%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV400^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:35:28 AM UTC 2026
% Result : Theorem 240.42s 30.57s
% Output : CNFRefutation 240.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 87 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 326 ( 0 equ; 0 cnn)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 1585 ( 123 ~; 200 |; 230 &;1020 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 319 ( 191 ^; 126 !; 2 ?; 319 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cQ: $i > $o ).
thf(decl_24,type,
cP: $i > $o ).
thf(decl_25,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_26,type,
esk2_1: ( $i > $o ) > $i ).
thf(decl_27,type,
epred1_1: ( $i > $o ) > $i > $o ).
thf(decl_28,type,
esk3_1: ( $i > $o ) > $i ).
thf(cTHM590_pme,conjecture,
? [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) )
& ! [X3: $i > $o] :
( ( ! [X2: $i] :
( ( X3 @ X2 )
=> ( cP @ X2 ) )
& ! [X2: $i] :
( ( X3 @ X2 )
=> ( cQ @ X2 ) ) )
=> ! [X2: $i] :
( ( X3 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ggMrZZg3KP/E---3.1_891344.p',cTHM590_pme) ).
thf(c_0_1,negated_conjecture,
~ ? [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) )
& ! [X3: $i > $o] :
( ( ! [X2: $i] :
( ( X3 @ X2 )
=> ( cP @ X2 ) )
& ! [X2: $i] :
( ( X3 @ X2 )
=> ( cQ @ X2 ) ) )
=> ! [X2: $i] :
( ( X3 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM590_pme]) ).
thf(c_0_2,negated_conjecture,
! [X11: $i > $o,X15: $i,X16: $i] :
( ( ~ ( epred1_1 @ X11 @ X15 )
| ( cP @ X15 )
| ( X11 @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ~ ( epred1_1 @ X11 @ X16 )
| ( cQ @ X16 )
| ( X11 @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ( epred1_1 @ X11 @ ( esk3_1 @ X11 ) )
| ( X11 @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ~ ( X11 @ ( esk3_1 @ X11 ) )
| ( X11 @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ~ ( epred1_1 @ X11 @ X15 )
| ( cP @ X15 )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ~ ( epred1_1 @ X11 @ X16 )
| ( cQ @ X16 )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ( epred1_1 @ X11 @ ( esk3_1 @ X11 ) )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ~ ( X11 @ ( esk3_1 @ X11 ) )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ( X11 @ ( esk1_1 @ X11 ) ) )
& ( ~ ( epred1_1 @ X11 @ X15 )
| ( cP @ X15 )
| ( X11 @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) )
& ( ~ ( epred1_1 @ X11 @ X16 )
| ( cQ @ X16 )
| ( X11 @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) )
& ( ( epred1_1 @ X11 @ ( esk3_1 @ X11 ) )
| ( X11 @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) )
& ( ~ ( X11 @ ( esk3_1 @ X11 ) )
| ( X11 @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) )
& ( ~ ( epred1_1 @ X11 @ X15 )
| ( cP @ X15 )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) )
& ( ~ ( epred1_1 @ X11 @ X16 )
| ( cQ @ X16 )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) )
& ( ( epred1_1 @ X11 @ ( esk3_1 @ X11 ) )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) )
& ( ~ ( X11 @ ( esk3_1 @ X11 ) )
| ~ ( cQ @ ( esk2_1 @ X11 ) )
| ~ ( cP @ ( esk1_1 @ X11 ) ) ) ),
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_1])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( cP @ X2 )
| ( X1 @ ( esk2_1 @ X1 ) )
| ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( epred1_1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X1: $i > $o] :
( ( epred1_1 @ X1 @ ( esk3_1 @ X1 ) )
| ( X1 @ ( esk2_1 @ X1 ) )
| ( X1 @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i > $o] :
( ( X1 @ ( esk2_1 @ X1 ) )
| ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( X1 @ ( esk3_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i > $o] :
( ( cP @ ( esk3_1 @ X1 ) )
| ( X1 @ ( esk1_1 @ X1 ) )
| ( X1 @ ( esk2_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( cQ @ X2 )
| ( X1 @ ( esk2_1 @ X1 ) )
| ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( epred1_1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
! [X55: $i > $o,X54: $i > $o] :
( ( ( X55
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X55 @ Z0 )
& ( X54 @ Z0 ) ) ) )
& ( X54
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X55 @ Z0 )
& ( X54 @ Z0 ) ) ) ) )
| ( ( X55
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X55 @ Z0 )
& ( X54 @ Z0 ) ) ) )
& ( X54
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X55 @ Z0 )
& ( X54 @ Z0 ) ) ) ) )
| ~ ( ( X55
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X55 @ Z0 )
