%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV021^5 : 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 : n015.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 233.64s 30.20s
% Output : CNFRefutation 233.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 1
% Syntax : Number of formulae : 70 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 422 ( 11 equ; 0 cnn)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 949 ( 96 ~; 146 |; 37 &; 644 @)
% ( 4 <=>; 18 =>; 0 <=; 4 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 137 ( 2 ^; 123 !; 12 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
cP: ( a > $o ) > $o ).
thf(decl_24,type,
esk1_1: ( a > $o ) > a ).
thf(decl_25,type,
epred1_1: a > a > $o ).
thf(decl_26,type,
epred2_1: ( a > a > $o ) > a > $o ).
thf(decl_27,type,
esk2_1: ( a > a > $o ) > a ).
thf(decl_28,type,
esk3_1: ( a > a > $o ) > a ).
thf(decl_29,type,
esk4_1: ( a > a > $o ) > a ).
thf(decl_30,type,
esk3_2: a > ( a > a > $o ) > a ).
thf(decl_31,type,
esk4_2: a > ( a > a > $o ) > a ).
thf(decl_36,type,
esk9_1: a > a ).
thf(decl_64,type,
esk37_1: a > a ).
thf(cTHM262_D_EXT2_pme,conjecture,
( ! [X1: a > $o,X2: a > $o] :
( ( ( X1 = X2 )
& ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ( ! [X3: a > $o] :
( ( cP @ X3 )
=> ? [X4: a] : ( X3 @ X4 ) )
& ! [X5: a] :
? [X3: a > $o] :
( ( cP @ X3 )
& ( X3 @ X5 ) )
& ! [X5: a,X6: a,X3: a > $o,X7: a > $o] :
( ( ( cP @ X3 )
& ( cP @ X7 )
& ( X3 @ X5 )
& ( X7 @ X5 )
& ( X3 @ X6 ) )
=> ( X7 @ X6 ) ) )
=> ? [X8: a > a > $o] :
( ( ^ [X9: a > $o] :
( ? [X4: a] : ( X9 @ X4 )
& ! [X5: a] :
( ( X9 @ X5 )
=> ! [X6: a] :
( ( X9 @ X6 )
<=> ( X8 @ X5 @ X6 ) ) ) ) )
= cP ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6sBU5Kt6Qn/E---3.1_3635863.p',cTHM262_D_EXT2_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ! [X1: a > $o,X2: a > $o] :
( ( ( X1 = X2 )
& ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ( ! [X3: a > $o] :
( ( cP @ X3 )
=> ? [X4: a] : ( X3 @ X4 ) )
& ! [X5: a] :
? [X3: a > $o] :
( ( cP @ X3 )
& ( X3 @ X5 ) )
& ! [X5: a,X6: a,X3: a > $o,X7: a > $o] :
( ( ( cP @ X3 )
& ( cP @ X7 )
& ( X3 @ X5 )
& ( X7 @ X5 )
& ( X3 @ X6 ) )
=> ( X7 @ X6 ) ) )
=> ? [X8: a > a > $o] :
( ( ^ [X9: a > $o] :
( ? [X4: a] : ( X9 @ X4 )
& ! [X5: a] :
( ( X9 @ X5 )
=> ! [X6: a] :
( ( X9 @ X6 )
<=> ( X8 @ X5 @ X6 ) ) ) ) )
= cP ) ) ),
inference(assume_negation,[status(cth)],[cTHM262_D_EXT2_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ! [X1: a > $o,X2: a > $o] :
( ( ( X1 = X2 )
& ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ( ! [X3: a > $o] :
( ( cP @ X3 )
=> ? [X4: a] : ( X3 @ X4 ) )
& ! [X5: a] :
? [X3: a > $o] :
( ( cP @ X3 )
& ( X3 @ X5 ) )
& ! [X5: a,X6: a,X3: a > $o,X7: a > $o] :
( ( ( cP @ X3 )
