TSTP Solution File: HAL001+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HAL001+2 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 : Thu Aug 31 01:53:27 EDT 2023
% Result : Theorem 31.07s 31.14s
% Output : CNFRefutation 31.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 56
% Syntax : Number of formulae : 159 ( 57 unt; 32 typ; 0 def)
% Number of atoms : 379 ( 102 equ)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 453 ( 201 ~; 207 |; 29 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 18 >; 36 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 26 ( 26 usr; 14 con; 0-6 aty)
% Number of variables : 223 ( 10 sgn; 83 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
morphism: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
element: ( $i * $i ) > $o ).
tff(decl_24,type,
apply: ( $i * $i ) > $i ).
tff(decl_25,type,
zero: $i > $i ).
tff(decl_26,type,
injection: $i > $o ).
tff(decl_27,type,
surjection: $i > $o ).
tff(decl_28,type,
exact: ( $i * $i ) > $o ).
tff(decl_29,type,
commute: ( $i * $i * $i * $i ) > $o ).
tff(decl_30,type,
subtract: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
alpha: $i ).
tff(decl_32,type,
a: $i ).
tff(decl_33,type,
b: $i ).
tff(decl_34,type,
beta: $i ).
tff(decl_35,type,
c: $i ).
tff(decl_36,type,
gamma: $i ).
tff(decl_37,type,
d: $i ).
tff(decl_38,type,
e: $i ).
tff(decl_39,type,
delta: $i ).
tff(decl_40,type,
r: $i ).
tff(decl_41,type,
f: $i ).
tff(decl_42,type,
g: $i ).
tff(decl_43,type,
h: $i ).
tff(decl_44,type,
gammma: $i ).
tff(decl_45,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_48,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk5_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
esk6_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
esk7_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_52,type,
esk8_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
esk9_3: ( $i * $i * $i ) > $i ).
fof(properties_for_injection,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2)
& apply(X1,X5) = apply(X1,X6) )
=> X5 = X6 ) )
=> injection(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',properties_for_injection) ).
fof(g_injection,conjecture,
injection(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_injection) ).
fof(subtract_in_domain,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> element(subtract(X2,X5,X6),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
fof(subtract_to_0,axiom,
! [X2,X4] :
( element(X4,X2)
=> subtract(X2,X4,X4) = zero(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',subtract_to_0) ).
fof(commute_properties,axiom,
! [X13,X14,X15,X16,X2,X17,X18,X3] :
( ( commute(X13,X14,X15,X16)
& morphism(X13,X2,X17)
& morphism(X14,X17,X3)
& morphism(X15,X2,X18)
& morphism(X16,X18,X3) )
=> ! [X8] :
( element(X8,X2)
=> apply(X14,apply(X13,X8)) = apply(X16,apply(X15,X8)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',commute_properties) ).
fof(morphism,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( ! [X4] :
( element(X4,X2)
=> element(apply(X1,X4),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(beta_h_g_delta_commute,axiom,
commute(beta,h,g,delta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
fof(injection_properties,axiom,
! [X1,X2,X3] :
( ( injection(X1)
& morphism(X1,X2,X3) )
=> ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2)
& apply(X1,X5) = apply(X1,X6) )
=> X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',injection_properties) ).
fof(h_morphism,axiom,
morphism(h,c,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_morphism) ).
fof(beta_morphism,axiom,
morphism(beta,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_morphism) ).
fof(properties_for_injection_2,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X4] :
( ( element(X4,X2)
& apply(X1,X4) = zero(X3) )
=> X4 = zero(X2) ) )
=> injection(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection_2) ).
fof(delta_morphism,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',delta_morphism) ).
fof(h_injection,hypothesis,
injection(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_injection) ).
fof(exact_properties,axiom,
! [X9,X10,X2,X11,X3] :
( ( exact(X9,X10)
& morphism(X9,X2,X11)
& morphism(X10,X11,X3) )
=> ! [X12] :
( ( element(X12,X11)
& apply(X10,X12) = zero(X3) )
<=> ? [X8] :
( element(X8,X2)
& apply(X9,X8) = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax',exact_properties) ).
fof(alpha_beta_exact,axiom,
exact(alpha,beta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_beta_exact) ).
