%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV021^6 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:34:44 AM UTC 2026
% Result : Theorem 1.83s 0.57s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 2
% Syntax : Number of formulae : 91 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 398 ( 9 equ; 0 cnn)
% Maximal formula atoms : 58 ( 4 avg)
% Number of connectives : 959 ( 143 ~; 196 |; 47 &; 550 @)
% ( 4 <=>; 18 =>; 0 <=; 1 <~>)
% Maximal formula depth : 32 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 156 ( 6 ^; 138 !; 12 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
cP: ( a > $o ) > $o ).
thf(decl_24,type,
cQ: a > a > $o ).
thf(decl_25,type,
esk1_1: ( a > $o ) > a ).
thf(decl_26,type,
epred1_1: a > a > $o ).
thf(decl_27,type,
epred2_0: a > $o ).
thf(decl_28,type,
esk2_0: a ).
thf(decl_29,type,
esk3_0: a ).
thf(decl_30,type,
epred3_0: a > $o ).
thf(decl_31,type,
esk4_0: a ).
thf(decl_32,type,
epred4_2: a > a > a > $o ).
thf(decl_40,type,
esk12_1: a > a ).
thf(cTHM262_D_EXT2_pme,conjecture,
( ! [X4: a > $o,X5: a > $o] :
( ( ( X4 = X5 )
& ( cP @ X4 ) )
=> ( cP @ X5 ) )
=> ( ( ! [X6: a > $o] :
( ( cP @ X6 )
=> ? [X7: a] : ( X6 @ X7 ) )
& ! [X8: a] :
? [X6: a > $o] :
( ( cP @ X6 )
& ( X6 @ X8 ) )
& ! [X8: a,X9: a,X6: a > $o,X10: a > $o] :
( ( ( cP @ X6 )
& ( cP @ X10 )
& ( X6 @ X8 )
& ( X10 @ X8 )
& ( X6 @ X9 ) )
=> ( X10 @ X9 ) ) )
=> ( ( ^ [X11: a > $o] :
( ? [X7: a] : ( X11 @ X7 )
& ! [X8: a] :
( ( X11 @ X8 )
=> ! [X9: a] :
( ( X11 @ X9 )
<=> ( cQ @ X8 @ X9 ) ) ) ) )
= cP ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uEORJhsUVh/E---3.1_433150.p',cTHM262_D_EXT2_pme) ).
thf(cQ_def,axiom,
( cQ
= ( ^ [X1: a,X2: a] :
? [X3: a > $o] :
( ( cP @ X3 )
& ( X3 @ X1 )
& ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uEORJhsUVh/E---3.1_433150.p',cQ_def) ).
thf(c_0_2,negated_conjecture,
~ ( ! [X4: a > $o,X5: a > $o] :
( ( ( X4 = X5 )
& ( cP @ X4 ) )
=> ( cP @ X5 ) )
=> ( ( ! [X6: a > $o] :
( ( cP @ X6 )
=> ? [X7: a] : ( X6 @ X7 ) )
& ! [X8: a] :
? [X6: a > $o] :
( ( cP @ X6 )
& ( X6 @ X8 ) )
& ! [X8: a,X9: a,X6: a > $o,X10: a > $o] :
( ( ( cP @ X6 )
& ( cP @ X10 )
& ( X6 @ X8 )
& ( X10 @ X8 )
& ( X6 @ X9 ) )
=> ( X10 @ X9 ) ) )
=> ( ( ^ [X11: a > $o] :
( ? [X7: a] : ( X11 @ X7 )
& ! [X8: a] :
( ( X11 @ X8 )
=> ! [X9: a] :
( ( X11 @ X9 )
<=> ( cQ @ X8 @ X9 ) ) ) ) )
= cP ) ) ),
inference(assume_negation,[status(cth)],[cTHM262_D_EXT2_pme]) ).
