%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM415^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:16:37 AM UTC 2026
% Result : Theorem 6.64s 1.10s
% Output : CNFRefutation 6.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 97 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 96 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 602 ( 6 ~; 0 |; 0 &; 596 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 162 ( 162 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 1 con; 0-4 aty)
% Number of variables : 190 ( 31 ^; 159 !; 0 ?; 190 :)
% 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_29,type,
six: ( $i > $i ) > $i > $i ).
thf(decl_30,type,
seven: ( $i > $i ) > $i > $i ).
thf(decl_31,type,
eight: ( $i > $i ) > $i > $i ).
thf(decl_32,type,
nine: ( $i > $i ) > $i > $i ).
thf(decl_33,type,
ten: ( $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_1316,type,
esk1280_1: $i > $i ).
thf(four_ax,axiom,
( four
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',four_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',three_ax) ).
thf(two_ax,axiom,
( two
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',two_ax) ).
thf(five_ax,axiom,
( five
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',five_ax) ).
thf(six_ax,axiom,
( six
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',six_ax) ).
thf(seven_ax,axiom,
( seven
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',seven_ax) ).
thf(eight_ax,axiom,
( eight
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',eight_ax) ).
thf(nine_ax,axiom,
( nine
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',nine_ax) ).
thf(ten_ax,axiom,
( ten
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',ten_ax) ).
thf(succ_ax,axiom,
( succ
= ( ^ [X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',succ_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/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',plus_ax) ).
thf(thm,conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.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/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',mult_ax) ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p',one_ax) ).
thf(c_0_14,plain,
! [X13: $i > $i,X14: $i] :
( ( four @ X13 @ X14 )
= ( X13 @ ( X13 @ ( X13 @ ( X13 @ X14 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[four_ax])]) ).
thf(c_0_15,plain,
! [X11: $i > $i,X12: $i] :
( ( three @ X11 @ X12 )
= ( X11 @ ( X11 @ ( X11 @ X12 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).
thf(c_0_16,plain,
! [X9: $i > $i,X10: $i] :
( ( two @ X9 @ X10 )
= ( X9 @ ( X9 @ X10 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).
thf(c_0_17,plain,
! [X15: $i > $i,X16: $i] :
( ( five @ X15 @ X16 )
= ( X15 @ ( X15 @ ( X15 @ ( X15 @ ( X15 @ X16 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[five_ax])]) ).
thf(c_0_18,plain,
! [X46: $i > $i,X47: $i] :
( ( four @ X46 @ X47 )
= ( X46 @ ( X46 @ ( X46 @ ( X46 @ X47 ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_14]) ).
thf(c_0_19,plain,
! [X44: $i > $i,X45: $i] :
( ( three @ X44 @ X45 )
= ( X44 @ ( X44 @ ( X44 @ X45 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
thf(c_0_20,plain,
! [X42: $i > $i,X43: $i] :
( ( two @ X42 @ X43 )
= ( X42 @ ( X42 @ X43 ) ) ),
inference(variable_rename,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
! [X17: $i > $i,X18: $i] :
( ( six @ X17 @ X18 )
= ( X17 @ ( X17 @ ( X17 @ ( X17 @ ( X17 @ ( X17 @ X18 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).
thf(c_0_22,plain,
! [X48: $i > $i,X49: $i] :
( ( five @ X48 @ X49 )
= ( X48 @ ( X48 @ ( X48 @ ( X48 @ ( X48 @ X49 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
thf(c_0_23,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_24,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
! [X19: $i > $i,X20: $i] :
( ( seven @ X19 @ X20 )
= ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ X20 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[seven_ax])]) ).
thf(c_0_27,plain,
! [X50: $i > $i,X51: $i] :
( ( six @ X50 @ X51 )
= ( X50 @ ( X50 @ ( X50 @ ( X50 @ ( X50 @ ( X50 @ X51 ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_21]) ).
thf(c_0_28,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( three @ X1 @ X2 ) )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_30,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( X1 @ ( two @ X1 @ X2 ) ) )
= ( two @ ( two @ X1 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
thf(c_0_31,plain,
! [X21: $i > $i,X22: $i] :
( ( eight @ X21 @ X22 )
= ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ ( X21 @ X22 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[eight_ax])]) ).