& ( cP @ X7 )
& ( X3 @ X5 )
& ( X7 @ X5 )
& ( X3 @ X6 ) )
=> ( X7 @ X6 ) ) )
=> ? [X8: a > a > $o] :
! [X21: a > $o] :
( ( ? [X4: a] : ( X21 @ X4 )
& ! [X5: a] :
( ( X21 @ X5 )
=> ! [X6: a] :
( ( X21 @ X6 )
<=> ( X8 @ X5 @ X6 ) ) ) )
<=> ( cP @ X21 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X22: a > $o,X23: a > $o,X24: a > $o,X26: a,X28: a,X29: a,X30: a > $o,X31: a > $o,X32: a > a > $o,X34: a,X38: a,X39: a,X40: a] :
( ( ( X22 != X23 )
| ~ ( cP @ X22 )
| ( cP @ X23 ) )
& ( ~ ( cP @ X24 )
| ( X24 @ ( esk1_1 @ X24 ) ) )
& ( cP @ ( epred1_1 @ X26 ) )
& ( epred1_1 @ X26 @ X26 )
& ( ~ ( cP @ X30 )
| ~ ( cP @ X31 )
| ~ ( X30 @ X28 )
| ~ ( X31 @ X28 )
| ~ ( X30 @ X29 )
| ( X31 @ X29 ) )
& ( ( epred2_1 @ X32 @ ( esk2_1 @ X32 ) )
| ~ ( epred2_1 @ X32 @ X34 )
| ~ ( cP @ ( epred2_1 @ X32 ) ) )
& ( ~ ( epred2_1 @ X32 @ ( esk3_1 @ X32 ) )
| ~ ( X32 @ ( esk2_1 @ X32 ) @ ( esk3_1 @ X32 ) )
| ~ ( epred2_1 @ X32 @ X34 )
| ~ ( cP @ ( epred2_1 @ X32 ) ) )
& ( ( epred2_1 @ X32 @ ( esk3_1 @ X32 ) )
| ( X32 @ ( esk2_1 @ X32 ) @ ( esk3_1 @ X32 ) )
| ~ ( epred2_1 @ X32 @ X34 )
| ~ ( cP @ ( epred2_1 @ X32 ) ) )
& ( ( epred2_1 @ X32 @ ( esk4_1 @ X32 ) )
| ( cP @ ( epred2_1 @ X32 ) ) )
& ( ~ ( epred2_1 @ X32 @ X39 )
| ( X32 @ X38 @ X39 )
| ~ ( epred2_1 @ X32 @ X38 )
| ( cP @ ( epred2_1 @ X32 ) ) )
& ( ~ ( X32 @ X38 @ X40 )
| ( epred2_1 @ X32 @ X40 )
| ~ ( epred2_1 @ X32 @ X38 )
| ( cP @ ( epred2_1 @ X32 ) ) ) ),
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_2])])])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X8: a > a > $o,X5: a,X4: a] :
( ( epred2_1 @ X8 @ X5 )
| ( cP @ ( epred2_1 @ X8 ) )
| ~ ( X8 @ X4 @ X5 )
| ~ ( epred2_1 @ X8 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X8: a > a > $o] :
( ( epred2_1 @ X8 @ ( esk4_1 @ X8 ) )
| ( cP @ ( epred2_1 @ X8 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: a > $o] :
( ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( cP @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X4: a] : ( cP @ ( epred1_1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X4: a,X8: a > a > $o] :
( ( epred2_1 @ X8 @ ( esk2_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ X4 )
| ~ ( cP @ ( epred2_1 @ X8 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X8: a > a > $o,X4: a] :
( ( cP @ ( epred2_1 @ X8 ) )
| ( epred2_1 @ X8 @ X4 )
| ~ ( X8 @ ( esk4_1 @ X8 ) @ X4 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_10,negated_conjecture,
! [X4: a] : ( epred1_1 @ X4 @ ( esk1_1 @ ( epred1_1 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_11,plain,
! [X4: a,X8: a > a > $o,X5: a] :
( ( epred2_1 @ X8 @ ( esk2_1 @ X8 ) )
| ( ( epred2_1 @ X8 )
!= ( epred1_1 @ X4 ) )
| ~ ( epred2_1 @ X8 @ X5 ) ),
inference(ext_sup,[status(thm)],[c_0_8,c_0_7]) ).
