TSTP Solution File: NUM799^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM799^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 : Sat May 4 08:58:01 EDT 2024
% Result : Theorem 18.04s 2.69s
% Output : CNFRefutation 18.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 111 ( 98 unt; 13 typ; 0 def)
% Number of atoms : 98 ( 97 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 533 ( 6 ~; 0 |; 0 &; 527 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 1 con; 0-4 aty)
% Number of variables : 202 ( 27 ^ 173 !; 2 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
zero: ( $i > $i ) > $i > $i ).
thf(decl_23,type,
one: ( $i > $i ) > $i > $i ).
thf(decl_24,type,
two: ( $i > $i ) > $i > $i ).
thf(decl_25,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
four: ( $i > $i ) > $i > $i ).
thf(decl_27,type,
five: ( $i > $i ) > $i > $i ).
thf(decl_28,type,
six: ( $i > $i ) > $i > $i ).
thf(decl_29,type,
seven: ( $i > $i ) > $i > $i ).
thf(decl_33,type,
succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_34,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_35,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_36,type,
esk1_2: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(decl_37,type,
esk2_1: ( ( $i > $i ) > $i > $i ) > $i ).
thf(two_ax,axiom,
( two
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',two_ax) ).
thf(four_ax,axiom,
( four
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',four_ax) ).
thf(succ_ax,axiom,
( succ
= ( ^ [X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',succ_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',three_ax) ).
thf(five_ax,axiom,
( five
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',five_ax) ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',one_ax) ).
thf(plus_ax,axiom,
( plus
= ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ X1 @ ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',plus_ax) ).
thf(six_ax,axiom,
( six
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',six_ax) ).
thf(seven_ax,axiom,
( seven
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',seven_ax) ).
thf(zero_ax,axiom,
( zero
= ( ^ [X1: $i > $i,X2: $i] : X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',zero_ax) ).
thf(thm,conjecture,
? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ four )
= ( plus @ five @ seven ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',thm) ).
thf(mult_ax,axiom,
( mult
= ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ ( X3 @ X1 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p',mult_ax) ).
thf(c_0_12,plain,
! [X10: $i > $i,X11: $i] :
( ( two @ X10 @ X11 )
= ( X10 @ ( X10 @ X11 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).
thf(c_0_13,plain,
! [X43: $i > $i,X44: $i] :
( ( two @ X43 @ X44 )
= ( X43 @ ( X43 @ X44 ) ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_14,plain,
! [X14: $i > $i,X15: $i] :
( ( four @ X14 @ X15 )
= ( X14 @ ( X14 @ ( X14 @ ( X14 @ X15 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[four_ax])]) ).
thf(c_0_15,plain,
! [X28: ( $i > $i ) > $i > $i,X29: $i > $i,X30: $i] :
( ( succ @ X28 @ X29 @ X30 )
= ( X29 @ ( X28 @ X29 @ X30 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[succ_ax])]) ).
thf(c_0_16,plain,
! [X12: $i > $i,X13: $i] :
( ( three @ X12 @ X13 )
= ( X12 @ ( X12 @ ( X12 @ X13 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).
thf(c_0_17,plain,
! [X16: $i > $i,X17: $i] :
( ( five @ X16 @ X17 )
= ( X16 @ ( X16 @ ( X16 @ ( X16 @ ( X16 @ X17 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[five_ax])]) ).
thf(c_0_18,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X47: $i > $i,X48: $i] :
( ( four @ X47 @ X48 )
= ( X47 @ ( X47 @ ( X47 @ ( X47 @ X48 ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X8: $i > $i,X9: $i] :
( ( one @ X8 @ X9 )
= ( X8 @ X9 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).
thf(c_0_21,plain,
! [X31: ( $i > $i ) > $i > $i,X32: ( $i > $i ) > $i > $i,X33: $i > $i,X34: $i] :
( ( plus @ X31 @ X32 @ X33 @ X34 )
= ( X31 @ X33 @ ( X32 @ X33 @ X34 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[plus_ax])]) ).
thf(c_0_22,plain,
! [X61: ( $i > $i ) > $i > $i,X62: $i > $i,X63: $i] :
( ( succ @ X61 @ X62 @ X63 )
= ( X62 @ ( X61 @ X62 @ X63 ) ) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
thf(c_0_23,plain,
! [X45: $i > $i,X46: $i] :
( ( three @ X45 @ X46 )
= ( X45 @ ( X45 @ ( X45 @ X46 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_16]) ).