& ( X54 @ Z0 ) ) ) )
& ( X54
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X55 @ Z0 )
& ( X54 @ Z0 ) ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X143: $i > $o,X142: $i > $o] :
( ( ( X143
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X143 @ Z0 )
& ( X142 @ Z0 ) ) ) )
& ( X142
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X143 @ Z0 )
& ( X142 @ Z0 ) ) ) ) )
| ( ( X143
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X143 @ Z0 )
& ( X142 @ Z0 ) ) ) )
& ( X142
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X143 @ Z0 )
& ( X142 @ Z0 ) ) ) ) )
| ( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X143 @ Z0 )
& ( X142 @ Z0 ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i > $o] :
( ( cQ @ ( esk3_1 @ X1 ) )
| ( X1 @ ( esk1_1 @ X1 ) )
| ( X1 @ ( esk2_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( cP @ X2 )
| ( X1 @ ( esk2_1 @ X1 ) )
| ~ ( epred1_1 @ X1 @ X2 )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X3
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
! [X120: $i > $o,X119: $i > $o] :
( ( ( X120
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X120 @ Z0 )
& ( X119 @ Z0 ) ) ) )
& ( X119
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X120 @ Z0 )
& ( X119 @ Z0 ) ) ) ) )
| ( ( X120
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X120 @ Z0 )
& ( X119 @ Z0 ) ) ) )
& ( X119
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X120 @ Z0 )
& ( X119 @ Z0 ) ) ) ) )
| ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X120 @ Z0 )
& ( X119 @ Z0 ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i > $o] :
( ( epred1_1 @ X1 @ ( esk3_1 @ X1 ) )
| ( X1 @ ( esk2_1 @ X1 ) )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( cQ @ X2 )
| ( X1 @ ( esk2_1 @ X1 ) )
| ~ ( epred1_1 @ X1 @ X2 )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_17,negated_conjecture,
! [X83: $i > $o,X82: $i > $o,X2: $i] :
( ( ( X83
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X83 @ Z0 )
& ( X82 @ Z0 ) ) ) )
& ( X82
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X83 @ Z0 )
& ( X82 @ Z0 ) ) ) ) )
| ( cP @ X2 )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X83 @ Z0 )
& ( X82 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X83 @ Z0 )
& ( X82 @ Z0 ) )
@ X2 ) ),
inference(primitive_enumeration,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i > $o] :
( ( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( X1 @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_14]) ).
thf(c_0_20,negated_conjecture,
! [X48: $i > $o,X47: $i > $o] :
( ( ( X48
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X48 @ Z0 )
& ( X47 @ Z0 ) ) ) )
& ( X47
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X48 @ Z0 )
& ( X47 @ Z0 ) ) ) ) )
| ( epred1_1
@ ^ [Z0: $i] :
( ( X48 @ Z0 )
& ( X47 @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X48 @ Z0 )
& ( X47 @ Z0 ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X48 @ Z0 )
& ( X47 @ Z0 ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_15]) ).
thf(c_0_21,negated_conjecture,
! [X69: $i > $o,X68: $i > $o,X2: $i] :
( ( ( X69
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X69 @ Z0 )
& ( X68 @ Z0 ) ) ) )
& ( X68
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X69 @ Z0 )
& ( X68 @ Z0 ) ) ) ) )
| ( cQ @ X2 )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X69 @ Z0 )
& ( X68 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X69 @ Z0 )
& ( X68 @ Z0 ) )
@ X2 ) ),
inference(primitive_enumeration,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i > $o] :
( ( X1 @ ( esk2_1 @ X1 ) )
| ~ ( X1 @ ( esk3_1 @ X1 ) )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i > $o,X3: $i > $o,X2: $i] :
( ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( cP @ X2 )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) )
@ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
( ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( epred1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i > $o,X3: $i > $o,X2: $i] :
( ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( cQ @ X2 )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) )
@ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X3
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X3
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_8]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X3
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_9]) ).