thf(c_0_3,plain,
( cQ
= ( ^ [Z0: a,Z1: a] :
? [X3: a > $o] :
( ( cP @ X3 )
& ( X3 @ Z0 )
& ( X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cQ_def]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X4: a > $o,X5: a > $o] :
( ( ( X4 = X5 )
& ( cP @ X4 ) )
=> ( cP @ X5 ) )
=> ( ( ! [X6: a > $o] :
( ( cP @ X6 )
=> ? [X7: a] : ( X6 @ X7 ) )
& ! [X8: a] :
? [X6: a > $o] :
( ( cP @ X6 )
& ( X6 @ X8 ) )
& ! [X8: a,X9: a,X6: a > $o,X10: a > $o] :
( ( ( cP @ X6 )
& ( cP @ X10 )
& ( X6 @ X8 )
& ( X10 @ X8 )
& ( X6 @ X9 ) )
=> ( X10 @ X9 ) ) )
=> ! [X23: a > $o] :
( ( ? [X7: a] : ( X23 @ X7 )
& ! [X8: a] :
( ( X23 @ X8 )
=> ! [X9: a] :
( ( X23 @ X9 )
<=> ? [X22: a > $o] :
( ( cP @ X22 )
& ( X22 @ X8 )
& ( X22 @ X9 ) ) ) ) )
<=> ( cP @ X23 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2]),c_0_3])]) ).
thf(c_0_5,negated_conjecture,
! [X24: a > $o,X25: a > $o,X26: a > $o,X28: a,X30: a,X31: a,X32: a > $o,X33: a > $o,X35: a,X38: a > $o,X41: a,X42: a,X44: a > $o] :
( ( ( X24 != X25 )
| ~ ( cP @ X24 )
| ( cP @ X25 ) )
& ( ~ ( cP @ X26 )
| ( X26 @ ( esk1_1 @ X26 ) ) )
& ( cP @ ( epred1_1 @ X28 ) )
& ( epred1_1 @ X28 @ X28 )
& ( ~ ( cP @ X32 )
| ~ ( cP @ X33 )
| ~ ( X32 @ X30 )
| ~ ( X33 @ X30 )
| ~ ( X32 @ X31 )
| ( X33 @ X31 ) )
& ( ( epred2_0 @ esk2_0 )
| ~ ( epred2_0 @ X35 )
| ~ ( cP @ epred2_0 ) )
& ( ~ ( epred2_0 @ esk3_0 )
| ~ ( cP @ X38 )
| ~ ( X38 @ esk2_0 )
| ~ ( X38 @ esk3_0 )
| ~ ( epred2_0 @ X35 )
| ~ ( cP @ epred2_0 ) )
& ( ( cP @ epred3_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X35 )
| ~ ( cP @ epred2_0 ) )
& ( ( epred3_0 @ esk2_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X35 )
| ~ ( cP @ epred2_0 ) )
& ( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X35 )
| ~ ( cP @ epred2_0 ) )
& ( ( epred2_0 @ esk4_0 )
| ( cP @ epred2_0 ) )
& ( ( cP @ ( epred4_2 @ X41 @ X42 ) )
| ~ ( epred2_0 @ X42 )
| ~ ( epred2_0 @ X41 )
| ( cP @ epred2_0 ) )
& ( ( epred4_2 @ X41 @ X42 @ X41 )
| ~ ( epred2_0 @ X42 )
| ~ ( epred2_0 @ X41 )
| ( cP @ epred2_0 ) )
& ( ( epred4_2 @ X41 @ X42 @ X42 )
| ~ ( epred2_0 @ X42 )
| ~ ( epred2_0 @ X41 )
| ( cP @ epred2_0 ) )
& ( ~ ( cP @ X44 )
| ~ ( X44 @ X41 )
| ~ ( X44 @ X42 )
| ( epred2_0 @ X42 )
| ~ ( epred2_0 @ X41 )
| ( cP @ epred2_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(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: a,X4: a > $o,X3: a > $o,X2: a] :
( ( X4 @ X2 )
| ~ ( cP @ X3 )
| ~ ( cP @ X4 )
| ~ ( X3 @ X1 )
| ~ ( X4 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: a] : ( cP @ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: a,X2: a,X3: a > $o,X7: a] :
( ( epred1_1 @ X1 @ X2 )
| ~ ( epred1_1 @ X1 @ X7 )
| ~ ( cP @ X3 )
| ~ ( X3 @ X2 )
| ~ ( X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: a] : ( epred1_1 @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
! [X3: a > $o,X2: a,X1: a] :
( ( epred1_1 @ X1 @ X2 )
| ~ ( cP @ X3 )
| ~ ( X3 @ X2 )
| ~ ( X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X7: a,X2: a,X1: a] :
( ( epred1_1 @ X1 @ X2 )
| ~ ( epred1_1 @ X7 @ X2 )
| ~ ( epred1_1 @ X7 @ X1 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X3: a > $o] :
( ( X3 @ ( esk1_1 @ X3 ) )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,negated_conjecture,
! [X3: a > $o,X2: a,X1: a] :
( ( epred2_0 @ X2 )
| ( cP @ epred2_0 )
| ~ ( cP @ X3 )
| ~ ( X3 @ X1 )
| ~ ( X3 @ X2 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_14,negated_conjecture,
! [X2: a,X1: a] :
( ( epred1_1 @ X1 @ X2 )
| ~ ( epred1_1 @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X1: a] : ( epred1_1 @ X1 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
thf(c_0_16,negated_conjecture,
! [X1: a,X3: a > $o,X2: a] :
( ( epred2_0 @ X1 )
| ~ ( cP @ X3 )
| ~ ( epred2_0 @ X2 )
| ~ ( X3 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(csr,[status(thm)],[c_0_13,c_0_6]) ).
