%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : HAL004+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n027.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 12:45:05 EDT 2022
% Result : Theorem 7.36s 2.35s
% Output : CNFRefutation 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 145 ( 33 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 188 ( 88 ~; 74 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 95 ( 0 sgn 38 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(delta_morphism,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_morphism) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
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(beta_h_g_delta_commute,axiom,
commute(beta,h,g,delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
fof(h_morphism,axiom,
morphism(h,c,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_morphism) ).
fof(beta_morphism,axiom,
morphism(beta,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_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(beta_surjection,axiom,
surjection(beta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta_surjection) ).
fof(h_surjection,hypothesis,
surjection(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_surjection) ).
fof(c_0_11,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]) ).
fof(c_0_12,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_11])])])]) ).
fof(c_0_13,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_14,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_12]) ).
cnf(c_0_15,plain,
( element(apply(X3,X1),X4)
| ~ element(X1,X2)
| ~ morphism(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
morphism(delta,e,r),
inference(split_conjunct,[status(thm)],[delta_morphism]) ).
cnf(c_0_17,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
cnf(c_0_18,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_14]) ).
cnf(c_0_19,plain,
( element(apply(delta,X1),r)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
fof(c_0_21,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_22,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_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,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_21]) ).
cnf(c_0_24,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(X2,apply(X3,X1))
| apply(X2,apply(X3,X1)) != apply(delta,esk9_0)
| ~ commute(X3,X2,g,delta)
| ~ element(X1,b)
| ~ element(X1,X4)
| ~ morphism(delta,X5,X6)
| ~ morphism(g,X4,X5)
| ~ morphism(X2,X7,X6)
| ~ morphism(X3,X4,X7) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
commute(beta,h,g,delta),
inference(split_conjunct,[status(thm)],[beta_h_g_delta_commute]) ).
cnf(c_0_26,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,esk9_0)
| ~ element(X1,b)
| ~ 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_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,esk9_0)
| ~ element(X1,b)
| ~ element(X1,X2)
| ~ morphism(g,X2,e)
| ~ morphism(h,X3,r)
| ~ morphism(beta,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,esk9_0)
| ~ element(X1,b)
| ~ morphism(h,X2,r)
| ~ morphism(beta,b,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_29,plain,
morphism(h,c,r),
inference(split_conjunct,[status(thm)],[h_morphism]) ).
cnf(c_0_30,plain,
morphism(beta,b,c),
inference(split_conjunct,[status(thm)],[beta_morphism]) ).
fof(c_0_31,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_32,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,esk9_0)
| ~ element(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,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_31]) ).
cnf(c_0_34,plain,
surjection(beta),
inference(split_conjunct,[status(thm)],[beta_surjection]) ).
cnf(c_0_35,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_31]) ).
cnf(c_0_36,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_32,c_0_33]),c_0_34])]) ).
cnf(c_0_37,plain,
( element(esk3_4(beta,b,c,X1),b)
| ~ element(X1,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_34])]) ).
cnf(c_0_38,hypothesis,
surjection(h),
inference(split_conjunct,[status(thm)],[h_surjection]) ).
cnf(c_0_39,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(X1,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_30])]) ).
cnf(c_0_40,plain,
( element(esk3_4(h,c,r,X1),c)
| ~ element(X1,r) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
( apply(h,esk3_4(h,c,r,X1)) != apply(delta,esk9_0)
| ~ element(X1,r) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
~ element(apply(delta,esk9_0),r),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_33]),c_0_38]),c_0_29])])]) ).
cnf(c_0_43,negated_conjecture,
element(esk9_0,e),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_19]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HAL004+1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue Jun 7 21:40:12 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.45 # ENIGMATIC: Selected SinE mode:
% 0.19/0.45 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.19/0.45 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.19/0.45 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 7.36/2.35 # ENIGMATIC: Solved by autoschedule:
% 7.36/2.35 # No SInE strategy applied
% 7.36/2.35 # Trying AutoSched0 for 150 seconds
% 7.36/2.35 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S059A
% 7.36/2.35 # and selection function SelectComplexExceptUniqMaxPosHorn.
% 7.36/2.35 #
% 7.36/2.35 # Preprocessing time : 0.027 s
% 7.36/2.35 # Presaturation interreduction done
% 7.36/2.35
% 7.36/2.35 # Proof found!
% 7.36/2.35 # SZS status Theorem
% 7.36/2.35 # SZS output start CNFRefutation
% See solution above
% 7.36/2.35 # Training examples: 0 positive, 0 negative
% 7.36/2.35
% 7.36/2.35 # -------------------------------------------------
% 7.36/2.35 # User time : 0.056 s
% 7.36/2.35 # System time : 0.007 s
% 7.36/2.35 # Total time : 0.062 s
% 7.36/2.35 # Maximum resident set size: 7120 pages
% 7.36/2.35
%------------------------------------------------------------------------------