thf(c_0_24,plain,
! [X18: $i > $i,X19: $i] :
( ( six @ X18 @ X19 )
= ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ X19 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).
thf(c_0_25,plain,
! [X49: $i > $i,X50: $i] :
( ( five @ X49 @ X50 )
= ( X49 @ ( X49 @ ( X49 @ ( X49 @ ( X49 @ X50 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
thf(c_0_26,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( two @ X1 ) @ X2 )
= ( X1 @ ( X1 @ ( two @ X1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
thf(c_0_27,plain,
! [X1: $i > $i,X2: $i] :
( ( four @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_28,plain,
! [X41: $i > $i,X42: $i] :
( ( one @ X41 @ X42 )
= ( X41 @ X42 ) ),
inference(variable_rename,[status(thm)],[c_0_20]) ).
thf(c_0_29,plain,
! [X64: ( $i > $i ) > $i > $i,X65: ( $i > $i ) > $i > $i,X66: $i > $i,X67: $i] :
( ( plus @ X64 @ X65 @ X66 @ X67 )
= ( X64 @ X66 @ ( X65 @ X66 @ X67 ) ) ),
inference(variable_rename,[status(thm)],[c_0_21]) ).
thf(c_0_30,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( succ @ X3 @ X1 @ X2 )
= ( X1 @ ( X3 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_31,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_32,plain,
! [X51: $i > $i,X52: $i] :
( ( six @ X51 @ X52 )
= ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ X52 ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_24]) ).
thf(c_0_33,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_34,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( two @ X1 ) @ X2 )
= ( two @ X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
thf(c_0_35,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( two @ X1 ) @ X2 )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_27]) ).
thf(c_0_36,plain,
! [X20: $i > $i,X21: $i] :
( ( seven @ X20 @ X21 )
= ( X20 @ ( X20 @ ( X20 @ ( X20 @ ( X20 @ ( X20 @ ( X20 @ X21 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[seven_ax])]) ).
thf(c_0_37,plain,
! [X1: $i > $i,X2: $i] :
( ( one @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_38,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ X3 @ X4 @ X1 @ X2 )
= ( X3 @ X1 @ ( X4 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_39,plain,
! [X6: $i > $i,X7: $i] :
( ( zero @ X6 @ X7 )
= X7 ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[zero_ax])]) ).
thf(c_0_40,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ three @ X1 @ X2 )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_27]) ).
thf(c_0_41,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( four @ X1 @ X2 ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_33,c_0_27]) ).
thf(c_0_43,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ X2 ) )
= ( X1 @ ( two @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
thf(c_0_44,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ ( X1 @ X2 ) ) )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_45,plain,
! [X53: $i > $i,X54: $i] :
( ( seven @ X53 @ X54 )
= ( X53 @ ( X53 @ ( X53 @ ( X53 @ ( X53 @ ( X53 @ ( X53 @ X54 ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_36]) ).
thf(c_0_46,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ one @ X3 @ X1 @ X2 )
= ( X1 @ ( X3 @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_47,plain,
! [X39: $i > $i,X40: $i] :
( ( zero @ X39 @ X40 )
= X40 ),
inference(variable_rename,[status(thm)],[c_0_39]) ).
thf(c_0_48,negated_conjecture,
~ ? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ four )
= ( plus @ five @ seven ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_49,plain,
! [X35: ( $i > $i ) > $i > $i,X36: ( $i > $i ) > $i > $i,X37: $i > $i,X38: $i] :
( ( mult @ X35 @ X36 @ X37 @ X38 )
= ( X35 @ ( X36 @ X37 ) @ X38 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).
thf(c_0_50,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( three @ X1 @ X2 ) )
= ( four @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
thf(c_0_51,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( five @ X1 @ X2 ) )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_27]),c_0_42]) ).
thf(c_0_52,plain,
! [X1: $i > $i,X2: $i] :
( ( four @ X1 @ ( X1 @ X2 ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_44]),c_0_42]) ).
thf(c_0_53,plain,
! [X1: $i > $i,X2: $i] :
( ( seven @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_54,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( two @ ( X3 @ X1 ) @ X2 )
= ( plus @ X3 @ X3 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_38]) ).