fof(alpha_g_f_gamma_commute,axiom,
commute(alpha,g,f,gamma),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_g_f_gamma_commute) ).
fof(injection_properties_2,axiom,
! [X1,X2,X3] :
( ( injection(X1)
& morphism(X1,X2,X3) )
=> ! [X4] :
( ( element(X4,X2)
& apply(X1,X4) = zero(X3) )
=> X4 = zero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties_2) ).
fof(alpha_morphism,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).
fof(gamma_morphism,axiom,
morphism(gamma,d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_morphism) ).
fof(alpha_injection,axiom,
injection(alpha),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_injection) ).
fof(f_morphism,axiom,
morphism(f,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_morphism) ).
fof(f_injection,hypothesis,
injection(f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_injection) ).
fof(gamma_injection,axiom,
injection(gamma),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_injection) ).
fof(c_0_24,plain,
! [X28,X29,X30] :
( ( element(esk1_2(X28,X29),X29)
| ~ morphism(X28,X29,X30)
| injection(X28) )
& ( element(esk2_2(X28,X29),X29)
| ~ morphism(X28,X29,X30)
| injection(X28) )
& ( apply(X28,esk1_2(X28,X29)) = apply(X28,esk2_2(X28,X29))
| ~ morphism(X28,X29,X30)
| injection(X28) )
& ( esk1_2(X28,X29) != esk2_2(X28,X29)
| ~ morphism(X28,X29,X30)
| injection(X28) ) ),
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)],[properties_for_injection])])])])])]) ).
fof(c_0_25,negated_conjecture,
~ injection(g),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[g_injection])]) ).
fof(c_0_26,plain,
! [X78,X79,X80] :
( ~ element(X79,X78)
| ~ element(X80,X78)
| element(subtract(X78,X79,X80),X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_in_domain])]) ).
cnf(c_0_27,plain,
( element(esk1_2(X1,X2),X2)
| injection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_29,negated_conjecture,
~ injection(g),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X81,X82] :
( ~ element(X82,X81)
| subtract(X81,X82,X82) = zero(X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_to_0])]) ).
fof(c_0_31,plain,
! [X60,X61,X62,X63,X64,X65,X66,X67,X68] :
( ~ commute(X60,X61,X62,X63)
| ~ morphism(X60,X64,X65)
| ~ morphism(X61,X65,X67)
| ~ morphism(X62,X64,X66)
| ~ morphism(X63,X66,X67)
| ~ element(X68,X64)
| apply(X61,apply(X60,X68)) = apply(X63,apply(X62,X68)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commute_properties])])]) ).
fof(c_0_32,plain,
! [X19,X20,X21,X22] :
( ( ~ element(X22,X20)
| element(apply(X19,X22),X21)
| ~ morphism(X19,X20,X21) )
& ( apply(X19,zero(X20)) = zero(X21)
| ~ morphism(X19,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])]) ).
cnf(c_0_33,plain,
( element(subtract(X2,X1,X3),X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
element(esk1_2(g,b),b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
( subtract(X2,X1,X1) = zero(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( apply(X2,apply(X1,X9)) = apply(X4,apply(X3,X9))
| ~ commute(X1,X2,X3,X4)
| ~ morphism(X1,X5,X6)
| ~ morphism(X2,X6,X7)
| ~ morphism(X3,X5,X8)
| ~ morphism(X4,X8,X7)
| ~ element(X9,X5) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
commute(beta,h,g,delta),
inference(split_conjunct,[status(thm)],[beta_h_g_delta_commute]) ).
fof(c_0_38,plain,
! [X23,X24,X25,X26,X27] :
( ~ injection(X23)
| ~ morphism(X23,X24,X25)
| ~ element(X26,X24)
| ~ element(X27,X24)
| apply(X23,X26) != apply(X23,X27)
| X26 = X27 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[injection_properties])])]) ).
cnf(c_0_39,plain,
( apply(X1,zero(X2)) = zero(X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
morphism(h,c,r),
inference(split_conjunct,[status(thm)],[h_morphism]) ).
cnf(c_0_41,plain,
( element(apply(X3,X1),X4)
| ~ element(X1,X2)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
morphism(beta,b,c),
inference(split_conjunct,[status(thm)],[beta_morphism]) ).
