TSTP Solution File: LCL475+1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : LCL475+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 : 300s
% DateTime : Mon May 20 23:46:35 EDT 2024
% Result : Theorem 38.89s 5.33s
% Output : CNFRefutation 38.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 20
% Syntax : Number of formulae : 128 ( 56 unt; 0 def)
% Number of atoms : 238 ( 27 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 199 ( 89 ~; 88 |; 10 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 236 ( 39 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(cn1,axiom,
( cn1
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn1) ).
fof(luka_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_modus_ponens) ).
fof(luka_cn1,axiom,
cn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn1) ).
fof(cn2,axiom,
( cn2
<=> ! [X4,X5] : is_a_theorem(implies(X4,implies(not(X4),X5))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn2) ).
fof(luka_cn2,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn2) ).
fof(cn3,axiom,
( cn3
<=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(luka_cn3,axiom,
cn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn3) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(luka_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_op_or) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',substitution_of_equivalents) ).
fof(luka_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_op_equiv) ).
fof(principia_r1,conjecture,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(c_0_20,plain,
! [X7,X8] :
( ( ~ modus_ponens
| ~ is_a_theorem(X7)
| ~ is_a_theorem(implies(X7,X8))
| is_a_theorem(X8) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])]) ).
fof(c_0_21,plain,
! [X83,X84,X85] :
( ( ~ cn1
| is_a_theorem(implies(implies(X83,X84),implies(implies(X84,X85),implies(X83,X85)))) )
& ( ~ is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0))))
| cn1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn1])])])])]) ).
cnf(c_0_22,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[luka_modus_ponens]) ).
cnf(c_0_24,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ cn1 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
cn1,
inference(split_conjunct,[status(thm)],[luka_cn1]) ).
fof(c_0_26,plain,
! [X89,X90] :
( ( ~ cn2
| is_a_theorem(implies(X89,implies(not(X89),X90))) )
& ( ~ is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0)))
| cn2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn2])])])])]) ).
cnf(c_0_27,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_28,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_29,plain,
( is_a_theorem(implies(X1,implies(not(X1),X2)))
| ~ cn2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
cn2,
inference(split_conjunct,[status(thm)],[luka_cn2]) ).
cnf(c_0_31,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
fof(c_0_35,plain,
! [X93] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(X93),X93),X93)) )
& ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
| cn3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])])]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(not(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_37,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(X3),X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
cn3,
inference(split_conjunct,[status(thm)],[luka_cn3]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X4,X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_44,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(not(X3),X4),X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_42]) ).
cnf(c_0_45,plain,
( is_a_theorem(implies(implies(not(X1),X1),X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_46,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_47,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(implies(not(X2),X4),X3)) ),
inference(spm,[status(thm)],[c_0_46,c_0_33]) ).
cnf(c_0_48,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X3),X3))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X3),X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_52,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X2),X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_45]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_54,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_51]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X2),X3),implies(implies(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_31,c_0_43]) ).
cnf(c_0_56,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(not(X2),X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X4,X2),X3)))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_54]) ).
cnf(c_0_58,plain,
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(implies(implies(not(X1),X1),X2),X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_55]) ).
cnf(c_0_59,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(implies(implies(X2,X4),implies(X1,X4)),X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_60]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)),
inference(spm,[status(thm)],[c_0_61,c_0_53]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_65,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_62,c_0_59]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_62,c_0_64]) ).
cnf(c_0_67,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_65]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(X1,implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_36,c_0_66]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(not(X1),X4),X2),X3))),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_70,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(implies(X3,X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
( is_a_theorem(implies(implies(implies(not(X1),X2),X3),X4))
| ~ is_a_theorem(implies(implies(X1,X3),X4)) ),
inference(spm,[status(thm)],[c_0_27,c_0_69]) ).
fof(c_0_72,plain,
! [X123,X124] :
( ~ op_implies_or
| implies(X123,X124) = or(not(X123),X124) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])]) ).
cnf(c_0_73,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_62,c_0_33]) ).
fof(c_0_75,plain,
! [X119,X120] :
( ~ op_and
| and(X119,X120) = not(or(not(X119),not(X120))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])]) ).
cnf(c_0_76,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
cnf(c_0_78,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
inference(spm,[status(thm)],[c_0_27,c_0_64]) ).