thf(c_0_32,plain,
! [X52: $i > $i,X53: $i] :
( ( seven @ X52 @ X53 )
= ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ X53 ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_26]) ).
thf(c_0_33,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_34,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( four @ X1 @ X2 ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_24]),c_0_29]) ).
thf(c_0_35,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( two @ X1 ) @ X2 )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_24]),c_0_29]) ).
thf(c_0_36,plain,
! [X23: $i > $i,X24: $i] :
( ( nine @ X23 @ X24 )
= ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ ( X23 @ X24 ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[nine_ax])]) ).
thf(c_0_37,plain,
! [X54: $i > $i,X55: $i] :
( ( eight @ X54 @ X55 )
= ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ ( X54 @ X55 ) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
thf(c_0_38,plain,
! [X1: $i > $i,X2: $i] :
( ( seven @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_39,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( five @ X1 @ X2 ) )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_24]),c_0_29]),c_0_34]) ).
thf(c_0_40,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_24,c_0_24]),c_0_29]),c_0_34]) ).
thf(c_0_41,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ ( X1 @ X2 ) )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_30]),c_0_35]) ).
thf(c_0_42,plain,
! [X25: $i > $i,X26: $i] :
( ( ten @ X25 @ X26 )
= ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ ( X25 @ X26 ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ten_ax])]) ).
thf(c_0_43,plain,
! [X56: $i > $i,X57: $i] :
( ( nine @ X56 @ X57 )
= ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ ( X56 @ X57 ) ) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_36]) ).
thf(c_0_44,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_37]) ).
thf(c_0_45,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( six @ X1 @ X2 ) )
= ( seven @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_24]),c_0_29]),c_0_34]),c_0_39]) ).
thf(c_0_46,plain,
! [X27: ( $i > $i ) > $i > $i,X28: $i > $i,X29: $i] :
( ( succ @ X27 @ X28 @ X29 )
= ( X28 @ ( X27 @ X28 @ X29 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[succ_ax])]) ).
thf(c_0_47,plain,
! [X1: $i > $i,X2: $i] :
( ( four @ X1 @ ( X1 @ X2 ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_48,plain,
! [X58: $i > $i,X59: $i] :
( ( ten @ X58 @ X59 )
= ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ ( X58 @ X59 ) ) ) ) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_42]) ).
thf(c_0_49,plain,
! [X1: $i > $i,X2: $i] :
( ( nine @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_24]),c_0_29]),c_0_34]),c_0_39]),c_0_45]) ).
thf(c_0_51,plain,
! [X60: ( $i > $i ) > $i > $i,X61: $i > $i,X62: $i] :
( ( succ @ X60 @ X61 @ X62 )
= ( X61 @ ( X60 @ X61 @ X62 ) ) ),
inference(variable_rename,[status(thm)],[c_0_46]) ).
thf(c_0_52,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( X1 @ ( two @ X1 @ X2 ) ) )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_30,c_0_35]) ).
thf(c_0_53,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ ( X1 @ X2 ) ) )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_25]),c_0_35]) ).
thf(c_0_54,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ ( X1 @ X2 ) )
= ( three @ ( two @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_35]),c_0_47]) ).
thf(c_0_55,plain,
! [X30: ( $i > $i ) > $i > $i,X31: ( $i > $i ) > $i > $i,X32: $i > $i,X33: $i] :
( ( plus @ X30 @ X31 @ X32 @ X33 )
= ( X30 @ X32 @ ( X31 @ X32 @ X33 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[plus_ax])]) ).
thf(c_0_56,plain,
! [X1: $i > $i,X2: $i] :
( ( ten @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_57,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( eight @ X1 @ X2 ) )
= ( nine @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_24]),c_0_29]),c_0_34]),c_0_39]),c_0_45]),c_0_50]) ).
thf(c_0_58,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_51]) ).
thf(c_0_59,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ ( two @ X1 ) @ X2 )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_34]),c_0_39]),c_0_47]),c_0_54]) ).
