%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU774^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:27:44 AM UTC 2026
% Result : Theorem 0.22s 0.26s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 362 ( 54 equ; 0 cnn)
% Maximal formula atoms : 91 ( 6 avg)
% Number of connectives : 2093 ( 155 ~; 209 |; 20 &;1645 @)
% ( 1 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 160 ( 12 ^; 148 !; 0 ?; 160 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
kpair: $i > $i > $i ).
thf(decl_26,type,
cartprod: $i > $i > $i ).
thf(decl_27,type,
breln: $i > $i > $i > $o ).
thf(decl_28,type,
eqbreln: $o ).
thf(decl_29,type,
breln1: $i > $i > $o ).
thf(decl_30,type,
esk1_4: $i > $i > $i > $i > $i ).
thf(decl_31,type,
esk2_4: $i > $i > $i > $i > $i ).
thf(decl_32,type,
esk3_4: $i > $i > $i > $i > $i ).
thf(decl_33,type,
esk4_4: $i > $i > $i > $i > $i ).
thf(decl_34,type,
esk5_0: $i ).
thf(decl_35,type,
esk6_0: $i ).
thf(decl_36,type,
esk7_0: $i ).
thf(breln1,axiom,
( breln1
= ( ^ [X1: $i,X4: $i] : ( breln @ X1 @ X1 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fUORoJ2mhz/E---3.1_155611.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fUORoJ2mhz/E---3.1_155611.p',breln) ).
thf(eqbreln1,conjecture,
( eqbreln
=> ! [X1: $i,X4: $i] :
( ( breln1 @ X1 @ X4 )
=> ! [X5: $i] :
( ( breln1 @ X1 @ X5 )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X5 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X4 ) ) ) )
=> ( X4 = X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fUORoJ2mhz/E---3.1_155611.p',eqbreln1) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( breln @ X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( breln @ X1 @ X2 @ X5 )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X5 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X4 ) ) ) )
=> ( X4 = X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fUORoJ2mhz/E---3.1_155611.p',eqbreln) ).
thf(c_0_4,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1]) ).
thf(c_0_5,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_6,negated_conjecture,
~ ( eqbreln
=> ! [X1: $i,X4: $i] :
( ( breln1 @ X1 @ X4 )
=> ! [X5: $i] :
( ( breln1 @ X1 @ X5 )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X5 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X4 ) ) ) )
=> ( X4 = X5 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[eqbreln1]) ).
thf(c_0_7,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_8,axiom,
( eqbreln
= ( ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ! [X5: $i] :
( ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X5 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X4 ) ) ) )
=> ( X4 = X5 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_5]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X23: $i,X24: $i,X25: $i] :
( ( subset @ X25 @ ( cartprod @ X23 @ X24 ) )
=> ! [X26: $i] :
( ( subset @ X26 @ ( cartprod @ X23 @ X24 ) )
=> ( ! [X27: $i] :
( ( in @ X27 @ X23 )
=> ! [X28: $i] :
( ( in @ X28 @ X24 )
=> ( ( in @ ( kpair @ X27 @ X28 ) @ X25 )
=> ( in @ ( kpair @ X27 @ X28 ) @ X26 ) ) ) )
=> ( ! [X29: $i] :
( ( in @ X29 @ X23 )
=> ! [X30: $i] :
( ( in @ X30 @ X24 )
=> ( ( in @ ( kpair @ X29 @ X30 ) @ X26 )
=> ( in @ ( kpair @ X29 @ X30 ) @ X25 ) ) ) )
=> ( X25 = X26 ) ) ) ) )
=> ! [X1: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X1 ) )
=> ! [X5: $i] :
( ( subset @ X5 @ ( cartprod @ X1 @ X1 ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X5 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X4 ) ) ) )
=> ( X4 = X5 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X31: $i,X32: $i,X33: $i,X34: $i,X42: $i,X43: $i,X44: $i,X45: $i] :
( ( ( in @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ( X33 = X34 )
| ( in @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ( X33 = X34 )
| ( in @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ( X33 = X34 )
| ( in @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ~ ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ( X33 = X34 )
| ( in @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ( X33 = X34 )
| ( in @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ( X33 = X34 )
| ( in @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ( X33 = X34 )
| ( in @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ~ ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ( X33 = X34 )
| ( in @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ( X33 = X34 )
| ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ( X33 = X34 )
| ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ( X33 = X34 )
| ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ~ ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ( X33 = X34 )
| ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ X31 )
| ( X33 = X34 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) @ X32 )
