%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG253^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 07:44:44 AM UTC 2026
% Result : Theorem 0.31s 0.30s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 195 ( 6 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1183 ( 79 ~; 167 |; 17 &; 862 @)
% ( 4 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 169 ( 0 ^; 169 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_24,type,
ap: term > term > term ).
thf(decl_25,type,
lam: term > term ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_27,type,
id: subst ).
thf(decl_29,type,
push: term > subst > subst ).
thf(decl_31,type,
var: term > $o ).
thf(decl_40,type,
induction2lem: $o ).
thf(decl_114,type,
induction2_lthm: $o ).
thf(decl_132,type,
induction2: $o ).
thf(decl_143,type,
axvarid: $o ).
thf(decl_145,type,
esk1_1: ( term > $o ) > term ).
thf(decl_146,type,
esk2_1: ( term > $o ) > term ).
thf(decl_147,type,
esk3_1: ( term > $o ) > term ).
thf(decl_148,type,
esk4_3: ( term > $o ) > term > subst > term ).
thf(decl_149,type,
epred1_0: term > $o ).
thf(decl_150,type,
esk5_1: term > term ).
thf(decl_151,type,
esk6_0: term ).
thf(thm,conjecture,
induction2_lthm,
file('/export/starexec/sandbox2/tmp/tmp.I5smYmN8Zt/E---3.1_3180284.p',thm) ).
thf(induction2_lthm,axiom,
( induction2_lthm
<=> ( axvarid
=> ( induction2lem
=> induction2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.I5smYmN8Zt/E---3.1_3180284.p',induction2_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.I5smYmN8Zt/E---3.1_3180284.p',axvarid) ).
thf(induction2lem,axiom,
( induction2lem
<=> ! [X6: term > $o] :
( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ! [X2: term] :
( ( X6 @ X2 )
=> ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term,X3: subst] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ( X6 @ ( sub @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.I5smYmN8Zt/E---3.1_3180284.p',induction2lem) ).
thf(induction2,axiom,
( induction2
<=> ! [X6: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) )
=> ( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ! [X2: term] :
( ( X6 @ X2 )
=> ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term] : ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.I5smYmN8Zt/E---3.1_3180284.p',induction2) ).
thf(c_0_5,negated_conjecture,
~ induction2_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_6,axiom,
( induction2_lthm
= ( ! [X44: term] :
( ( sub @ X44 @ id )
= X44 )
=> ( ! [X45: term > $o] :
( ! [X46: term,X47: term] :
( ( X45 @ X46 )
=> ( ( X45 @ X47 )
=> ( X45 @ ( ap @ X46 @ X47 ) ) ) )
=> ( ! [X48: term] :
( ! [X49: term] :
( ( X45 @ X49 )
=> ( X45 @ ( sub @ X48 @ ( push @ X49 @ id ) ) ) )
=> ( X45 @ ( lam @ X48 ) ) )
=> ! [X50: term,X51: subst] :
( ! [X52: term] :
( ( var @ X52 )
=> ( X45 @ ( sub @ X52 @ X51 ) ) )
=> ( X45 @ ( sub @ X50 @ X51 ) ) ) ) )
=> ! [X53: term > $o] :
( ! [X54: term] :
( ( var @ X54 )
=> ( X53 @ X54 ) )
=> ( ! [X55: term,X56: term] :
( ( X53 @ X55 )
=> ( ( X53 @ X56 )
=> ( X53 @ ( ap @ X55 @ X56 ) ) ) )
=> ( ! [X57: term] :
( ! [X58: term] :
( ( X53 @ X58 )
=> ( X53 @ ( sub @ X57 @ ( push @ X58 @ id ) ) ) )
=> ( X53 @ ( lam @ X57 ) ) )
=> ! [X59: term] : ( X53 @ X59 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[induction2_lthm,axvarid]),induction2lem]),induction2]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X60: term] :
( ( sub @ X60 @ id )
= X60 )
=> ( ! [X61: term > $o] :
( ! [X62: term,X63: term] :
( ( X61 @ X62 )
=> ( ( X61 @ X63 )
=> ( X61 @ ( ap @ X62 @ X63 ) ) ) )
=> ( ! [X64: term] :
( ! [X65: term] :
( ( X61 @ X65 )