thf(c_0_60,negated_conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_61,plain,
! [X63: ( $i > $i ) > $i > $i,X64: ( $i > $i ) > $i > $i,X65: $i > $i,X66: $i] :
( ( plus @ X63 @ X64 @ X65 @ X66 )
= ( X63 @ X65 @ ( X64 @ X65 @ X66 ) ) ),
inference(variable_rename,[status(thm)],[c_0_55]) ).
thf(c_0_62,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( nine @ X1 @ X2 ) )
= ( ten @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_24]),c_0_29]),c_0_34]),c_0_39]),c_0_45]),c_0_50]),c_0_57]) ).
thf(c_0_63,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ three @ X1 @ X2 )
= ( four @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_29,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_59]),c_0_45]),c_0_50]) ).
thf(c_0_65,negated_conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
thf(c_0_66,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_61]) ).
thf(c_0_67,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ ( seven @ X1 @ X2 ) )
= ( ten @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_50]),c_0_57]),c_0_62]) ).
thf(c_0_68,plain,
! [X34: ( $i > $i ) > $i > $i,X35: ( $i > $i ) > $i > $i,X36: $i > $i,X37: $i] :
( ( mult @ X34 @ X35 @ X36 @ X37 )
= ( X34 @ ( X35 @ X36 ) @ X37 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).
thf(c_0_69,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( succ @ ( succ @ X3 ) @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X3 @ X1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_58,c_0_58]) ).
thf(c_0_70,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ ( five @ X1 @ X2 ) )
= ( eight @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_45]),c_0_50]) ).
thf(c_0_71,plain,
( ( succ @ three )
= four ),
inference(pos_ext,[status(thm)],[c_0_63]) ).
thf(c_0_72,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ four @ X1 @ X2 )
= ( five @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_58]) ).
thf(c_0_73,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ ( two @ X1 ) @ X2 )
= ( ten @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_64]),c_0_57]),c_0_62]) ).
thf(c_0_74,negated_conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
inference(fof_nnf,[status(thm)],[c_0_65]) ).
thf(c_0_75,plain,
! [X1: $i > $i,X2: $i] :
( ( plus @ three @ seven @ X1 @ X2 )
= ( ten @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_76,plain,
! [X67: ( $i > $i ) > $i > $i,X68: ( $i > $i ) > $i > $i,X69: $i > $i,X70: $i] :
( ( mult @ X67 @ X68 @ X69 @ X70 )
= ( X67 @ ( X68 @ X69 ) @ X70 ) ),
inference(variable_rename,[status(thm)],[c_0_68]) ).
thf(c_0_77,plain,
! [X7: $i > $i,X8: $i] :
( ( one @ X7 @ X8 )
= ( X7 @ X8 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).
thf(c_0_78,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( five @ X1 ) @ X2 )
= ( ten @ X1 @ X2 ) ),
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_69,c_0_70]),c_0_71]),c_0_72]),c_0_25]),c_0_57]),c_0_62]) ).
thf(c_0_79,plain,
! [X1: $i > $i] :
( ( five @ ( two @ X1 ) )
= ( ten @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_73]) ).
thf(c_0_80,plain,
! [X1: $i > $i] :
( ( two @ ( two @ X1 ) )
= ( four @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_35]) ).
thf(c_0_81,negated_conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
!= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_82,plain,
( ( plus @ three @ seven )
= ten ),
inference(pos_ext,[status(thm)],[c_0_75]) ).
thf(c_0_83,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_76]) ).
thf(c_0_84,plain,
! [X40: $i > $i,X41: $i] :
( ( one @ X40 @ X41 )
= ( X40 @ X41 ) ),
inference(variable_rename,[status(thm)],[c_0_77]) ).
thf(c_0_85,plain,
! [X1: $i > $i] :
( ( two @ ( five @ X1 ) )
= ( ten @ X1 ) ),
inference(pos_ext,[status(thm)],[c_0_78]) ).
thf(c_0_86,plain,
! [X1: $i > $i] :
( ( ten @ ( two @ X1 ) )
= ( five @ ( four @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_87,negated_conjecture,
( ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) )
!= ( mult @ two @ ten ) ),
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
thf(c_0_88,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_83]) ).