| ( X33 = X34 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ( X33 = X34 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( ~ ( in @ ( kpair @ ( esk3_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk4_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X33 )
| ( X33 = X34 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X31 @ X32 @ X33 @ X34 ) @ ( esk2_4 @ X31 @ X32 @ X33 @ X34 ) ) @ X34 )
| ~ ( subset @ X34 @ ( cartprod @ X31 @ X32 ) )
| ~ ( subset @ X33 @ ( cartprod @ X31 @ X32 ) ) )
& ( subset @ esk6_0 @ ( cartprod @ esk5_0 @ esk5_0 ) )
& ( subset @ esk7_0 @ ( cartprod @ esk5_0 @ esk5_0 ) )
& ( ~ ( in @ X42 @ esk5_0 )
| ~ ( in @ X43 @ esk5_0 )
| ~ ( in @ ( kpair @ X42 @ X43 ) @ esk6_0 )
| ( in @ ( kpair @ X42 @ X43 ) @ esk7_0 ) )
& ( ~ ( in @ X44 @ esk5_0 )
| ~ ( in @ X45 @ esk5_0 )
| ~ ( in @ ( kpair @ X44 @ X45 ) @ esk7_0 )
| ( in @ ( kpair @ X44 @ X45 ) @ esk6_0 ) )
& ( esk6_0 != esk7_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_9])])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( X3 = X4 )
| ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ esk6_0 )
| ~ ( in @ X1 @ esk5_0 )
| ~ ( in @ X2 @ esk5_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ esk7_0 )
| ~ ( in @ X1 @ esk5_0 )
| ~ ( in @ X2 @ esk5_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ( X3 = X4 )
| ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( esk6_0 = X1 )
| ( in @ ( esk1_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ X2 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ ( esk4_4 @ X2 @ X3 @ esk6_0 @ X1 ) ) @ esk7_0 )
| ~ ( in @ ( esk4_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( in @ ( esk3_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( subset @ esk6_0 @ ( cartprod @ X2 @ X3 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ( X3 = X4 )
| ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,negated_conjecture,
esk6_0 != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ( X3 = X4 )
| ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_19,negated_conjecture,
subset @ esk7_0 @ ( cartprod @ esk5_0 @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ( X3 = X4 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( esk6_0 = X1 )
| ( in @ ( kpair @ ( esk1_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ ( esk2_4 @ X2 @ X3 @ esk6_0 @ X1 ) ) @ esk7_0 )
| ( in @ ( esk3_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ X2 )
| ~ ( in @ ( esk2_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( in @ ( esk1_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( subset @ esk6_0 @ ( cartprod @ X2 @ X3 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ( X3 = X4 )
| ( in @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ X1 )
| ~ ( in @ ( esk4_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk3_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ esk6_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ esk7_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( X1 = esk7_0 )
| ( in @ ( esk1_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) @ esk5_0 )
| ( in @ ( esk4_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk5_0 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,negated_conjecture,
subset @ esk6_0 @ ( cartprod @ esk5_0 @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ( X3 = X4 )
| ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ X1 )
| ~ ( in @ ( esk2_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk1_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ esk7_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ esk6_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_17]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ( X1 = esk7_0 )
| ( in @ ( esk2_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) @ esk5_0 )
| ( in @ ( esk3_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk5_0 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
thf(c_0_29,negated_conjecture,
( ( in @ ( esk1_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk3_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_19])]),c_0_17]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ( X3 = X4 )
| ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( X3 = X4 )
| ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( X1 = esk7_0 )
| ( in @ ( kpair @ ( esk3_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) @ ( esk4_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) ) @ esk7_0 )
| ( in @ ( kpair @ ( esk1_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) @ ( esk2_4 @ esk5_0 @ esk5_0 @ X1 @ esk7_0 ) ) @ X1 )
| ~ ( subset @ X1 @ ( cartprod @ esk5_0 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
thf(c_0_33,negated_conjecture,
( ( in @ ( esk3_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk1_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]),c_0_25])]),c_0_17]) ).