=> ( X61 @ ( sub @ X64 @ ( push @ X65 @ id ) ) ) )
=> ( X61 @ ( lam @ X64 ) ) )
=> ! [X66: term,X67: subst] :
( ! [X68: term] :
( ( var @ X68 )
=> ( X61 @ ( sub @ X68 @ X67 ) ) )
=> ( X61 @ ( sub @ X66 @ X67 ) ) ) ) )
=> ! [X69: term > $o] :
( ! [X70: term] :
( ( var @ X70 )
=> ( X69 @ X70 ) )
=> ( ! [X71: term,X72: term] :
( ( X69 @ X71 )
=> ( ( X69 @ X72 )
=> ( X69 @ ( ap @ X71 @ X72 ) ) ) )
=> ( ! [X73: term] :
( ! [X74: term] :
( ( X69 @ X74 )
=> ( X69 @ ( sub @ X73 @ ( push @ X74 @ id ) ) ) )
=> ( X69 @ ( lam @ X73 ) ) )
=> ! [X75: term] : ( X69 @ X75 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X76: term,X77: term > $o,X81: term,X82: term,X83: subst,X86: term,X87: term,X88: term,X89: term] :
( ( ( sub @ X76 @ id )
= X76 )
& ( ( var @ ( esk4_3 @ X77 @ X82 @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ X81 )
| ( X77 @ ( sub @ ( esk3_1 @ X77 ) @ ( push @ X81 @ id ) ) )
| ( X77 @ ( esk1_1 @ X77 ) ) )
& ( ~ ( X77 @ ( sub @ ( esk4_3 @ X77 @ X82 @ X83 ) @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ X81 )
| ( X77 @ ( sub @ ( esk3_1 @ X77 ) @ ( push @ X81 @ id ) ) )
| ( X77 @ ( esk1_1 @ X77 ) ) )
& ( ( var @ ( esk4_3 @ X77 @ X82 @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ ( lam @ ( esk3_1 @ X77 ) ) )
| ( X77 @ ( esk1_1 @ X77 ) ) )
& ( ~ ( X77 @ ( sub @ ( esk4_3 @ X77 @ X82 @ X83 ) @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ ( lam @ ( esk3_1 @ X77 ) ) )
| ( X77 @ ( esk1_1 @ X77 ) ) )
& ( ( var @ ( esk4_3 @ X77 @ X82 @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ X81 )
| ( X77 @ ( sub @ ( esk3_1 @ X77 ) @ ( push @ X81 @ id ) ) )
| ( X77 @ ( esk2_1 @ X77 ) ) )
& ( ~ ( X77 @ ( sub @ ( esk4_3 @ X77 @ X82 @ X83 ) @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ X81 )
| ( X77 @ ( sub @ ( esk3_1 @ X77 ) @ ( push @ X81 @ id ) ) )
| ( X77 @ ( esk2_1 @ X77 ) ) )
& ( ( var @ ( esk4_3 @ X77 @ X82 @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ ( lam @ ( esk3_1 @ X77 ) ) )
| ( X77 @ ( esk2_1 @ X77 ) ) )
& ( ~ ( X77 @ ( sub @ ( esk4_3 @ X77 @ X82 @ X83 ) @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ ( lam @ ( esk3_1 @ X77 ) ) )
| ( X77 @ ( esk2_1 @ X77 ) ) )
& ( ( var @ ( esk4_3 @ X77 @ X82 @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ X81 )
| ( X77 @ ( sub @ ( esk3_1 @ X77 ) @ ( push @ X81 @ id ) ) )
| ~ ( X77 @ ( ap @ ( esk1_1 @ X77 ) @ ( esk2_1 @ X77 ) ) ) )
& ( ~ ( X77 @ ( sub @ ( esk4_3 @ X77 @ X82 @ X83 ) @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ X81 )
| ( X77 @ ( sub @ ( esk3_1 @ X77 ) @ ( push @ X81 @ id ) ) )
| ~ ( X77 @ ( ap @ ( esk1_1 @ X77 ) @ ( esk2_1 @ X77 ) ) ) )
& ( ( var @ ( esk4_3 @ X77 @ X82 @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ ( lam @ ( esk3_1 @ X77 ) ) )
| ~ ( X77 @ ( ap @ ( esk1_1 @ X77 ) @ ( esk2_1 @ X77 ) ) ) )
& ( ~ ( X77 @ ( sub @ ( esk4_3 @ X77 @ X82 @ X83 ) @ X83 ) )
| ( X77 @ ( sub @ X82 @ X83 ) )
| ~ ( X77 @ ( lam @ ( esk3_1 @ X77 ) ) )
| ~ ( X77 @ ( ap @ ( esk1_1 @ X77 ) @ ( esk2_1 @ X77 ) ) ) )
& ( ~ ( var @ X86 )
| ( epred1_0 @ X86 ) )
& ( ~ ( epred1_0 @ X87 )
| ~ ( epred1_0 @ X88 )
| ( epred1_0 @ ( ap @ X87 @ X88 ) ) )
& ( ( epred1_0 @ ( esk5_1 @ X89 ) )
| ( epred1_0 @ ( lam @ X89 ) ) )
& ( ~ ( epred1_0 @ ( sub @ X89 @ ( push @ ( esk5_1 @ X89 ) @ id ) ) )
| ( epred1_0 @ ( lam @ X89 ) ) )
& ~ ( epred1_0 @ esk6_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X6: term > $o,X1: term,X3: subst,X2: term] :
( ( var @ ( esk4_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk2_1 @ X6 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( esk5_1 @ X1 ) )
| ( epred1_0 @ ( lam @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X6: term > $o,X1: term,X3: subst,X2: term] :
