnf(c_0_158,plain,
( lhs_atom24(X1)
| element(esk11_1(X1),a) ),
c_0_110,
[final] ).
cnf(c_0_159,plain,
( lhs_atom24(X1)
| element(esk7_1(X1),r) ),
c_0_111,
[final] ).
cnf(c_0_160,plain,
( lhs_atom24(X1)
| element(esk8_1(X1),b) ),
c_0_112,
[final] ).
cnf(c_0_161,plain,
( lhs_atom24(X1)
| apply(delta,X1) = esk7_1(X1) ),
c_0_113,
[final] ).
cnf(c_0_162,plain,
lhs_atom23,
c_0_114,
[final] ).
cnf(c_0_163,plain,
lhs_atom22,
c_0_115,
[final] ).
cnf(c_0_164,plain,
lhs_atom21,
c_0_116,
[final] ).
cnf(c_0_165,plain,
lhs_atom20,
c_0_117,
[final] ).
cnf(c_0_166,plain,
lhs_atom19,
c_0_118,
[final] ).
cnf(c_0_167,plain,
lhs_atom18,
c_0_119,
[final] ).
cnf(c_0_168,plain,
lhs_atom17,
c_0_120,
[final] ).
cnf(c_0_169,plain,
lhs_atom16,
c_0_121,
[final] ).
cnf(c_0_170,plain,
lhs_atom15,
c_0_122,
[final] ).
cnf(c_0_171,plain,
lhs_atom14,
c_0_123,
[final] ).
cnf(c_0_172,plain,
lhs_atom13,
c_0_124,
[final] ).
cnf(c_0_173,plain,
lhs_atom12,
c_0_125,
[final] ).
cnf(c_0_174,plain,
lhs_atom11,
c_0_126,
[final] ).
cnf(c_0_175,plain,
lhs_atom10,
c_0_127,
[final] ).
cnf(c_0_176,plain,
lhs_atom9,
c_0_128,
[final] ).
% End CNF derivation
cnf(c_0_129_0,axiom,
( commute(X4,X3,X2,X1)
| ~ morphism(X4,X5,X6)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X5,X8)
| ~ morphism(X1,X8,X7)
| apply(X3,apply(X4,sk1_esk6_8(X1,X2,X3,X4,X8,X6,X5,X7))) != apply(X1,apply(X2,sk1_esk6_8(X1,X2,X3,X4,X8,X6,X5,X7))) ),
inference(unfold_definition,[status(thm)],[c_0_129,def_lhs_atom5]) ).
cnf(c_0_130_0,axiom,
( commute(X4,X3,X2,X1)
| element(sk1_esk6_8(X1,X2,X3,X4,X8,X6,X5,X7),X5)
| ~ morphism(X4,X5,X6)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X5,X8)
| ~ morphism(X1,X8,X7) ),
inference(unfold_definition,[status(thm)],[c_0_130,def_lhs_atom5]) ).
cnf(c_0_131_0,axiom,
( exact(X2,X1)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5)
| apply(X2,X6) != sk1_esk4_5(X1,X2,X3,X4,X5)
| ~ element(X6,X3)
| apply(X1,sk1_esk4_5(X1,X2,X3,X4,X5)) != zero(X5)
| ~ element(sk1_esk4_5(X1,X2,X3,X4,X5),X4) ),
inference(unfold_definition,[status(thm)],[c_0_131,def_lhs_atom4]) ).
cnf(c_0_132_0,axiom,
( exact(X2,X1)
| apply(X1,sk1_esk4_5(X1,X2,X3,X4,X5)) = zero(X5)
| apply(X2,sk1_esk5_5(X1,X2,X3,X4,X5)) = sk1_esk4_5(X1,X2,X3,X4,X5)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(unfold_definition,[status(thm)],[c_0_132,def_lhs_atom4]) ).
cnf(c_0_133_0,axiom,
( exact(X2,X1)
| element(sk1_esk4_5(X1,X2,X3,X4,X5),X4)
| apply(X2,sk1_esk5_5(X1,X2,X3,X4,X5)) = sk1_esk4_5(X1,X2,X3,X4,X5)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(unfold_definition,[status(thm)],[c_0_133,def_lhs_atom4]) ).
cnf(c_0_134_0,axiom,
( exact(X2,X1)
| apply(X1,sk1_esk4_5(X1,X2,X3,X4,X5)) = zero(X5)
| element(sk1_esk5_5(X1,X2,X3,X4,X5),X3)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(unfold_definition,[status(thm)],[c_0_134,def_lhs_atom4]) ).
cnf(c_0_135_0,axiom,
( exact(X2,X1)
| element(sk1_esk4_5(X1,X2,X3,X4,X5),X4)
| element(sk1_esk5_5(X1,X2,X3,X4,X5),X3)
| ~ morphism(X2,X3,X4)
| ~ morphism(X1,X4,X5) ),
inference(unfold_definition,[status(thm)],[c_0_135,def_lhs_atom4]) ).
cnf(c_0_136_0,axiom,
( ~ morphism(X1,X2,X5)
| apply(X1,subtract(X2,X3,X4)) = subtract(X5,apply(X1,X3),apply(X1,X4))
| ~ element(X4,X2)
| ~ element(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_136,def_lhs_atom1]) ).
cnf(c_0_137_0,axiom,
( surjection(X1)
| ~ morphism(X1,X2,X3)
| apply(X1,X4) != sk1_esk3_3(X1,X2,X3)
| ~ element(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_137,def_lhs_atom3]) ).
cnf(c_0_138_0,axiom,
( surjection(X1)
| element(sk1_esk3_3(X1,X2,X3),X3)
| ~ morphism(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_138,def_lhs_atom3]) ).
cnf(c_0_139_0,axiom,
( injection(X1)
| apply(X1,sk1_esk2_2(X1,X2)) = apply(X1,sk1_esk1_2(X1,X2))
| ~ morphism(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_139,def_lhs_atom2]) ).
cnf(c_0_140_0,axiom,
( ~ element(X1,e)
| apply(g,subtract(b,sk1_esk12_1(X1),sk1_esk13_1(X1))) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_140,def_lhs_atom24]) ).
cnf(c_0_141_0,axiom,
( injection(X1)
| ~ morphism(X1,X2,X3)
| sk1_esk2_2(X1,X2) != sk1_esk1_2(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_141,def_lhs_atom2]) ).
cnf(c_0_142_0,axiom,
( injection(X1)
| element(sk1_esk1_2(X1,X2),X2)
| ~ morphism(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_142,def_lhs_atom2]) ).
cnf(c_0_143_0,axiom,
( injection(X1)
| element(sk1_esk2_2(X1,X2),X2)
| ~ morphism(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_143,def_lhs_atom2]) ).
cnf(c_0_144_0,axiom,
( ~ morphism(X1,X2,X3)
| element(apply(X1,X4),X3)
| ~ element(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_144,def_lhs_atom1]) ).
cnf(c_0_145_0,axiom,
( subtract(X2,X3,subtract(X2,X3,X1)) = X1
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_145,def_lhs_atom8]) ).
cnf(c_0_146_0,axiom,
( element(subtract(X2,X3,X1),X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_146,def_lhs_atom6]) ).
cnf(c_0_147_0,axiom,
( ~ element(X1,e)
| subtract(e,apply(g,sk1_esk9_1(X1)),X1) = sk1_esk10_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_147,def_lhs_atom24]) ).
cnf(c_0_148_0,axiom,
( ~ morphism(X1,X2,X3)
| apply(X1,zero(X2)) = zero(X3) ),
inference(unfold_definition,[status(thm)],[c_0_148,def_lhs_atom1]) ).
