%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO246^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:44:04 AM UTC 2026
% Result : Theorem 0.47s 0.39s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 62 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 2 equ; 0 cnn)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 645 ( 64 ~; 116 |; 20 &; 420 @)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 336 ( 336 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 127 ( 4 ^; 105 !; 18 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
epred1_1: ( ( ( a > $o ) > $o ) > $o ) > ( a > $o ) > $o ).
thf(decl_24,type,
epred2_1: ( ( ( a > $o ) > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(decl_25,type,
epred3_0: ( ( a > $o ) > $o ) > $o ).
thf(decl_26,type,
epred4_0: ( a > $o ) > $o ).
thf(decl_27,type,
epred5_1: ( ( a > $o ) > $o ) > a > $o ).
thf(decl_28,type,
esk1_0: a ).
thf(decl_29,type,
epred6_0: ( a > $o ) > $o ).
thf(decl_30,type,
epred7_1: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(decl_31,type,
epred8_1: ( ( a > $o ) > $o ) > a > $o ).
thf(decl_32,type,
epred9_0: ( ( a > $o ) > $o ) > a > $o ).
thf(cTHM535,conjecture,
( ! [X1: ( ( a > $o ) > $o ) > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ? [X3: a > $o] : ( X2 @ X3 ) )
=> ? [X4: ( ( a > $o ) > $o ) > a > $o] :
! [X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X2 @ ( X4 @ X2 ) ) ) )
=> ! [X5: ( ( a > $o ) > $o ) > $o] :
( ( ? [X2: ( a > $o ) > $o] : ( X5 @ X2 )
& ! [X2: ( a > $o ) > $o] :
( ( X5 @ X2 )
=> ? [X6: a > $o] : ( X2 @ X6 ) ) )
=> ( ( ^ [X7: a] :
! [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
=> ? [X9: a > $o] :
( ( X8 @ X9 )
& ( X9 @ X7 ) ) ) )
= ( ^ [X7: a] :
? [X4: ( ( a > $o ) > $o ) > a > $o] :
! [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
=> ( ( X8 @ ( X4 @ X8 ) )
& ( X4 @ X8 @ X7 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3jevS3idKG/E---3.1_321106.p',cTHM535) ).
thf(c_0_1,negated_conjecture,
~ ( ! [X1: ( ( a > $o ) > $o ) > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ? [X3: a > $o] : ( X2 @ X3 ) )
=> ? [X4: ( ( a > $o ) > $o ) > a > $o] :
! [X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X2 @ ( X4 @ X2 ) ) ) )
=> ! [X5: ( ( a > $o ) > $o ) > $o] :
( ( ? [X2: ( a > $o ) > $o] : ( X5 @ X2 )
& ! [X2: ( a > $o ) > $o] :
( ( X5 @ X2 )
=> ? [X6: a > $o] : ( X2 @ X6 ) ) )
=> ( ( ^ [X7: a] :
! [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
=> ? [X9: a > $o] :
( ( X8 @ X9 )
& ( X9 @ X7 ) ) ) )
= ( ^ [X7: a] :
? [X4: ( ( a > $o ) > $o ) > a > $o] :
! [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
=> ( ( X8 @ ( X4 @ X8 ) )
& ( X4 @ X8 @ X7 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM535]) ).