thf(c_0_17,negated_conjecture,
! [X1: a] : ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) @ X1 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: a,X2: a,X7: a] :
( ( epred2_0 @ X1 )
| ~ ( epred1_1 @ X2 @ X1 )
| ~ ( epred1_1 @ X2 @ X7 )
| ~ ( epred2_0 @ X7 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_7]) ).
thf(c_0_19,negated_conjecture,
! [X2: a,X1: a] :
( ( cP @ ( epred4_2 @ X1 @ X2 ) )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X2 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_20,negated_conjecture,
( ( epred2_0 @ esk4_0 )
| ( cP @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_21,negated_conjecture,
! [X2: a,X1: a] :
( ( epred1_1 @ X1 @ X2 )
| ~ ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ X2 ) ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
thf(c_0_22,negated_conjecture,
! [X2: a,X1: a] :
( ( epred4_2 @ X1 @ X2 @ X1 )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X2 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_23,negated_conjecture,
! [X1: a,X2: a] :
( ( epred2_0 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) )
| ~ ( epred1_1 @ X1 @ X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
thf(c_0_24,negated_conjecture,
! [X1: a] :
( ( cP @ ( epred4_2 @ X1 @ esk4_0 ) )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_25,negated_conjecture,
! [X2: a,X1: a] :
( ( epred4_2 @ X1 @ X2 @ X2 )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X2 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_26,negated_conjecture,
! [X1: a] : ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) ) ) @ X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
thf(c_0_27,negated_conjecture,
! [X1: a] :
( ( epred4_2 @ X1 @ esk4_0 @ X1 )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
thf(c_0_28,negated_conjecture,
! [X1: a] :
( ( epred2_0 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) )
| ~ ( epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_9]) ).
thf(c_0_29,negated_conjecture,
( ( cP @ ( epred4_2 @ esk4_0 @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
thf(c_0_30,negated_conjecture,
! [X1: a] :
( ( epred4_2 @ X1 @ esk4_0 @ esk4_0 )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
thf(c_0_31,negated_conjecture,
! [X1: a,X3: a > $o,X2: a] :
( ( epred1_1 @ X1 @ X2 )
| ~ ( X3 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) )
| ~ ( cP @ X3 )
| ~ ( X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
thf(c_0_32,negated_conjecture,
! [X1: a] : ( epred1_1 @ X1 @ ( esk1_1 @ ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
thf(c_0_33,negated_conjecture,
! [X1: a] :
( ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) @ esk4_0 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_34,negated_conjecture,
! [X1: a] :
( ( cP @ ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) @ esk4_0 ) )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
thf(c_0_35,negated_conjecture,
! [X1: a,X3: a > $o,X2: a] :
( ( epred4_2 @ esk4_0 @ esk4_0 @ X1 )
| ( cP @ epred2_0 )
| ~ ( epred4_2 @ esk4_0 @ esk4_0 @ X2 )
| ~ ( cP @ X3 )
| ~ ( X3 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_29]) ).