cnf(c_0_149_0,axiom,
( ~ element(X2,X1)
| subtract(X1,X2,X2) = zero(X1) ),
inference(unfold_definition,[status(thm)],[c_0_149,def_lhs_atom7]) ).
cnf(c_0_150_0,axiom,
( ~ element(X1,e)
| apply(gamma,apply(f,sk1_esk11_1(X1))) = sk1_esk10_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_150,def_lhs_atom24]) ).
cnf(c_0_151_0,axiom,
( ~ element(X1,e)
| apply(g,apply(alpha,sk1_esk11_1(X1))) = sk1_esk10_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_151,def_lhs_atom24]) ).
cnf(c_0_152_0,axiom,
( ~ element(X1,e)
| apply(h,apply(beta,sk1_esk8_1(X1))) = sk1_esk7_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_152,def_lhs_atom24]) ).
cnf(c_0_153_0,axiom,
( ~ element(X1,e)
| apply(delta,apply(g,sk1_esk8_1(X1))) = sk1_esk7_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_153,def_lhs_atom24]) ).
cnf(c_0_154_0,axiom,
( ~ element(X1,e)
| element(sk1_esk12_1(X1),b) ),
inference(unfold_definition,[status(thm)],[c_0_154,def_lhs_atom24]) ).
cnf(c_0_155_0,axiom,
( ~ element(X1,e)
| element(sk1_esk13_1(X1),b) ),
inference(unfold_definition,[status(thm)],[c_0_155,def_lhs_atom24]) ).
cnf(c_0_156_0,axiom,
( ~ element(X1,e)
| element(sk1_esk9_1(X1),b) ),
inference(unfold_definition,[status(thm)],[c_0_156,def_lhs_atom24]) ).
cnf(c_0_157_0,axiom,
( ~ element(X1,e)
| element(sk1_esk10_1(X1),e) ),
inference(unfold_definition,[status(thm)],[c_0_157,def_lhs_atom24]) ).
cnf(c_0_158_0,axiom,
( ~ element(X1,e)
| element(sk1_esk11_1(X1),a) ),
inference(unfold_definition,[status(thm)],[c_0_158,def_lhs_atom24]) ).
cnf(c_0_159_0,axiom,
( ~ element(X1,e)
| element(sk1_esk7_1(X1),r) ),
inference(unfold_definition,[status(thm)],[c_0_159,def_lhs_atom24]) ).
cnf(c_0_160_0,axiom,
( ~ element(X1,e)
| element(sk1_esk8_1(X1),b) ),
inference(unfold_definition,[status(thm)],[c_0_160,def_lhs_atom24]) ).
cnf(c_0_161_0,axiom,
( ~ element(X1,e)
| apply(delta,X1) = sk1_esk7_1(X1) ),
inference(unfold_definition,[status(thm)],[c_0_161,def_lhs_atom24]) ).
cnf(c_0_162_0,axiom,
commute(beta,h,g,delta),
inference(unfold_definition,[status(thm)],[c_0_162,def_lhs_atom23]) ).
cnf(c_0_163_0,axiom,
commute(alpha,g,f,gamma),
inference(unfold_definition,[status(thm)],[c_0_163,def_lhs_atom22]) ).
cnf(c_0_164_0,axiom,
exact(gammma,delta),
inference(unfold_definition,[status(thm)],[c_0_164,def_lhs_atom21]) ).
cnf(c_0_165_0,axiom,
exact(alpha,beta),
inference(unfold_definition,[status(thm)],[c_0_165,def_lhs_atom20]) ).
cnf(c_0_166_0,axiom,
surjection(delta),
inference(unfold_definition,[status(thm)],[c_0_166,def_lhs_atom19]) ).
cnf(c_0_167_0,axiom,
surjection(beta),
inference(unfold_definition,[status(thm)],[c_0_167,def_lhs_atom18]) ).
cnf(c_0_168_0,axiom,
injection(gamma),
inference(unfold_definition,[status(thm)],[c_0_168,def_lhs_atom17]) ).
cnf(c_0_169_0,axiom,
injection(alpha),
inference(unfold_definition,[status(thm)],[c_0_169,def_lhs_atom16]) ).
cnf(c_0_170_0,axiom,
morphism(h,c,r),
inference(unfold_definition,[status(thm)],[c_0_170,def_lhs_atom15]) ).
cnf(c_0_171_0,axiom,
morphism(g,b,e),
inference(unfold_definition,[status(thm)],[c_0_171,def_lhs_atom14]) ).
cnf(c_0_172_0,axiom,
morphism(f,a,d),
inference(unfold_definition,[status(thm)],[c_0_172,def_lhs_atom13]) ).
cnf(c_0_173_0,axiom,
morphism(delta,e,r),
inference(unfold_definition,[status(thm)],[c_0_173,def_lhs_atom12]) ).
cnf(c_0_174_0,axiom,
morphism(gamma,d,e),
inference(unfold_definition,[status(thm)],[c_0_174,def_lhs_atom11]) ).
cnf(c_0_175_0,axiom,
morphism(beta,b,c),
inference(unfold_definition,[status(thm)],[c_0_175,def_lhs_atom10]) ).
cnf(c_0_176_0,axiom,
morphism(alpha,a,b),
inference(unfold_definition,[status(thm)],[c_0_176,def_lhs_atom9]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X10,X11,X5,X12,X8] :
( ( exact(X10,X11)
& morphism(X10,X5,X12)
& morphism(X11,X12,X8) )
=> ! [X13] :
( ( element(X13,X12)
& apply(X11,X13) = zero(X8) )
<=> ? [X9] :
( element(X9,X5)
& apply(X10,X9) = X13 ) ) ),
file('<stdin>',exact_properties) ).
fof(c_0_1_002,axiom,
! [X1,X2,X3,X4,X5,X6,X7,X8] :
( ( commute(X1,X2,X3,X4)
& morphism(X1,X5,X6)
& morphism(X2,X6,X8)
& morphism(X3,X5,X7)
& morphism(X4,X7,X8) )
=> ! [X9] :
( element(X9,X5)
=> apply(X2,apply(X1,X9)) = apply(X4,apply(X3,X9)) ) ),
file('<stdin>',commute_properties) ).
fof(c_0_2_003,axiom,
! [X14,X5,X8] :
( ( surjection(X14)
& morphism(X14,X5,X8) )
=> ! [X15] :
( element(X15,X8)
=> ? [X9] :
( element(X9,X5)
& apply(X14,X9) = X15 ) ) ),
file('<stdin>',surjection_properties) ).
fof(c_0_3_004,axiom,
! [X14,X5,X8] :
( ( injection(X14)
& morphism(X14,X5,X8) )
=> ! [X16,X17] :
( ( element(X16,X5)
& element(X17,X5)
& apply(X14,X16) = apply(X14,X17) )
=> X16 = X17 ) ),
file('<stdin>',injection_properties) ).
fof(c_0_4_005,axiom,
! [X10,X11,X5,X12,X8] :
( ( exact(X10,X11)
& morphism(X10,X5,X12)
& morphism(X11,X12,X8) )
=> ! [X13] :
( ( element(X13,X12)
& apply(X11,X13) = zero(X8) )
<=> ? [X9] :
( element(X9,X5)
& apply(X10,X9) = X13 ) ) ),
c_0_0 ).
fof(c_0_5_006,axiom,
! [X1,X2,X3,X4,X5,X6,X7,X8] :
( ( commute(X1,X2,X3,X4)
& morphism(X1,X5,X6)
& morphism(X2,X6,X8)
& morphism(X3,X5,X7)
& morphism(X4,X7,X8) )
=> ! [X9] :
( element(X9,X5)
=> apply(X2,apply(X1,X9)) = apply(X4,apply(X3,X9)) ) ),
c_0_1 ).