thf(c_0_2,negated_conjecture,
~ ( ! [X1: ( ( a > $o ) > $o ) > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ? [X3: a > $o] : ( X2 @ X3 ) )
=> ? [X4: ( ( a > $o ) > $o ) > a > $o] :
! [X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X2 @ ( X4 @ X2 ) ) ) )
=> ! [X5: ( ( a > $o ) > $o ) > $o] :
( ( ? [X2: ( a > $o ) > $o] : ( X5 @ X2 )
& ! [X2: ( a > $o ) > $o] :
( ( X5 @ X2 )
=> ? [X6: a > $o] : ( X2 @ X6 ) ) )
=> ! [X19: a] :
( ! [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
=> ? [X9: a > $o] :
( ( X8 @ X9 )
& ( X9 @ X19 ) ) )
<=> ? [X4: ( ( a > $o ) > $o ) > a > $o] :
! [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
=> ( ( X8 @ ( X4 @ X8 ) )
& ( X4 @ X8 @ X19 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X20: ( ( a > $o ) > $o ) > $o,X22: a > $o,X24: ( a > $o ) > $o,X27: ( a > $o ) > $o,X31: a > $o,X32: ( ( a > $o ) > $o ) > a > $o,X34: ( a > $o ) > $o,X37: ( a > $o ) > $o] :
( ( ( X20 @ ( epred1_1 @ X20 ) )
| ~ ( X20 @ X24 )
| ( X24 @ ( epred2_1 @ X20 @ X24 ) ) )
& ( ~ ( epred1_1 @ X20 @ X22 )
| ~ ( X20 @ X24 )
| ( X24 @ ( epred2_1 @ X20 @ X24 ) ) )
& ( epred3_0 @ epred4_0 )
& ( ~ ( epred3_0 @ X27 )
| ( X27 @ ( epred5_1 @ X27 ) ) )
& ( ( epred3_0 @ ( epred7_1 @ X32 ) )
| ( epred3_0 @ epred6_0 ) )
& ( ~ ( epred7_1 @ X32 @ ( X32 @ ( epred7_1 @ X32 ) ) )
| ~ ( X32 @ ( epred7_1 @ X32 ) @ esk1_0 )
| ( epred3_0 @ epred6_0 ) )
& ( ( epred3_0 @ ( epred7_1 @ X32 ) )
| ~ ( epred6_0 @ X31 )
| ~ ( X31 @ esk1_0 ) )
& ( ~ ( epred7_1 @ X32 @ ( X32 @ ( epred7_1 @ X32 ) ) )
| ~ ( X32 @ ( epred7_1 @ X32 ) @ esk1_0 )
| ~ ( epred6_0 @ X31 )
| ~ ( X31 @ esk1_0 ) )
& ( ( X37 @ ( epred9_0 @ X37 ) )
| ~ ( epred3_0 @ X37 )
| ( X34 @ ( epred8_1 @ X34 ) )
| ~ ( epred3_0 @ X34 ) )
& ( ( epred9_0 @ X37 @ esk1_0 )
| ~ ( epred3_0 @ X37 )
| ( X34 @ ( epred8_1 @ X34 ) )
| ~ ( epred3_0 @ X34 ) )
& ( ( X37 @ ( epred9_0 @ X37 ) )
| ~ ( epred3_0 @ X37 )
| ( epred8_1 @ X34 @ esk1_0 )
| ~ ( epred3_0 @ X34 ) )
& ( ( epred9_0 @ X37 @ esk1_0 )
| ~ ( epred3_0 @ X37 )
| ( epred8_1 @ X34 @ esk1_0 )
| ~ ( epred3_0 @ X34 ) ) ),
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_2])])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X2: ( a > $o ) > $o,X8: ( a > $o ) > $o] :
( ( X2 @ ( epred9_0 @ X2 ) )
| ( X8 @ ( epred8_1 @ X8 ) )
| ~ ( epred3_0 @ X2 )
| ~ ( epred3_0 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred3_0 @ ( epred7_1 @ X4 ) )
| ( epred3_0 @ epred6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X2: ( a > $o ) > $o,X8: ( a > $o ) > $o] :
( ( X2 @ ( epred9_0 @ X2 ) )
| ( epred8_1 @ X8 @ esk1_0 )
| ~ ( epred3_0 @ X2 )
| ~ ( epred3_0 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X2: ( a > $o ) > $o,X8: ( a > $o ) > $o] :
( ( epred9_0 @ X2 @ esk1_0 )
| ( X8 @ ( epred8_1 @ X8 ) )
| ~ ( epred3_0 @ X2 )
| ~ ( epred3_0 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X2: ( a > $o ) > $o,X8: ( a > $o ) > $o] :
( ( epred9_0 @ X2 @ esk1_0 )
| ( epred8_1 @ X8 @ esk1_0 )
| ~ ( epred3_0 @ X2 )
| ~ ( epred3_0 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred3_0 @ epred6_0 )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_10,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred8_1 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred3_0 @ epred6_0 )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
thf(c_0_11,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred9_0 @ X2 @ esk1_0 )
| ( epred3_0 @ epred6_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
thf(c_0_12,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred8_1 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred9_0 @ X2 @ esk1_0 )
| ( epred3_0 @ epred6_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
thf(c_0_13,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred3_0 @ epred6_0 )
| ~ ( epred7_1 @ X4 @ ( X4 @ ( epred7_1 @ X4 ) ) )
| ~ ( X4 @ ( epred7_1 @ X4 ) @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_14,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) )
| ( epred7_1 @ X13 @ ( epred8_1 @ ( epred7_1 @ X13 ) ) )
| ( epred3_0 @ epred6_0 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_5]) ).