thf(c_0_29,negated_conjecture,
! [X34: $i > $o,X33: $i > $o] :
( ( ( X34
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X34 @ Z0 )
& ( X33 @ Z0 ) ) ) )
& ( X33
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X34 @ Z0 )
& ( X33 @ Z0 ) ) ) ) )
| ~ ( ( X34
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X34 @ Z0 )
& ( X33 @ Z0 ) ) ) )
& ( X33
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X34 @ Z0 )
& ( X33 @ Z0 ) ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X34 @ Z0 )
& ( X33 @ Z0 ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_22]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i] :
( ( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_31,negated_conjecture,
( ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
thf(c_0_32,negated_conjecture,
! [X2: $i] :
( ( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i > $o] :
( ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( X1 @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X3
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_14]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X3
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_29]) ).
thf(c_0_36,negated_conjecture,
( ( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_37,negated_conjecture,
( ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
thf(c_0_38,negated_conjecture,
( ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_39,negated_conjecture,
( cP
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_24]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( epred1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X3
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_20]) ).
thf(c_0_41,negated_conjecture,
! [X2: $i] :
( ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_38]),c_0_39])])]) ).
thf(c_0_42,negated_conjecture,
( ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
thf(c_0_43,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( cP @ X2 )
| ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( epred1_1 @ X1 @ X2 )
| ~ ( cQ @ ( esk2_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_44,negated_conjecture,
! [X3: $i > $o,X1: $i > $o] :
( ( X1
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( X3
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_29]) ).
thf(c_0_45,negated_conjecture,
( ( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i > $o] :
( ( epred1_1 @ X1 @ ( esk3_1 @ X1 ) )
| ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( cQ @ ( esk2_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( cQ @ X2 )
| ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( epred1_1 @ X1 @ X2 )
| ~ ( cQ @ ( esk2_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_48,negated_conjecture,
! [X76: $i > $o,X75: $i > $o,X2: $i] :
( ( ( X76
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X76 @ Z0 )
& ( X75 @ Z0 ) ) ) )
& ( X75
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X76 @ Z0 )
& ( X75 @ Z0 ) ) ) ) )
| ( cP @ X2 )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X76 @ Z0 )
& ( X75 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X76 @ Z0 )
& ( X75 @ Z0 ) )
@ X2 ) ),
inference(primitive_enumeration,[status(thm)],[c_0_43]) ).
thf(c_0_49,negated_conjecture,
! [X2: $i] :
( ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_38]),c_0_39])])]) ).
thf(c_0_50,negated_conjecture,
( ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ~ ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_38]) ).
thf(c_0_51,negated_conjecture,
! [X41: $i > $o,X40: $i > $o] :
( ( ( X41
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X41 @ Z0 )
& ( X40 @ Z0 ) ) ) )
& ( X40
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X41 @ Z0 )
& ( X40 @ Z0 ) ) ) ) )
| ( epred1_1
@ ^ [Z0: $i] :
( ( X41 @ Z0 )
& ( X40 @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X41 @ Z0 )
& ( X40 @ Z0 ) ) ) )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X41 @ Z0 )
& ( X40 @ Z0 ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_46]) ).
thf(c_0_52,negated_conjecture,
! [X62: $i > $o,X61: $i > $o,X2: $i] :
( ( ( X62
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X62 @ Z0 )
& ( X61 @ Z0 ) ) ) )
& ( X61
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X62 @ Z0 )
& ( X61 @ Z0 ) ) ) ) )
| ( cQ @ X2 )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X62 @ Z0 )
& ( X61 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X62 @ Z0 )
& ( X61 @ Z0 ) )
@ X2 ) ),
inference(primitive_enumeration,[status(thm)],[c_0_47]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i > $o] :
( ( X1 @ ( esk1_1 @ X1 ) )
| ~ ( X1 @ ( esk3_1 @ X1 ) )
| ~ ( cQ @ ( esk2_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i > $o,X3: $i > $o,X2: $i] :
( ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ( cP @ X2 )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) )
@ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_48]) ).