fof(c_0_6_007,axiom,
! [X14,X5,X8] :
( ( surjection(X14)
& morphism(X14,X5,X8) )
=> ! [X15] :
( element(X15,X8)
=> ? [X9] :
( element(X9,X5)
& apply(X14,X9) = X15 ) ) ),
c_0_2 ).
fof(c_0_7_008,axiom,
! [X14,X5,X8] :
( ( injection(X14)
& morphism(X14,X5,X8) )
=> ! [X16,X17] :
( ( element(X16,X5)
& element(X17,X5)
& apply(X14,X16) = apply(X14,X17) )
=> X16 = X17 ) ),
c_0_3 ).
fof(c_0_8_009,plain,
! [X14,X15,X16,X17,X18,X19,X21,X22] :
( ( element(esk1_6(X14,X15,X16,X17,X18,X19),X16)
| ~ element(X19,X17)
| apply(X15,X19) != zero(X18)
| ~ exact(X14,X15)
| ~ morphism(X14,X16,X17)
| ~ morphism(X15,X17,X18) )
& ( apply(X14,esk1_6(X14,X15,X16,X17,X18,X19)) = X19
| ~ element(X19,X17)
| apply(X15,X19) != zero(X18)
| ~ exact(X14,X15)
| ~ morphism(X14,X16,X17)
| ~ morphism(X15,X17,X18) )
& ( element(X21,X17)
| ~ element(X22,X16)
| apply(X14,X22) != X21
| ~ exact(X14,X15)
| ~ morphism(X14,X16,X17)
| ~ morphism(X15,X17,X18) )
& ( apply(X15,X21) = zero(X18)
| ~ element(X22,X16)
| apply(X14,X22) != X21
| ~ exact(X14,X15)
| ~ morphism(X14,X16,X17)
| ~ morphism(X15,X17,X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
fof(c_0_9_010,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17,X18] :
( ~ commute(X10,X11,X12,X13)
| ~ morphism(X10,X14,X15)
| ~ morphism(X11,X15,X17)
| ~ morphism(X12,X14,X16)
| ~ morphism(X13,X16,X17)
| ~ element(X18,X14)
| apply(X11,apply(X10,X18)) = apply(X13,apply(X12,X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_10_011,plain,
! [X16,X17,X18,X19] :
( ( element(esk2_4(X16,X17,X18,X19),X17)
| ~ element(X19,X18)
| ~ surjection(X16)
| ~ morphism(X16,X17,X18) )
& ( apply(X16,esk2_4(X16,X17,X18,X19)) = X19
| ~ element(X19,X18)
| ~ surjection(X16)
| ~ morphism(X16,X17,X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_11_012,plain,
! [X18,X19,X20,X21,X22] :
( ~ injection(X18)
| ~ morphism(X18,X19,X20)
| ~ element(X21,X19)
| ~ element(X22,X19)
| apply(X18,X21) != apply(X18,X22)
| X21 = X22 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12_013,plain,
( apply(X4,esk1_6(X4,X1,X5,X2,X3,X6)) = X6
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_014,plain,
( element(esk1_6(X4,X1,X5,X2,X3,X6),X5)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14_015,plain,
( apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ element(X3,X6)
| ~ morphism(X4,X7,X8)
| ~ morphism(X5,X6,X7)
| ~ morphism(X1,X9,X8)
| ~ morphism(X2,X6,X9)
| ~ commute(X2,X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15_016,plain,
( apply(X1,esk2_4(X1,X2,X3,X4)) = X4
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16_017,plain,
( element(esk2_4(X1,X2,X3,X4),X2)
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17_018,plain,
( apply(X1,X7) = zero(X3)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18_019,plain,
( element(X7,X2)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19_020,plain,
( X1 = X2
| apply(X3,X1) != apply(X3,X2)
| ~ element(X2,X4)
| ~ element(X1,X4)
| ~ morphism(X3,X4,X5)
| ~ injection(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20_021,plain,
( apply(X4,esk1_6(X4,X1,X5,X2,X3,X6)) = X6
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
c_0_12,
[final] ).
cnf(c_0_21_022,plain,
( element(esk1_6(X4,X1,X5,X2,X3,X6),X5)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
c_0_13,
[final] ).
cnf(c_0_22_023,plain,
( apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ element(X3,X6)
| ~ morphism(X4,X7,X8)
| ~ morphism(X5,X6,X7)
| ~ morphism(X1,X9,X8)
| ~ morphism(X2,X6,X9)
| ~ commute(X2,X1,X5,X4) ),
c_0_14,
[final] ).
cnf(c_0_23_024,plain,
( apply(X1,esk2_4(X1,X2,X3,X4)) = X4
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
c_0_15,
[final] ).
cnf(c_0_24_025,plain,
( element(esk2_4(X1,X2,X3,X4),X2)
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
c_0_16,
[final] ).
cnf(c_0_25_026,plain,
( apply(X1,X7) = zero(X3)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
c_0_17,
[final] ).
cnf(c_0_26_027,plain,
( element(X7,X2)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
c_0_18,
[final] ).
cnf(c_0_27_028,plain,
( X1 = X2
| apply(X3,X1) != apply(X3,X2)
| ~ element(X2,X4)
| ~ element(X1,X4)
| ~ morphism(X3,X4,X5)
| ~ injection(X3) ),
c_0_19,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_20_0,axiom,
( apply(X4,sk2_esk1_6(X4,X1,X5,X2,X3,X6)) = X6
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_20]) ).
cnf(c_0_20_1,axiom,
( ~ morphism(X1,X2,X3)
| apply(X4,sk2_esk1_6(X4,X1,X5,X2,X3,X6)) = X6
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_20]) ).
cnf(c_0_20_2,axiom,
( ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X4,sk2_esk1_6(X4,X1,X5,X2,X3,X6)) = X6
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_20]) ).
cnf(c_0_20_3,axiom,
( ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X4,sk2_esk1_6(X4,X1,X5,X2,X3,X6)) = X6
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_20]) ).
cnf(c_0_20_4,axiom,
( apply(X1,X6) != zero(X3)
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X4,sk2_esk1_6(X4,X1,X5,X2,X3,X6)) = X6
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_20]) ).
cnf(c_0_20_5,axiom,
( ~ element(X6,X2)
| apply(X1,X6) != zero(X3)
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X4,sk2_esk1_6(X4,X1,X5,X2,X3,X6)) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_20]) ).
cnf(c_0_21_0,axiom,
( element(sk2_esk1_6(X4,X1,X5,X2,X3,X6),X5)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_21]) ).
cnf(c_0_21_1,axiom,
( ~ morphism(X1,X2,X3)
| element(sk2_esk1_6(X4,X1,X5,X2,X3,X6),X5)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_21]) ).
cnf(c_0_21_2,axiom,
( ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(sk2_esk1_6(X4,X1,X5,X2,X3,X6),X5)
| ~ exact(X4,X1)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_21]) ).
cnf(c_0_21_3,axiom,
( ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(sk2_esk1_6(X4,X1,X5,X2,X3,X6),X5)
| apply(X1,X6) != zero(X3)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_21]) ).
cnf(c_0_21_4,axiom,
( apply(X1,X6) != zero(X3)
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(sk2_esk1_6(X4,X1,X5,X2,X3,X6),X5)
| ~ element(X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_21]) ).
