%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:11:59 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 13 equ; 0 cnn)
% Maximal formula atoms : 38 ( 3 avg)
% Number of connectives : 957 ( 117 ~; 207 |; 16 &; 606 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 175 ( 28 ^; 147 !; 0 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_29,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_53,type,
transitive: ( $i > $i > $o ) > $o ).
thf(decl_63,type,
epred1_0: $i > $i > $o ).
thf(decl_64,type,
epred2_0: $i > $o ).
thf(decl_65,type,
esk1_0: $i ).
thf(decl_66,type,
esk2_0: $i ).
thf(decl_67,type,
esk3_0: $i ).
thf(decl_68,type,
esk4_0: $i ).
thf(decl_69,type,
esk5_0: $i ).
thf(decl_70,type,
esk6_0: $i ).
thf(decl_71,type,
esk7_2: ( $i > $o ) > $i > $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WwiWgMQo5j/E---3.1_4031228.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WwiWgMQo5j/E---3.1_4031228.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WwiWgMQo5j/E---3.1_4031228.p',mor) ).
thf(thm,conjecture,
! [X10: $i > $i > $o] :
( ! [X28: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X10 @ X28 ) @ ( mbox @ X10 @ ( mbox @ X10 @ X28 ) ) ) )
<=> ( transitive @ X10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.WwiWgMQo5j/E---3.1_4031228.p',thm) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WwiWgMQo5j/E---3.1_4031228.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WwiWgMQo5j/E---3.1_4031228.p',mvalid) ).
thf(transitive,axiom,
( transitive
= ( ^ [X10: $i > $i > $o] :
! [X1: $i,X36: $i,X33: $i] :
( ( ( X10 @ X1 @ X36 )
& ( X10 @ X36 @ X33 ) )
=> ( X10 @ X1 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WwiWgMQo5j/E---3.1_4031228.p',transitive) ).
thf(c_0_7,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_8,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_9,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_10,negated_conjecture,
~ ! [X10: $i > $i > $o] :
( ! [X28: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X10 @ X28 ) @ ( mbox @ X10 @ ( mbox @ X10 @ X28 ) ) ) )
<=> ( transitive @ X10 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_11,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_12,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X12: $i] :
( ( Z0 @ Z2 @ X12 )
=> ( Z1 @ X12 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_13,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_14,plain,
( transitive
= ( ^ [Z0: $i > $i > $o] :
! [X1: $i,X36: $i,X33: $i] :
( ( ( Z0 @ X1 @ X36 )
& ( Z0 @ X36 @ X33 ) )
=> ( Z0 @ X1 @ X33 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_15,negated_conjecture,
~ ! [X10: $i > $i > $o] :
( ! [X28: $i > $o,X60: $i] :
( ~ ! [X57: $i] :
( ( X10 @ X60 @ X57 )
=> ( X28 @ X57 ) )
| ! [X59: $i] :
( ( X10 @ X60 @ X59 )
=> ! [X58: $i] :
( ( X10 @ X59 @ X58 )
=> ( X28 @ X58 ) ) ) )
<=> ! [X61: $i,X62: $i,X63: $i] :
( ( ( X10 @ X61 @ X62 )
& ( X10 @ X62 @ X63 ) )
=> ( X10 @ X61 @ X63 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X67: $i,X73: $i > $o,X74: $i,X76: $i,X77: $i,X78: $i,X79: $i,X80: $i] :
( ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ~ ( epred1_0 @ esk1_0 @ X67 )
| ( epred2_0 @ X67 ) )
& ( ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ esk1_0 @ X67 )
| ( epred2_0 @ X67 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred1_0 @ esk1_0 @ X67 )
| ( epred2_0 @ X67 ) )
& ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) )
& ( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ~ ( epred2_0 @ esk3_0 ) )
& ( ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred2_0 @ esk3_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred2_0 @ esk3_0 ) )
& ( ( epred1_0 @ X74 @ ( esk7_2 @ X73 @ X74 ) )
| ~ ( epred1_0 @ X74 @ X76 )
| ~ ( epred1_0 @ X76 @ X77 )
| ( X73 @ X77 )
| ~ ( epred1_0 @ X78 @ X79 )
| ~ ( epred1_0 @ X79 @ X80 )
| ( epred1_0 @ X78 @ X80 ) )
& ( ~ ( X73 @ ( esk7_2 @ X73 @ X74 ) )
| ~ ( epred1_0 @ X74 @ X76 )
| ~ ( epred1_0 @ X76 @ X77 )
| ( X73 @ X77 )
| ~ ( epred1_0 @ X78 @ X79 )
| ~ ( epred1_0 @ X79 @ X80 )
| ( epred1_0 @ X78 @ X80 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i > $o,X1: $i,X3: $i,X15: $i,X13: $i,X12: $i,X20: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( X2 @ X12 )
| ( epred1_0 @ X13 @ X20 )
| ~ ( epred1_0 @ X1 @ X3 )
| ~ ( epred1_0 @ X3 @ X12 )
| ~ ( epred1_0 @ X13 @ X15 )