thf(c_0_55,negated_conjecture,
( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_42]),c_0_50]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( epred1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X3
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_51]) ).
thf(c_0_57,negated_conjecture,
! [X1: $i > $o,X3: $i > $o,X2: $i] :
( ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ( cQ @ X2 )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) )
@ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_52]) ).
thf(c_0_58,negated_conjecture,
! [X27: $i > $o,X26: $i > $o] :
( ( ( X27
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X27 @ Z0 )
& ( X26 @ Z0 ) ) ) )
& ( X26
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X27 @ Z0 )
& ( X26 @ Z0 ) ) ) ) )
| ~ ( ( X27
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X27 @ Z0 )
& ( X26 @ Z0 ) ) ) )
& ( X26
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X27 @ Z0 )
& ( X26 @ Z0 ) ) ) ) )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X27 @ Z0 )
& ( X26 @ Z0 ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_53]) ).
thf(c_0_59,negated_conjecture,
! [X2: $i] :
( ( cQ
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_60,negated_conjecture,
( ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_56,c_0_55]) ).
thf(c_0_61,negated_conjecture,
! [X2: $i] :
( ( cQ
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_55]) ).
thf(c_0_62,negated_conjecture,
! [X3: $i > $o,X1: $i > $o] :
( ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( X3
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X3 @ Z0 )
& ( X1 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_58]) ).
thf(c_0_63,negated_conjecture,
( ( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_64,negated_conjecture,
( ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_61,c_0_60]) ).
thf(c_0_65,negated_conjecture,
! [X1: $i > $o,X3: $i > $o,X2: $i] :
( ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( cP @ X2 )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) )
@ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_48]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( epred1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_51]) ).
thf(c_0_67,negated_conjecture,
( cQ
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_55])]),c_0_64]) ).
thf(c_0_68,negated_conjecture,
! [X2: $i] :
( ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_55]) ).
thf(c_0_69,negated_conjecture,
( ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_55]) ).
thf(c_0_70,negated_conjecture,
! [X2: $i] :
( ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cQ @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_55]),c_0_67])]) ).
thf(c_0_71,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ( X1
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X3
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_58]) ).
thf(c_0_72,negated_conjecture,
( ( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_73,negated_conjecture,
( ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) )
| ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_70,c_0_69]) ).
thf(c_0_74,negated_conjecture,
! [X1: $i > $o] :
( ~ ( X1 @ ( esk3_1 @ X1 ) )
| ~ ( cQ @ ( esk2_1 @ X1 ) )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_75,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( cP @ X2 )
| ~ ( epred1_1 @ X1 @ X2 )
| ~ ( cQ @ ( esk2_1 @ X1 ) )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_76,negated_conjecture,
( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_55])]),c_0_73]) ).
thf(c_0_77,negated_conjecture,
! [X1: $i > $o] :
( ( epred1_1 @ X1 @ ( esk3_1 @ X1 ) )
| ~ ( cQ @ ( esk2_1 @ X1 ) )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_78,negated_conjecture,
! [X20: $i > $o,X19: $i > $o] :
( ~ ( ( X20
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X20 @ Z0 )
& ( X19 @ Z0 ) ) ) )
& ( X19
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X20 @ Z0 )
& ( X19 @ Z0 ) ) ) ) )
| ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X20 @ Z0 )
& ( X19 @ Z0 ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X20 @ Z0 )
& ( X19 @ Z0 ) ) ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_74]) ).
thf(c_0_79,negated_conjecture,
! [X2: $i] :
( ( cP @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_55])]) ).
thf(c_0_80,negated_conjecture,
( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_76]),c_0_55])]) ).
