%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM799^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:17:09 AM UTC 2026
% Result : Theorem 23.91s 3.75s
% Output : CNFRefutation 23.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 98 ( 98 unt; 0 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 : 190 ( 190 >; 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_23,type,
zero: ( $i > $i ) > $i > $i ).
thf(decl_24,type,
one: ( $i > $i ) > $i > $i ).
thf(decl_25,type,
two: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_27,type,
four: ( $i > $i ) > $i > $i ).
thf(decl_28,type,
five: ( $i > $i ) > $i > $i ).
thf(decl_29,type,
six: ( $i > $i ) > $i > $i ).
thf(decl_30,type,
seven: ( $i > $i ) > $i > $i ).
thf(decl_34,type,
succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_35,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_36,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_37,type,
esk1_2: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(decl_38,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.ECAX4KrcFK/E---3.1_672120.p',two_ax) ).
thf(four_ax,axiom,
( four
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ECAX4KrcFK/E---3.1_672120.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.ECAX4KrcFK/E---3.1_672120.p',succ_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ECAX4KrcFK/E---3.1_672120.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.ECAX4KrcFK/E---3.1_672120.p',five_ax) ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ECAX4KrcFK/E---3.1_672120.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.ECAX4KrcFK/E---3.1_672120.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.ECAX4KrcFK/E---3.1_672120.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.ECAX4KrcFK/E---3.1_672120.p',seven_ax) ).
thf(zero_ax,axiom,
( zero
= ( ^ [X1: $i > $i,X2: $i] : X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ECAX4KrcFK/E---3.1_672120.p',zero_ax) ).
thf(thm,conjecture,
? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ four )
= ( plus @ five @ seven ) ),
file('/export/starexec/sandbox2/tmp/tmp.ECAX4KrcFK/E---3.1_672120.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.ECAX4KrcFK/E---3.1_672120.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
% 0.00/0.03 % Problem : NUM799^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.18 % Computer : n006.cluster.edu
% 0.13/0.18 % Model : x86_64 x86_64
% 0.13/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.18 % Memory : 8046.5625MB
% 0.13/0.18 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Tue Sep 29 13:00:09 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.23 Running higher-order theorem proving
% 0.13/0.25 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.ECAX4KrcFK/E---3.1_672120.p
% 23.91/3.75 % Version: 3.5.1-ho
% 23.91/3.75 % Preprocessing class: HSSSSMSSMSSNHHN.
% 23.91/3.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.91/3.75 % Starting pre_casc_2 with 1500s (5) cores
% 23.91/3.75 % Starting sh2 with 300s (1) cores
% 23.91/3.75 % Starting sh3 with 300s (1) cores
% 23.91/3.75 % Starting new_ho_10 with 300s (1) cores
% 23.91/3.75 % pre_casc_2 with pid 672133 completed with status 0
% 23.91/3.75 % Result found by pre_casc_2
% 23.91/3.75 % Preprocessing class: HSSSSMSSMSSNHHN.
% 23.91/3.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.91/3.75 % Starting pre_casc_2 with 1500s (5) cores
% 23.91/3.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.91/3.75 % No SInE strategy applied
% 23.91/3.75 % Search class: HUUPM-FFSF32-DHHSFMNN
% 23.91/3.75 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 23.91/3.75 % Starting SubtermCWHack with 151s (1) cores
% 23.91/3.75 % Starting pre_casc_2 with 901s (1) cores
% 23.91/3.75 % Starting sh2 with 151s (1) cores
% 23.91/3.75 % Starting sh3 with 151s (1) cores
% 23.91/3.75 % Starting sh9 with 146s (1) cores
% 23.91/3.75 % sh3 with pid 672143 completed with status 0
% 23.91/3.75 % Result found by sh3
% 23.91/3.75 % Preprocessing class: HSSSSMSSMSSNHHN.
% 23.91/3.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.91/3.75 % Starting pre_casc_2 with 1500s (5) cores
% 23.91/3.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.91/3.75 % No SInE strategy applied
% 23.91/3.75 % Search class: HUUPM-FFSF32-DHHSFMNN
% 23.91/3.75 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 23.91/3.75 % Starting SubtermCWHack with 151s (1) cores
% 23.91/3.75 % Starting pre_casc_2 with 901s (1) cores
% 23.91/3.75 % Starting sh2 with 151s (1) cores
% 23.91/3.75 % Starting sh3 with 151s (1) cores
% 23.91/3.75 % Preprocessing time : 0.001 s
% 23.91/3.75 % Presaturation interreduction done
% 23.91/3.75
% 23.91/3.75 % Proof found!