| ~ ( epred1_0 @ X15 @ X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_18,negated_conjecture,
( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X2: $i > $o,X1: $i,X12: $i,X3: $i,X13: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ X3 @ esk3_0 )
| ( X2 @ X12 )
| ~ ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ X13 @ X12 )
| ~ ( epred1_0 @ X1 @ X13 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ X3 @ esk3_0 )
| ( X2 @ esk3_0 )
| ~ ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( X2 @ esk3_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i > $o,X1: $i,X12: $i,X3: $i,X13: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ X3 @ esk3_0 )
| ( X2 @ X12 )
| ~ ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ X13 @ X12 )
| ~ ( epred1_0 @ X1 @ X13 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i,X15: $i,X13: $i,X12: $i,X20: $i] :
( ( X2 @ X12 )
| ( epred1_0 @ X13 @ X20 )
| ~ ( X2 @ ( esk7_2 @ X2 @ X1 ) )
| ~ ( epred1_0 @ X1 @ X3 )
| ~ ( epred1_0 @ X3 @ X12 )
| ~ ( epred1_0 @ X13 @ X15 )
| ~ ( epred1_0 @ X15 @ X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i > $o] :
( ( epred2_0 @ ( esk7_2 @ X2 @ esk1_0 ) )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( X2 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
thf(c_0_28,negated_conjecture,
( ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ X3 @ esk3_0 )
| ( X2 @ esk3_0 )
| ~ ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
thf(c_0_30,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X3: $i,X15: $i,X13: $i,X12: $i] :
( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ X3 )
| ( epred2_0 @ X12 )
| ~ ( epred1_0 @ esk1_0 @ X13 )
| ~ ( epred1_0 @ X15 @ X3 )
| ~ ( epred1_0 @ X1 @ X15 )
| ~ ( epred1_0 @ X13 @ X12 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_33,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( X2 @ esk3_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X12: $i,X3: $i,X13: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ X1 @ X3 )
| ( epred2_0 @ X12 )
| ~ ( epred1_0 @ esk2_0 @ X12 )
| ~ ( epred1_0 @ X13 @ X3 )
| ~ ( epred1_0 @ X1 @ X13 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
thf(c_0_35,negated_conjecture,
! [X2: $i > $o] :
( ( epred2_0 @ ( esk7_2 @ X2 @ esk1_0 ) )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( X2 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30]) ).
thf(c_0_36,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ~ ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ X3 )
| ~ ( epred1_0 @ X12 @ X3 )
| ~ ( epred1_0 @ X1 @ X12 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_28]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i,X3: $i,X15: $i,X13: $i,X12: $i] :
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ X3 )
| ( epred2_0 @ X12 )
| ~ ( epred1_0 @ esk1_0 @ X13 )
| ~ ( epred1_0 @ X15 @ X3 )
| ~ ( epred1_0 @ X1 @ X15 )
| ~ ( epred1_0 @ X13 @ X12 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_35]),c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_18]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X12: $i,X3: $i,X13: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ X1 @ X3 )
| ( epred2_0 @ X12 )
| ~ ( epred1_0 @ esk2_0 @ X12 )
| ~ ( epred1_0 @ X13 @ X3 )
| ~ ( epred1_0 @ X1 @ X13 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
thf(c_0_41,negated_conjecture,
( ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ X3 )
| ~ ( epred1_0 @ X12 @ X3 )
| ~ ( epred1_0 @ X1 @ X12 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_22]),c_0_36]) ).
thf(c_0_43,negated_conjecture,
epred1_0 @ esk5_0 @ esk6_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_41]),c_0_28]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_22]) ).
thf(c_0_45,negated_conjecture,
! [X2: $i > $o,X1: $i,X12: $i,X3: $i,X13: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ X3 @ esk6_0 )
| ( X2 @ X12 )
| ~ ( epred1_0 @ X3 @ esk5_0 )
| ~ ( epred1_0 @ X13 @ X12 )
| ~ ( epred1_0 @ X1 @ X13 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
thf(c_0_46,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_30]) ).
thf(c_0_47,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ X3 @ esk6_0 )
| ( X2 @ esk6_0 )
| ~ ( epred1_0 @ X3 @ esk5_0 )
| ~ ( epred1_0 @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
thf(c_0_48,negated_conjecture,
epred1_0 @ esk4_0 @ esk5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_46]),c_0_36]) ).
