TSTP Solution File: HAL004+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HAL004+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n004.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 01:53:28 EDT 2023
% Result : Theorem 14.17s 14.36s
% Output : CNFRefutation 14.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 47
% Syntax : Number of formulae : 129 ( 24 unt; 32 typ; 0 def)
% Number of atoms : 265 ( 69 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 319 ( 151 ~; 134 |; 21 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 17 >; 34 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 26 ( 26 usr; 15 con; 0-6 aty)
% Number of variables : 178 ( 5 sgn; 64 !; 5 ?; 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_0: $i ).
fof(subtract_in_domain,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> element(subtract(X2,X5,X6),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_in_domain) ).
fof(subtract_to_0,axiom,
! [X2,X4] :
( element(X4,X2)
=> subtract(X2,X4,X4) = zero(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_to_0) ).
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/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(surjection_properties,axiom,
! [X1,X2,X3] :
( ( surjection(X1)
& morphism(X1,X2,X3) )
=> ! [X7] :
( element(X7,X3)
=> ? [X8] :
( element(X8,X2)
& apply(X1,X8) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',surjection_properties) ).
fof(delta_morphism,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_morphism) ).
fof(lemma3,conjecture,
! [X19] :
( element(X19,e)
=> ? [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('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma3) ).
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/sandbox2/benchmark/Axioms/HAL001+0.ax',commute_properties) ).
fof(h_morphism,axiom,
morphism(h,c,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_morphism) ).
fof(h_surjection,hypothesis,
surjection(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_surjection) ).
fof(beta_h_g_delta_commute,axiom,
commute(beta,h,g,delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
fof(subtract_distribution,axiom,
! [X1,X2,X3] :
( morphism(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('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(beta_morphism,axiom,
morphism(beta,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_morphism) ).
fof(beta_surjection,axiom,
surjection(beta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_surjection) ).
fof(subtract_cancellation,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> subtract(X2,X5,subtract(X2,X5,X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(c_0_15,plain,
! [X81,X82,X83] :
( ~ element(X82,X81)
| ~ element(X83,X81)
| element(subtract(X81,X82,X83),X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_in_domain])]) ).
fof(c_0_16,plain,
! [X84,X85] :
( ~ element(X85,X84)
| subtract(X84,X85,X85) = zero(X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_to_0])]) ).
fof(c_0_17,plain,
! [X22,X23,X24,X25] :
( ( ~ element(X25,X23)
| element(apply(X22,X25),X24)
| ~ morphism(X22,X23,X24) )
& ( apply(X22,zero(X23)) = zero(X24)
| ~ morphism(X22,X23,X24) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])]) ).
cnf(c_0_18,plain,
( element(subtract(X2,X1,X3),X2)
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( subtract(X2,X1,X1) = zero(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X36,X37,X38,X39] :
( ( element(esk3_4(X36,X37,X38,X39),X37)
| ~ element(X39,X38)
| ~ surjection(X36)
| ~ morphism(X36,X37,X38) )
& ( apply(X36,esk3_4(X36,X37,X38,X39)) = X39
| ~ element(X39,X38)
| ~ surjection(X36)
| ~ morphism(X36,X37,X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[surjection_properties])])])])]) ).
cnf(c_0_21,plain,
( element(apply(X3,X1),X4)
| ~ element(X1,X2)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
morphism(delta,e,r),
inference(split_conjunct,[status(thm)],[delta_morphism]) ).
fof(c_0_23,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X20,X21] :
( element(X20,r)
& apply(delta,X19) = X20
& element(X21,b)
& apply(h,apply(beta,X21)) = X20
& apply(delta,apply(g,X21)) = X20 ) ),
inference(assume_negation,[status(cth)],[lemma3]) ).
cnf(c_0_24,plain,
( element(zero(X1),X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( element(esk3_4(X1,X2,X3,X4),X2)
| ~ element(X4,X3)
| ~ surjection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( element(apply(delta,X1),r)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_27,negated_conjecture,
! [X95,X96] :
( element(esk9_0,e)
& ( ~ element(X95,r)
| apply(delta,esk9_0) != X95
| ~ element(X96,b)
| apply(h,apply(beta,X96)) != X95
| apply(delta,apply(g,X96)) != X95 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_28,plain,
! [X63,X64,X65,X66,X67,X68,X69,X70,X71] :
( ~ commute(X63,X64,X65,X66)
| ~ morphism(X63,X67,X68)
| ~ morphism(X64,X68,X70)
| ~ morphism(X65,X67,X69)
| ~ morphism(X66,X69,X70)
| ~ element(X71,X67)
| apply(X64,apply(X63,X71)) = apply(X66,apply(X65,X71)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commute_properties])])]) ).
cnf(c_0_29,plain,
( element(zero(X1),X1)
| ~ surjection(X2)
| ~ element(X3,X4)
| ~ morphism(X2,X1,X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
morphism(h,c,r),
inference(split_conjunct,[status(thm)],[h_morphism]) ).