thf(c_0_81,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( cQ @ X2 )
| ~ ( epred1_1 @ X1 @ X2 )
| ~ ( cQ @ ( esk2_1 @ X1 ) )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i > $o,X3: $i > $o] :
( ~ ( cQ
@ ( esk2_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( cP
@ ( esk1_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X1
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) )
| ~ ( X3
@ ( esk3_1
@ ^ [Z0: $i] :
( ( X1 @ Z0 )
& ( X3 @ Z0 ) ) ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_78]) ).
thf(c_0_83,negated_conjecture,
( cP
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_84,negated_conjecture,
! [X2: $i] :
( ( cQ @ X2 )
| ~ ( epred1_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) )
@ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_76]),c_0_55])]) ).
thf(c_0_85,negated_conjecture,
~ ( cQ
@ ( esk3_1
@ ^ [Z0: $i] :
( ( cP @ Z0 )
& ( cQ @ Z0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_55]),c_0_76])]) ).
thf(c_0_86,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_80]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV400^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.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
% 0.08/0.18 % DateTime : Tue Sep 29 15:43:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.ggMrZZg3KP/E---3.1_891344.p
% 240.42/30.57 % Version: 3.5.1-ho
% 240.42/30.57 % Preprocessing class: HSSSSMSSSSSNSSA.
% 240.42/30.57 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 240.42/30.57 % Starting post_as_ho12 with 300s (1) cores
% 240.42/30.57 % Starting new_bool_9 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho1 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho4 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho2 with 300s (1) cores
% 240.42/30.57 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 240.42/30.57 % Starting full_lambda_10 with 300s (1) cores
% 240.42/30.57 % Starting new_ho_8 with 300s (1) cores
% 240.42/30.57 % ehoh_best2_full_lfho with pid 891362 completed with status 0
% 240.42/30.57 % Result found by ehoh_best2_full_lfho
% 240.42/30.57 % Preprocessing class: HSSSSMSSSSSNSSA.
% 240.42/30.57 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 240.42/30.57 % Starting post_as_ho12 with 300s (1) cores
% 240.42/30.57 % Starting new_bool_9 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho1 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho4 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho2 with 300s (1) cores
% 240.42/30.57 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 240.42/30.57 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 240.42/30.57 % No SInE strategy applied
% 240.42/30.57 % Search class: HGHNF-FFSF11-SSSFFMBN
% 240.42/30.57 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 240.42/30.57 % Starting SubtermCWHack with 28s (1) cores
% 240.42/30.57 % SubtermCWHack with pid 891370 completed with status 8
% 240.42/30.57 % Starting ehoh_best2_full_lfho with 31s (1) cores
% 240.42/30.57 % ehoh_best2_full_lfho with pid 891730 completed with status 0
% 240.42/30.57 % Result found by ehoh_best2_full_lfho
% 240.42/30.57 % Preprocessing class: HSSSSMSSSSSNSSA.
% 240.42/30.57 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 240.42/30.57 % Starting post_as_ho12 with 300s (1) cores
% 240.42/30.57 % Starting new_bool_9 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho1 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho4 with 300s (1) cores
% 240.42/30.57 % Starting post_as_ho2 with 300s (1) cores
% 240.42/30.57 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 240.42/30.57 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 240.42/30.57 % No SInE strategy applied
% 240.42/30.57 % Search class: HGHNF-FFSF11-SSSFFMBN
% 240.42/30.57 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 240.42/30.57 % Starting SubtermCWHack with 28s (1) cores
% 240.42/30.57 % SubtermCWHack with pid 891370 completed with status 8
% 240.42/30.57 % Starting ehoh_best2_full_lfho with 31s (1) cores
% 240.42/30.57 % Preprocessing time : 0.001 s
% 240.42/30.57
% 240.42/30.57 % Proof found!