( ( var @ ( esk4_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk1_1 @ X6 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( lam @ X1 ) )
| ~ ( epred1_0 @ ( sub @ X1 @ ( push @ ( esk5_1 @ X1 ) @ id ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ ( esk5_1 @ X1 ) @ id ) ) )
| ( var @ ( esk4_3 @ epred1_0 @ X2 @ X3 ) )
| ( epred1_0 @ ( esk2_1 @ epred1_0 ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ( epred1_0 @ ( lam @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( var @ ( esk4_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk2_1 @ X6 ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ ( esk5_1 @ X1 ) @ id ) ) )
| ( var @ ( esk4_3 @ epred1_0 @ X2 @ X3 ) )
| ( epred1_0 @ ( esk1_1 @ epred1_0 ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ( epred1_0 @ ( lam @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
thf(c_0_16,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( var @ ( esk4_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk1_1 @ X6 ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
! [X1: term,X6: term > $o,X3: subst,X2: term] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk2_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk4_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_18,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_19,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ X1 )
| ~ ( var @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_20,negated_conjecture,
! [X1: term,X3: subst] :
( ( var @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) )
| ( epred1_0 @ ( esk2_1 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_21,negated_conjecture,
! [X1: term,X6: term > $o,X3: subst,X2: term] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ( X6 @ ( esk1_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk4_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_22,negated_conjecture,
! [X1: term,X3: subst] :
( ( var @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) )
| ( epred1_0 @ ( esk1_1 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_16]) ).
thf(c_0_23,negated_conjecture,
! [X6: term > $o,X2: term,X1: term] :
( ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X1 @ id ) ) )
| ( X6 @ ( esk2_1 @ X6 ) )
| ( X6 @ X2 )
| ~ ( X6 @ ( esk4_3 @ X6 @ X2 @ id ) )
| ~ ( X6 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
thf(c_0_24,negated_conjecture,
! [X1: term,X3: subst] :
( ( epred1_0 @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( esk2_1 @ epred1_0 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_25,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk2_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk4_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_26,negated_conjecture,
! [X6: term > $o,X2: term,X1: term] :
( ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X1 @ id ) ) )
| ( X6 @ ( esk1_1 @ X6 ) )
| ( X6 @ X2 )
| ~ ( X6 @ ( esk4_3 @ X6 @ X2 @ id ) )
| ~ ( X6 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_18]) ).
thf(c_0_27,negated_conjecture,
! [X1: term,X3: subst] :
( ( epred1_0 @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( esk1_1 @ epred1_0 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
thf(c_0_28,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( esk1_1 @ X6 ) )
| ~ ( X6 @ ( sub @ ( esk4_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_29,negated_conjecture,
! [X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ ( esk2_1 @ epred1_0 ) )
| ( epred1_0 @ X2 )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18])]) ).