thf(c_0_15,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) )
| ( epred8_1 @ ( epred7_1 @ X13 ) @ esk1_0 )
| ( epred3_0 @ epred6_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_5]) ).
thf(c_0_16,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred9_0 @ ( epred7_1 @ X13 ) @ esk1_0 )
| ( epred3_0 @ epred6_0 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_5]) ).
thf(c_0_17,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred9_0 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred8_1 @ ( epred7_1 @ X13 ) @ esk1_0 )
| ( epred3_0 @ epred6_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_5]) ).
thf(c_0_18,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) )
| ( epred3_0 @ epred6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred9_0 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred3_0 @ epred6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_17]) ).
thf(c_0_20,negated_conjecture,
epred3_0 @ epred6_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X2: ( a > $o ) > $o] :
( ( epred6_0 @ ( epred8_1 @ epred6_0 ) )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_20]) ).
thf(c_0_22,negated_conjecture,
! [X2: ( a > $o ) > $o] :
( ( epred8_1 @ epred6_0 @ esk1_0 )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X3: a > $o] :
( ( epred3_0 @ ( epred7_1 @ X4 ) )
| ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_24,negated_conjecture,
( ( epred6_0 @ ( epred9_0 @ epred6_0 ) )
| ( epred6_0 @ ( epred8_1 @ epred6_0 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
thf(c_0_25,negated_conjecture,
( ( epred6_0 @ ( epred9_0 @ epred6_0 ) )
| ( epred8_1 @ epred6_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred6_0 @ ( epred9_0 @ epred6_0 ) )
| ( epred3_0 @ ( epred7_1 @ X4 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
thf(c_0_27,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred6_0 @ ( epred9_0 @ epred6_0 ) )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_26]) ).
thf(c_0_28,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred8_1 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred6_0 @ ( epred9_0 @ epred6_0 ) )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X3: a > $o] :
( ~ ( epred7_1 @ X4 @ ( X4 @ ( epred7_1 @ X4 ) ) )
| ~ ( X4 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_30,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred6_0 @ ( epred9_0 @ epred6_0 ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
thf(c_0_31,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred8_1 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred6_0 @ ( epred9_0 @ epred6_0 ) ) ),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
thf(c_0_32,negated_conjecture,
! [X2: ( a > $o ) > $o] :
( ( epred6_0 @ ( epred8_1 @ epred6_0 ) )
| ( epred9_0 @ X2 @ esk1_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_20]) ).
thf(c_0_33,negated_conjecture,
! [X2: ( a > $o ) > $o] :
( ( epred8_1 @ epred6_0 @ esk1_0 )
| ( epred9_0 @ X2 @ esk1_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_20]) ).
thf(c_0_34,negated_conjecture,
! [X3: a > $o] :
( ( epred6_0 @ ( epred9_0 @ epred6_0 ) )
| ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_35,negated_conjecture,
( ( epred9_0 @ epred6_0 @ esk1_0 )
| ( epred6_0 @ ( epred8_1 @ epred6_0 ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
thf(c_0_36,negated_conjecture,
( ( epred9_0 @ epred6_0 @ esk1_0 )
| ( epred8_1 @ epred6_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
thf(c_0_37,negated_conjecture,
epred6_0 @ ( epred9_0 @ epred6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_24]) ).
thf(c_0_38,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred9_0 @ epred6_0 @ esk1_0 )
| ( epred3_0 @ ( epred7_1 @ X4 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_35]),c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] : ( epred3_0 @ ( epred7_1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_37]),c_0_38]) ).
thf(c_0_40,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred9_0 @ X2 @ esk1_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_39]) ).
thf(c_0_41,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred8_1 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred9_0 @ X2 @ esk1_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_39]) ).
thf(c_0_42,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) )
| ( epred8_1 @ epred6_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
thf(c_0_43,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred9_0 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred8_1 @ epred6_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
thf(c_0_44,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_39]) ).
thf(c_0_45,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X2: ( a > $o ) > $o] :
( ( epred8_1 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( X2 @ ( epred9_0 @ X2 ) )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_39]) ).