thf(c_0_12,negated_conjecture,
( ( epred2_1 @ epred1_1 @ ( esk1_1 @ ( epred1_1 @ ( esk4_1 @ epred1_1 ) ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,plain,
! [X4: a,X8: a > a > $o,X5: a] :
( ( epred2_1 @ X8 @ ( esk2_1 @ X8 ) )
| ( ( epred1_1 @ X4 @ ( esk3_2 @ X4 @ X8 ) )
<~> ( epred2_1 @ X8 @ ( esk3_2 @ X4 @ X8 ) ) )
| ~ ( epred2_1 @ X8 @ X5 ) ),
inference(neg_ext,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X4: a] :
( ( cP @ ( epred2_1 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ X4 )
| ~ ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ ( esk4_1 @ epred1_1 ) ) ) @ X4 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_12]) ).
thf(c_0_15,plain,
! [X4: a,X8: a > a > $o,X5: a] :
( ( epred2_1 @ X8 @ ( esk3_2 @ X4 @ X8 ) )
| ( epred1_1 @ X4 @ ( esk3_2 @ X4 @ X8 ) )
| ( epred2_1 @ X8 @ ( esk2_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ X5 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
( ( epred2_1 @ epred1_1 @ ( esk1_1 @ ( epred1_1 @ ( esk1_1 @ ( epred1_1 @ ( esk4_1 @ epred1_1 ) ) ) ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
thf(c_0_17,negated_conjecture,
! [X4: a,X8: a > a > $o,X5: a] :
( ( X8 @ X5 @ X4 )
| ( cP @ ( epred2_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ X4 )
| ~ ( epred2_1 @ X8 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_18,negated_conjecture,
! [X4: a] :
( ( epred2_1 @ epred1_1 @ ( esk3_2 @ X4 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk2_1 @ epred1_1 ) )
| ( epred1_1 @ X4 @ ( esk3_2 @ X4 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X4: a,X8: a > a > $o] :
( ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) )
| ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ X4 )
| ~ ( cP @ ( epred2_1 @ X8 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_20,negated_conjecture,
! [X8: a > a > $o,X4: a] :
( ( X8 @ ( esk4_1 @ X8 ) @ X4 )
| ( cP @ ( epred2_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ X4 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_5]) ).
thf(c_0_21,negated_conjecture,
( ( epred2_1 @ epred1_1 @ ( esk3_2 @ ( esk4_1 @ epred1_1 ) @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk2_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
thf(c_0_22,plain,
! [X4: a,X8: a > a > $o,X5: a] :
( ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) )
| ( ( epred2_1 @ X8 )
!= ( epred1_1 @ X4 ) )
| ~ ( epred2_1 @ X8 @ X5 ) ),
inference(ext_sup,[status(thm)],[c_0_19,c_0_7]) ).
thf(c_0_23,plain,
! [X4: a,X8: a > a > $o] :
( ( epred2_1 @ X8 @ ( esk2_1 @ X8 ) )
| ~ ( epred1_1 @ X4 @ ( esk3_2 @ X4 @ X8 ) )
| ~ ( epred2_1 @ X8 @ ( esk3_2 @ X4 @ X8 ) ) ),
inference(condense,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_13])]) ).
thf(c_0_24,negated_conjecture,
( ( epred1_1 @ ( esk4_1 @ epred1_1 ) @ ( esk3_2 @ ( esk4_1 @ epred1_1 ) @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk2_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X4: a,X8: a > a > $o] :
( ~ ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) )
| ~ ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ X4 )
| ~ ( cP @ ( epred2_1 @ X8 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_26,negated_conjecture,
! [X4: a] :
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk3_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) )
| ( ( epred1_1 @ X4 )
!= ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
thf(c_0_27,plain,
( ( epred2_1 @ epred1_1 @ ( esk2_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
thf(c_0_28,negated_conjecture,
! [X8: a > a > $o] :
( ~ ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) )
| ~ ( cP @ ( epred2_1 @ X8 ) ) ),
inference(condense,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X4: a] :
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk3_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) )
| ( ( epred1_1 @ X4 @ ( esk9_1 @ X4 ) )
<~> ( epred2_1 @ epred1_1 @ ( esk9_1 @ X4 ) ) ) ),
inference(neg_ext,[status(thm)],[c_0_26]) ).