cnf(c_0_43,plain,
( element(subtract(b,X1,esk1_2(g,b)),b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
subtract(b,esk1_2(g,b),esk1_2(g,b)) = zero(b),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
fof(c_0_45,plain,
! [X95,X96,X97] :
( ( element(esk9_3(X95,X96,X97),X96)
| ~ morphism(X95,X96,X97)
| injection(X95) )
& ( apply(X95,esk9_3(X95,X96,X97)) = zero(X97)
| ~ morphism(X95,X96,X97)
| injection(X95) )
& ( esk9_3(X95,X96,X97) != zero(X96)
| ~ morphism(X95,X96,X97)
| injection(X95) ) ),
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)],[properties_for_injection_2])])])])])]) ).
cnf(c_0_46,plain,
( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
| ~ element(X1,X2)
| ~ morphism(delta,X3,X4)
| ~ morphism(g,X2,X3)
| ~ morphism(h,X5,X4)
| ~ morphism(beta,X2,X5) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,plain,
morphism(delta,e,r),
inference(split_conjunct,[status(thm)],[delta_morphism]) ).
cnf(c_0_48,plain,
( X4 = X5
| ~ injection(X1)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2)
| ~ element(X5,X2)
| apply(X1,X4) != apply(X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,plain,
apply(h,zero(c)) = zero(r),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_50,hypothesis,
injection(h),
inference(split_conjunct,[status(thm)],[h_injection]) ).
cnf(c_0_51,plain,
( element(apply(beta,X1),c)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_52,plain,
element(zero(b),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_34]),c_0_44]) ).
cnf(c_0_53,plain,
apply(beta,zero(b)) = zero(c),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_54,plain,
( element(esk9_3(X1,X2,X3),X2)
| injection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
| ~ element(X1,X2)
| ~ morphism(g,X2,e)
| ~ morphism(h,X3,r)
| ~ morphism(beta,X2,X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,plain,
( apply(X1,esk9_3(X1,X2,X3)) = zero(X3)
| injection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( X1 = zero(c)
| apply(h,X1) != zero(r)
| ~ element(zero(c),X2)
| ~ element(X1,X2)
| ~ morphism(h,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_58,plain,
element(zero(c),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_59,plain,
element(esk9_3(g,b,e),b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_28]),c_0_29]) ).
cnf(c_0_60,plain,
( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
| ~ element(X1,b)
| ~ morphism(h,X2,r)
| ~ morphism(beta,b,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_28]) ).
cnf(c_0_61,plain,
apply(g,esk9_3(g,b,e)) = zero(e),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_28]),c_0_29]) ).
cnf(c_0_62,plain,
apply(delta,zero(e)) = zero(r),
inference(spm,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_63,plain,
( X1 = zero(c)
| apply(h,X1) != zero(r)
| ~ element(X1,c)
| ~ morphism(h,c,X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
element(apply(beta,esk9_3(g,b,e)),c),
inference(spm,[status(thm)],[c_0_51,c_0_59]) ).
cnf(c_0_65,plain,
( apply(h,apply(beta,esk9_3(g,b,e))) = zero(r)
| ~ morphism(h,X1,r)
| ~ morphism(beta,b,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_59]),c_0_61]),c_0_62]) ).
fof(c_0_66,plain,
! [X43,X44,X45,X46,X47,X48,X50,X51] :
( ( element(esk5_6(X43,X44,X45,X46,X47,X48),X45)
| ~ element(X48,X46)
| apply(X44,X48) != zero(X47)
| ~ exact(X43,X44)
| ~ morphism(X43,X45,X46)
| ~ morphism(X44,X46,X47) )
& ( apply(X43,esk5_6(X43,X44,X45,X46,X47,X48)) = X48
| ~ element(X48,X46)
| apply(X44,X48) != zero(X47)
| ~ exact(X43,X44)
| ~ morphism(X43,X45,X46)
| ~ morphism(X44,X46,X47) )
& ( element(X50,X46)
| ~ element(X51,X45)
| apply(X43,X51) != X50
| ~ exact(X43,X44)
| ~ morphism(X43,X45,X46)
| ~ morphism(X44,X46,X47) )
& ( apply(X44,X50) = zero(X47)
| ~ element(X51,X45)
| apply(X43,X51) != X50
| ~ exact(X43,X44)
| ~ morphism(X43,X45,X46)
| ~ morphism(X44,X46,X47) ) ),
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)],[exact_properties])])])])])]) ).