thf(c_0_34,negated_conjecture,
in @ ( esk1_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19]),c_0_25])]),c_0_17]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( esk6_0 = X1 )
| ( in @ ( kpair @ ( esk1_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ ( esk2_4 @ X2 @ X3 @ esk6_0 @ X1 ) ) @ esk6_0 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ ( esk4_4 @ X2 @ X3 @ esk6_0 @ X1 ) ) @ esk7_0 )
| ~ ( in @ ( esk4_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( in @ ( esk3_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( subset @ esk6_0 @ ( cartprod @ X2 @ X3 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_12]) ).
thf(c_0_36,negated_conjecture,
( ( in @ ( kpair @ ( esk1_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ ( esk2_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) ) @ esk6_0 )
| ( in @ ( kpair @ ( esk3_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_17]) ).
thf(c_0_37,negated_conjecture,
in @ ( esk3_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
thf(c_0_38,negated_conjecture,
( ( in @ ( kpair @ ( esk1_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ ( esk2_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) ) @ esk6_0 )
| ~ ( in @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_25]),c_0_19])]),c_0_17]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( X3 = X4 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_40,negated_conjecture,
( ( in @ ( kpair @ ( esk1_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ ( esk2_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) ) @ esk7_0 )
| ~ ( in @ ( esk2_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_38]),c_0_34])]) ).
thf(c_0_41,negated_conjecture,
( ~ ( in @ ( kpair @ ( esk3_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) ) @ esk6_0 )
| ~ ( in @ ( esk2_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_19]),c_0_25])]),c_0_17]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( X3 = X4 )
| ( in @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ( X3 = X4 )
| ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_44,negated_conjecture,
( ~ ( in @ ( kpair @ ( esk3_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) ) @ esk7_0 )
| ~ ( in @ ( esk2_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_12]),c_0_37])]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ( X3 = X4 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( esk6_0 = X1 )
| ( in @ ( esk2_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ X3 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ ( esk4_4 @ X2 @ X3 @ esk6_0 @ X1 ) ) @ esk7_0 )
| ~ ( in @ ( esk4_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( in @ ( esk3_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( subset @ esk6_0 @ ( cartprod @ X2 @ X3 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_42,c_0_12]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ( X3 = X4 )
| ( in @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_48,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ( X3 = X4 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( esk6_0 = X1 )
| ( in @ ( kpair @ ( esk1_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ ( esk2_4 @ X2 @ X3 @ esk6_0 @ X1 ) ) @ esk7_0 )
| ( in @ ( esk4_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ X3 )
| ~ ( in @ ( esk2_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( in @ ( esk1_4 @ X2 @ X3 @ esk6_0 @ X1 ) @ esk5_0 )
| ~ ( subset @ esk6_0 @ ( cartprod @ X2 @ X3 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_43]) ).
thf(c_0_50,negated_conjecture,
( ~ ( in @ ( esk2_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_19]),c_0_25])]),c_0_17]),c_0_40]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk2_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ X2 )
| ~ ( in @ ( esk4_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk3_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ esk6_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ esk7_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_17]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk4_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ X2 )
| ~ ( in @ ( esk2_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk1_4 @ X1 @ X2 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ esk7_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ esk6_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_17]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk4_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ( X3 = X4 )
| ( in @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_54,negated_conjecture,
~ ( in @ ( esk4_4 @ esk5_0 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_37]),c_0_25]),c_0_19])]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk4_4 @ X1 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( in @ ( esk1_4 @ X1 @ esk5_0 @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ esk7_0 @ ( cartprod @ X1 @ esk5_0 ) )
| ~ ( subset @ esk6_0 @ ( cartprod @ X1 @ esk5_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_17]) ).
thf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_34]),c_0_19]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU774^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:30:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.fUORoJ2mhz/E---3.1_155611.p
% 0.22/0.26 % Version: 3.5.1-ho
% 0.22/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.26 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.26 % Starting sh4l with 300s (1) cores
% 0.22/0.26 % Starting ho_unfolding_2 with 300s (1) cores
% 0.22/0.26 % post_as_ho5 with pid 155625 completed with status 0
% 0.22/0.26 % Result found by post_as_ho5
% 0.22/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.26 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.22/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.26 % Search class: HGUSF-FFMF33-SSFFMFNN
% 0.22/0.26 % partial match(2): HGUSF-FFMF32-SFFFMFNN
% 0.22/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.26 % SubtermCWHack with pid 155628 completed with status 0
% 0.22/0.26 % Result found by SubtermCWHack
% 0.22/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.26 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.22/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.26 % Search class: HGUSF-FFMF33-SSFFMFNN
% 0.22/0.26 % partial match(2): HGUSF-FFMF32-SFFFMFNN
% 0.22/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.26 % Preprocessing time : 0.001 s
% 0.22/0.26
% 0.22/0.26 % Proof found!