% 240.42/30.57 % SZS status Theorem
% 240.42/30.57 % SZS output start CNFRefutation
% See solution above
% 240.42/30.58 % Parsed axioms : 3
% 240.42/30.58 % Removed by relevancy pruning/SinE : 0
% 240.42/30.58 % Initial clauses : 18
% 240.42/30.58 % Removed in clause preprocessing : 2
% 240.42/30.58 % Initial clauses in saturation : 16
% 240.42/30.58 % Processed clauses : 1145
% 240.42/30.58 % ...of these trivial : 8
% 240.42/30.58 % ...subsumed : 235
% 240.42/30.58 % ...remaining for further processing : 901
% 240.42/30.58 % Other redundant clauses eliminated : 406
% 240.42/30.58 % Clauses deleted for lack of memory : 0
% 240.42/30.58 % Backward-subsumed : 44
% 240.42/30.58 % Backward-rewritten : 36
% 240.42/30.58 % Generated clauses : 12848
% 240.42/30.58 % ...of the previous two non-redundant : 12100
% 240.42/30.58 % ...aggressively subsumed : 0
% 240.42/30.58 % Contextual simplify-reflections : 12
% 240.42/30.58 % Paramodulations : 11273
% 240.42/30.58 % Factorizations : 0
% 240.42/30.58 % NegExts : 26
% 240.42/30.58 % Equation resolutions : 412
% 240.42/30.58 % Disequality decompositions : 0
% 240.42/30.58 % Total rewrite steps : 3371
% 240.42/30.58 % ...of those cached : 3362
% 240.42/30.58 % Propositional unsat checks : 0
% 240.42/30.58 % Propositional check models : 0
% 240.42/30.58 % Propositional check unsatisfiable : 0
% 240.42/30.58 % Propositional clauses : 0
% 240.42/30.58 % Propositional clauses after purity: 0
% 240.42/30.58 % Propositional unsat core size : 0
% 240.42/30.58 % Propositional preprocessing time : 0.000
% 240.42/30.58 % Propositional encoding time : 0.000
% 240.42/30.58 % Propositional solver time : 0.000
% 240.42/30.58 % Success case prop preproc time : 0.000
% 240.42/30.58 % Success case prop encoding time : 0.000
% 240.42/30.58 % Success case prop solver time : 0.000
% 240.42/30.58 % Current number of processed clauses : 736
% 240.42/30.58 % Positive orientable unit clauses : 11
% 240.42/30.58 % Positive unorientable unit clauses: 0
% 240.42/30.58 % Negative unit clauses : 1
% 240.42/30.58 % Non-unit-clauses : 724
% 240.42/30.58 % Current number of unprocessed clauses: 10909
% 240.42/30.58 % ...number of literals in the above : 110556
% 240.42/30.58 % Current number of archived formulas : 0
% 240.42/30.58 % Current number of archived clauses : 165
% 240.42/30.58 % Clause-clause subsumption calls (NU) : 494953
% 240.42/30.58 % Rec. Clause-clause subsumption calls : 51486
% 240.42/30.58 % Non-unit clause-clause subsumptions : 291
% 240.42/30.58 % Unit Clause-clause subsumption calls : 2559
% 240.42/30.58 % Rewrite failures with RHS unbound : 0
% 240.42/30.58 % BW rewrite match attempts : 84
% 240.42/30.58 % BW rewrite match successes : 6
% 240.42/30.58 % Condensation attempts : 0
% 240.42/30.58 % Condensation successes : 0
% 240.42/30.58 % Termbank termtop insertions : 3276762
% 240.42/30.58 % Search garbage collected termcells : 234
% 240.42/30.58
% 240.42/30.58 % -------------------------------------------------
% 240.42/30.58 % User time : 30.265 s
% 240.42/30.58 % System time : 0.041 s
% 240.42/30.58 % Total time : 30.306 s
% 240.42/30.58 % Maximum resident set size: 3884 pages
% 240.42/30.58
% 240.42/30.58 % -------------------------------------------------
% 240.42/30.58 % User time : 30.266 s
% 240.42/30.58 % System time : 0.048 s
% 240.42/30.58 % Total time : 30.315 s
% 240.42/30.58 % Maximum resident set size: 4864 pages
% 240.42/30.58 % E exiting
%------------------------------------------------------------------------------