cnf(c_0_67,plain,
( apply(beta,esk9_3(g,b,e)) = zero(c)
| apply(h,apply(beta,esk9_3(g,b,e))) != zero(r)
| ~ morphism(h,c,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
apply(h,apply(beta,esk9_3(g,b,e))) = zero(r),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_40]),c_0_42])]) ).
cnf(c_0_69,plain,
( apply(X1,esk5_6(X1,X2,X3,X4,X5,X6)) = X6
| ~ element(X6,X4)
| apply(X2,X6) != zero(X5)
| ~ exact(X1,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_70,plain,
( apply(beta,esk9_3(g,b,e)) = zero(c)
| ~ morphism(h,c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_71,plain,
( apply(X1,esk5_6(X1,beta,X2,X3,X4,zero(b))) = zero(b)
| zero(c) != zero(X4)
| ~ exact(X1,beta)
| ~ element(zero(b),X3)
| ~ morphism(beta,X3,X4)
| ~ morphism(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_53]) ).
cnf(c_0_72,plain,
exact(alpha,beta),
inference(split_conjunct,[status(thm)],[alpha_beta_exact]) ).
cnf(c_0_73,plain,
( element(esk5_6(X1,X2,X3,X4,X5,X6),X3)
| ~ element(X6,X4)
| apply(X2,X6) != zero(X5)
| ~ exact(X1,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,plain,
apply(beta,esk9_3(g,b,e)) = zero(c),
inference(spm,[status(thm)],[c_0_70,c_0_40]) ).
cnf(c_0_75,plain,
( apply(alpha,esk5_6(alpha,beta,X1,X2,X3,zero(b))) = zero(b)
| zero(c) != zero(X3)
| ~ element(zero(b),X2)
| ~ morphism(beta,X2,X3)
| ~ morphism(alpha,X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,plain,
( element(esk5_6(X1,beta,X2,X3,X4,esk9_3(g,b,e)),X2)
| zero(c) != zero(X4)
| ~ exact(X1,beta)
| ~ element(esk9_3(g,b,e),X3)
| ~ morphism(beta,X3,X4)
| ~ morphism(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,plain,
( apply(X1,esk5_6(X1,beta,X2,X3,X4,esk9_3(g,b,e))) = esk9_3(g,b,e)
| zero(c) != zero(X4)
| ~ exact(X1,beta)
| ~ element(esk9_3(g,b,e),X3)
| ~ morphism(beta,X3,X4)
| ~ morphism(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_74]) ).
cnf(c_0_78,plain,
( apply(alpha,esk5_6(alpha,beta,X1,X2,c,zero(b))) = zero(b)
| ~ element(zero(b),X2)
| ~ morphism(beta,X2,c)
| ~ morphism(alpha,X1,X2) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_79,plain,
( element(esk5_6(X1,beta,X2,X3,X4,zero(b)),X2)
| zero(c) != zero(X4)
| ~ exact(X1,beta)
| ~ element(zero(b),X3)
| ~ morphism(beta,X3,X4)
| ~ morphism(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_53]) ).
cnf(c_0_80,plain,
commute(alpha,g,f,gamma),
inference(split_conjunct,[status(thm)],[alpha_g_f_gamma_commute]) ).
cnf(c_0_81,plain,
( element(esk5_6(alpha,beta,X1,X2,X3,esk9_3(g,b,e)),X1)
| zero(c) != zero(X3)
| ~ element(esk9_3(g,b,e),X2)
| ~ morphism(beta,X2,X3)
| ~ morphism(alpha,X1,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_72]) ).
cnf(c_0_82,plain,
( apply(alpha,esk5_6(alpha,beta,X1,X2,X3,esk9_3(g,b,e))) = esk9_3(g,b,e)
| zero(c) != zero(X3)
| ~ element(esk9_3(g,b,e),X2)
| ~ morphism(beta,X2,X3)
| ~ morphism(alpha,X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_72]) ).
fof(c_0_83,plain,
! [X91,X92,X93,X94] :
( ~ injection(X91)
| ~ morphism(X91,X92,X93)
| ~ element(X94,X92)
| apply(X91,X94) != zero(X93)
| X94 = zero(X92) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[injection_properties_2])])]) ).