thf(c_0_89,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ X3 @ X3 @ X1 @ X2 )
= ( two @ ( X3 @ X1 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_66]) ).
thf(c_0_90,plain,
! [X1: $i > $i,X2: $i] :
( ( one @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_91,plain,
! [X1: $i > $i] :
( ( five @ ( four @ X1 ) )
= ( two @ ( ten @ X1 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_79]),c_0_86]) ).
thf(c_0_92,negated_conjecture,
( ( ten @ ( plus @ one @ one @ esk1280_1 ) )
!= ( two @ ( ten @ esk1280_1 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_87]),c_0_88]),c_0_88]),c_0_85]),c_0_88]) ).
thf(c_0_93,plain,
! [X3: ( $i > $i ) > $i > $i,X1: $i > $i] :
( ( plus @ X3 @ X3 @ X1 )
= ( two @ ( X3 @ X1 ) ) ),
inference(pos_ext,[status(thm)],[c_0_89]) ).
thf(c_0_94,plain,
! [X1: $i > $i] :
( ( one @ X1 )
= X1 ),
inference(pos_ext,[status(thm)],[c_0_90]) ).
thf(c_0_95,plain,
! [X1: $i > $i] :
( ( ten @ ( two @ X1 ) )
= ( two @ ( ten @ X1 ) ) ),
inference(rw,[status(thm)],[c_0_86,c_0_91]) ).
thf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM415^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 11:53:35 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.GR9QbnFPyv/E---3.1_4193580.p
% 6.64/1.10 % Version: 3.5.1-ho
% 6.64/1.10 % Preprocessing class: HSSSSMSSMSSNHHN.
% 6.64/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.64/1.10 % Starting pre_casc_2 with 1500s (5) cores
% 6.64/1.10 % Starting sh2 with 300s (1) cores
% 6.64/1.10 % Starting sh3 with 300s (1) cores
% 6.64/1.10 % Starting new_ho_10 with 300s (1) cores
% 6.64/1.10 % pre_casc_2 with pid 4193593 completed with status 0
% 6.64/1.10 % Result found by pre_casc_2
% 6.64/1.10 % Preprocessing class: HSSSSMSSMSSNHHN.
% 6.64/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.64/1.10 % Starting pre_casc_2 with 1500s (5) cores
% 6.64/1.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.64/1.10 % No SInE strategy applied
% 6.64/1.10 % Search class: HUUPM-FFSF32-DHHSFMNN
% 6.64/1.10 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 6.64/1.10 % Starting SubtermCWHack with 151s (1) cores
% 6.64/1.10 % Starting pre_casc_2 with 901s (1) cores
% 6.64/1.10 % Starting sh2 with 151s (1) cores
% 6.64/1.10 % Starting sh3 with 151s (1) cores
% 6.64/1.10 % Starting sh9 with 146s (1) cores
% 6.64/1.10 % sh9 with pid 4193604 completed with status 0
% 6.64/1.10 % Result found by sh9
% 6.64/1.10 % Preprocessing class: HSSSSMSSMSSNHHN.
% 6.64/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.64/1.10 % Starting pre_casc_2 with 1500s (5) cores
% 6.64/1.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.64/1.10 % No SInE strategy applied
% 6.64/1.10 % Search class: HUUPM-FFSF32-DHHSFMNN
% 6.64/1.10 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 6.64/1.10 % Starting SubtermCWHack with 151s (1) cores
% 6.64/1.10 % Starting pre_casc_2 with 901s (1) cores
% 6.64/1.10 % Starting sh2 with 151s (1) cores
% 6.64/1.10 % Starting sh3 with 151s (1) cores
% 6.64/1.10 % Starting sh9 with 146s (1) cores
% 6.64/1.10 % Preprocessing time : 0.001 s
% 6.64/1.10 % Presaturation interreduction done
% 6.64/1.10
% 6.64/1.10 % Proof found!