thf(c_0_55,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ one @ X3 @ X1 @ X2 )
= ( succ @ X3 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
thf(c_0_56,plain,
! [X1: $i > $i,X2: $i] :
( ( zero @ X1 @ X2 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_57,negated_conjecture,
! [X72: ( $i > $i ) > $i > $i] :
( ( mult @ X72 @ four )
!= ( plus @ five @ seven ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])]) ).
thf(c_0_58,plain,
! [X68: ( $i > $i ) > $i > $i,X69: ( $i > $i ) > $i > $i,X70: $i > $i,X71: $i] :
( ( mult @ X68 @ X69 @ X70 @ X71 )
= ( X68 @ ( X69 @ X70 ) @ X71 ) ),
inference(variable_rename,[status(thm)],[c_0_49]) ).
thf(c_0_59,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ ( X1 @ ( X1 @ X2 ) ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_31]),c_0_50]),c_0_42]) ).
thf(c_0_60,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( three @ X1 ) @ X2 )
= ( X1 @ ( five @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_50]),c_0_42]) ).
thf(c_0_61,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ five @ X1 @ X2 )
= ( six @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_51]) ).
thf(c_0_62,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( five @ X1 @ X2 ) )
= ( five @ X1 @ ( X1 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_31]),c_0_50]),c_0_42]),c_0_52]) ).
thf(c_0_63,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( X1 @ ( five @ X1 @ X2 ) ) )
= ( seven @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_27]),c_0_42]) ).
thf(c_0_64,plain,
! [X3: ( $i > $i ) > $i > $i,X1: $i > $i] :
( ( two @ ( X3 @ X1 ) )
= ( plus @ X3 @ X3 @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_54]) ).
thf(c_0_65,plain,
! [X3: ( $i > $i ) > $i > $i,X1: $i > $i] :
( ( plus @ one @ X3 @ X1 )
= ( succ @ X3 @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_55]) ).
thf(c_0_66,plain,
! [X1: $i > $i] :
( ( one @ X1 )
= X1 ),
inference(pos_ext,[status(thm)],[c_0_37]) ).
thf(c_0_67,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ zero @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_56]) ).
thf(c_0_68,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( five @ X1 @ X2 ) )
= ( three @ ( two @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_18]),c_0_35]),c_0_42]) ).
thf(c_0_69,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ four )
!= ( plus @ five @ seven ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_70,plain,
! [X1: $i > $i,X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( mult @ X3 @ X4 @ X1 @ X2 )
= ( X3 @ ( X4 @ X1 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_71,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ ( X1 @ X2 ) )
= ( two @ ( three @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_59]) ).
thf(c_0_72,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( three @ X1 ) @ X2 )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_60]),c_0_61]) ).
thf(c_0_73,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( three @ X1 ) @ ( X1 @ ( five @ X1 @ X2 ) ) )
= ( four @ ( three @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_31]),c_0_50]),c_0_42]),c_0_18]) ).
thf(c_0_74,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ X1 @ ( X1 @ X2 ) )
= ( seven @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_62]),c_0_61]),c_0_63]) ).
thf(c_0_75,plain,
! [X1: $i > $i] :
( ( succ @ one @ X1 )
= ( two @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
thf(c_0_76,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( two @ ( succ @ X3 @ X1 ) @ ( X1 @ ( X3 @ X1 @ X2 ) ) )
= ( three @ ( succ @ X3 @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_18]) ).
thf(c_0_77,plain,
! [X1: $i > $i] :
( ( succ @ zero @ X1 )
= X1 ),
inference(pos_ext,[status(thm)],[c_0_67]) ).
thf(c_0_78,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ ( two @ X1 ) @ X2 )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_68]),c_0_61]) ).
thf(c_0_79,plain,
! [X1: $i > $i] :
( ( two @ ( two @ X1 ) )
= ( four @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_35]) ).
thf(c_0_80,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( X3 @ ( four @ ( esk1_2 @ X3 ) ) @ ( esk2_1 @ X3 ) )
!= ( plus @ five @ seven @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_69]),c_0_70]) ).
thf(c_0_81,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ ( X1 @ X2 ) )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_82,plain,
! [X1: $i > $i,X2: $i] :
( ( seven @ X1 @ ( five @ X1 @ X2 ) )
= ( four @ ( three @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_72]),c_0_74]) ).
thf(c_0_83,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ X3 @ one @ X1 @ X2 )
= ( X3 @ X1 @ ( X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
thf(c_0_84,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ one @ X1 @ X2 )
= ( two @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_66]) ).