cnf(c_0_84,plain,
( apply(alpha,esk5_6(alpha,beta,X1,b,c,zero(b))) = zero(b)
| ~ morphism(alpha,X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_52]),c_0_42])]) ).
cnf(c_0_85,plain,
morphism(alpha,a,b),
inference(split_conjunct,[status(thm)],[alpha_morphism]) ).
cnf(c_0_86,plain,
( element(esk5_6(alpha,beta,X1,X2,X3,zero(b)),X1)
| zero(c) != zero(X3)
| ~ element(zero(b),X2)
| ~ morphism(beta,X2,X3)
| ~ morphism(alpha,X1,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_72]) ).
cnf(c_0_87,plain,
( apply(gamma,apply(f,X1)) = apply(g,apply(alpha,X1))
| ~ element(X1,X2)
| ~ morphism(gamma,X3,X4)
| ~ morphism(f,X2,X3)
| ~ morphism(g,X5,X4)
| ~ morphism(alpha,X2,X5) ),
inference(spm,[status(thm)],[c_0_36,c_0_80]) ).
cnf(c_0_88,plain,
morphism(gamma,d,e),
inference(split_conjunct,[status(thm)],[gamma_morphism]) ).
cnf(c_0_89,plain,
( element(esk5_6(alpha,beta,X1,X2,c,esk9_3(g,b,e)),X1)
| ~ element(esk9_3(g,b,e),X2)
| ~ morphism(beta,X2,c)
| ~ morphism(alpha,X1,X2) ),
inference(er,[status(thm)],[c_0_81]) ).
cnf(c_0_90,plain,
( apply(alpha,esk5_6(alpha,beta,X1,X2,c,esk9_3(g,b,e))) = esk9_3(g,b,e)
| ~ element(esk9_3(g,b,e),X2)
| ~ morphism(beta,X2,c)
| ~ morphism(alpha,X1,X2) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_91,plain,
( X4 = zero(X2)
| ~ injection(X1)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2)
| apply(X1,X4) != zero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_92,plain,
apply(alpha,esk5_6(alpha,beta,a,b,c,zero(b))) = zero(b),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_93,plain,
injection(alpha),
inference(split_conjunct,[status(thm)],[alpha_injection]) ).
cnf(c_0_94,plain,
( element(esk5_6(alpha,beta,X1,X2,c,zero(b)),X1)
| ~ element(zero(b),X2)
| ~ morphism(beta,X2,c)
| ~ morphism(alpha,X1,X2) ),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_95,plain,
( apply(gamma,apply(f,X1)) = apply(g,apply(alpha,X1))
| ~ element(X1,X2)
| ~ morphism(f,X2,d)
| ~ morphism(g,X3,e)
| ~ morphism(alpha,X2,X3) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,plain,
morphism(f,a,d),
inference(split_conjunct,[status(thm)],[f_morphism]) ).
cnf(c_0_97,plain,
( element(esk5_6(alpha,beta,X1,b,c,esk9_3(g,b,e)),X1)
| ~ morphism(alpha,X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_42]),c_0_59])]) ).
cnf(c_0_98,plain,
( apply(alpha,esk5_6(alpha,beta,X1,b,c,esk9_3(g,b,e))) = esk9_3(g,b,e)
| ~ morphism(alpha,X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_42]),c_0_59])]) ).
cnf(c_0_99,plain,
( esk5_6(alpha,beta,a,b,c,zero(b)) = zero(X1)
| zero(b) != zero(X2)
| ~ element(esk5_6(alpha,beta,a,b,c,zero(b)),X1)
| ~ morphism(alpha,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]) ).
cnf(c_0_100,plain,
( element(esk5_6(alpha,beta,X1,b,c,zero(b)),X1)
| ~ morphism(alpha,X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_42]),c_0_52])]) ).
cnf(c_0_101,plain,
( apply(gamma,apply(f,X1)) = apply(g,apply(alpha,X1))
| ~ element(X1,a)
| ~ morphism(g,X2,e)
| ~ morphism(alpha,a,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,plain,
element(esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)),a),
inference(spm,[status(thm)],[c_0_97,c_0_85]) ).