thf(c_0_30,negated_conjecture,
! [X4: a] :
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ X4 )
| ( cP @ ( epred2_1 @ epred1_1 ) )
| ~ ( epred2_1 @ epred1_1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
thf(c_0_31,plain,
! [X4: a,X8: a > a > $o] :
( ( ( epred2_1 @ X8 )
!= ( epred1_1 @ X4 ) )
| ~ ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) ) ),
inference(ext_sup,[status(thm)],[c_0_28,c_0_7]) ).
thf(c_0_32,negated_conjecture,
! [X4: a] :
( ( cP @ ( epred2_1 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ X4 )
| ~ ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ X4 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_27]) ).
thf(c_0_33,negated_conjecture,
! [X4: a] :
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk9_1 @ X4 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) )
| ( epred1_1 @ X4 @ ( esk9_1 @ X4 ) ) ),
inference(csr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_29]),c_0_30]) ).
thf(c_0_34,plain,
! [X4: a,X8: a > a > $o] :
( ( ( epred1_1 @ X4 @ ( esk4_2 @ X4 @ X8 ) )
<~> ( epred2_1 @ X8 @ ( esk4_2 @ X4 @ X8 ) ) )
| ~ ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) ) ),
inference(neg_ext,[status(thm)],[c_0_31]) ).
thf(c_0_35,negated_conjecture,
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,plain,
! [X4: a,X8: a > a > $o] :
( ( epred2_1 @ X8 @ ( esk4_2 @ X4 @ X8 ) )
| ( epred1_1 @ X4 @ ( esk4_2 @ X4 @ X8 ) )
| ~ ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_34]) ).
thf(c_0_37,negated_conjecture,
( ( epred2_1 @ epred1_1 @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) )
| ( epred2_1 @ epred1_1 @ ( esk3_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
thf(c_0_38,plain,
! [X4: a] :
( ( epred2_1 @ epred1_1 @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) )
| ( epred2_1 @ epred1_1 @ ( esk4_2 @ X4 @ epred1_1 ) )
| ( epred1_1 @ X4 @ ( esk4_2 @ X4 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_37]) ).
thf(c_0_39,negated_conjecture,
( ( epred2_1 @ epred1_1 @ ( esk4_2 @ ( esk4_1 @ epred1_1 ) @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_38]) ).
thf(c_0_40,plain,
! [X4: a,X8: a > a > $o] :
( ~ ( epred1_1 @ X4 @ ( esk4_2 @ X4 @ X8 ) )
| ~ ( epred2_1 @ X8 @ ( esk4_2 @ X4 @ X8 ) )
| ~ ( X8 @ ( esk2_1 @ X8 ) @ ( esk3_1 @ X8 ) )
| ~ ( epred2_1 @ X8 @ ( esk3_1 @ X8 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_34]) ).
thf(c_0_41,negated_conjecture,
( ( epred1_1 @ ( esk4_1 @ epred1_1 ) @ ( esk4_2 @ ( esk4_1 @ epred1_1 ) @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
thf(c_0_42,negated_conjecture,
! [X4: a] :
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ( epred2_1 @ epred1_1 @ ( esk3_1 @ epred1_1 ) )
| ~ ( epred2_1 @ epred1_1 @ ( esk9_1 @ X4 ) )
| ~ ( epred1_1 @ X4 @ ( esk9_1 @ X4 ) ) ),
inference(csr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_29]),c_0_19]) ).
thf(c_0_43,plain,
( ( epred2_1 @ epred1_1 @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32]),c_0_35]),c_0_39]) ).
thf(c_0_44,negated_conjecture,
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) )
| ~ ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_30]) ).
thf(c_0_45,negated_conjecture,
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk9_1 @ ( esk2_1 @ epred1_1 ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
thf(c_0_46,negated_conjecture,
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_47,plain,
! [X4: a] :
( ( cP @ ( epred2_1 @ epred1_1 ) )
| ( ( epred1_1 @ X4 )
!= ( epred2_1 @ epred1_1 ) )
| ~ ( epred2_1 @ epred1_1 @ ( esk3_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_46]) ).