cnf(c_0_79,plain,
is_a_theorem(implies(not(X1),implies(X1,implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
fof(c_0_80,plain,
! [X117,X118] :
( ~ op_or
| or(X117,X118) = not(and(not(X117),not(X118))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_81,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_83,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(not(not(implies(X1,X2))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
and(X1,X2) = not(implies(X1,not(X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_87,plain,
op_or,
inference(split_conjunct,[status(thm)],[luka_op_or]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(not(not(implies(not(X1),X1))),X1)),
inference(spm,[status(thm)],[c_0_78,c_0_84]) ).
cnf(c_0_89,plain,
not(not(implies(not(X1),not(not(X2))))) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_90,plain,
is_a_theorem(implies(implies(not(X1),X1),not(not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_82]) ).
cnf(c_0_91,plain,
( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(not(X4),X5),X2),X3)))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_42]) ).
cnf(c_0_92,plain,
( is_a_theorem(implies(implies(X1,implies(not(X2),X2)),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_59]) ).
cnf(c_0_93,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_27,c_0_74]) ).
cnf(c_0_94,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_36,c_0_90]) ).
cnf(c_0_95,plain,
( is_a_theorem(implies(implies(implies(not(X1),X2),X3),X3))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_91]) ).
fof(c_0_96,plain,
! [X11,X12] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X11,X12))
| X11 = X12 )
& ( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents )
& ( esk3_0 != esk4_0
| substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])]) ).
fof(c_0_97,plain,
! [X125,X126] :
( ~ op_equiv
| equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).
cnf(c_0_98,plain,
( is_a_theorem(implies(implies(not(X1),X2),X1))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_92]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
( is_a_theorem(implies(implies(X1,not(X2)),implies(X1,X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_95]) ).
cnf(c_0_101,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_102,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_103,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_104,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[luka_op_equiv]) ).
cnf(c_0_105,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_98]) ).
cnf(c_0_106,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_78,c_0_99]) ).
cnf(c_0_107,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,not(X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_100]) ).
cnf(c_0_108,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
cnf(c_0_109,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
cnf(c_0_110,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,not(X1))) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,plain,
( is_a_theorem(implies(implies(X1,not(X2)),X3))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_59]) ).
cnf(c_0_112,plain,
( X1 = X2
| ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_86]) ).
cnf(c_0_113,plain,
( is_a_theorem(not(implies(X1,not(X2))))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
fof(c_0_114,negated_conjecture,
~ r1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[principia_r1])]) ).
cnf(c_0_115,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
fof(c_0_116,plain,
! [X95] :
( ( ~ r1
| is_a_theorem(implies(or(X95,X95),X95)) )
& ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])]) ).
fof(c_0_117,negated_conjecture,
~ r1,
inference(fof_nnf,[status(thm)],[c_0_114]) ).
cnf(c_0_118,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_70,c_0_33]) ).
cnf(c_0_119,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_106]),c_0_94])]) ).
cnf(c_0_120,plain,
( r1
| ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_121,negated_conjecture,
~ r1,
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_122,plain,
implies(not(X1),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_41]),c_0_118])]) ).
cnf(c_0_123,plain,
implies(not(X1),X2) = or(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_119]),c_0_119]) ).
cnf(c_0_124,plain,
~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)),
inference(sr,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,plain,
or(X1,X1) = X1,
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_127,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : LCL475+1 : TPTP v8.2.0. Released v3.3.0.
% 0.02/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n027.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon May 20 02:24:53 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.89/5.33 # Version: 3.1.0
% 38.89/5.33 # Preprocessing class: FSMSSLSSSSSNFFN.
% 38.89/5.33 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.89/5.33 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 38.89/5.33 # Starting new_bool_3 with 300s (1) cores
% 38.89/5.33 # Starting new_bool_1 with 300s (1) cores
% 38.89/5.33 # Starting sh5l with 300s (1) cores
% 38.89/5.33 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 26325 completed with status 0
% 38.89/5.33 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 38.89/5.33 # Preprocessing class: FSMSSLSSSSSNFFN.
% 38.89/5.33 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.89/5.33 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 38.89/5.33 # No SInE strategy applied
% 38.89/5.33 # Search class: FGUSF-FFMM21-MFFFFFNN
% 38.89/5.33 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 38.89/5.33 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 38.89/5.33 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 38.89/5.33 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 38.89/5.33 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 38.89/5.33 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 38.89/5.33 # G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 26339 completed with status 0
% 38.89/5.33 # Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 38.89/5.33 # Preprocessing class: FSMSSLSSSSSNFFN.
% 38.89/5.33 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.89/5.33 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 38.89/5.33 # No SInE strategy applied
% 38.89/5.33 # Search class: FGUSF-FFMM21-MFFFFFNN
% 38.89/5.33 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 38.89/5.33 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 38.89/5.33 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 38.89/5.33 # Preprocessing time : 0.002 s
% 38.89/5.33 # Presaturation interreduction done
% 38.89/5.33
% 38.89/5.33 # Proof found!