cnf(c_0_103,plain,
apply(alpha,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) = esk9_3(g,b,e),
inference(spm,[status(thm)],[c_0_98,c_0_85]) ).
cnf(c_0_104,plain,
( esk5_6(alpha,beta,a,b,c,zero(b)) = zero(X1)
| ~ element(esk5_6(alpha,beta,a,b,c,zero(b)),X1)
| ~ morphism(alpha,X1,b) ),
inference(er,[status(thm)],[c_0_99]) ).
cnf(c_0_105,plain,
element(esk5_6(alpha,beta,a,b,c,zero(b)),a),
inference(spm,[status(thm)],[c_0_100,c_0_85]) ).
cnf(c_0_106,plain,
( apply(gamma,apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)))) = zero(e)
| ~ morphism(g,X1,e)
| ~ morphism(alpha,a,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_61]) ).
cnf(c_0_107,plain,
apply(f,zero(a)) = zero(d),
inference(spm,[status(thm)],[c_0_39,c_0_96]) ).
cnf(c_0_108,hypothesis,
injection(f),
inference(split_conjunct,[status(thm)],[f_injection]) ).
cnf(c_0_109,plain,
esk5_6(alpha,beta,a,b,c,zero(b)) = zero(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_85]),c_0_105])]) ).
cnf(c_0_110,plain,
apply(gamma,apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)))) = zero(e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_28]),c_0_85])]) ).
cnf(c_0_111,plain,
injection(gamma),
inference(split_conjunct,[status(thm)],[gamma_injection]) ).
cnf(c_0_112,plain,
( X1 = zero(a)
| apply(f,X1) != zero(d)
| ~ element(zero(a),X2)
| ~ element(X1,X2)
| ~ morphism(f,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_107]),c_0_108])]) ).
cnf(c_0_113,plain,
element(zero(a),a),
inference(rw,[status(thm)],[c_0_105,c_0_109]) ).
cnf(c_0_114,plain,
( apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) = zero(X1)
| zero(e) != zero(X2)
| ~ element(apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))),X1)
| ~ morphism(gamma,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_110]),c_0_111])]) ).
cnf(c_0_115,plain,
( element(apply(f,X1),d)
| ~ element(X1,a) ),
inference(spm,[status(thm)],[c_0_41,c_0_96]) ).
cnf(c_0_116,plain,
( X1 = zero(a)
| apply(f,X1) != zero(d)
| ~ element(X1,a)
| ~ morphism(f,a,X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_117,plain,
( apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) = zero(X1)
| ~ element(apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))),X1)
| ~ morphism(gamma,X1,e) ),
inference(er,[status(thm)],[c_0_114]) ).
cnf(c_0_118,plain,
element(apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))),d),
inference(spm,[status(thm)],[c_0_115,c_0_102]) ).
cnf(c_0_119,plain,
( esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)) = zero(a)
| apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) != zero(d)
| ~ morphism(f,a,X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_102]) ).
cnf(c_0_120,plain,
apply(f,esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e))) = zero(d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_88]),c_0_118])]) ).
cnf(c_0_121,plain,
( esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)) = zero(a)
| ~ morphism(f,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_122,plain,
esk5_6(alpha,beta,a,b,c,esk9_3(g,b,e)) = zero(a),
inference(spm,[status(thm)],[c_0_121,c_0_96]) ).
cnf(c_0_123,plain,
apply(alpha,zero(a)) = zero(b),
inference(spm,[status(thm)],[c_0_39,c_0_85]) ).
cnf(c_0_124,plain,
( injection(X1)
| esk9_3(X1,X2,X3) != zero(X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_125,plain,
esk9_3(g,b,e) = zero(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_122]),c_0_123]) ).
cnf(c_0_126,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL001+2 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 02:40:01 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 31.07/31.14 % Version : CSE_E---1.5
% 31.07/31.14 % Problem : theBenchmark.p
% 31.07/31.14 % Proof found
% 31.07/31.14 % SZS status Theorem for theBenchmark.p
% 31.07/31.14 % SZS output start Proof
% See solution above
% 31.07/31.15 % Total time : 30.590000 s
% 31.07/31.15 % SZS output end Proof
% 31.07/31.15 % Total time : 30.595000 s
%------------------------------------------------------------------------------