% 6.64/1.10 % SZS status Theorem
% 6.64/1.10 % SZS output start CNFRefutation
% See solution above
% 6.64/1.10 % Parsed axioms : 29
% 6.64/1.10 % Removed by relevancy pruning/SinE : 0
% 6.64/1.10 % Initial clauses : 29
% 6.64/1.10 % Removed in clause preprocessing : 14
% 6.64/1.10 % Initial clauses in saturation : 15
% 6.64/1.10 % Processed clauses : 2504
% 6.64/1.10 % ...of these trivial : 771
% 6.64/1.10 % ...subsumed : 8
% 6.64/1.10 % ...remaining for further processing : 1725
% 6.64/1.10 % Other redundant clauses eliminated : 0
% 6.64/1.10 % Clauses deleted for lack of memory : 0
% 6.64/1.10 % Backward-subsumed : 0
% 6.64/1.10 % Backward-rewritten : 476
% 6.64/1.10 % Generated clauses : 45751
% 6.64/1.10 % ...of the previous two non-redundant : 43064
% 6.64/1.10 % ...aggressively subsumed : 0
% 6.64/1.10 % Contextual simplify-reflections : 0
% 6.64/1.10 % Paramodulations : 43404
% 6.64/1.10 % Factorizations : 0
% 6.64/1.10 % NegExts : 2116
% 6.64/1.10 % Equation resolutions : 0
% 6.64/1.10 % Disequality decompositions : 0
% 6.64/1.10 % Total rewrite steps : 57343
% 6.64/1.10 % ...of those cached : 44874
% 6.64/1.10 % Propositional unsat checks : 0
% 6.64/1.10 % Propositional check models : 0
% 6.64/1.10 % Propositional check unsatisfiable : 0
% 6.64/1.10 % Propositional clauses : 0
% 6.64/1.10 % Propositional clauses after purity: 0
% 6.64/1.10 % Propositional unsat core size : 0
% 6.64/1.10 % Propositional preprocessing time : 0.000
% 6.64/1.10 % Propositional encoding time : 0.000
% 6.64/1.10 % Propositional solver time : 0.000
% 6.64/1.10 % Success case prop preproc time : 0.000
% 6.64/1.10 % Success case prop encoding time : 0.000
% 6.64/1.10 % Success case prop solver time : 0.000
% 6.64/1.10 % Current number of processed clauses : 1234
% 6.64/1.10 % Positive orientable unit clauses : 484
% 6.64/1.10 % Positive unorientable unit clauses: 27
% 6.64/1.10 % Negative unit clauses : 1
% 6.64/1.10 % Non-unit-clauses : 722
% 6.64/1.10 % Current number of unprocessed clauses: 40356
% 6.64/1.10 % ...number of literals in the above : 43103
% 6.64/1.10 % Current number of archived formulas : 0
% 6.64/1.10 % Current number of archived clauses : 491
% 6.64/1.10 % Clause-clause subsumption calls (NU) : 223515
% 6.64/1.10 % Rec. Clause-clause subsumption calls : 4317
% 6.64/1.10 % Non-unit clause-clause subsumptions : 1
% 6.64/1.10 % Unit Clause-clause subsumption calls : 367
% 6.64/1.10 % Rewrite failures with RHS unbound : 0
% 6.64/1.10 % BW rewrite match attempts : 90336
% 6.64/1.10 % BW rewrite match successes : 523
% 6.64/1.10 % Condensation attempts : 2504
% 6.64/1.10 % Condensation successes : 0
% 6.64/1.10 % Termbank termtop insertions : 2333344
% 6.64/1.10 % Search garbage collected termcells : 76
% 6.64/1.10
% 6.64/1.10 % -------------------------------------------------
% 6.64/1.10 % User time : 0.869 s
% 6.64/1.10 % System time : 0.029 s
% 6.64/1.10 % Total time : 0.898 s
% 6.64/1.10 % Maximum resident set size: 3648 pages
% 6.64/1.10
% 6.64/1.10 % -------------------------------------------------
% 6.64/1.10 % User time : 4.275 s
% 6.64/1.10 % System time : 0.171 s
% 6.64/1.10 % Total time : 4.445 s
% 6.64/1.10 % Maximum resident set size: 4864 pages
% 6.64/1.10 % E exiting
%------------------------------------------------------------------------------