cnf(c_0_21_5,axiom,
( ~ element(X6,X2)
| apply(X1,X6) != zero(X3)
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(sk2_esk1_6(X4,X1,X5,X2,X3,X6),X5) ),
inference(literals_permutation,[status(thm)],[c_0_21]) ).
cnf(c_0_22_0,axiom,
( apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ element(X3,X6)
| ~ morphism(X4,X7,X8)
| ~ morphism(X5,X6,X7)
| ~ morphism(X1,X9,X8)
| ~ morphism(X2,X6,X9)
| ~ commute(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_22]) ).
cnf(c_0_22_1,axiom,
( ~ element(X3,X6)
| apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ morphism(X4,X7,X8)
| ~ morphism(X5,X6,X7)
| ~ morphism(X1,X9,X8)
| ~ morphism(X2,X6,X9)
| ~ commute(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_22]) ).
cnf(c_0_22_2,axiom,
( ~ morphism(X4,X7,X8)
| ~ element(X3,X6)
| apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ morphism(X5,X6,X7)
| ~ morphism(X1,X9,X8)
| ~ morphism(X2,X6,X9)
| ~ commute(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_22]) ).
cnf(c_0_22_3,axiom,
( ~ morphism(X5,X6,X7)
| ~ morphism(X4,X7,X8)
| ~ element(X3,X6)
| apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ morphism(X1,X9,X8)
| ~ morphism(X2,X6,X9)
| ~ commute(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_22]) ).
cnf(c_0_22_4,axiom,
( ~ morphism(X1,X9,X8)
| ~ morphism(X5,X6,X7)
| ~ morphism(X4,X7,X8)
| ~ element(X3,X6)
| apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ morphism(X2,X6,X9)
| ~ commute(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_22]) ).
cnf(c_0_22_5,axiom,
( ~ morphism(X2,X6,X9)
| ~ morphism(X1,X9,X8)
| ~ morphism(X5,X6,X7)
| ~ morphism(X4,X7,X8)
| ~ element(X3,X6)
| apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3))
| ~ commute(X2,X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_22]) ).
cnf(c_0_22_6,axiom,
( ~ commute(X2,X1,X5,X4)
| ~ morphism(X2,X6,X9)
| ~ morphism(X1,X9,X8)
| ~ morphism(X5,X6,X7)
| ~ morphism(X4,X7,X8)
| ~ element(X3,X6)
| apply(X1,apply(X2,X3)) = apply(X4,apply(X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_22]) ).
cnf(c_0_23_0,axiom,
( apply(X1,sk2_esk2_4(X1,X2,X3,X4)) = X4
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_23]) ).
cnf(c_0_23_1,axiom,
( ~ morphism(X1,X2,X3)
| apply(X1,sk2_esk2_4(X1,X2,X3,X4)) = X4
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_23]) ).
cnf(c_0_23_2,axiom,
( ~ surjection(X1)
| ~ morphism(X1,X2,X3)
| apply(X1,sk2_esk2_4(X1,X2,X3,X4)) = X4
| ~ element(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_23]) ).
cnf(c_0_23_3,axiom,
( ~ element(X4,X3)
| ~ surjection(X1)
| ~ morphism(X1,X2,X3)
| apply(X1,sk2_esk2_4(X1,X2,X3,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_23]) ).
cnf(c_0_24_0,axiom,
( element(sk2_esk2_4(X1,X2,X3,X4),X2)
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_24]) ).
cnf(c_0_24_1,axiom,
( ~ morphism(X1,X2,X3)
| element(sk2_esk2_4(X1,X2,X3,X4),X2)
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_24]) ).
cnf(c_0_24_2,axiom,
( ~ surjection(X1)
| ~ morphism(X1,X2,X3)
| element(sk2_esk2_4(X1,X2,X3,X4),X2)
| ~ element(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_24]) ).
cnf(c_0_24_3,axiom,
( ~ element(X4,X3)
| ~ surjection(X1)
| ~ morphism(X1,X2,X3)
| element(sk2_esk2_4(X1,X2,X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_24]) ).
cnf(c_0_25_0,axiom,
( apply(X1,X7) = zero(X3)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_25]) ).
cnf(c_0_25_1,axiom,
( ~ morphism(X1,X2,X3)
| apply(X1,X7) = zero(X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_25]) ).
cnf(c_0_25_2,axiom,
( ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X1,X7) = zero(X3)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_25]) ).
cnf(c_0_25_3,axiom,
( ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X1,X7) = zero(X3)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_25]) ).
cnf(c_0_25_4,axiom,
( apply(X4,X6) != X7
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X1,X7) = zero(X3)
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_25]) ).
cnf(c_0_25_5,axiom,
( ~ element(X6,X5)
| apply(X4,X6) != X7
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| apply(X1,X7) = zero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_25]) ).
cnf(c_0_26_0,axiom,
( element(X7,X2)
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_26]) ).
cnf(c_0_26_1,axiom,
( ~ morphism(X1,X2,X3)
| element(X7,X2)
| ~ morphism(X4,X5,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_26]) ).
cnf(c_0_26_2,axiom,
( ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(X7,X2)
| ~ exact(X4,X1)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_26]) ).
cnf(c_0_26_3,axiom,
( ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(X7,X2)
| apply(X4,X6) != X7
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_26]) ).
cnf(c_0_26_4,axiom,
( apply(X4,X6) != X7
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(X7,X2)
| ~ element(X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_26]) ).
cnf(c_0_26_5,axiom,
( ~ element(X6,X5)
| apply(X4,X6) != X7
| ~ exact(X4,X1)
| ~ morphism(X4,X5,X2)
| ~ morphism(X1,X2,X3)
| element(X7,X2) ),
inference(literals_permutation,[status(thm)],[c_0_26]) ).
cnf(c_0_27_0,axiom,
( X1 = X2
| apply(X3,X1) != apply(X3,X2)
| ~ element(X2,X4)
| ~ element(X1,X4)
| ~ morphism(X3,X4,X5)
| ~ injection(X3) ),
inference(literals_permutation,[status(thm)],[c_0_27]) ).
cnf(c_0_27_1,axiom,
( apply(X3,X1) != apply(X3,X2)
| X1 = X2
| ~ element(X2,X4)
| ~ element(X1,X4)
| ~ morphism(X3,X4,X5)
| ~ injection(X3) ),
inference(literals_permutation,[status(thm)],[c_0_27]) ).
cnf(c_0_27_2,axiom,
( ~ element(X2,X4)
| apply(X3,X1) != apply(X3,X2)
| X1 = X2
| ~ element(X1,X4)
| ~ morphism(X3,X4,X5)
| ~ injection(X3) ),
inference(literals_permutation,[status(thm)],[c_0_27]) ).
cnf(c_0_27_3,axiom,
( ~ element(X1,X4)
| ~ element(X2,X4)
| apply(X3,X1) != apply(X3,X2)
| X1 = X2
| ~ morphism(X3,X4,X5)
| ~ injection(X3) ),
inference(literals_permutation,[status(thm)],[c_0_27]) ).
cnf(c_0_27_4,axiom,
( ~ morphism(X3,X4,X5)
| ~ element(X1,X4)
| ~ element(X2,X4)
| apply(X3,X1) != apply(X3,X2)
| X1 = X2
| ~ injection(X3) ),
inference(literals_permutation,[status(thm)],[c_0_27]) ).
cnf(c_0_27_5,axiom,
( ~ injection(X3)
| ~ morphism(X3,X4,X5)
| ~ element(X1,X4)
| ~ element(X2,X4)
| apply(X3,X1) != apply(X3,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_27]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_029,conjecture,
surjection(g),
file('<stdin>',g_surjection) ).