cnf(c_0_31,hypothesis,
surjection(h),
inference(split_conjunct,[status(thm)],[h_surjection]) ).
cnf(c_0_32,plain,
( element(zero(r),r)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
element(esk9_0,e),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,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_28]) ).
cnf(c_0_35,plain,
commute(beta,h,g,delta),
inference(split_conjunct,[status(thm)],[beta_h_g_delta_commute]) ).
fof(c_0_36,plain,
! [X89,X90,X91,X92,X93] :
( ~ morphism(X89,X90,X91)
| ~ element(X92,X90)
| ~ element(X93,X90)
| apply(X89,subtract(X90,X92,X93)) = subtract(X91,apply(X89,X92),apply(X89,X93)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_distribution])])]) ).
cnf(c_0_37,plain,
morphism(beta,b,c),
inference(split_conjunct,[status(thm)],[beta_morphism]) ).
cnf(c_0_38,plain,
surjection(beta),
inference(split_conjunct,[status(thm)],[beta_surjection]) ).
cnf(c_0_39,plain,
( element(zero(c),c)
| ~ element(X1,r) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_40,negated_conjecture,
element(zero(r),r),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,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_34,c_0_35]) ).
fof(c_0_42,plain,
! [X86,X87,X88] :
( ~ element(X87,X86)
| ~ element(X88,X86)
| subtract(X86,X87,subtract(X86,X87,X88)) = X88 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])]) ).
cnf(c_0_43,plain,
( apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5))
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2)
| ~ element(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_45,plain,
( apply(X1,zero(X2)) = zero(X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_46,plain,
( element(zero(b),b)
| ~ element(X1,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_37]),c_0_38])]) ).
cnf(c_0_47,negated_conjecture,
element(zero(c),c),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( ~ element(X1,r)
| apply(delta,esk9_0) != X1
| ~ element(X2,b)
| apply(h,apply(beta,X2)) != X1
| apply(delta,apply(g,X2)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_49,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_41,c_0_22]) ).
cnf(c_0_50,plain,
( subtract(X2,X1,subtract(X2,X1,X3)) = X3
| ~ element(X1,X2)
| ~ element(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( subtract(e,apply(g,X1),apply(g,X2)) = apply(g,subtract(b,X1,X2))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
apply(g,zero(b)) = zero(e),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
element(zero(b),b),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,apply(g,X1))
| apply(delta,apply(g,X1)) != apply(delta,esk9_0)
| ~ element(apply(delta,apply(g,X1)),r)
| ~ element(X1,b) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_56,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_49,c_0_44]) ).
cnf(c_0_57,plain,
( subtract(X1,X2,zero(X1)) = X2
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_19]) ).
cnf(c_0_58,plain,
( subtract(e,apply(g,X1),zero(e)) = apply(g,subtract(b,X1,zero(b)))
| ~ element(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_59,plain,
( subtract(r,apply(delta,X1),apply(delta,X2)) = apply(delta,subtract(e,X1,X2))
| ~ element(X2,e)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_60,plain,
apply(delta,zero(e)) = zero(r),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_61,negated_conjecture,
element(zero(e),e),
inference(spm,[status(thm)],[c_0_24,c_0_33]) ).
cnf(c_0_62,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,apply(g,X1))
| apply(delta,apply(g,X1)) != apply(delta,esk9_0)
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_26]),c_0_55]) ).
cnf(c_0_63,plain,
( apply(h,apply(beta,X1)) = apply(delta,apply(g,X1))
| ~ element(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_30]),c_0_37])]) ).
cnf(c_0_64,plain,
( apply(g,subtract(b,X1,zero(b))) = apply(g,X1)
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_55]) ).
cnf(c_0_65,plain,
( subtract(r,apply(delta,X1),zero(r)) = apply(delta,subtract(e,X1,zero(e)))
| ~ element(X1,e) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_66,negated_conjecture,
( apply(delta,apply(g,X1)) != apply(delta,esk9_0)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
( apply(g,subtract(b,subtract(b,X1,zero(b)),zero(b))) = subtract(e,apply(g,X1),zero(e))
| ~ element(subtract(b,X1,zero(b)),b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_58,c_0_64]) ).
cnf(c_0_68,plain,
( apply(delta,subtract(e,X1,zero(e))) = apply(delta,X1)
| ~ element(X1,e) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_65]),c_0_26]) ).
cnf(c_0_69,plain,
( subtract(r,apply(h,X1),apply(h,X2)) = apply(h,subtract(c,X1,X2))
| ~ element(X2,c)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_30]) ).