thf(c_0_85,plain,
( ( succ @ one )
= two ),
inference(pos_ext,[status(thm)],[c_0_75]) ).
thf(c_0_86,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ X2 ) )
= ( three @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_56]),c_0_77]),c_0_77]) ).
thf(c_0_87,plain,
! [X1: $i > $i] :
( ( three @ ( two @ X1 ) )
= ( six @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_78]) ).
thf(c_0_88,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ ( two @ X1 ) @ X2 )
= ( three @ ( four @ X1 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_89,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( five @ ( esk1_2 @ X3 ) @ ( seven @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) )
!= ( X3 @ ( four @ ( esk1_2 @ X3 ) ) @ ( esk2_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_80,c_0_38]) ).
thf(c_0_90,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ ( seven @ X1 @ X2 ) )
= ( four @ ( three @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_63]),c_0_74]),c_0_82]) ).
thf(c_0_91,plain,
! [X1: $i > $i,X2: $i] :
( ( plus @ two @ one @ X1 @ X2 )
= ( three @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_86]) ).
thf(c_0_92,plain,
! [X1: $i > $i] :
( ( two @ ( three @ X1 ) )
= ( six @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_72]) ).
thf(c_0_93,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( six @ X1 ) @ X2 )
= ( three @ ( four @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_87]),c_0_88]) ).
thf(c_0_94,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( four @ ( three @ ( esk1_2 @ X3 ) ) @ ( esk2_1 @ X3 ) )
!= ( X3 @ ( four @ ( esk1_2 @ X3 ) ) @ ( esk2_1 @ X3 ) ) ),
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_95,plain,
( ( plus @ two @ one )
= three ),
inference(pos_ext,[status(thm)],[c_0_91]) ).
thf(c_0_96,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ ( four @ X1 ) @ X2 )
= ( four @ ( three @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_92]),c_0_93]) ).
thf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_91]),c_0_95]),c_0_95]),c_0_96]),c_0_95]),c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : NUM799^1 : TPTP v8.1.2. Released v3.7.0.
% 0.02/0.09 % Command : run_E %s %d THM
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Fri May 3 09:33:24 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.11/0.35 Running higher-order theorem proving
% 0.11/0.35 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.6fHzGN0XRp/E---3.1_4220.p
% 18.04/2.69 # Version: 3.1.0-ho
% 18.04/2.69 # Preprocessing class: HSSSSMSSMSSNHHN.
% 18.04/2.69 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.04/2.69 # Starting pre_casc_2 with 1500s (5) cores
% 18.04/2.69 # Starting sh2 with 300s (1) cores
% 18.04/2.69 # Starting sh3 with 300s (1) cores
% 18.04/2.69 # Starting new_ho_10 with 300s (1) cores
% 18.04/2.69 # new_ho_10 with pid 4343 completed with status 0
% 18.04/2.69 # Result found by new_ho_10
% 18.04/2.69 # Preprocessing class: HSSSSMSSMSSNHHN.
% 18.04/2.69 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.04/2.69 # Starting pre_casc_2 with 1500s (5) cores
% 18.04/2.69 # Starting sh2 with 300s (1) cores
% 18.04/2.69 # Starting sh3 with 300s (1) cores
% 18.04/2.69 # Starting new_ho_10 with 300s (1) cores
% 18.04/2.69 # No SInE strategy applied
% 18.04/2.69 # Search class: HUUPM-FFSF32-DHHSFMNN
% 18.04/2.69 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 18.04/2.69 # Starting pre_casc_2 with 181s (1) cores
% 18.04/2.69 # pre_casc_2 with pid 4351 completed with status 0
% 18.04/2.69 # Result found by pre_casc_2
% 18.04/2.69 # Preprocessing class: HSSSSMSSMSSNHHN.
% 18.04/2.69 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.04/2.69 # Starting pre_casc_2 with 1500s (5) cores
% 18.04/2.69 # Starting sh2 with 300s (1) cores
% 18.04/2.69 # Starting sh3 with 300s (1) cores
% 18.04/2.69 # Starting new_ho_10 with 300s (1) cores
% 18.04/2.69 # No SInE strategy applied
% 18.04/2.69 # Search class: HUUPM-FFSF32-DHHSFMNN
% 18.04/2.69 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 18.04/2.69 # Starting pre_casc_2 with 181s (1) cores
% 18.04/2.69 # Preprocessing time : 0.001 s
% 18.04/2.69 # Presaturation interreduction done
% 18.04/2.69
% 18.04/2.69 # Proof found!