fof(c_0_1_030,hypothesis,
surjection(h),
file('<stdin>',h_surjection) ).
fof(c_0_2_031,hypothesis,
surjection(f),
file('<stdin>',f_surjection) ).
fof(c_0_3_032,negated_conjecture,
~ surjection(g),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_4_033,hypothesis,
surjection(h),
c_0_1 ).
fof(c_0_5_034,hypothesis,
surjection(f),
c_0_2 ).
fof(c_0_6_035,negated_conjecture,
~ surjection(g),
c_0_3 ).
fof(c_0_7_036,hypothesis,
surjection(h),
c_0_4 ).
fof(c_0_8_037,hypothesis,
surjection(f),
c_0_5 ).
cnf(c_0_9_038,negated_conjecture,
~ surjection(g),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10_039,hypothesis,
surjection(h),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11_040,hypothesis,
surjection(f),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12_041,negated_conjecture,
~ surjection(g),
c_0_9,
[final] ).
cnf(c_0_13_042,hypothesis,
surjection(h),
c_0_10,
[final] ).
cnf(c_0_14_043,hypothesis,
surjection(f),
c_0_11,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_84,plain,
( ~ element(X0,X1)
| apply(X2,X0) != sk1_esk3_3(X2,X1,X3)
| ~ morphism(X2,X1,X3)
| surjection(X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_137_0) ).
cnf(c_849136,plain,
( ~ element(X0,X1)
| apply(X2,X0) != sk1_esk3_3(X2,X1,X3)
| ~ morphism(X2,X1,X3)
| surjection(X2) ),
inference(copy,[status(esa)],[c_84]) ).
cnf(c_849220,plain,
( ~ morphism(X0,X1,X2)
| ~ element(subtract(X1,X3,X4),X1)
| surjection(X0)
| apply(X0,subtract(X1,X3,X4)) != sk1_esk3_3(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_849136]) ).
cnf(c_849500,plain,
( ~ morphism(g,b,e)
| ~ element(subtract(b,X0,X1),b)
| surjection(g)
| apply(g,subtract(b,X0,X1)) != sk1_esk3_3(g,b,e) ),
inference(instantiation,[status(thm)],[c_849220]) ).
cnf(c_849682,plain,
( ~ morphism(g,b,e)
| ~ element(subtract(b,sk1_esk12_1(sk1_esk3_3(g,b,e)),sk1_esk13_1(sk1_esk3_3(g,b,e))),b)
| surjection(g)
| apply(g,subtract(b,sk1_esk12_1(sk1_esk3_3(g,b,e)),sk1_esk13_1(sk1_esk3_3(g,b,e)))) != sk1_esk3_3(g,b,e) ),
inference(instantiation,[status(thm)],[c_849500]) ).
cnf(c_75,plain,
( ~ element(X0,X1)
| ~ element(X2,X1)
| element(subtract(X1,X0,X2),X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_146_0) ).
cnf(c_228,plain,
( ~ element(X0,X1)
| ~ element(X2,X1)
| element(subtract(X1,X0,X2),X1) ),
inference(copy,[status(esa)],[c_75]) ).
cnf(c_46376,plain,
( ~ element(sk1_esk12_1(sk1_esk3_3(g,b,e)),b)
| element(subtract(b,sk1_esk12_1(sk1_esk3_3(g,b,e)),X0),b)
| ~ element(X0,b) ),
inference(instantiation,[status(thm)],[c_228]) ).
cnf(c_46872,plain,
( ~ element(sk1_esk13_1(sk1_esk3_3(g,b,e)),b)
| ~ element(sk1_esk12_1(sk1_esk3_3(g,b,e)),b)
| element(subtract(b,sk1_esk12_1(sk1_esk3_3(g,b,e)),sk1_esk13_1(sk1_esk3_3(g,b,e))),b) ),
inference(instantiation,[status(thm)],[c_46376]) ).
cnf(c_67,plain,
( element(sk1_esk12_1(X0),b)
| ~ element(X0,e) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_154_0) ).
cnf(c_220,plain,
( element(sk1_esk12_1(X0),b)
| ~ element(X0,e) ),
inference(copy,[status(esa)],[c_67]) ).
cnf(c_46259,plain,
( element(sk1_esk12_1(sk1_esk3_3(g,b,e)),b)
| ~ element(sk1_esk3_3(g,b,e),e) ),
inference(instantiation,[status(thm)],[c_220]) ).
cnf(c_66,plain,
( element(sk1_esk13_1(X0),b)
| ~ element(X0,e) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_155_0) ).
cnf(c_219,plain,
( element(sk1_esk13_1(X0),b)
| ~ element(X0,e) ),
inference(copy,[status(esa)],[c_66]) ).
cnf(c_46260,plain,
( element(sk1_esk13_1(sk1_esk3_3(g,b,e)),b)
| ~ element(sk1_esk3_3(g,b,e),e) ),
inference(instantiation,[status(thm)],[c_219]) ).
cnf(c_81,plain,
( apply(g,subtract(b,sk1_esk12_1(X0),sk1_esk13_1(X0))) = X0
| ~ element(X0,e) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_140_0) ).
cnf(c_234,plain,
( apply(g,subtract(b,sk1_esk12_1(X0),sk1_esk13_1(X0))) = X0
| ~ element(X0,e) ),
inference(copy,[status(esa)],[c_81]) ).
cnf(c_46266,plain,
( ~ element(sk1_esk3_3(g,b,e),e)
| apply(g,subtract(b,sk1_esk12_1(sk1_esk3_3(g,b,e)),sk1_esk13_1(sk1_esk3_3(g,b,e)))) = sk1_esk3_3(g,b,e) ),
inference(instantiation,[status(thm)],[c_234]) ).
cnf(c_83,plain,
( ~ morphism(X0,X1,X2)
| element(sk1_esk3_3(X0,X1,X2),X2)
| surjection(X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_138_0) ).
cnf(c_236,plain,
( ~ morphism(X0,X1,X2)
| element(sk1_esk3_3(X0,X1,X2),X2)
| surjection(X0) ),
inference(copy,[status(esa)],[c_83]) ).
cnf(c_46158,plain,
( ~ morphism(g,b,e)
| element(sk1_esk3_3(g,b,e),e)
| surjection(g) ),
inference(instantiation,[status(thm)],[c_236]) ).
cnf(c_50,plain,
morphism(g,b,e),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_171_0) ).
cnf(c_93,negated_conjecture,
~ surjection(g),
file('/export/starexec/sandbox/tmp/iprover_modulo_906ea0.p',c_0_12) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_849682,c_46872,c_46259,c_46260,c_46266,c_46158,c_50,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HAL003+3 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : iprover_modulo %s %d
% 0.13/0.35 % Computer : n022.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 : 600
% 0.13/0.35 % DateTime : Tue Jun 7 21:25:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.21/0.42 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.42 % FOF problem with conjecture
% 0.21/0.42 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_b1a371.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_906ea0.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_bba23e | grep -v "SZS"
% 0.21/0.45
% 0.21/0.45 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.45
% 0.21/0.45 %
% 0.21/0.45 % ------ iProver source info
% 0.21/0.45
% 0.21/0.45 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.45 % git: non_committed_changes: true
% 0.21/0.45 % git: last_make_outside_of_git: true
% 0.21/0.45
% 0.21/0.45 %
% 0.21/0.45 % ------ Input Options
% 0.21/0.45
% 0.21/0.45 % --out_options all
% 0.21/0.45 % --tptp_safe_out true
% 0.21/0.45 % --problem_path ""
% 0.21/0.45 % --include_path ""
% 0.21/0.45 % --clausifier .//eprover
% 0.21/0.45 % --clausifier_options --tstp-format
% 0.21/0.45 % --stdin false
% 0.21/0.45 % --dbg_backtrace false
% 0.21/0.45 % --dbg_dump_prop_clauses false
% 0.21/0.45 % --dbg_dump_prop_clauses_file -
% 0.21/0.45 % --dbg_out_stat false
% 0.21/0.45
% 0.21/0.45 % ------ General Options
% 0.21/0.45
% 0.21/0.45 % --fof false
% 0.21/0.45 % --time_out_real 150.
