%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM801^1 : 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 08:17:45 AM UTC 2026
% Result : Theorem 6.89s 1.20s
% Output : CNFRefutation 6.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 71 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 421 ( 6 ~; 0 |; 0 &; 415 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 171 ( 171 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 1 con; 0-4 aty)
% Number of variables : 159 ( 25 ^; 130 !; 4 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
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_30,type,
seven: ( $i > $i ) > $i > $i ).
thf(decl_31,type,
eight: ( $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_3: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(decl_42,type,
esk6_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.iW4ZXAdQ6Y/E---3.1_672573.p',two_ax) ).
thf(four_ax,axiom,
( four
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iW4ZXAdQ6Y/E---3.1_672573.p',four_ax) ).
thf(five_ax,axiom,
( five
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iW4ZXAdQ6Y/E---3.1_672573.p',five_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.iW4ZXAdQ6Y/E---3.1_672573.p',succ_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iW4ZXAdQ6Y/E---3.1_672573.p',three_ax) ).
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.iW4ZXAdQ6Y/E---3.1_672573.p',mult_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.iW4ZXAdQ6Y/E---3.1_672573.p',seven_ax) ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iW4ZXAdQ6Y/E---3.1_672573.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.iW4ZXAdQ6Y/E---3.1_672573.p',plus_ax) ).
thf(thm,conjecture,
? [X3: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ four )
= ( plus @ five @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iW4ZXAdQ6Y/E---3.1_672573.p',thm) ).
thf(eight_ax,axiom,
( eight
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iW4ZXAdQ6Y/E---3.1_672573.p',eight_ax) ).
thf(c_0_11,plain,
! [X11: $i > $i,X12: $i] :
( ( two @ X11 @ X12 )
= ( X11 @ ( X11 @ X12 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).
thf(c_0_12,plain,
! [X44: $i > $i,X45: $i] :
( ( two @ X44 @ X45 )
= ( X44 @ ( X44 @ X45 ) ) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
thf(c_0_13,plain,
! [X15: $i > $i,X16: $i] :
( ( four @ X15 @ X16 )
= ( X15 @ ( X15 @ ( X15 @ ( X15 @ X16 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[four_ax])]) ).
thf(c_0_14,plain,
! [X17: $i > $i,X18: $i] :
( ( five @ X17 @ X18 )
= ( X17 @ ( X17 @ ( X17 @ ( X17 @ ( X17 @ X18 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[five_ax])]) ).
thf(c_0_15,plain,
! [X29: ( $i > $i ) > $i > $i,X30: $i > $i,X31: $i] :
( ( succ @ X29 @ X30 @ X31 )
= ( X30 @ ( X29 @ X30 @ X31 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[succ_ax])]) ).
thf(c_0_16,plain,
! [X13: $i > $i,X14: $i] :
( ( three @ X13 @ X14 )
= ( X13 @ ( X13 @ ( X13 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).
thf(c_0_17,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X48: $i > $i,X49: $i] :
( ( four @ X48 @ X49 )
= ( X48 @ ( X48 @ ( X48 @ ( X48 @ X49 ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X36: ( $i > $i ) > $i > $i,X37: ( $i > $i ) > $i > $i,X38: $i > $i,X39: $i] :
( ( mult @ X36 @ X37 @ X38 @ X39 )
= ( X36 @ ( X37 @ X38 ) @ X39 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).
thf(c_0_20,plain,
! [X21: $i > $i,X22: $i] :
( ( seven @ X21 @ X22 )
= ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ X22 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[seven_ax])]) ).
thf(c_0_21,plain,
! [X50: $i > $i,X51: $i] :
( ( five @ X50 @ X51 )
= ( X50 @ ( X50 @ ( X50 @ ( X50 @ ( X50 @ X51 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_14]) ).
thf(c_0_22,plain,
! [X9: $i > $i,X10: $i] :
( ( one @ X9 @ X10 )
= ( X9 @ X10 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).
thf(c_0_23,plain,
! [X32: ( $i > $i ) > $i > $i,X33: ( $i > $i ) > $i > $i,X34: $i > $i,X35: $i] :
( ( plus @ X32 @ X33 @ X34 @ X35 )
= ( X32 @ X34 @ ( X33 @ X34 @ X35 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[plus_ax])]) ).
thf(c_0_24,plain,
! [X62: ( $i > $i ) > $i > $i,X63: $i > $i,X64: $i] :
( ( succ @ X62 @ X63 @ X64 )
= ( X63 @ ( X62 @ X63 @ X64 ) ) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
thf(c_0_25,plain,
! [X46: $i > $i,X47: $i] :
( ( three @ X46 @ X47 )
= ( X46 @ ( X46 @ ( X46 @ X47 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_16]) ).