thf(c_0_49,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk4_0 @ esk6_0 )
| ( X2 @ esk6_0 )
| ~ ( epred1_0 @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X12: $i,X15: $i,X13: $i,X3: $i,X20: $i] :
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ X1 @ esk6_0 )
| ( epred1_0 @ X1 @ X3 )
| ( epred1_0 @ X12 @ X13 )
| ~ ( epred1_0 @ X1 @ esk5_0 )
| ~ ( epred1_0 @ X15 @ X13 )
| ~ ( epred1_0 @ X12 @ X15 )
| ~ ( epred1_0 @ X20 @ X3 )
| ~ ( epred1_0 @ X1 @ X20 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i,X3: $i,X12: $i,X13: $i] :
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ X1 @ esk6_0 )
| ( epred1_0 @ X3 @ esk6_0 )
| ( epred1_0 @ X3 @ X12 )
| ~ ( epred1_0 @ X3 @ esk5_0 )
| ~ ( epred1_0 @ X1 @ esk5_0 )
| ~ ( epred1_0 @ X13 @ X12 )
| ~ ( epred1_0 @ X3 @ X13 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
thf(c_0_52,negated_conjecture,
( ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ X1 @ esk6_0 )
| ( epred1_0 @ X3 @ esk6_0 )
| ~ ( epred1_0 @ X1 @ esk5_0 )
| ~ ( epred1_0 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_43]) ).
thf(c_0_54,negated_conjecture,
! [X2: $i > $o,X1: $i,X12: $i,X3: $i,X13: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ X3 @ esk3_0 )
| ( X2 @ X12 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ X13 @ X12 )
| ~ ( epred1_0 @ X1 @ X13 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_52]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ X1 @ esk6_0 )
| ~ ( epred1_0 @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_48]) ).
thf(c_0_56,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ X3 @ esk3_0 )
| ( X2 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_52]) ).
thf(c_0_57,negated_conjecture,
epred1_0 @ esk4_0 @ esk6_0,
inference(spm,[status(thm)],[c_0_55,c_0_48]) ).
thf(c_0_58,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_59,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ X3 @ esk3_0 )
| ( X2 @ esk3_0 )
| ~ ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
thf(c_0_61,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_57])]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_57])]) ).
thf(c_0_63,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( epred1_0 @ X1 @ ( esk7_2 @ X2 @ X1 ) )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( X2 @ esk3_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_64,negated_conjecture,
( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_65,negated_conjecture,
! [X2: $i > $o] :
( ( epred2_0 @ ( esk7_2 @ X2 @ esk1_0 ) )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( X2 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_61])]) ).
thf(c_0_66,negated_conjecture,
~ ( epred2_0 @ esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_57])]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i,X3: $i,X15: $i,X13: $i,X12: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ X3 )
| ( epred2_0 @ X12 )
| ~ ( epred1_0 @ esk1_0 @ X13 )
| ~ ( epred1_0 @ X15 @ X3 )
| ~ ( epred1_0 @ X1 @ X15 )
| ~ ( epred1_0 @ X13 @ X12 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_65]),c_0_66]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i,X12: $i,X3: $i,X13: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ X3 )
| ( epred2_0 @ X12 )
| ~ ( epred1_0 @ esk2_0 @ X12 )
| ~ ( epred1_0 @ X13 @ X3 )
| ~ ( epred1_0 @ X1 @ X13 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_61]) ).
thf(c_0_69,negated_conjecture,
epred1_0 @ esk2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_57])]) ).
thf(c_0_70,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ X3 )
| ~ ( epred1_0 @ X12 @ X3 )
| ~ ( epred1_0 @ X1 @ X12 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_66]) ).
thf(c_0_71,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_69]) ).
thf(c_0_72,negated_conjecture,
epred1_0 @ esk1_0 @ esk3_0,
inference(spm,[status(thm)],[c_0_71,c_0_61]) ).
thf(c_0_73,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_72]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/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 09:14:48 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 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.WwiWgMQo5j/E---3.1_4031228.p
% 0.08/0.17 % Version: 3.5.1-ho
% 0.08/0.17 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.17 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.17 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.17 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.17 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.17 % full_lambda_8 with pid 4031244 completed with status 0
% 0.08/0.17 % Result found by full_lambda_8
% 0.08/0.17 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.17 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.17 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.17 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.17 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.17 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.17 % No SInE strategy applied
% 0.08/0.17 % Search class: HGHNF-FFSS22-SHSSMSBN
% 0.08/0.17 % partial match(1): HGUNF-FFSS22-SHSSMSBN
% 0.08/0.17 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.17 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.17 % SubtermCWHack with pid 4031251 completed with status 0
% 0.08/0.17 % Result found by SubtermCWHack
% 0.08/0.17 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.17 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.17 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.17 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.17 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.17 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.17 % No SInE strategy applied
% 0.08/0.17 % Search class: HGHNF-FFSS22-SHSSMSBN
% 0.08/0.17 % partial match(1): HGUNF-FFSS22-SHSSMSBN
% 0.08/0.17 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.17 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.17 % Preprocessing time : 0.001 s
% 0.08/0.17
% 0.08/0.17 % Proof found!