% 0.22/0.26 % SZS status Theorem
% 0.22/0.26 % SZS output start CNFRefutation
% See solution above
% 0.22/0.26 % Parsed axioms : 11
% 0.22/0.26 % Removed by relevancy pruning/SinE : 7
% 0.22/0.26 % Initial clauses : 21
% 0.22/0.26 % Removed in clause preprocessing : 0
% 0.22/0.26 % Initial clauses in saturation : 21
% 0.22/0.26 % Processed clauses : 83
% 0.22/0.26 % ...of these trivial : 1
% 0.22/0.26 % ...subsumed : 14
% 0.22/0.26 % ...remaining for further processing : 68
% 0.22/0.26 % Other redundant clauses eliminated : 0
% 0.22/0.26 % Clauses deleted for lack of memory : 0
% 0.22/0.26 % Backward-subsumed : 8
% 0.22/0.26 % Backward-rewritten : 4
% 0.22/0.26 % Generated clauses : 92
% 0.22/0.26 % ...of the previous two non-redundant : 72
% 0.22/0.26 % ...aggressively subsumed : 0
% 0.22/0.26 % Contextual simplify-reflections : 3
% 0.22/0.26 % Paramodulations : 92
% 0.22/0.26 % Factorizations : 0
% 0.22/0.26 % NegExts : 0
% 0.22/0.26 % Equation resolutions : 0
% 0.22/0.26 % Disequality decompositions : 0
% 0.22/0.26 % Total rewrite steps : 101
% 0.22/0.26 % ...of those cached : 95
% 0.22/0.26 % Propositional unsat checks : 0
% 0.22/0.26 % Propositional check models : 0
% 0.22/0.26 % Propositional check unsatisfiable : 0
% 0.22/0.26 % Propositional clauses : 0
% 0.22/0.26 % Propositional clauses after purity: 0
% 0.22/0.26 % Propositional unsat core size : 0
% 0.22/0.26 % Propositional preprocessing time : 0.000
% 0.22/0.26 % Propositional encoding time : 0.000
% 0.22/0.26 % Propositional solver time : 0.000
% 0.22/0.26 % Success case prop preproc time : 0.000
% 0.22/0.26 % Success case prop encoding time : 0.000
% 0.22/0.26 % Success case prop solver time : 0.000
% 0.22/0.26 % Current number of processed clauses : 56
% 0.22/0.26 % Positive orientable unit clauses : 6
% 0.22/0.26 % Positive unorientable unit clauses: 0
% 0.22/0.26 % Negative unit clauses : 2
% 0.22/0.26 % Non-unit-clauses : 48
% 0.22/0.26 % Current number of unprocessed clauses: 8
% 0.22/0.26 % ...number of literals in the above : 46
% 0.22/0.26 % Current number of archived formulas : 0
% 0.22/0.26 % Current number of archived clauses : 12
% 0.22/0.26 % Clause-clause subsumption calls (NU) : 338
% 0.22/0.26 % Rec. Clause-clause subsumption calls : 41
% 0.22/0.26 % Non-unit clause-clause subsumptions : 23
% 0.22/0.26 % Unit Clause-clause subsumption calls : 34
% 0.22/0.26 % Rewrite failures with RHS unbound : 0
% 0.22/0.26 % BW rewrite match attempts : 14
% 0.22/0.26 % BW rewrite match successes : 3
% 0.22/0.26 % Condensation attempts : 0
% 0.22/0.26 % Condensation successes : 0
% 0.22/0.26 % Termbank termtop insertions : 7172
% 0.22/0.26 % Search garbage collected termcells : 676
% 0.22/0.26
% 0.22/0.26 % -------------------------------------------------
% 0.22/0.26 % User time : 0.009 s
% 0.22/0.26 % System time : 0.002 s
% 0.22/0.26 % Total time : 0.011 s
% 0.22/0.26 % Maximum resident set size: 3640 pages
% 0.22/0.26
% 0.22/0.26 % -------------------------------------------------
% 0.22/0.26 % User time : 0.011 s
% 0.22/0.26 % System time : 0.006 s
% 0.22/0.26 % Total time : 0.016 s
% 0.22/0.26 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------