thf(c_0_36,negated_conjecture,
( ( epred4_2 @ esk4_0 @ esk4_0 @ esk4_0 )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
thf(c_0_37,negated_conjecture,
! [X1: a,X2: a] :
( ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ X1 ) ) @ X2 )
| ~ ( epred1_1 @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_7])]) ).
thf(c_0_38,negated_conjecture,
( ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) @ esk4_0 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
thf(c_0_39,negated_conjecture,
( ( cP @ ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
thf(c_0_40,negated_conjecture,
! [X3: a > $o,X1: a] :
( ( epred4_2 @ esk4_0 @ esk4_0 @ X1 )
| ( cP @ epred2_0 )
| ~ ( cP @ X3 )
| ~ ( X3 @ esk4_0 )
| ~ ( X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X1: a,X2: a,X7: a] :
( ( epred2_0 @ X1 )
| ~ ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ X2 ) ) @ X7 )
| ~ ( epred1_1 @ X2 @ X1 )
| ~ ( epred2_0 @ X7 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_37]) ).
thf(c_0_42,negated_conjecture,
! [X1: a] :
( ( epred1_1 @ esk4_0 @ X1 )
| ( cP @ epred2_0 )
| ~ ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) @ esk4_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_39]) ).
thf(c_0_43,negated_conjecture,
( ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) @ esk4_0 @ ( esk1_1 @ ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) @ esk4_0 ) ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_39]) ).
thf(c_0_44,negated_conjecture,
! [X2: a,X1: a] :
( ( epred4_2 @ esk4_0 @ esk4_0 @ X1 )
| ( cP @ epred2_0 )
| ~ ( epred1_1 @ X2 @ esk4_0 )
| ~ ( epred1_1 @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_7]) ).
thf(c_0_45,plain,
! [X1: a] :
( ( cP @ epred2_0 )
| ( ( epred4_2 @ X1 @ esk4_0 )
!= epred2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(ext_eqfact,[status(thm)],[c_0_24]) ).
thf(c_0_46,negated_conjecture,
! [X1: a,X2: a] :
( ( epred2_0 @ X1 )
| ~ ( epred1_1 @ X2 @ X1 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_17]) ).
thf(c_0_47,negated_conjecture,
( ( epred1_1 @ esk4_0 @ ( esk1_1 @ ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) @ esk4_0 ) ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_48,negated_conjecture,
! [X1: a] :
( ( epred4_2 @ esk4_0 @ esk4_0 @ X1 )
| ( cP @ epred2_0 )
| ~ ( epred1_1 @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_9]) ).
thf(c_0_49,plain,
! [X1: a] :
( ( cP @ epred2_0 )
| ( ( epred4_2 @ X1 @ esk4_0 @ ( esk12_1 @ X1 ) )
<~> ( epred2_0 @ ( esk12_1 @ X1 ) ) )
| ~ ( epred2_0 @ X1 ) ),
inference(neg_ext,[status(thm)],[c_0_45]) ).
thf(c_0_50,negated_conjecture,
( ( epred2_0 @ ( esk1_1 @ ( epred4_2 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) @ esk4_0 ) ) )
| ( cP @ epred2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20]) ).
thf(c_0_51,negated_conjecture,
( ( epred4_2 @ esk4_0 @ esk4_0 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_15]) ).
thf(c_0_52,plain,
! [X1: a] :
( ( epred4_2 @ X1 @ esk4_0 @ ( esk12_1 @ X1 ) )
| ( epred2_0 @ ( esk12_1 @ X1 ) )
| ( cP @ epred2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_49]) ).
thf(c_0_53,negated_conjecture,
! [X2: a,X1: a] :
( ( epred2_0 @ X1 )
| ~ ( epred2_0 @ ( esk1_1 @ ( epred1_1 @ X2 ) ) )
| ~ ( epred1_1 @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_9]) ).
thf(c_0_54,negated_conjecture,
( ( epred2_0 @ ( esk1_1 @ ( epred1_1 @ esk4_0 ) ) )
| ( cP @ epred2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_47]),c_0_50]) ).
thf(c_0_55,negated_conjecture,
! [X1: a] :
( ( epred1_1 @ esk4_0 @ X1 )
| ( cP @ epred2_0 )
| ~ ( epred4_2 @ esk4_0 @ esk4_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_51]),c_0_29]) ).