% 0.08/0.17 % SZS status Theorem
% 0.08/0.17 % SZS output start CNFRefutation
% See solution above
% 0.08/0.17 % Parsed axioms : 78
% 0.08/0.17 % Removed by relevancy pruning/SinE : 0
% 0.08/0.17 % Initial clauses : 55
% 0.08/0.17 % Removed in clause preprocessing : 41
% 0.08/0.17 % Initial clauses in saturation : 14
% 0.08/0.17 % Processed clauses : 280
% 0.08/0.17 % ...of these trivial : 0
% 0.08/0.17 % ...subsumed : 117
% 0.08/0.17 % ...remaining for further processing : 163
% 0.08/0.17 % Other redundant clauses eliminated : 0
% 0.08/0.17 % Clauses deleted for lack of memory : 0
% 0.08/0.17 % Backward-subsumed : 64
% 0.08/0.17 % Backward-rewritten : 63
% 0.08/0.17 % Generated clauses : 644
% 0.08/0.17 % ...of the previous two non-redundant : 632
% 0.08/0.17 % ...aggressively subsumed : 0
% 0.08/0.17 % Contextual simplify-reflections : 15
% 0.08/0.17 % Paramodulations : 644
% 0.08/0.17 % Factorizations : 0
% 0.08/0.17 % NegExts : 0
% 0.08/0.17 % Equation resolutions : 0
% 0.08/0.17 % Disequality decompositions : 0
% 0.08/0.17 % Total rewrite steps : 71
% 0.08/0.17 % ...of those cached : 65
% 0.08/0.17 % Propositional unsat checks : 0
% 0.08/0.17 % Propositional check models : 0
% 0.08/0.17 % Propositional check unsatisfiable : 0
% 0.08/0.17 % Propositional clauses : 0
% 0.08/0.17 % Propositional clauses after purity: 0
% 0.08/0.17 % Propositional unsat core size : 0
% 0.08/0.17 % Propositional preprocessing time : 0.000
% 0.08/0.17 % Propositional encoding time : 0.000
% 0.08/0.17 % Propositional solver time : 0.000
% 0.08/0.17 % Success case prop preproc time : 0.000
% 0.08/0.17 % Success case prop encoding time : 0.000
% 0.08/0.17 % Success case prop solver time : 0.000
% 0.08/0.17 % Current number of processed clauses : 36
% 0.08/0.17 % Positive orientable unit clauses : 7
% 0.08/0.17 % Positive unorientable unit clauses: 0
% 0.08/0.17 % Negative unit clauses : 1
% 0.08/0.17 % Non-unit-clauses : 28
% 0.08/0.17 % Current number of unprocessed clauses: 84
% 0.08/0.17 % ...number of literals in the above : 676
% 0.08/0.17 % Current number of archived formulas : 0
% 0.08/0.17 % Current number of archived clauses : 127
% 0.08/0.17 % Clause-clause subsumption calls (NU) : 1877
% 0.08/0.17 % Rec. Clause-clause subsumption calls : 676
% 0.08/0.17 % Non-unit clause-clause subsumptions : 182
% 0.08/0.17 % Unit Clause-clause subsumption calls : 22
% 0.08/0.17 % Rewrite failures with RHS unbound : 0
% 0.08/0.17 % BW rewrite match attempts : 5
% 0.08/0.17 % BW rewrite match successes : 5
% 0.08/0.17 % Condensation attempts : 0
% 0.08/0.17 % Condensation successes : 0
% 0.08/0.17 % Termbank termtop insertions : 21780
% 0.08/0.17 % Search garbage collected termcells : 535
% 0.08/0.17
% 0.08/0.17 % -------------------------------------------------
% 0.08/0.17 % User time : 0.021 s
% 0.08/0.17 % System time : 0.001 s
% 0.08/0.17 % Total time : 0.023 s
% 0.08/0.17 % Maximum resident set size: 3720 pages
% 0.08/0.17
% 0.08/0.17 % -------------------------------------------------
% 0.08/0.17 % User time : 0.024 s
% 0.08/0.17 % System time : 0.003 s
% 0.08/0.17 % Total time : 0.027 s
% 0.08/0.17 % Maximum resident set size: 5120 pages
% 0.08/0.17 % E exiting
%------------------------------------------------------------------------------