cnf(c_0_70,plain,
( element(apply(h,X1),r)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_71,plain,
( subtract(c,apply(beta,X1),apply(beta,X2)) = apply(beta,subtract(b,X1,X2))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
cnf(c_0_72,plain,
( element(apply(beta,X1),c)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_73,negated_conjecture,
( apply(delta,subtract(e,apply(g,X1),zero(e))) != apply(delta,esk9_0)
| ~ element(subtract(b,subtract(b,X1,zero(b)),zero(b)),b)
| ~ element(subtract(b,X1,zero(b)),b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,plain,
( apply(delta,apply(g,subtract(b,X1,zero(b)))) = apply(delta,apply(g,X1))
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_58]),c_0_55]) ).
cnf(c_0_75,plain,
( element(apply(g,subtract(b,X1,zero(b))),e)
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_58]),c_0_61])]),c_0_55]) ).
cnf(c_0_76,plain,
( subtract(r,apply(h,X1),apply(h,subtract(c,X1,X2))) = apply(h,X2)
| ~ element(X2,c)
| ~ element(X1,c) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_69]),c_0_70]),c_0_70]) ).
cnf(c_0_77,plain,
( subtract(c,apply(beta,X1),apply(beta,subtract(b,X1,X2))) = apply(beta,X2)
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_71]),c_0_72]),c_0_72]) ).
cnf(c_0_78,plain,
( element(apply(beta,subtract(b,X1,X2)),c)
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_71]),c_0_72]),c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( apply(delta,subtract(e,apply(g,X1),zero(e))) != apply(delta,esk9_0)
| ~ element(subtract(b,X1,zero(b)),b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_73,c_0_57]) ).
cnf(c_0_80,plain,
( apply(delta,subtract(e,apply(g,subtract(b,X1,zero(b))),zero(e))) = subtract(r,apply(delta,apply(g,X1)),zero(r))
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_74]),c_0_75]) ).
cnf(c_0_81,plain,
( subtract(r,apply(h,apply(beta,X1)),apply(h,apply(beta,X2))) = apply(h,apply(beta,subtract(b,X1,X2)))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_72]),c_0_78]) ).
cnf(c_0_82,plain,
apply(beta,zero(b)) = zero(c),
inference(spm,[status(thm)],[c_0_45,c_0_37]) ).
cnf(c_0_83,plain,
apply(h,zero(c)) = zero(r),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_84,negated_conjecture,
( subtract(r,apply(delta,apply(g,X1)),zero(r)) != apply(delta,esk9_0)
| ~ element(subtract(b,subtract(b,X1,zero(b)),zero(b)),b)
| ~ element(subtract(b,X1,zero(b)),b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
( subtract(r,apply(h,apply(beta,X1)),zero(r)) = apply(h,apply(beta,subtract(b,X1,zero(b))))
| ~ element(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_53])]) ).
cnf(c_0_86,negated_conjecture,
( subtract(r,apply(delta,apply(g,X1)),zero(r)) != apply(delta,esk9_0)
| ~ element(subtract(b,X1,zero(b)),b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_84,c_0_57]) ).
cnf(c_0_87,plain,
( subtract(r,apply(delta,apply(g,X1)),zero(r)) = apply(h,apply(beta,subtract(b,X1,zero(b))))
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_85,c_0_63]) ).
cnf(c_0_88,negated_conjecture,
( apply(h,apply(beta,subtract(b,X1,zero(b)))) != apply(delta,esk9_0)
| ~ element(subtract(b,X1,zero(b)),b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_89,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,esk9_0)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_88,c_0_57]) ).
cnf(c_0_90,plain,
( apply(X1,esk3_4(X1,X2,X3,X4)) = X4
| ~ element(X4,X3)
| ~ surjection(X1)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_91,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(esk3_4(beta,X2,X3,X1),b)
| ~ element(X1,X3)
| ~ morphism(beta,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_38])]) ).
cnf(c_0_92,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(X1,X2)
| ~ morphism(beta,b,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_25]),c_0_38])]) ).
cnf(c_0_93,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[c_0_92,c_0_37]) ).
cnf(c_0_94,negated_conjecture,
( ~ element(esk3_4(h,X1,X2,apply(delta,esk9_0)),c)
| ~ element(apply(delta,esk9_0),X2)
| ~ morphism(h,X1,X2) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_90]),c_0_31])])]) ).
cnf(c_0_95,negated_conjecture,
( ~ element(apply(delta,esk9_0),X1)
| ~ morphism(h,c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_25]),c_0_31])]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_26]),c_0_30]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL004+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 02:28:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 14.17/14.36 % Version : CSE_E---1.5
% 14.17/14.36 % Problem : theBenchmark.p
% 14.17/14.36 % Proof found
% 14.17/14.36 % SZS status Theorem for theBenchmark.p
% 14.17/14.36 % SZS output start Proof
% See solution above
% 14.17/14.37 % Total time : 13.797000 s
% 14.17/14.37 % SZS output end Proof
% 14.17/14.37 % Total time : 13.801000 s
%------------------------------------------------------------------------------