% 18.04/2.69 # SZS status Theorem
% 18.04/2.69 # SZS output start CNFRefutation
% See solution above
% 18.04/2.69 # Parsed axioms : 29
% 18.04/2.69 # Removed by relevancy pruning/SinE : 0
% 18.04/2.69 # Initial clauses : 29
% 18.04/2.69 # Removed in clause preprocessing : 14
% 18.04/2.69 # Initial clauses in saturation : 15
% 18.04/2.69 # Processed clauses : 2772
% 18.04/2.69 # ...of these trivial : 1628
% 18.04/2.69 # ...subsumed : 322
% 18.04/2.69 # ...remaining for further processing : 822
% 18.04/2.69 # Other redundant clauses eliminated : 0
% 18.04/2.69 # Clauses deleted for lack of memory : 0
% 18.04/2.69 # Backward-subsumed : 0
% 18.04/2.69 # Backward-rewritten : 226
% 18.04/2.69 # Generated clauses : 91748
% 18.04/2.69 # ...of the previous two non-redundant : 77168
% 18.04/2.69 # ...aggressively subsumed : 0
% 18.04/2.69 # Contextual simplify-reflections : 0
% 18.04/2.69 # Paramodulations : 91254
% 18.04/2.69 # Factorizations : 0
% 18.04/2.69 # NegExts : 25
% 18.04/2.69 # Equation resolutions : 0
% 18.04/2.69 # Disequality decompositions : 0
% 18.04/2.69 # Total rewrite steps : 334405
% 18.04/2.69 # ...of those cached : 312723
% 18.04/2.69 # Propositional unsat checks : 0
% 18.04/2.69 # Propositional check models : 0
% 18.04/2.69 # Propositional check unsatisfiable : 0
% 18.04/2.69 # Propositional clauses : 0
% 18.04/2.69 # Propositional clauses after purity: 0
% 18.04/2.69 # Propositional unsat core size : 0
% 18.04/2.69 # Propositional preprocessing time : 0.000
% 18.04/2.69 # Propositional encoding time : 0.000
% 18.04/2.69 # Propositional solver time : 0.000
% 18.04/2.69 # Success case prop preproc time : 0.000
% 18.04/2.69 # Success case prop encoding time : 0.000
% 18.04/2.69 # Success case prop solver time : 0.000
% 18.04/2.69 # Current number of processed clauses : 581
% 18.04/2.69 # Positive orientable unit clauses : 456
% 18.04/2.69 # Positive unorientable unit clauses: 49
% 18.04/2.69 # Negative unit clauses : 76
% 18.04/2.69 # Non-unit-clauses : 0
% 18.04/2.69 # Current number of unprocessed clauses: 73207
% 18.04/2.69 # ...number of literals in the above : 73207
% 18.04/2.69 # Current number of archived formulas : 0
% 18.04/2.69 # Current number of archived clauses : 241
% 18.04/2.69 # Clause-clause subsumption calls (NU) : 0
% 18.04/2.69 # Rec. Clause-clause subsumption calls : 0
% 18.04/2.69 # Non-unit clause-clause subsumptions : 0
% 18.04/2.69 # Unit Clause-clause subsumption calls : 2042
% 18.04/2.69 # Rewrite failures with RHS unbound : 0
% 18.04/2.69 # BW rewrite match attempts : 52390
% 18.04/2.69 # BW rewrite match successes : 331
% 18.04/2.69 # Condensation attempts : 2772
% 18.04/2.69 # Condensation successes : 0
% 18.04/2.69 # Termbank termtop insertions : 5169964
% 18.04/2.69 # Search garbage collected termcells : 87
% 18.04/2.69
% 18.04/2.69 # -------------------------------------------------
% 18.04/2.69 # User time : 2.224 s
% 18.04/2.69 # System time : 0.076 s
% 18.04/2.69 # Total time : 2.300 s
% 18.04/2.69 # Maximum resident set size: 1708 pages
% 18.04/2.69
% 18.04/2.69 # -------------------------------------------------
% 18.04/2.69 # User time : 2.226 s
% 18.04/2.69 # System time : 0.077 s
% 18.04/2.69 # Total time : 2.303 s
% 18.04/2.69 # Maximum resident set size: 1740 pages
% 18.04/2.69 % E---3.1 exiting
% 18.04/2.70 % E exiting
%------------------------------------------------------------------------------