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_17,c_0_17]) ).
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_18]) ).
thf(c_0_28,negated_conjecture,
~ ? [X3: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ four )
= ( plus @ five @ X4 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_29,plain,
! [X69: ( $i > $i ) > $i > $i,X70: ( $i > $i ) > $i > $i,X71: $i > $i,X72: $i] :
( ( mult @ X69 @ X70 @ X71 @ X72 )
= ( X69 @ ( X70 @ X71 ) @ X72 ) ),
inference(variable_rename,[status(thm)],[c_0_19]) ).
thf(c_0_30,plain,
! [X23: $i > $i,X24: $i] :
( ( eight @ X23 @ X24 )
= ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ X24 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[eight_ax])]) ).
thf(c_0_31,plain,
! [X54: $i > $i,X55: $i] :
( ( seven @ X54 @ X55 )
= ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ X55 ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_20]) ).
thf(c_0_32,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_33,plain,
! [X42: $i > $i,X43: $i] :
( ( one @ X42 @ X43 )
= ( X42 @ X43 ) ),
inference(variable_rename,[status(thm)],[c_0_22]) ).
thf(c_0_34,plain,
! [X65: ( $i > $i ) > $i > $i,X66: ( $i > $i ) > $i > $i,X67: $i > $i,X68: $i] :
( ( plus @ X65 @ X66 @ X67 @ X68 )
= ( X65 @ X67 @ ( X66 @ X67 @ X68 ) ) ),
inference(variable_rename,[status(thm)],[c_0_23]) ).
thf(c_0_35,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_24]) ).
thf(c_0_36,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_37,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( two @ X1 ) @ X2 )
= ( two @ X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
thf(c_0_38,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_17]),c_0_27]) ).
thf(c_0_39,negated_conjecture,
! [X73: ( $i > $i ) > $i > $i,X74: ( $i > $i ) > $i > $i] :
( ( mult @ X73 @ four )
!= ( plus @ five @ X74 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
thf(c_0_40,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_29]) ).
thf(c_0_41,plain,
! [X56: $i > $i,X57: $i] :
( ( eight @ X56 @ X57 )
= ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ X57 ) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
thf(c_0_42,plain,
! [X1: $i > $i,X2: $i] :
( ( seven @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_43,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( four @ X1 @ X2 ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_32,c_0_27]) ).
thf(c_0_44,plain,
! [X1: $i > $i,X2: $i] :
( ( one @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_45,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_34]) ).
thf(c_0_46,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ three @ X1 @ X2 )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_27]) ).
thf(c_0_47,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ X2 ) )
= ( X1 @ ( two @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
thf(c_0_48,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ ( X1 @ X2 ) ) )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_49,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ four )
!= ( plus @ five @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_50,plain,
! [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i] :
( ( mult @ X3 @ X4 @ X1 )
= ( X3 @ ( X4 @ X1 ) ) ),
inference(pos_ext,[status(thm)],[c_0_40]) ).
thf(c_0_51,plain,
! [X1: $i > $i] :
( ( two @ ( two @ X1 ) )
= ( four @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_38]) ).
thf(c_0_52,plain,
! [X1: $i > $i,X2: $i] :
( ( eight @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_53,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( X1 @ ( five @ X1 @ X2 ) ) )
= ( seven @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_27]),c_0_43]) ).
thf(c_0_54,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_44,c_0_45]) ).
thf(c_0_55,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( three @ X1 @ X2 ) )
= ( four @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
thf(c_0_56,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_47,c_0_48]),c_0_48]),c_0_43]) ).
thf(c_0_57,negated_conjecture,
! [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i] :
( ( X3 @ ( four @ ( esk1_3 @ X4 @ X3 ) ) )
!= ( plus @ five @ X4 @ ( esk1_3 @ X4 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_49]),c_0_50]) ).
thf(c_0_58,plain,
! [X1: $i > $i] :
( ( two @ ( four @ X1 ) )
= ( four @ ( two @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_51,c_0_51]) ).