% 0.21/0.45 % --time_out_prep_mult 0.2
% 0.21/0.45 % --time_out_virtual -1.
% 0.21/0.45 % --schedule none
% 0.21/0.45 % --ground_splitting input
% 0.21/0.45 % --splitting_nvd 16
% 0.21/0.45 % --non_eq_to_eq false
% 0.21/0.45 % --prep_gs_sim true
% 0.21/0.45 % --prep_unflatten false
% 0.21/0.45 % --prep_res_sim true
% 0.21/0.45 % --prep_upred true
% 0.21/0.45 % --res_sim_input true
% 0.21/0.45 % --clause_weak_htbl true
% 0.21/0.45 % --gc_record_bc_elim false
% 0.21/0.45 % --symbol_type_check false
% 0.21/0.45 % --clausify_out false
% 0.21/0.45 % --large_theory_mode false
% 0.21/0.45 % --prep_sem_filter none
% 0.21/0.45 % --prep_sem_filter_out false
% 0.21/0.45 % --preprocessed_out false
% 0.21/0.45 % --sub_typing false
% 0.21/0.45 % --brand_transform false
% 0.21/0.45 % --pure_diseq_elim true
% 0.21/0.45 % --min_unsat_core false
% 0.21/0.45 % --pred_elim true
% 0.21/0.45 % --add_important_lit false
% 0.21/0.45 % --soft_assumptions false
% 0.21/0.45 % --reset_solvers false
% 0.21/0.45 % --bc_imp_inh []
% 0.21/0.45 % --conj_cone_tolerance 1.5
% 0.21/0.45 % --prolific_symb_bound 500
% 0.21/0.45 % --lt_threshold 2000
% 0.21/0.45
% 0.21/0.45 % ------ SAT Options
% 0.21/0.45
% 0.21/0.45 % --sat_mode false
% 0.21/0.45 % --sat_fm_restart_options ""
% 0.21/0.45 % --sat_gr_def false
% 0.21/0.45 % --sat_epr_types true
% 0.21/0.45 % --sat_non_cyclic_types false
% 0.21/0.45 % --sat_finite_models false
% 0.21/0.45 % --sat_fm_lemmas false
% 0.21/0.45 % --sat_fm_prep false
% 0.21/0.45 % --sat_fm_uc_incr true
% 0.21/0.45 % --sat_out_model small
% 0.21/0.45 % --sat_out_clauses false
% 0.21/0.45
% 0.21/0.45 % ------ QBF Options
% 0.21/0.45
% 0.21/0.45 % --qbf_mode false
% 0.21/0.45 % --qbf_elim_univ true
% 0.21/0.45 % --qbf_sk_in true
% 0.21/0.45 % --qbf_pred_elim true
% 0.21/0.45 % --qbf_split 32
% 0.21/0.45
% 0.21/0.45 % ------ BMC1 Options
% 0.21/0.45
% 0.21/0.45 % --bmc1_incremental false
% 0.21/0.45 % --bmc1_axioms reachable_all
% 0.21/0.45 % --bmc1_min_bound 0
% 0.21/0.45 % --bmc1_max_bound -1
% 0.21/0.45 % --bmc1_max_bound_default -1
% 0.21/0.45 % --bmc1_symbol_reachability true
% 0.21/0.45 % --bmc1_property_lemmas false
% 0.21/0.45 % --bmc1_k_induction false
% 0.21/0.45 % --bmc1_non_equiv_states false
% 0.21/0.45 % --bmc1_deadlock false
% 0.21/0.45 % --bmc1_ucm false
% 0.21/0.45 % --bmc1_add_unsat_core none
% 0.21/0.45 % --bmc1_unsat_core_children false
% 0.21/0.45 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.45 % --bmc1_out_stat full
% 0.21/0.45 % --bmc1_ground_init false
% 0.21/0.45 % --bmc1_pre_inst_next_state false
% 0.21/0.45 % --bmc1_pre_inst_state false
% 0.21/0.45 % --bmc1_pre_inst_reach_state false
% 0.21/0.45 % --bmc1_out_unsat_core false
% 0.21/0.45 % --bmc1_aig_witness_out false
% 0.21/0.45 % --bmc1_verbose false
% 0.21/0.45 % --bmc1_dump_clauses_tptp false
% 0.21/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.46 % --bmc1_dump_file -
% 0.21/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.46 % --bmc1_ucm_extend_mode 1
% 0.21/0.46 % --bmc1_ucm_init_mode 2
% 0.21/0.46 % --bmc1_ucm_cone_mode none
% 0.21/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.46 % --bmc1_ucm_relax_model 4
% 0.21/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.46 % --bmc1_ucm_layered_model none
% 0.21/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.46
% 0.21/0.46 % ------ AIG Options
% 0.21/0.46
% 0.21/0.46 % --aig_mode false
% 0.21/0.46
% 0.21/0.46 % ------ Instantiation Options
% 0.21/0.46
% 0.21/0.46 % --instantiation_flag true
% 0.21/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.46 % --inst_solver_per_active 750
% 0.21/0.46 % --inst_solver_calls_frac 0.5
% 0.21/0.46 % --inst_passive_queue_type priority_queues
% 0.21/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.46 % --inst_passive_queues_freq [25;2]
% 0.21/0.46 % --inst_dismatching true
% 0.21/0.46 % --inst_eager_unprocessed_to_passive true
% 0.21/0.46 % --inst_prop_sim_given true
% 0.21/0.46 % --inst_prop_sim_new false
% 0.21/0.46 % --inst_orphan_elimination true
% 0.21/0.46 % --inst_learning_loop_flag true
% 0.21/0.46 % --inst_learning_start 3000
% 0.21/0.46 % --inst_learning_factor 2
% 0.21/0.46 % --inst_start_prop_sim_after_learn 3
% 0.21/0.46 % --inst_sel_renew solver
% 0.21/0.46 % --inst_lit_activity_flag true
% 0.21/0.46 % --inst_out_proof true
% 0.21/0.46
% 0.21/0.46 % ------ Resolution Options
% 0.21/0.46
% 0.21/0.46 % --resolution_flag true
% 0.21/0.46 % --res_lit_sel kbo_max
% 0.21/0.46 % --res_to_prop_solver none
% 0.21/0.46 % --res_prop_simpl_new false
% 0.21/0.46 % --res_prop_simpl_given false
% 0.21/0.46 % --res_passive_queue_type priority_queues
% 0.21/0.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.21/0.46 % --res_passive_queues_freq [15;5]
% 0.21/0.46 % --res_forward_subs full
% 0.21/0.46 % --res_backward_subs full
% 0.21/0.46 % --res_forward_subs_resolution true
% 0.21/0.46 % --res_backward_subs_resolution true
% 0.21/0.46 % --res_orphan_elimination false
% 0.21/0.46 % --res_time_limit 1000.