thf(c_0_48,negated_conjecture,
( ( epred2_1 @ epred1_1 @ ( esk3_1 @ epred1_1 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
thf(c_0_49,plain,
! [X4: a] :
( ( cP @ ( epred2_1 @ epred1_1 ) )
| ( ( epred1_1 @ X4 @ ( esk37_1 @ X4 ) )
<~> ( epred2_1 @ epred1_1 @ ( esk37_1 @ X4 ) ) ) ),
inference(csr,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_47]),c_0_48]) ).
thf(c_0_50,plain,
! [X4: a] :
( ( epred2_1 @ epred1_1 @ ( esk37_1 @ X4 ) )
| ( cP @ ( epred2_1 @ epred1_1 ) )
| ( epred1_1 @ X4 @ ( esk37_1 @ X4 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_49]) ).
thf(c_0_51,negated_conjecture,
( ( epred2_1 @ epred1_1 @ ( esk37_1 @ ( esk4_1 @ epred1_1 ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_50]) ).
thf(c_0_52,negated_conjecture,
! [X1: a > $o,X4: a,X2: a > $o,X5: a] :
( ( X2 @ X5 )
| ~ ( cP @ X1 )
| ~ ( cP @ X2 )
| ~ ( X1 @ X4 )
| ~ ( X2 @ X4 )
| ~ ( X1 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_53,plain,
! [X4: a] :
( ( cP @ ( epred2_1 @ epred1_1 ) )
| ~ ( epred2_1 @ epred1_1 @ ( esk37_1 @ X4 ) )
| ~ ( epred1_1 @ X4 @ ( esk37_1 @ X4 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_49]) ).
thf(c_0_54,negated_conjecture,
( ( epred1_1 @ ( esk4_1 @ epred1_1 ) @ ( esk37_1 @ ( esk4_1 @ epred1_1 ) ) )
| ( cP @ ( epred2_1 @ epred1_1 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_51]) ).
thf(c_0_55,negated_conjecture,
! [X1: a > $o,X5: a,X4: a,X6: a] :
( ( epred1_1 @ X4 @ X5 )
| ~ ( epred1_1 @ X4 @ X6 )
| ~ ( cP @ X1 )
| ~ ( X1 @ X5 )
| ~ ( X1 @ X6 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_7]) ).
thf(c_0_56,negated_conjecture,
! [X4: a] : ( epred1_1 @ X4 @ X4 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_57,plain,
cP @ ( epred2_1 @ epred1_1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_51]) ).
thf(c_0_58,negated_conjecture,
! [X1: a > $o,X5: a,X4: a] :
( ( epred1_1 @ X4 @ X5 )
| ~ ( cP @ X1 )
| ~ ( X1 @ X5 )
| ~ ( X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_59,negated_conjecture,
! [X4: a] :
( ( epred2_1 @ epred1_1 @ ( esk2_1 @ epred1_1 ) )
| ~ ( epred2_1 @ epred1_1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_57]) ).
thf(c_0_60,negated_conjecture,
epred2_1 @ epred1_1 @ ( esk1_1 @ ( epred2_1 @ epred1_1 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_57]) ).
thf(c_0_61,negated_conjecture,
! [X5: a,X4: a] :
( ( epred1_1 @ X4 @ X5 )
| ~ ( epred2_1 @ epred1_1 @ X5 )
| ~ ( epred2_1 @ epred1_1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_57]) ).
thf(c_0_62,negated_conjecture,
! [X1: a > $o,X4: a,X5: a] :
( ( epred2_1 @ epred1_1 @ X4 )
| ~ ( epred2_1 @ epred1_1 @ X5 )
| ~ ( cP @ X1 )
| ~ ( X1 @ X4 )
| ~ ( X1 @ X5 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_57]) ).
thf(c_0_63,negated_conjecture,
epred2_1 @ epred1_1 @ ( esk2_1 @ epred1_1 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_64,negated_conjecture,
~ ( epred2_1 @ epred1_1 @ ( esk3_1 @ epred1_1 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_61]),c_0_57])]),c_0_59]) ).