thf(c_0_30,negated_conjecture,
! [X1: term,X6: term > $o] :
( ( X6 @ ( esk2_1 @ X6 ) )
| ( X6 @ X1 )
| ~ ( X6 @ ( esk4_3 @ X6 @ X1 @ id ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_18]) ).
thf(c_0_31,negated_conjecture,
! [X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ ( esk1_1 @ epred1_0 ) )
| ( epred1_0 @ X2 )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18])]) ).
thf(c_0_32,negated_conjecture,
! [X1: term,X6: term > $o] :
( ( X6 @ ( esk1_1 @ X6 ) )
| ( X6 @ X1 )
| ~ ( X6 @ ( esk4_3 @ X6 @ X1 @ id ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_18]) ).
thf(c_0_33,negated_conjecture,
! [X1: term,X2: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ ( esk5_1 @ X1 ) @ id ) ) )
| ( epred1_0 @ ( esk2_1 @ epred1_0 ) )
| ( epred1_0 @ ( lam @ X1 ) )
| ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_10]) ).
thf(c_0_34,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( esk2_1 @ epred1_0 ) )
| ( epred1_0 @ X1 )
| ~ ( epred1_0 @ ( lam @ ( esk3_1 @ epred1_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_18])]) ).
thf(c_0_35,negated_conjecture,
! [X1: term,X2: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ ( esk5_1 @ X1 ) @ id ) ) )
| ( epred1_0 @ ( esk1_1 @ epred1_0 ) )
| ( epred1_0 @ ( lam @ X1 ) )
| ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_10]) ).
thf(c_0_36,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( esk1_1 @ epred1_0 ) )
| ( epred1_0 @ X1 )
| ~ ( epred1_0 @ ( lam @ ( esk3_1 @ epred1_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_18])]) ).
thf(c_0_37,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( esk2_1 @ epred1_0 ) )
| ( epred1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_33]),c_0_34]) ).
thf(c_0_38,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( esk1_1 @ epred1_0 ) )
| ( epred1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_35]),c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X3: subst,X2: term,X1: term,X6: term > $o] :
( ( var @ ( esk4_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ~ ( X6 @ X2 )
| ~ ( X6 @ ( ap @ ( esk1_1 @ X6 ) @ ( esk2_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_40,negated_conjecture,
! [X1: term,X2: term] :
( ( epred1_0 @ ( ap @ X1 @ X2 ) )
| ~ ( epred1_0 @ X1 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_41,negated_conjecture,
epred1_0 @ ( esk2_1 @ epred1_0 ),
inference(ef,[status(thm)],[c_0_37]) ).
thf(c_0_42,negated_conjecture,
epred1_0 @ ( esk1_1 @ epred1_0 ),
inference(ef,[status(thm)],[c_0_38]) ).
thf(c_0_43,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( var @ ( esk4_3 @ epred1_0 @ X2 @ X3 ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).
thf(c_0_44,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( var @ ( esk4_3 @ X6 @ X1 @ X3 ) )
| ( X6 @ ( sub @ X1 @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) )
| ~ ( X6 @ ( ap @ ( esk1_1 @ X6 ) @ ( esk2_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_45,negated_conjecture,
! [X1: term,X3: subst,X2: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ( X6 @ ( sub @ ( esk3_1 @ X6 ) @ ( push @ X2 @ id ) ) )
| ~ ( X6 @ ( sub @ ( esk4_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ X2 )
| ~ ( X6 @ ( ap @ ( esk1_1 @ X6 ) @ ( esk2_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_46,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ ( esk5_1 @ X1 ) @ id ) ) )
| ( var @ ( esk4_3 @ epred1_0 @ X2 @ X3 ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ( epred1_0 @ ( lam @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_10]) ).
thf(c_0_47,negated_conjecture,
! [X1: term,X3: subst] :
( ( var @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) )
| ~ ( epred1_0 @ ( lam @ ( esk3_1 @ epred1_0 ) ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_40]),c_0_16]),c_0_14]) ).
thf(c_0_48,negated_conjecture,
! [X3: subst,X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ ( sub @ X2 @ X3 ) )
| ~ ( epred1_0 @ ( sub @ ( esk4_3 @ epred1_0 @ X2 @ X3 ) @ X3 ) )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_40]),c_0_41]),c_0_42])]) ).
thf(c_0_49,negated_conjecture,
! [X1: term,X3: subst] :
( ( var @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_46]),c_0_47]) ).