thf(c_0_46,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred9_0 @ epred6_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
thf(c_0_47,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] :
( ( epred8_1 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred9_0 @ epred6_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
thf(c_0_48,negated_conjecture,
! [X3: a > $o] :
( ( epred8_1 @ epred6_0 @ esk1_0 )
| ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42]),c_0_43]) ).
thf(c_0_49,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) )
| ( epred7_1 @ X13 @ ( epred8_1 @ ( epred7_1 @ X13 ) ) ) ),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
thf(c_0_50,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) )
| ( epred8_1 @ ( epred7_1 @ X13 ) @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_39]) ).
thf(c_0_51,negated_conjecture,
! [X3: a > $o] :
( ( epred9_0 @ epred6_0 @ esk1_0 )
| ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_46]),c_0_47]) ).
thf(c_0_52,negated_conjecture,
epred8_1 @ epred6_0 @ esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_37]),c_0_36]) ).
thf(c_0_53,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred7_1 @ X4 @ ( epred8_1 @ ( epred7_1 @ X4 ) ) )
| ( epred9_0 @ ( epred7_1 @ X13 ) @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_39]) ).
thf(c_0_54,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X13: ( ( a > $o ) > $o ) > a > $o] :
( ( epred9_0 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ( epred8_1 @ ( epred7_1 @ X13 ) @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
thf(c_0_55,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X3: a > $o] :
( ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) )
| ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_49]),c_0_50]) ).
thf(c_0_56,negated_conjecture,
epred9_0 @ epred6_0 @ esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_35]),c_0_52])]) ).
thf(c_0_57,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o,X3: a > $o] :
( ( epred9_0 @ ( epred7_1 @ X4 ) @ esk1_0 )
| ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_53]),c_0_54]) ).
thf(c_0_58,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] : ( epred7_1 @ X4 @ ( epred9_0 @ ( epred7_1 @ X4 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_56])]) ).
thf(c_0_59,negated_conjecture,
! [X4: ( ( a > $o ) > $o ) > a > $o] : ( epred9_0 @ ( epred7_1 @ X4 ) @ esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_37]),c_0_56])]) ).
thf(c_0_60,negated_conjecture,
! [X3: a > $o] :
( ~ ( epred6_0 @ X3 )
| ~ ( X3 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_58]),c_0_59])]) ).
thf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_37]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO246^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n011.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:41:01 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.33 Running higher-order theorem proving
% 0.25/0.35 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.3jevS3idKG/E---3.1_321106.p
% 0.47/0.39 % Version: 3.5.1-ho
% 0.47/0.39 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.47/0.39 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.47/0.39 % Starting sh2lt with 1200s (4) cores
% 0.47/0.39 % Starting new_ho_10_unif with 300s (1) cores
% 0.47/0.39 % Starting full_lambda_6 with 300s (1) cores
% 0.47/0.39 % Starting post_as_ho1 with 300s (1) cores
% 0.47/0.39 % Starting ehoh_best3_rw with 300s (1) cores
% 0.47/0.39 % sh2lt with pid 321122 completed with status 0
% 0.47/0.39 % Result found by sh2lt
% 0.47/0.39 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.47/0.39 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.47/0.39 % Starting sh2lt with 1200s (4) cores
% 0.47/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.47/0.39 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.47/0.39 % Search class: HGHNF-FFSF00-SHHFFMBN
% 0.47/0.39 % Scheduled 5 strats onto 4 cores with 1200 seconds (1200 total)
% 0.47/0.39 % Starting SubtermCWHack with 121s (1) cores
% 0.47/0.39 % Starting new_ho_10 with 721s (1) cores
% 0.47/0.39 % Starting full_lambda_3 with 121s (1) cores
% 0.47/0.39 % Starting ho_unfolding_6 with 121s (1) cores
% 0.47/0.39 % SubtermCWHack with pid 321127 completed with status 0
% 0.47/0.39 % Result found by SubtermCWHack
% 0.47/0.39 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.47/0.39 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.47/0.39 % Starting sh2lt with 1200s (4) cores
% 0.47/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.47/0.39 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.47/0.39 % Search class: HGHNF-FFSF00-SHHFFMBN
% 0.47/0.39 % Scheduled 5 strats onto 4 cores with 1200 seconds (1200 total)
% 0.47/0.39 % Starting SubtermCWHack with 121s (1) cores
% 0.47/0.39 % Preprocessing time : 0.001 s
% 0.47/0.39
% 0.47/0.39 % Proof found!