thf(c_0_65,negated_conjecture,
! [X1: a > $o,X4: a] :
( ( epred2_1 @ epred1_1 @ X4 )
| ~ ( X1 @ ( esk2_1 @ epred1_1 ) )
| ~ ( cP @ X1 )
| ~ ( X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_66,negated_conjecture,
! [X4: a] :
( ( epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ) )
| ~ ( epred2_1 @ epred1_1 @ X4 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_57]),c_0_64]) ).
thf(c_0_67,negated_conjecture,
! [X5: a,X4: a] :
( ( epred2_1 @ epred1_1 @ X4 )
| ~ ( epred2_1 @ epred1_1 @ X5 )
| ~ ( epred1_1 @ X5 @ X4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_61]),c_0_7]),c_0_63])]) ).
thf(c_0_68,negated_conjecture,
epred1_1 @ ( esk2_1 @ epred1_1 ) @ ( esk3_1 @ epred1_1 ),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_63])]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV021^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:04:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.6sBU5Kt6Qn/E---3.1_3635863.p
% 233.64/30.20 % Version: 3.5.1-ho
% 233.64/30.20 % Preprocessing class: HSMSSMSSSSSNHHA.
% 233.64/30.20 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 233.64/30.20 % Starting full_lambda_6 with 900s (3) cores
% 233.64/30.20 % Starting post_as_ho1 with 300s (1) cores
% 233.64/30.20 % Starting lpo6_lambda_fix with 300s (1) cores
% 233.64/30.20 % Starting ho_unfolding_1 with 300s (1) cores
% 233.64/30.20 % Starting new_ho_10_unif with 300s (1) cores
% 233.64/30.20 % Starting ho_unfolding_2 with 300s (1) cores
% 233.64/30.20 % ho_unfolding_1 with pid 3635879 completed with status 0
% 233.64/30.20 % Result found by ho_unfolding_1
% 233.64/30.20 % Preprocessing class: HSMSSMSSSSSNHHA.
% 233.64/30.20 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 233.64/30.20 % Starting full_lambda_6 with 900s (3) cores
% 233.64/30.20 % Starting post_as_ho1 with 300s (1) cores
% 233.64/30.20 % Starting lpo6_lambda_fix with 300s (1) cores
% 233.64/30.20 % Starting ho_unfolding_1 with 300s (1) cores
% 233.64/30.20 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 233.64/30.20 % No SInE strategy applied
% 233.64/30.20 % Search class: HGHNS-FFSF11-SHHFFMBN
% 233.64/30.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 233.64/30.20 % Starting SubtermCWHack with 28s (1) cores
% 233.64/30.20 % SubtermCWHack with pid 3635887 completed with status 8
% 233.64/30.20 % Starting ho_unfolding_1 with 31s (1) cores
% 233.64/30.20 % ho_unfolding_1 with pid 3635933 completed with status 0
% 233.64/30.20 % Result found by ho_unfolding_1
% 233.64/30.20 % Preprocessing class: HSMSSMSSSSSNHHA.
% 233.64/30.20 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 233.64/30.20 % Starting full_lambda_6 with 900s (3) cores
% 233.64/30.20 % Starting post_as_ho1 with 300s (1) cores
% 233.64/30.20 % Starting lpo6_lambda_fix with 300s (1) cores
% 233.64/30.20 % Starting ho_unfolding_1 with 300s (1) cores
% 233.64/30.20 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 233.64/30.20 % No SInE strategy applied
% 233.64/30.20 % Search class: HGHNS-FFSF11-SHHFFMBN
% 233.64/30.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 233.64/30.20 % Starting SubtermCWHack with 28s (1) cores
% 233.64/30.20 % SubtermCWHack with pid 3635887 completed with status 8
% 233.64/30.20 % Starting ho_unfolding_1 with 31s (1) cores
% 233.64/30.20 % Preprocessing time : 0.001 s
% 233.64/30.20 % Presaturation interreduction done
% 233.64/30.20
% 233.64/30.20 % Proof found!