% 38.89/5.33 # SZS status Theorem
% 38.89/5.33 # SZS output start CNFRefutation
% See solution above
% 38.89/5.33 # Parsed axioms : 43
% 38.89/5.33 # Removed by relevancy pruning/SinE : 0
% 38.89/5.33 # Initial clauses : 72
% 38.89/5.33 # Removed in clause preprocessing : 0
% 38.89/5.33 # Initial clauses in saturation : 72
% 38.89/5.33 # Processed clauses : 12664
% 38.89/5.33 # ...of these trivial : 492
% 38.89/5.33 # ...subsumed : 10160
% 38.89/5.33 # ...remaining for further processing : 2012
% 38.89/5.33 # Other redundant clauses eliminated : 0
% 38.89/5.33 # Clauses deleted for lack of memory : 0
% 38.89/5.33 # Backward-subsumed : 94
% 38.89/5.33 # Backward-rewritten : 295
% 38.89/5.33 # Generated clauses : 305904
% 38.89/5.33 # ...of the previous two non-redundant : 277663
% 38.89/5.33 # ...aggressively subsumed : 0
% 38.89/5.33 # Contextual simplify-reflections : 0
% 38.89/5.33 # Paramodulations : 305904
% 38.89/5.33 # Factorizations : 0
% 38.89/5.33 # NegExts : 0
% 38.89/5.33 # Equation resolutions : 0
% 38.89/5.33 # Disequality decompositions : 0
% 38.89/5.33 # Total rewrite steps : 108051
% 38.89/5.33 # ...of those cached : 96824
% 38.89/5.33 # Propositional unsat checks : 0
% 38.89/5.33 # Propositional check models : 0
% 38.89/5.33 # Propositional check unsatisfiable : 0
% 38.89/5.33 # Propositional clauses : 0
% 38.89/5.33 # Propositional clauses after purity: 0
% 38.89/5.33 # Propositional unsat core size : 0
% 38.89/5.33 # Propositional preprocessing time : 0.000
% 38.89/5.33 # Propositional encoding time : 0.000
% 38.89/5.33 # Propositional solver time : 0.000
% 38.89/5.33 # Success case prop preproc time : 0.000
% 38.89/5.33 # Success case prop encoding time : 0.000
% 38.89/5.33 # Success case prop solver time : 0.000
% 38.89/5.33 # Current number of processed clauses : 1562
% 38.89/5.33 # Positive orientable unit clauses : 719
% 38.89/5.33 # Positive unorientable unit clauses: 19
% 38.89/5.33 # Negative unit clauses : 3
% 38.89/5.33 # Non-unit-clauses : 821
% 38.89/5.33 # Current number of unprocessed clauses: 252846
% 38.89/5.33 # ...number of literals in the above : 407179
% 38.89/5.33 # Current number of archived formulas : 0
% 38.89/5.33 # Current number of archived clauses : 450
% 38.89/5.33 # Clause-clause subsumption calls (NU) : 283705
% 38.89/5.33 # Rec. Clause-clause subsumption calls : 282873
% 38.89/5.33 # Non-unit clause-clause subsumptions : 10243
% 38.89/5.33 # Unit Clause-clause subsumption calls : 49567
% 38.89/5.33 # Rewrite failures with RHS unbound : 20
% 38.89/5.33 # BW rewrite match attempts : 118058
% 38.89/5.33 # BW rewrite match successes : 646
% 38.89/5.33 # Condensation attempts : 0
% 38.89/5.33 # Condensation successes : 0
% 38.89/5.33 # Termbank termtop insertions : 6582192
% 38.89/5.33 # Search garbage collected termcells : 1095
% 38.89/5.33
% 38.89/5.33 # -------------------------------------------------
% 38.89/5.33 # User time : 4.617 s
% 38.89/5.33 # System time : 0.177 s
% 38.89/5.33 # Total time : 4.794 s
% 38.89/5.33 # Maximum resident set size: 1988 pages
% 38.89/5.33
% 38.89/5.33 # -------------------------------------------------
% 38.89/5.33 # User time : 23.150 s
% 38.89/5.33 # System time : 0.918 s
% 38.89/5.33 # Total time : 24.068 s
% 38.89/5.33 # Maximum resident set size: 1744 pages
% 38.89/5.33 % E---3.1 exiting
% 38.89/5.33 % E exiting
%------------------------------------------------------------------------------