% 0.47/0.39 % SZS status Theorem
% 0.47/0.39 % SZS output start CNFRefutation
% See solution above
% 0.47/0.39 % Parsed axioms : 2
% 0.47/0.39 % Removed by relevancy pruning/SinE : 1
% 0.47/0.39 % Initial clauses : 12
% 0.47/0.39 % Removed in clause preprocessing : 0
% 0.47/0.39 % Initial clauses in saturation : 12
% 0.47/0.39 % Processed clauses : 192
% 0.47/0.39 % ...of these trivial : 0
% 0.47/0.39 % ...subsumed : 46
% 0.47/0.39 % ...remaining for further processing : 146
% 0.47/0.39 % Other redundant clauses eliminated : 0
% 0.47/0.39 % Clauses deleted for lack of memory : 0
% 0.47/0.39 % Backward-subsumed : 43
% 0.47/0.39 % Backward-rewritten : 71
% 0.47/0.39 % Generated clauses : 282
% 0.47/0.39 % ...of the previous two non-redundant : 273
% 0.47/0.39 % ...aggressively subsumed : 0
% 0.47/0.39 % Contextual simplify-reflections : 31
% 0.47/0.39 % Paramodulations : 278
% 0.47/0.39 % Factorizations : 0
% 0.47/0.39 % NegExts : 0
% 0.47/0.39 % Equation resolutions : 0
% 0.47/0.39 % Disequality decompositions : 0
% 0.47/0.39 % Total rewrite steps : 96
% 0.47/0.39 % ...of those cached : 81
% 0.47/0.39 % Propositional unsat checks : 0
% 0.47/0.39 % Propositional check models : 0
% 0.47/0.39 % Propositional check unsatisfiable : 0
% 0.47/0.39 % Propositional clauses : 0
% 0.47/0.39 % Propositional clauses after purity: 0
% 0.47/0.39 % Propositional unsat core size : 0
% 0.47/0.39 % Propositional preprocessing time : 0.000
% 0.47/0.39 % Propositional encoding time : 0.000
% 0.47/0.39 % Propositional solver time : 0.000
% 0.47/0.39 % Success case prop preproc time : 0.000
% 0.47/0.39 % Success case prop encoding time : 0.000
% 0.47/0.39 % Success case prop solver time : 0.000
% 0.47/0.39 % Current number of processed clauses : 32
% 0.47/0.39 % Positive orientable unit clauses : 14
% 0.47/0.39 % Positive unorientable unit clauses: 0
% 0.47/0.39 % Negative unit clauses : 0
% 0.47/0.39 % Non-unit-clauses : 18
% 0.47/0.39 % Current number of unprocessed clauses: 5
% 0.47/0.39 % ...number of literals in the above : 14
% 0.47/0.39 % Current number of archived formulas : 0
% 0.47/0.39 % Current number of archived clauses : 115
% 0.47/0.39 % Clause-clause subsumption calls (NU) : 618
% 0.47/0.39 % Rec. Clause-clause subsumption calls : 409
% 0.47/0.39 % Non-unit clause-clause subsumptions : 99
% 0.47/0.39 % Unit Clause-clause subsumption calls : 57
% 0.47/0.39 % Rewrite failures with RHS unbound : 0
% 0.47/0.39 % BW rewrite match attempts : 14
% 0.47/0.39 % BW rewrite match successes : 14
% 0.47/0.39 % Condensation attempts : 0
% 0.47/0.39 % Condensation successes : 0
% 0.47/0.39 % Termbank termtop insertions : 6729
% 0.47/0.39 % Search garbage collected termcells : 474
% 0.47/0.39
% 0.47/0.39 % -------------------------------------------------
% 0.47/0.39 % User time : 0.017 s
% 0.47/0.39 % System time : 0.003 s
% 0.47/0.39 % Total time : 0.020 s
% 0.47/0.39 % Maximum resident set size: 3896 pages
% 0.47/0.39
% 0.47/0.39 % -------------------------------------------------
% 0.47/0.39 % User time : 0.049 s
% 0.47/0.39 % System time : 0.011 s
% 0.47/0.39 % Total time : 0.060 s
% 0.47/0.39 % Maximum resident set size: 4864 pages
% 0.47/0.39 % E exiting
%------------------------------------------------------------------------------