% 0.21/0.46 % --res_out_proof true
% 0.21/0.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_b1a371.s
% 0.21/0.46 % --modulo true
% 0.21/0.46
% 0.21/0.46 % ------ Combination Options
% 0.21/0.46
% 0.21/0.46 % --comb_res_mult 1000
% 0.21/0.46 % --comb_inst_mult 300
% 0.21/0.46 % ------
% 0.21/0.46
% 0.21/0.46 % ------ Parsing...% successful
% 0.21/0.46
% 0.21/0.46 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.21/0.46
% 0.21/0.46 % ------ Proving...
% 0.21/0.46 % ------ Problem Properties
% 0.21/0.46
% 0.21/0.46 %
% 0.21/0.46 % EPR false
% 0.21/0.46 % Horn false
% 0.21/0.46 % Has equality true
% 0.21/0.46
% 0.21/0.46 % % ------ Input Options Time Limit: Unbounded
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % % ------ Current options:
% 0.21/0.46
% 0.21/0.46 % ------ Input Options
% 0.21/0.46
% 0.21/0.46 % --out_options all
% 0.21/0.46 % --tptp_safe_out true
% 0.21/0.46 % --problem_path ""
% 0.21/0.46 % --include_path ""
% 0.21/0.46 % --clausifier .//eprover
% 0.21/0.46 % --clausifier_options --tstp-format
% 0.21/0.46 % --stdin false
% 0.21/0.46 % --dbg_backtrace false
% 0.21/0.46 % --dbg_dump_prop_clauses false
% 0.21/0.46 % --dbg_dump_prop_clauses_file -
% 0.21/0.46 % --dbg_out_stat false
% 0.21/0.46
% 0.21/0.46 % ------ General Options
% 0.21/0.46
% 0.21/0.46 % --fof false
% 0.21/0.46 % --time_out_real 150.
% 0.21/0.46 % --time_out_prep_mult 0.2
% 0.21/0.46 % --time_out_virtual -1.
% 0.21/0.46 % --schedule none
% 0.21/0.46 % --ground_splitting input
% 0.21/0.46 % --splitting_nvd 16
% 0.21/0.46 % --non_eq_to_eq false
% 0.21/0.46 % --prep_gs_sim true
% 0.21/0.46 % --prep_unflatten false
% 0.21/0.46 % --prep_res_sim true
% 0.21/0.46 % --prep_upred true
% 0.21/0.46 % --res_sim_input true
% 0.21/0.46 % --clause_weak_htbl true
% 0.21/0.46 % --gc_record_bc_elim false
% 0.21/0.46 % --symbol_type_check false
% 0.21/0.46 % --clausify_out false
% 0.21/0.46 % --large_theory_mode false
% 0.21/0.46 % --prep_sem_filter none
% 0.21/0.46 % --prep_sem_filter_out false
% 0.21/0.46 % --preprocessed_out false
% 0.21/0.46 % --sub_typing false
% 0.21/0.46 % --brand_transform false
% 0.21/0.46 % --pure_diseq_elim true
% 0.21/0.46 % --min_unsat_core false
% 0.21/0.46 % --pred_elim true
% 0.21/0.46 % --add_important_lit false
% 0.21/0.46 % --soft_assumptions false
% 0.21/0.46 % --reset_solvers false
% 0.21/0.46 % --bc_imp_inh []
% 0.21/0.46 % --conj_cone_tolerance 1.5
% 0.21/0.46 % --prolific_symb_bound 500
% 0.21/0.46 % --lt_threshold 2000
% 0.21/0.46
% 0.21/0.46 % ------ SAT Options
% 0.21/0.46
% 0.21/0.46 % --sat_mode false
% 0.21/0.46 % --sat_fm_restart_options ""
% 0.21/0.46 % --sat_gr_def false
% 0.21/0.46 % --sat_epr_types true
% 0.21/0.46 % --sat_non_cyclic_types false
% 0.21/0.46 % --sat_finite_models false
% 0.21/0.46 % --sat_fm_lemmas false
% 0.21/0.46 % --sat_fm_prep false
% 0.21/0.46 % --sat_fm_uc_incr true
% 0.21/0.46 % --sat_out_model small
% 0.21/0.46 % --sat_out_clauses false
% 0.21/0.46
% 0.21/0.46 % ------ QBF Options
% 0.21/0.46
% 0.21/0.46 % --qbf_mode false
% 0.21/0.46 % --qbf_elim_univ true
% 0.21/0.46 % --qbf_sk_in true
% 0.21/0.46 % --qbf_pred_elim true
% 0.21/0.46 % --qbf_split 32
% 0.21/0.46
% 0.21/0.46 % ------ BMC1 Options
% 0.21/0.46
% 0.21/0.46 % --bmc1_incremental false
% 0.21/0.46 % --bmc1_axioms reachable_all
% 0.21/0.46 % --bmc1_min_bound 0
% 0.21/0.46 % --bmc1_max_bound -1
% 0.21/0.46 % --bmc1_max_bound_default -1
% 0.21/0.46 % --bmc1_symbol_reachability true
% 0.21/0.46 % --bmc1_property_lemmas false
% 0.21/0.46 % --bmc1_k_induction false
% 0.21/0.46 % --bmc1_non_equiv_states false
% 0.21/0.46 % --bmc1_deadlock false
% 0.21/0.46 % --bmc1_ucm false
% 0.21/0.46 % --bmc1_add_unsat_core none
% 0.21/0.46 % --bmc1_unsat_core_children false
% 0.21/0.46 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.46 % --bmc1_out_stat full
% 0.21/0.46 % --bmc1_ground_init false
% 0.21/0.46 % --bmc1_pre_inst_next_state false
% 0.21/0.46 % --bmc1_pre_inst_state false
% 0.21/0.46 % --bmc1_pre_inst_reach_state false
% 0.21/0.46 % --bmc1_out_unsat_core false
% 0.21/0.46 % --bmc1_aig_witness_out false
% 0.21/0.46 % --bmc1_verbose false
% 0.21/0.46 % --bmc1_dump_clauses_tptp false
% 0.21/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.46 % --bmc1_dump_file -
% 0.21/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.46 % --bmc1_ucm_extend_mode 1
% 0.21/0.46 % --bmc1_ucm_init_mode 2
% 0.21/0.46 % --bmc1_ucm_cone_mode none
% 0.21/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.46 % --bmc1_ucm_relax_model 4
% 0.21/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.46 % --bmc1_ucm_layered_model none
% 0.21/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.46
% 0.21/0.46 % ------ AIG Options
% 0.21/0.46
% 0.21/0.46 % --aig_mode false
% 0.21/0.46
% 0.21/0.46 % ------ Instantiation Options
% 0.21/0.46
% 0.21/0.46 % --instantiation_flag true
% 0.21/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.46 % --inst_solver_per_active 750
% 0.21/0.46 % --inst_solver_calls_frac 0.5
% 0.21/0.46 % --inst_passive_queue_type priority_queues
% 0.21/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.46 % --inst_passive_queues_freq [25;2]
% 0.21/0.46 % --inst_dismatching true
% 0.21/0.46 % --inst_eager_unprocessed_to_passive true
% 0.21/0.46 % --inst_prop_sim_given true
% 91.80/92.05 % --inst_prop_sim_new false
% 91.80/92.05 % --inst_orphan_elimination true
% 91.80/92.05 % --inst_learning_loop_flag true
% 91.80/92.05 % --inst_learning_start 3000
% 91.80/92.05 % --inst_learning_factor 2
% 91.80/92.05 % --inst_start_prop_sim_after_learn 3
% 91.80/92.05 % --inst_sel_renew solver
% 91.80/92.05 % --inst_lit_activity_flag true
% 91.80/92.05 % --inst_out_proof true
% 91.80/92.05
% 91.80/92.05 % ------ Resolution Options
% 91.80/92.05
% 91.80/92.05 % --resolution_flag true
% 91.80/92.05 % --res_lit_sel kbo_max
% 91.80/92.05 % --res_to_prop_solver none
% 91.80/92.05 % --res_prop_simpl_new false
% 91.80/92.05 % --res_prop_simpl_given false
% 91.80/92.05 % --res_passive_queue_type priority_queues
% 91.80/92.05 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 91.80/92.05 % --res_passive_queues_freq [15;5]
% 91.80/92.05 % --res_forward_subs full
% 91.80/92.05 % --res_backward_subs full
% 91.80/92.05 % --res_forward_subs_resolution true
% 91.80/92.05 % --res_backward_subs_resolution true
% 91.80/92.05 % --res_orphan_elimination false
% 91.80/92.05 % --res_time_limit 1000.