thf(c_0_56,negated_conjecture,
( ( epred4_2 @ esk4_0 @ esk4_0 @ ( esk12_1 @ esk4_0 ) )
| ( epred2_0 @ ( esk12_1 @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_20]) ).
thf(c_0_57,negated_conjecture,
! [X1: a] :
( ( cP @ epred2_0 )
| ( epred2_0 @ X1 )
| ~ ( epred1_1 @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_58,negated_conjecture,
( ( epred2_0 @ ( esk12_1 @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
thf(c_0_59,negated_conjecture,
( ( cP @ ( epred4_2 @ ( esk12_1 @ esk4_0 ) @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_58]) ).
thf(c_0_60,negated_conjecture,
! [X2: a,X1: a] :
( ( cP @ epred2_0 )
| ( epred1_1 @ X1 @ X2 )
| ~ ( epred4_2 @ ( esk12_1 @ esk4_0 ) @ esk4_0 @ X2 )
| ~ ( epred4_2 @ ( esk12_1 @ esk4_0 ) @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_59]) ).
thf(c_0_61,negated_conjecture,
( ( epred4_2 @ ( esk12_1 @ esk4_0 ) @ esk4_0 @ esk4_0 )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
thf(c_0_62,negated_conjecture,
! [X1: a] :
( ( epred1_1 @ X1 @ esk4_0 )
| ( cP @ epred2_0 )
| ~ ( epred4_2 @ ( esk12_1 @ esk4_0 ) @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_63,negated_conjecture,
( ( epred4_2 @ ( esk12_1 @ esk4_0 ) @ esk4_0 @ ( esk12_1 @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_58]) ).
thf(c_0_64,negated_conjecture,
( ( epred1_1 @ ( esk12_1 @ esk4_0 ) @ esk4_0 )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_65,negated_conjecture,
( ( epred1_1 @ esk4_0 @ ( esk12_1 @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_64]) ).
thf(c_0_66,plain,
! [X1: a] :
( ( cP @ epred2_0 )
| ~ ( epred4_2 @ X1 @ esk4_0 @ ( esk12_1 @ X1 ) )
| ~ ( epred2_0 @ ( esk12_1 @ X1 ) )
| ~ ( epred2_0 @ X1 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_49]) ).
thf(c_0_67,negated_conjecture,
( ( epred4_2 @ esk4_0 @ esk4_0 @ ( esk12_1 @ esk4_0 ) )
| ( cP @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_65]) ).
thf(c_0_68,negated_conjecture,
! [X1: a] :
( ( epred2_0 @ esk2_0 )
| ~ ( epred2_0 @ X1 )
| ~ ( cP @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_69,plain,
cP @ epred2_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_20]),c_0_58]) ).
thf(c_0_70,negated_conjecture,
! [X1: a] :
( ( cP @ epred3_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X1 )
| ~ ( cP @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_71,negated_conjecture,
! [X1: a] :
( ( epred2_0 @ esk2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
thf(c_0_72,negated_conjecture,
epred2_0 @ ( esk1_1 @ epred2_0 ),
inference(spm,[status(thm)],[c_0_12,c_0_69]) ).
thf(c_0_73,negated_conjecture,
! [X1: a] :
( ( epred2_0 @ esk3_0 )
| ( cP @ epred3_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_69])]) ).
thf(c_0_74,negated_conjecture,
epred2_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_75,negated_conjecture,
! [X1: a] :
( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X1 )
| ~ ( cP @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_76,negated_conjecture,
( ( cP @ epred3_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_77,negated_conjecture,
! [X1: a] :
( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_69])]) ).
thf(c_0_78,negated_conjecture,
! [X1: a] :
( ( epred3_0 @ esk2_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X1 )
| ~ ( cP @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_79,negated_conjecture,
! [X2: a,X1: a] :
( ( epred2_0 @ esk3_0 )
| ( epred1_1 @ X1 @ X2 )
| ~ ( epred3_0 @ X2 )
| ~ ( epred3_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_76]) ).
thf(c_0_80,negated_conjecture,
( ( epred2_0 @ esk3_0 )
| ( epred3_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_77,c_0_74]) ).
thf(c_0_81,negated_conjecture,
! [X1: a] :
( ( epred3_0 @ esk2_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_69])]) ).