% 233.64/30.20 % SZS status Theorem
% 233.64/30.20 % SZS output start CNFRefutation
% See solution above
% 233.64/30.20 % Parsed axioms : 3
% 233.64/30.20 % Removed by relevancy pruning/SinE : 0
% 233.64/30.20 % Initial clauses : 13
% 233.64/30.20 % Removed in clause preprocessing : 3
% 233.64/30.20 % Initial clauses in saturation : 10
% 233.64/30.20 % Processed clauses : 5912
% 233.64/30.20 % ...of these trivial : 155
% 233.64/30.20 % ...subsumed : 4843
% 233.64/30.20 % ...remaining for further processing : 914
% 233.64/30.20 % Other redundant clauses eliminated : 0
% 233.64/30.20 % Clauses deleted for lack of memory : 0
% 233.64/30.20 % Backward-subsumed : 39
% 233.64/30.20 % Backward-rewritten : 358
% 233.64/30.20 % Generated clauses : 34215
% 233.64/30.20 % ...of the previous two non-redundant : 29412
% 233.64/30.20 % ...aggressively subsumed : 0
% 233.64/30.20 % Contextual simplify-reflections : 16
% 233.64/30.20 % Paramodulations : 34102
% 233.64/30.20 % Factorizations : 18
% 233.64/30.20 % NegExts : 36
% 233.64/30.20 % Equation resolutions : 0
% 233.64/30.20 % Disequality decompositions : 0
% 233.64/30.20 % Total rewrite steps : 7408
% 233.64/30.20 % ...of those cached : 6756
% 233.64/30.20 % Propositional unsat checks : 0
% 233.64/30.20 % Propositional check models : 0
% 233.64/30.20 % Propositional check unsatisfiable : 0
% 233.64/30.20 % Propositional clauses : 0
% 233.64/30.20 % Propositional clauses after purity: 0
% 233.64/30.20 % Propositional unsat core size : 0
% 233.64/30.20 % Propositional preprocessing time : 0.000
% 233.64/30.20 % Propositional encoding time : 0.000
% 233.64/30.20 % Propositional solver time : 0.000
% 233.64/30.20 % Success case prop preproc time : 0.000
% 233.64/30.20 % Success case prop encoding time : 0.000
% 233.64/30.20 % Success case prop solver time : 0.000
% 233.64/30.20 % Current number of processed clauses : 486
% 233.64/30.20 % Positive orientable unit clauses : 30
% 233.64/30.20 % Positive unorientable unit clauses: 0
% 233.64/30.20 % Negative unit clauses : 1
% 233.64/30.20 % Non-unit-clauses : 455
% 233.64/30.20 % Current number of unprocessed clauses: 22695
% 233.64/30.20 % ...number of literals in the above : 86033
% 233.64/30.20 % Current number of archived formulas : 0
% 233.64/30.20 % Current number of archived clauses : 428
% 233.64/30.20 % Clause-clause subsumption calls (NU) : 285612
% 233.64/30.20 % Rec. Clause-clause subsumption calls : 167103
% 233.64/30.20 % Non-unit clause-clause subsumptions : 4898
% 233.64/30.20 % Unit Clause-clause subsumption calls : 433
% 233.64/30.20 % Rewrite failures with RHS unbound : 0
% 233.64/30.20 % BW rewrite match attempts : 1129
% 233.64/30.20 % BW rewrite match successes : 29
% 233.64/30.20 % Condensation attempts : 5912
% 233.64/30.20 % Condensation successes : 3
% 233.64/30.20 % Termbank termtop insertions : 957933
% 233.64/30.20 % Search garbage collected termcells : 609
% 233.64/30.20
% 233.64/30.20 % -------------------------------------------------
% 233.64/30.20 % User time : 28.566 s
% 233.64/30.20 % System time : 0.479 s
% 233.64/30.20 % Total time : 29.045 s
% 233.64/30.20 % Maximum resident set size: 3640 pages
% 233.64/30.20
% 233.64/30.20 % -------------------------------------------------
% 233.64/30.20 % User time : 28.568 s
% 233.64/30.20 % System time : 0.485 s
% 233.64/30.20 % Total time : 29.053 s
% 233.64/30.20 % Maximum resident set size: 4864 pages
% 233.64/30.20 % E exiting
%------------------------------------------------------------------------------