thf(c_0_50,negated_conjecture,
! [X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ X2 )
| ~ ( epred1_0 @ ( esk4_3 @ epred1_0 @ X2 @ id ) )
| ~ ( epred1_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_18]),c_0_18]) ).
thf(c_0_51,negated_conjecture,
! [X1: term,X3: subst] :
( ( epred1_0 @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) )
| ( epred1_0 @ ( sub @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_49]) ).
thf(c_0_52,negated_conjecture,
! [X2: term,X1: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ X1 @ id ) ) )
| ( epred1_0 @ X2 )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_18])]) ).
thf(c_0_53,negated_conjecture,
! [X1: term,X2: term] :
( ( epred1_0 @ ( sub @ ( esk3_1 @ epred1_0 ) @ ( push @ ( esk5_1 @ X1 ) @ id ) ) )
| ( epred1_0 @ ( lam @ X1 ) )
| ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_10]) ).
thf(c_0_54,negated_conjecture,
! [X3: subst,X1: term,X6: term > $o] :
( ( X6 @ ( sub @ X1 @ X3 ) )
| ~ ( X6 @ ( sub @ ( esk4_3 @ X6 @ X1 @ X3 ) @ X3 ) )
| ~ ( X6 @ ( lam @ ( esk3_1 @ X6 ) ) )
| ~ ( X6 @ ( ap @ ( esk1_1 @ X6 ) @ ( esk2_1 @ X6 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_55,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( lam @ ( esk3_1 @ epred1_0 ) ) )
| ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_53]) ).
thf(c_0_56,negated_conjecture,
! [X1: term,X3: subst] :
( ( epred1_0 @ ( sub @ X1 @ X3 ) )
| ~ ( epred1_0 @ ( sub @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) @ X3 ) )
| ~ ( epred1_0 @ ( lam @ ( esk3_1 @ epred1_0 ) ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_28]),c_0_25]) ).
thf(c_0_57,negated_conjecture,
epred1_0 @ ( lam @ ( esk3_1 @ epred1_0 ) ),
inference(ef,[status(thm)],[c_0_55]) ).
thf(c_0_58,negated_conjecture,
! [X1: term,X3: subst] :
( ( epred1_0 @ ( sub @ X1 @ X3 ) )
| ~ ( epred1_0 @ ( sub @ ( esk4_3 @ epred1_0 @ X1 @ X3 ) @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
thf(c_0_59,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ X1 )
| ~ ( epred1_0 @ ( esk4_3 @ epred1_0 @ X1 @ id ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_18]),c_0_18]) ).
thf(c_0_60,negated_conjecture,
~ ( epred1_0 @ esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_61,negated_conjecture,
! [X1: term] : ( epred1_0 @ X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_18])]) ).
thf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG253^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n010.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 17:33:03 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.26 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.I5smYmN8Zt/E---3.1_3180284.p
% 0.31/0.30 % Version: 3.5.1-ho
% 0.31/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.31/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.31/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.31/0.30 % Starting post_as_ho5 with 300s (1) cores
% 0.31/0.30 % Starting post_as_ho10 with 300s (1) cores
% 0.31/0.30 % post_as_ho5 with pid 3180299 completed with status 0
% 0.31/0.30 % Result found by post_as_ho5
% 0.31/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.31/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.31/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.31/0.30 % Starting post_as_ho5 with 300s (1) cores
% 0.31/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.31/0.30 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.31/0.30 % Search class: HGUSF-FFMF31-MHFMMMBN
% 0.31/0.30 % partial match(1): HGUSS-FFMF31-MHFMMMBN
% 0.31/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.31/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.31/0.30 % SubtermCWHack with pid 3180301 completed with status 0
% 0.31/0.30 % Result found by SubtermCWHack
% 0.31/0.30 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.31/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.31/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.31/0.30 % Starting post_as_ho5 with 300s (1) cores
% 0.31/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.31/0.30 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.31/0.30 % Search class: HGUSF-FFMF31-MHFMMMBN
% 0.31/0.30 % partial match(1): HGUSS-FFMF31-MHFMMMBN
% 0.31/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.31/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.31/0.30 % Preprocessing time : 0.001 s
% 0.31/0.30
% 0.31/0.30 % Proof found!