thf(c_0_82,negated_conjecture,
! [X3: a > $o,X1: a] :
( ~ ( epred2_0 @ esk3_0 )
| ~ ( cP @ X3 )
| ~ ( X3 @ esk2_0 )
| ~ ( X3 @ esk3_0 )
| ~ ( epred2_0 @ X1 )
| ~ ( cP @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_83,negated_conjecture,
! [X1: a] :
( ( epred1_1 @ X1 @ esk3_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred3_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_84,negated_conjecture,
( ( epred2_0 @ esk3_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_74]) ).
thf(c_0_85,negated_conjecture,
! [X3: a > $o] :
( ~ ( cP @ epred2_0 )
| ~ ( epred2_0 @ esk3_0 )
| ~ ( cP @ X3 )
| ~ ( X3 @ esk2_0 )
| ~ ( X3 @ esk3_0 ) ),
inference(condense,[status(thm)],[c_0_82]) ).
thf(c_0_86,negated_conjecture,
( ( epred1_1 @ esk2_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
thf(c_0_87,negated_conjecture,
! [X3: a > $o] :
( ~ ( epred2_0 @ esk3_0 )
| ~ ( cP @ X3 )
| ~ ( X3 @ esk2_0 )
| ~ ( X3 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_69])]) ).
thf(c_0_88,negated_conjecture,
epred2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_86]),c_0_74])]) ).
thf(c_0_89,negated_conjecture,
! [X3: a > $o] :
( ~ ( cP @ X3 )
| ~ ( X3 @ esk2_0 )
| ~ ( X3 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88])]) ).
thf(c_0_90,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_69]),c_0_74]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV021^6 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n017.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:56:21 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.uEORJhsUVh/E---3.1_433150.p
% 1.83/0.57 % Version: 3.5.1-ho
% 1.83/0.57 % Preprocessing class: HSMSSMSSSLSNHHA.
% 1.83/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.83/0.57 % Starting sh3 with 1500s (5) cores
% 1.83/0.57 % Starting lpo8_s with 300s (1) cores
% 1.83/0.57 % Starting lpo6_lambda_fix with 300s (1) cores
% 1.83/0.57 % Starting pre_casc_5 with 300s (1) cores
% 1.83/0.57 % sh3 with pid 433163 completed with status 0
% 1.83/0.57 % Result found by sh3
% 1.83/0.57 % Preprocessing class: HSMSSMSSSLSNHHA.
% 1.83/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.83/0.57 % Starting sh3 with 1500s (5) cores
% 1.83/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.83/0.57 % No SInE strategy applied
% 1.83/0.57 % Search class: HGHNS-FFSF11-SHHFMSBN
% 1.83/0.57 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.83/0.57 % Starting SubtermCWHack with 151s (1) cores
% 1.83/0.57 % Starting sh3 with 750s (1) cores
% 1.83/0.57 % Starting lpo1_def_fix with 188s (1) cores
% 1.83/0.57 % Starting post_as_ho9 with 188s (1) cores
% 1.83/0.57 % Starting lpo8_s with 188s (1) cores
% 1.83/0.57 % lpo8_s with pid 433174 completed with status 0
% 1.83/0.57 % Result found by lpo8_s
% 1.83/0.57 % Preprocessing class: HSMSSMSSSLSNHHA.
% 1.83/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.83/0.57 % Starting sh3 with 1500s (5) cores
% 1.83/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.83/0.57 % No SInE strategy applied
% 1.83/0.57 % Search class: HGHNS-FFSF11-SHHFMSBN
% 1.83/0.57 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.83/0.57 % Starting SubtermCWHack with 151s (1) cores
% 1.83/0.57 % Starting sh3 with 750s (1) cores
% 1.83/0.57 % Starting lpo1_def_fix with 188s (1) cores
% 1.83/0.57 % Starting post_as_ho9 with 188s (1) cores
% 1.83/0.57 % Starting lpo8_s with 188s (1) cores
% 1.83/0.57 % Preprocessing time : 0.001 s
% 1.83/0.57 % Presaturation interreduction done
% 1.83/0.57
% 1.83/0.57 % Proof found!