thf(c_0_59,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ ( five @ X1 @ X2 ) ) )
= ( four @ ( two @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_17]),c_0_17]),c_0_38]),c_0_43]) ).
thf(c_0_60,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( seven @ X1 @ X2 ) )
= ( eight @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_27]),c_0_43]),c_0_53]) ).
thf(c_0_61,plain,
! [X1: $i > $i,X2: $i] :
( ( plus @ one @ four @ X1 @ X2 )
= ( five @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
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_36]),c_0_55]),c_0_43]),c_0_56]) ).
thf(c_0_63,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( plus @ five @ X3 @ ( esk1_3 @ X3 @ two ) )
!= ( four @ ( two @ ( esk1_3 @ X3 @ two ) ) ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_64,plain,
! [X1: $i > $i,X2: $i] :
( ( four @ ( two @ X1 ) @ X2 )
= ( eight @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_59]),c_0_53]),c_0_60]) ).
thf(c_0_65,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ X3 @ three @ X1 @ X2 )
= ( X3 @ X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_45,c_0_36]) ).
thf(c_0_66,plain,
( ( plus @ one @ four )
= five ),
inference(pos_ext,[status(thm)],[c_0_61]) ).
thf(c_0_67,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ ( X1 @ ( X1 @ X2 ) ) )
= ( seven @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_27]),c_0_43]),c_0_53]),c_0_56]) ).
thf(c_0_68,plain,
! [X1: $i > $i,X2: $i] :
( ( seven @ X1 @ ( X1 @ X2 ) )
= ( eight @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_62]),c_0_53]),c_0_60]) ).
thf(c_0_69,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( plus @ five @ X3 @ ( esk1_3 @ X3 @ two ) @ ( esk6_1 @ X3 ) )
!= ( eight @ ( esk1_3 @ X3 @ two ) @ ( esk6_1 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_63]),c_0_64]) ).
thf(c_0_70,plain,
! [X1: $i > $i,X2: $i] :
( ( plus @ five @ three @ X1 @ X2 )
= ( eight @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_65]),c_0_66]),c_0_67]),c_0_68]) ).
thf(c_0_71,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_69,c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM801^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n006.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:00:24 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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.iW4ZXAdQ6Y/E---3.1_672573.p
% 6.89/1.20 % Version: 3.5.1-ho
% 6.89/1.20 % Preprocessing class: HSSSSMSSMSSNHHN.
% 6.89/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.89/1.20 % Starting pre_casc_2 with 1500s (5) cores
% 6.89/1.20 % Starting sh2 with 300s (1) cores
% 6.89/1.20 % Starting sh3 with 300s (1) cores
% 6.89/1.20 % Starting new_ho_10 with 300s (1) cores
% 6.89/1.20 % pre_casc_2 with pid 672586 completed with status 0
% 6.89/1.20 % Result found by pre_casc_2
% 6.89/1.20 % Preprocessing class: HSSSSMSSMSSNHHN.
% 6.89/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.89/1.20 % Starting pre_casc_2 with 1500s (5) cores
% 6.89/1.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.89/1.20 % No SInE strategy applied
% 6.89/1.20 % Search class: HUUPM-FFSF32-DHHSFMNN
% 6.89/1.20 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 6.89/1.20 % Starting SubtermCWHack with 151s (1) cores
% 6.89/1.20 % Starting pre_casc_2 with 901s (1) cores
% 6.89/1.20 % Starting sh2 with 151s (1) cores
% 6.89/1.20 % Starting sh3 with 151s (1) cores
% 6.89/1.20 % Starting sh9 with 146s (1) cores
% 6.89/1.20 % pre_casc_2 with pid 672592 completed with status 0
% 6.89/1.20 % Result found by pre_casc_2
% 6.89/1.20 % Preprocessing class: HSSSSMSSMSSNHHN.
% 6.89/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.89/1.20 % Starting pre_casc_2 with 1500s (5) cores
% 6.89/1.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.89/1.20 % No SInE strategy applied
% 6.89/1.20 % Search class: HUUPM-FFSF32-DHHSFMNN
% 6.89/1.20 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 6.89/1.20 % Starting SubtermCWHack with 151s (1) cores
% 6.89/1.20 % Starting pre_casc_2 with 901s (1) cores
% 6.89/1.20 % Preprocessing time : 0.001 s
% 6.89/1.20 % Presaturation interreduction done
% 6.89/1.20
% 6.89/1.20 % Proof found!