% 0.31/0.30 % SZS status Theorem
% 0.31/0.30 % SZS output start CNFRefutation
% See solution above
% 0.31/0.30 % Parsed axioms : 238
% 0.31/0.30 % Removed by relevancy pruning/SinE : 233
% 0.31/0.30 % Initial clauses : 18
% 0.31/0.30 % Removed in clause preprocessing : 0
% 0.31/0.30 % Initial clauses in saturation : 18
% 0.31/0.30 % Processed clauses : 75
% 0.31/0.30 % ...of these trivial : 2
% 0.31/0.30 % ...subsumed : 2
% 0.31/0.30 % ...remaining for further processing : 71
% 0.31/0.30 % Other redundant clauses eliminated : 0
% 0.31/0.30 % Clauses deleted for lack of memory : 0
% 0.31/0.30 % Backward-subsumed : 34
% 0.31/0.30 % Backward-rewritten : 19
% 0.31/0.30 % Generated clauses : 372
% 0.31/0.30 % ...of the previous two non-redundant : 234
% 0.31/0.30 % ...aggressively subsumed : 0
% 0.31/0.30 % Contextual simplify-reflections : 9
% 0.31/0.30 % Paramodulations : 354
% 0.31/0.30 % Factorizations : 18
% 0.31/0.30 % NegExts : 0
% 0.31/0.30 % Equation resolutions : 0
% 0.31/0.30 % Disequality decompositions : 0
% 0.31/0.30 % Total rewrite steps : 193
% 0.31/0.30 % ...of those cached : 168
% 0.31/0.30 % Propositional unsat checks : 0
% 0.31/0.30 % Propositional check models : 0
% 0.31/0.30 % Propositional check unsatisfiable : 0
% 0.31/0.30 % Propositional clauses : 0
% 0.31/0.30 % Propositional clauses after purity: 0
% 0.31/0.30 % Propositional unsat core size : 0
% 0.31/0.30 % Propositional preprocessing time : 0.000
% 0.31/0.30 % Propositional encoding time : 0.000
% 0.31/0.30 % Propositional solver time : 0.000
% 0.31/0.30 % Success case prop preproc time : 0.000
% 0.31/0.30 % Success case prop encoding time : 0.000
% 0.31/0.30 % Success case prop solver time : 0.000
% 0.31/0.30 % Current number of processed clauses : 18
% 0.31/0.30 % Positive orientable unit clauses : 2
% 0.31/0.30 % Positive unorientable unit clauses: 0
% 0.31/0.30 % Negative unit clauses : 0
% 0.31/0.30 % Non-unit-clauses : 16
% 0.31/0.30 % Current number of unprocessed clauses: 39
% 0.31/0.30 % ...number of literals in the above : 174
% 0.31/0.30 % Current number of archived formulas : 0
% 0.31/0.30 % Current number of archived clauses : 53
% 0.31/0.30 % Clause-clause subsumption calls (NU) : 442
% 0.31/0.30 % Rec. Clause-clause subsumption calls : 230
% 0.31/0.30 % Non-unit clause-clause subsumptions : 40
% 0.31/0.30 % Unit Clause-clause subsumption calls : 10
% 0.31/0.30 % Rewrite failures with RHS unbound : 0
% 0.31/0.30 % BW rewrite match attempts : 26
% 0.31/0.30 % BW rewrite match successes : 23
% 0.31/0.30 % Condensation attempts : 0
% 0.31/0.30 % Condensation successes : 0
% 0.31/0.30 % Termbank termtop insertions : 16138
% 0.31/0.30 % Search garbage collected termcells : 2398
% 0.31/0.30
% 0.31/0.30 % -------------------------------------------------
% 0.31/0.30 % User time : 0.010 s
% 0.31/0.30 % System time : 0.005 s
% 0.31/0.30 % Total time : 0.015 s
% 0.31/0.30 % Maximum resident set size: 4236 pages
% 0.31/0.30
% 0.31/0.30 % -------------------------------------------------
% 0.31/0.30 % User time : 0.019 s
% 0.31/0.30 % System time : 0.009 s
% 0.31/0.30 % Total time : 0.029 s
% 0.31/0.30 % Maximum resident set size: 5120 pages
% 0.31/0.30 % E exiting
%------------------------------------------------------------------------------