% 91.80/92.05 % --res_out_proof true
% 91.80/92.05 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_b1a371.s
% 91.80/92.05 % --modulo true
% 91.80/92.05
% 91.80/92.05 % ------ Combination Options
% 91.80/92.05
% 91.80/92.05 % --comb_res_mult 1000
% 91.80/92.05 % --comb_inst_mult 300
% 91.80/92.05 % ------
% 91.80/92.05
% 91.80/92.05
% 91.80/92.05
% 91.80/92.05 % ------ Proving...
% 91.80/92.05 %
% 91.80/92.05
% 91.80/92.05
% 91.80/92.05 % ------ Statistics
% 91.80/92.05
% 91.80/92.05 % ------ General
% 91.80/92.05
% 91.80/92.05 % num_of_input_clauses: 96
% 91.80/92.05 % num_of_input_neg_conjectures: 1
% 91.80/92.05 % num_of_splits: 0
% 91.80/92.05 % num_of_split_atoms: 0
% 91.80/92.05 % num_of_sem_filtered_clauses: 0
% 91.80/92.05 % num_of_subtypes: 0
% 91.80/92.05 % monotx_restored_types: 0
% 91.80/92.05 % sat_num_of_epr_types: 0
% 91.80/92.05 % sat_num_of_non_cyclic_types: 0
% 91.80/92.05 % sat_guarded_non_collapsed_types: 0
% 91.80/92.05 % is_epr: 0
% 91.80/92.05 % is_horn: 0
% 91.80/92.05 % has_eq: 1
% 91.80/92.05 % num_pure_diseq_elim: 0
% 91.80/92.05 % simp_replaced_by: 0
% 91.80/92.05 % res_preprocessed: 4
% 91.80/92.05 % prep_upred: 0
% 91.80/92.05 % prep_unflattend: 0
% 91.80/92.05 % pred_elim_cands: 0
% 91.80/92.05 % pred_elim: 0
% 91.80/92.05 % pred_elim_cl: 0
% 91.80/92.05 % pred_elim_cycles: 0
% 91.80/92.05 % forced_gc_time: 0
% 91.80/92.05 % gc_basic_clause_elim: 0
% 91.80/92.05 % parsing_time: 0.006
% 91.80/92.05 % sem_filter_time: 0.
% 91.80/92.05 % pred_elim_time: 0.
% 91.80/92.05 % out_proof_time: 0.002
% 91.80/92.05 % monotx_time: 0.
% 91.80/92.05 % subtype_inf_time: 0.
% 91.80/92.05 % unif_index_cands_time: 0.159
% 91.80/92.05 % unif_index_add_time: 0.064
% 91.80/92.05 % total_time: 91.625
% 91.80/92.05 % num_of_symbols: 63
% 91.80/92.05 % num_of_terms: 570985
% 91.80/92.05
% 91.80/92.05 % ------ Propositional Solver
% 91.80/92.05
% 91.80/92.05 % prop_solver_calls: 21
% 91.80/92.05 % prop_fast_solver_calls: 7
% 91.80/92.05 % prop_num_of_clauses: 12183
% 91.80/92.05 % prop_preprocess_simplified: 13485
% 91.80/92.05 % prop_fo_subsumed: 0
% 91.80/92.05 % prop_solver_time: 0.005
% 91.80/92.05 % prop_fast_solver_time: 0.
% 91.80/92.05 % prop_unsat_core_time: 0.001
% 91.80/92.05
% 91.80/92.05 % ------ QBF
% 91.80/92.05
% 91.80/92.05 % qbf_q_res: 0
% 91.80/92.05 % qbf_num_tautologies: 0
% 91.80/92.05 % qbf_prep_cycles: 0
% 91.80/92.05
% 91.80/92.05 % ------ BMC1
% 91.80/92.05
% 91.80/92.05 % bmc1_current_bound: -1
% 91.80/92.05 % bmc1_last_solved_bound: -1
% 91.80/92.05 % bmc1_unsat_core_size: -1
% 91.80/92.05 % bmc1_unsat_core_parents_size: -1
% 91.80/92.05 % bmc1_merge_next_fun: 0
% 91.80/92.05 % bmc1_unsat_core_clauses_time: 0.
% 91.80/92.05
% 91.80/92.05 % ------ Instantiation
% 91.80/92.05
% 91.80/92.05 % inst_num_of_clauses: 410
% 91.80/92.05 % inst_num_in_passive: 107
% 91.80/92.05 % inst_num_in_active: 235
% 91.80/92.05 % inst_num_in_unprocessed: 65
% 91.80/92.05 % inst_num_of_loops: 237
% 91.88/92.06 % inst_num_of_learning_restarts: 1
% 91.88/92.06 % inst_num_moves_active_passive: 0
% 91.88/92.06 % inst_lit_activity: 120
% 91.88/92.06 % inst_lit_activity_moves: 0
% 91.88/92.06 % inst_num_tautologies: 0
% 91.88/92.06 % inst_num_prop_implied: 0
% 91.88/92.06 % inst_num_existing_simplified: 0
% 91.88/92.06 % inst_num_eq_res_simplified: 0
% 91.88/92.06 % inst_num_child_elim: 0
% 91.88/92.06 % inst_num_of_dismatching_blockings: 0
% 91.88/92.06 % inst_num_of_non_proper_insts: 330
% 91.88/92.06 % inst_num_of_duplicates: 114
% 91.88/92.06 % inst_inst_num_from_inst_to_res: 0
% 91.88/92.06 % inst_dismatching_checking_time: 0.804
% 91.88/92.06
% 91.88/92.06 % ------ Resolution
% 91.88/92.06
% 91.88/92.06 % res_num_of_clauses: 131313
% 91.88/92.06 % res_num_in_passive: 120278
% 91.88/92.06 % res_num_in_active: 10969
% 91.88/92.06 % res_num_of_loops: 11000
% 91.88/92.06 % res_forward_subset_subsumed: 28
% 91.88/92.06 % res_backward_subset_subsumed: 0
% 91.88/92.06 % res_forward_subsumed: 96
% 91.88/92.06 % res_backward_subsumed: 0
% 91.88/92.06 % res_forward_subsumption_resolution: 26
% 91.88/92.06 % res_backward_subsumption_resolution: 0
% 91.88/92.06 % res_clause_to_clause_subsumption: 601460
% 91.88/92.06 % res_orphan_elimination: 0
% 91.88/92.06 % res_tautology_del: 30
% 91.88/92.06 % res_num_eq_res_simplified: 0
% 91.88/92.06 % res_num_sel_changes: 0
% 91.88/92.06 % res_moves_from_active_to_pass: 0
% 91.88/92.06
% 91.88/92.06 % Status Unsatisfiable
% 91.88/92.06 % SZS status Theorem
% 91.88/92.06 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------