% 6.89/1.20 % SZS status Theorem
% 6.89/1.20 % SZS output start CNFRefutation
% See solution above
% 6.89/1.20 % Parsed axioms : 29
% 6.89/1.20 % Removed by relevancy pruning/SinE : 0
% 6.89/1.20 % Initial clauses : 29
% 6.89/1.20 % Removed in clause preprocessing : 14
% 6.89/1.20 % Initial clauses in saturation : 15
% 6.89/1.20 % Processed clauses : 2350
% 6.89/1.20 % ...of these trivial : 865
% 6.89/1.20 % ...subsumed : 594
% 6.89/1.20 % ...remaining for further processing : 891
% 6.89/1.20 % Other redundant clauses eliminated : 0
% 6.89/1.20 % Clauses deleted for lack of memory : 0
% 6.89/1.20 % Backward-subsumed : 0
% 6.89/1.20 % Backward-rewritten : 180
% 6.89/1.20 % Generated clauses : 55391
% 6.89/1.20 % ...of the previous two non-redundant : 48760
% 6.89/1.20 % ...aggressively subsumed : 0
% 6.89/1.20 % Contextual simplify-reflections : 0
% 6.89/1.20 % Paramodulations : 54863
% 6.89/1.20 % Factorizations : 0
% 6.89/1.20 % NegExts : 260
% 6.89/1.20 % Equation resolutions : 0
% 6.89/1.20 % Disequality decompositions : 0
% 6.89/1.20 % Total rewrite steps : 209938
% 6.89/1.20 % ...of those cached : 198094
% 6.89/1.20 % Propositional unsat checks : 0
% 6.89/1.20 % Propositional check models : 0
% 6.89/1.20 % Propositional check unsatisfiable : 0
% 6.89/1.20 % Propositional clauses : 0
% 6.89/1.20 % Propositional clauses after purity: 0
% 6.89/1.20 % Propositional unsat core size : 0
% 6.89/1.20 % Propositional preprocessing time : 0.000
% 6.89/1.20 % Propositional encoding time : 0.000
% 6.89/1.20 % Propositional solver time : 0.000
% 6.89/1.20 % Success case prop preproc time : 0.000
% 6.89/1.20 % Success case prop encoding time : 0.000
% 6.89/1.20 % Success case prop solver time : 0.000
% 6.89/1.20 % Current number of processed clauses : 696
% 6.89/1.20 % Positive orientable unit clauses : 284
% 6.89/1.20 % Positive unorientable unit clauses: 41
% 6.89/1.20 % Negative unit clauses : 371
% 6.89/1.20 % Non-unit-clauses : 0
% 6.89/1.20 % Current number of unprocessed clauses: 45777
% 6.89/1.20 % ...number of literals in the above : 45777
% 6.89/1.20 % Current number of archived formulas : 0
% 6.89/1.20 % Current number of archived clauses : 195
% 6.89/1.20 % Clause-clause subsumption calls (NU) : 0
% 6.89/1.20 % Rec. Clause-clause subsumption calls : 0
% 6.89/1.20 % Non-unit clause-clause subsumptions : 0
% 6.89/1.20 % Unit Clause-clause subsumption calls : 69188
% 6.89/1.20 % Rewrite failures with RHS unbound : 0
% 6.89/1.20 % BW rewrite match attempts : 57299
% 6.89/1.20 % BW rewrite match successes : 227
% 6.89/1.20 % Condensation attempts : 2350
% 6.89/1.20 % Condensation successes : 0
% 6.89/1.20 % Termbank termtop insertions : 2903572
% 6.89/1.20 % Search garbage collected termcells : 93
% 6.89/1.20
% 6.89/1.20 % -------------------------------------------------
% 6.89/1.20 % User time : 0.893 s
% 6.89/1.20 % System time : 0.040 s
% 6.89/1.20 % Total time : 0.933 s
% 6.89/1.20 % Maximum resident set size: 3648 pages
% 6.89/1.20
% 6.89/1.20 % -------------------------------------------------
% 6.89/1.20 % User time : 4.219 s
% 6.89/1.20 % System time : 0.185 s
% 6.89/1.20 % Total time : 4.404 s
% 6.89/1.20 % Maximum resident set size: 4864 pages
% 6.89/1.20 % E exiting
%------------------------------------------------------------------------------