% 23.91/3.75 % SZS status Theorem
% 23.91/3.75 % SZS output start CNFRefutation
% See solution above
% 23.91/3.75 % Parsed axioms : 29
% 23.91/3.75 % Removed by relevancy pruning/SinE : 0
% 23.91/3.75 % Initial clauses : 29
% 23.91/3.75 % Removed in clause preprocessing : 14
% 23.91/3.75 % Initial clauses in saturation : 15
% 23.91/3.75 % Processed clauses : 2772
% 23.91/3.75 % ...of these trivial : 1628
% 23.91/3.75 % ...subsumed : 322
% 23.91/3.75 % ...remaining for further processing : 822
% 23.91/3.75 % Other redundant clauses eliminated : 0
% 23.91/3.75 % Clauses deleted for lack of memory : 0
% 23.91/3.75 % Backward-subsumed : 0
% 23.91/3.75 % Backward-rewritten : 226
% 23.91/3.75 % Generated clauses : 91748
% 23.91/3.75 % ...of the previous two non-redundant : 77171
% 23.91/3.75 % ...aggressively subsumed : 0
% 23.91/3.75 % Contextual simplify-reflections : 0
% 23.91/3.75 % Paramodulations : 91254
% 23.91/3.75 % Factorizations : 0
% 23.91/3.75 % NegExts : 25
% 23.91/3.75 % Equation resolutions : 0
% 23.91/3.75 % Disequality decompositions : 0
% 23.91/3.75 % Total rewrite steps : 334397
% 23.91/3.75 % ...of those cached : 312721
% 23.91/3.75 % Propositional unsat checks : 0
% 23.91/3.75 % Propositional check models : 0
% 23.91/3.75 % Propositional check unsatisfiable : 0
% 23.91/3.75 % Propositional clauses : 0
% 23.91/3.75 % Propositional clauses after purity: 0
% 23.91/3.75 % Propositional unsat core size : 0
% 23.91/3.75 % Propositional preprocessing time : 0.000
% 23.91/3.75 % Propositional encoding time : 0.000
% 23.91/3.75 % Propositional solver time : 0.000
% 23.91/3.75 % Success case prop preproc time : 0.000
% 23.91/3.75 % Success case prop encoding time : 0.000
% 23.91/3.75 % Success case prop solver time : 0.000
% 23.91/3.75 % Current number of processed clauses : 581
% 23.91/3.75 % Positive orientable unit clauses : 456
% 23.91/3.75 % Positive unorientable unit clauses: 49
% 23.91/3.75 % Negative unit clauses : 76
% 23.91/3.75 % Non-unit-clauses : 0
% 23.91/3.75 % Current number of unprocessed clauses: 73210
% 23.91/3.75 % ...number of literals in the above : 73210
% 23.91/3.75 % Current number of archived formulas : 0
% 23.91/3.75 % Current number of archived clauses : 241
% 23.91/3.75 % Clause-clause subsumption calls (NU) : 0
% 23.91/3.75 % Rec. Clause-clause subsumption calls : 0
% 23.91/3.75 % Non-unit clause-clause subsumptions : 0
% 23.91/3.75 % Unit Clause-clause subsumption calls : 2042
% 23.91/3.75 % Rewrite failures with RHS unbound : 0
% 23.91/3.75 % BW rewrite match attempts : 52386
% 23.91/3.75 % BW rewrite match successes : 331
% 23.91/3.75 % Condensation attempts : 0
% 23.91/3.75 % Condensation successes : 0
% 23.91/3.75 % Termbank termtop insertions : 5170394
% 23.91/3.75 % Search garbage collected termcells : 87
% 23.91/3.75
% 23.91/3.75 % -------------------------------------------------
% 23.91/3.75 % User time : 3.183 s
% 23.91/3.75 % System time : 0.100 s
% 23.91/3.75 % Total time : 3.283 s
% 23.91/3.75 % Maximum resident set size: 3648 pages
% 23.91/3.75
% 23.91/3.75 % -------------------------------------------------
% 23.91/3.75 % User time : 16.337 s
% 23.91/3.75 % System time : 0.533 s
% 23.91/3.75 % Total time : 16.871 s
% 23.91/3.75 % Maximum resident set size: 4864 pages
% 23.91/3.75 % E exiting
%------------------------------------------------------------------------------