% 1.83/0.57 % SZS status Theorem
% 1.83/0.57 % SZS output start CNFRefutation
% See solution above
% 1.83/0.57 % Parsed axioms : 5
% 1.83/0.57 % Removed by relevancy pruning/SinE : 0
% 1.83/0.57 % Initial clauses : 18
% 1.83/0.57 % Removed in clause preprocessing : 4
% 1.83/0.57 % Initial clauses in saturation : 14
% 1.83/0.57 % Processed clauses : 1579
% 1.83/0.57 % ...of these trivial : 15
% 1.83/0.57 % ...subsumed : 1007
% 1.83/0.57 % ...remaining for further processing : 557
% 1.83/0.57 % Other redundant clauses eliminated : 0
% 1.83/0.57 % Clauses deleted for lack of memory : 0
% 1.83/0.57 % Backward-subsumed : 45
% 1.83/0.57 % Backward-rewritten : 337
% 1.83/0.57 % Generated clauses : 6432
% 1.83/0.57 % ...of the previous two non-redundant : 6066
% 1.83/0.57 % ...aggressively subsumed : 0
% 1.83/0.57 % Contextual simplify-reflections : 37
% 1.83/0.57 % Paramodulations : 6276
% 1.83/0.57 % Factorizations : 0
% 1.83/0.57 % NegExts : 44
% 1.83/0.57 % Equation resolutions : 0
% 1.83/0.57 % Disequality decompositions : 0
% 1.83/0.57 % Total rewrite steps : 726
% 1.83/0.57 % ...of those cached : 628
% 1.83/0.57 % Propositional unsat checks : 0
% 1.83/0.57 % Propositional check models : 0
% 1.83/0.57 % Propositional check unsatisfiable : 0
% 1.83/0.57 % Propositional clauses : 0
% 1.83/0.57 % Propositional clauses after purity: 0
% 1.83/0.57 % Propositional unsat core size : 0
% 1.83/0.57 % Propositional preprocessing time : 0.000
% 1.83/0.57 % Propositional encoding time : 0.000
% 1.83/0.57 % Propositional solver time : 0.000
% 1.83/0.57 % Success case prop preproc time : 0.000
% 1.83/0.57 % Success case prop encoding time : 0.000
% 1.83/0.57 % Success case prop solver time : 0.000
% 1.83/0.57 % Current number of processed clauses : 142
% 1.83/0.57 % Positive orientable unit clauses : 16
% 1.83/0.57 % Positive unorientable unit clauses: 0
% 1.83/0.57 % Negative unit clauses : 0
% 1.83/0.57 % Non-unit-clauses : 126
% 1.83/0.57 % Current number of unprocessed clauses: 3019
% 1.83/0.57 % ...number of literals in the above : 10425
% 1.83/0.57 % Current number of archived formulas : 0
% 1.83/0.57 % Current number of archived clauses : 415
% 1.83/0.57 % Clause-clause subsumption calls (NU) : 53779
% 1.83/0.57 % Rec. Clause-clause subsumption calls : 30572
% 1.83/0.57 % Non-unit clause-clause subsumptions : 1120
% 1.83/0.57 % Unit Clause-clause subsumption calls : 16
% 1.83/0.57 % Rewrite failures with RHS unbound : 0
% 1.83/0.57 % BW rewrite match attempts : 111
% 1.83/0.57 % BW rewrite match successes : 3
% 1.83/0.57 % Condensation attempts : 1579
% 1.83/0.57 % Condensation successes : 31
% 1.83/0.57 % Termbank termtop insertions : 139177
% 1.83/0.57 % Search garbage collected termcells : 738
% 1.83/0.57
% 1.83/0.57 % -------------------------------------------------
% 1.83/0.57 % User time : 0.205 s
% 1.83/0.57 % System time : 0.012 s
% 1.83/0.57 % Total time : 0.217 s
% 1.83/0.57 % Maximum resident set size: 3640 pages
% 1.83/0.57
% 1.83/0.57 % -------------------------------------------------
% 1.83/0.57 % User time : 1.361 s
% 1.83/0.57 % System time : 0.050 s
% 1.83/0.57 % Total time : 1.411 s
% 1.83/0.57 % Maximum resident set size: 4864 pages
% 1.83/0.57 % E exiting
%------------------------------------------------------------------------------