%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO067^4.002 : 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 : n019.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 08:42:17 AM UTC 2026
% Result : Theorem 23.62s 3.74s
% Output : CNFRefutation 23.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 259 ( 24 equ; 0 cnn)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 641 ( 63 ~; 101 |; 17 &; 439 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 2 con; 0-3 aty)
% Number of variables : 152 ( 56 ^; 96 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
irel: $i > $i > $o ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_29,type,
iatom: ( $i > $o ) > $i > $o ).
thf(decl_33,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_35,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
f: $i > $o ).
thf(decl_44,type,
p1: $i > $o ).
thf(decl_45,type,
p2: $i > $o ).
thf(decl_46,type,
esk1_1: $i > $i ).
thf(decl_47,type,
esk2_1: $i > $i ).
thf(decl_48,type,
esk3_1: $i > $i ).
thf(decl_49,type,
esk4_1: $i > $i ).
thf(decl_50,type,
esk5_1: $i > $i ).
thf(decl_51,type,
esk6_1: $i > $i ).
thf(decl_52,type,
esk7_1: $i > $i ).
thf(decl_53,type,
esk8_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',mor) ).
thf(iand,axiom,
( iand
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',iand) ).
thf(mand,axiom,
( mand
= ( ^ [X8: $i > $o,X9: $i > $o,X5: $i] :
( ( X8 @ X5 )
& ( X9 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',mand) ).
thf(ior,axiom,
( ior
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',ior) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',mbox_s4) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',iimplies) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',ivalid) ).
thf(axiom1,axiom,
ivalid @ ( iimplies @ ( ior @ ( iand @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( ior @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ f ) ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ f ) ) ) ) @ ( iatom @ f ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',axiom1) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',refl_axiom) ).
thf(trans_axiom,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',trans_axiom) ).
thf(con,conjecture,
ivalid @ ( iatom @ f ),
file('/export/starexec/sandbox/tmp/tmp.RPil1cMl9Z/E---3.1_1004271.p',con) ).
thf(c_0_14,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_15,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_16,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_17,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[iand]) ).
thf(c_0_18,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_19,plain,
( ior
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ! [X22: $i] :
( ( irel @ Z2 @ X22 )
=> ( Z0 @ X22 ) )
| ! [X23: $i] :
( ( irel @ Z2 @ X23 )
=> ( Z1 @ X23 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ior]) ).
thf(c_0_20,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X2: $i] :
( ( irel @ Z1 @ X2 )
=> ( Z0 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_21,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iimplies]) ).
thf(c_0_22,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_23,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_24,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_25,plain,
( ior
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ! [X22: $i] :
( ( irel @ Z2 @ X22 )
=> ( Z0 @ X22 ) )
| ! [X23: $i] :
( ( irel @ Z2 @ X23 )
=> ( Z1 @ X23 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_16]),c_0_20]) ).
thf(c_0_26,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).
thf(c_0_27,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_28,plain,
! [X47: $i] :
( ~ ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( ! [X43: $i] :
( ( irel @ X45 @ X43 )
=> ( ( p1 @ X43 )
& ( p2 @ X43 ) ) )
| ! [X44: $i] :
( ( irel @ X45 @ X44 )
=> ( ! [X41: $i] :
( ( irel @ X44 @ X41 )
=> ( ~ ! [X37: $i] :
( ( irel @ X41 @ X37 )
=> ( p1 @ X37 ) )
| ! [X38: $i] :
( ( irel @ X41 @ X38 )
=> ( f @ X38 ) ) ) )
| ! [X42: $i] :
( ( irel @ X44 @ X42 )
=> ( ~ ! [X39: $i] :
( ( irel @ X42 @ X39 )
=> ( p2 @ X39 ) )
| ! [X40: $i] :
( ( irel @ X42 @ X40 )
=> ( f @ X40 ) ) ) ) ) ) ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( f @ X46 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]) ).
thf(c_0_29,plain,
! [X53: $i,X58: $i,X61: $i,X63: $i] :
( ( ( irel @ X53 @ ( esk1_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ( irel @ ( esk1_1 @ X53 ) @ ( esk2_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ~ ( p1 @ ( esk2_1 @ X53 ) )
| ~ ( p2 @ ( esk2_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ( irel @ ( esk1_1 @ X53 ) @ ( esk3_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ( irel @ ( esk3_1 @ X53 ) @ ( esk4_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ~ ( irel @ ( esk4_1 @ X53 ) @ X58 )
| ( p1 @ X58 )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ( irel @ ( esk4_1 @ X53 ) @ ( esk5_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ~ ( f @ ( esk5_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ( irel @ ( esk3_1 @ X53 ) @ ( esk6_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ~ ( irel @ ( esk6_1 @ X53 ) @ X61 )
| ( p2 @ X61 )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ( irel @ ( esk6_1 @ X53 ) @ ( esk7_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) )
& ( ~ ( f @ ( esk7_1 @ X53 ) )
| ~ ( irel @ X53 @ X63 )
| ( f @ X63 ) ) ),
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_28])])])])])]) ).
thf(c_0_30,plain,
! [X49: $i] : ( irel @ X49 @ X49 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_31,plain,
! [X50: $i,X51: $i,X52: $i] :
( ~ ( irel @ X50 @ X51 )
| ~ ( irel @ X51 @ X52 )
| ( irel @ X50 @ X52 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_32,plain,
! [X1: $i,X2: $i] :
( ( irel @ ( esk1_1 @ X1 ) @ ( esk2_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_34,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_35,plain,
! [X1: $i] :
( ( irel @ ( esk1_1 @ X1 ) @ ( esk2_1 @ X1 ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_37,plain,
! [X1: $i,X2: $i] :
( ( irel @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_38,plain,
! [X1: $i,X2: $i] :
( ( f @ X2 )
| ~ ( f @ ( esk5_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_39,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk2_1 @ X2 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ ( esk1_1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_40,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
thf(c_0_41,plain,
! [X1: $i,X2: $i] :
( ( irel @ ( esk1_1 @ X1 ) @ ( esk3_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_42,plain,
! [X1: $i] :
( ( irel @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_33]) ).
thf(c_0_43,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( f @ ( esk5_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
thf(c_0_44,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_45,plain,
! [X1: $i,X2: $i] :
( ( irel @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_46,plain,
! [X1: $i,X2: $i] :
( ( f @ X2 )
| ~ ( f @ ( esk7_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_47,plain,
! [X1: $i,X2: $i] :
( ( irel @ ( esk3_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_48,plain,
! [X1: $i] :
( ( irel @ ( esk1_1 @ ( esk4_1 @ X1 ) ) @ ( esk3_1 @ ( esk4_1 @ X1 ) ) )
| ( f @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
thf(c_0_49,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk2_1 @ X2 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
thf(c_0_50,plain,
! [X1: $i] :
( ( irel @ ( esk6_1 @ ( esk4_1 @ X1 ) ) @ ( esk7_1 @ ( esk4_1 @ X1 ) ) )
| ( f @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_42]),c_0_43]) ).
thf(c_0_51,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( f @ ( esk7_1 @ ( esk4_1 @ X1 ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_42]),c_0_43]) ).
thf(c_0_52,plain,
! [X1: $i] :
( ( irel @ ( esk3_1 @ ( esk4_1 @ X1 ) ) @ ( esk6_1 @ ( esk4_1 @ X1 ) ) )
| ( f @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_42]),c_0_43]) ).
thf(c_0_53,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk3_1 @ ( esk4_1 @ X2 ) ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ ( esk1_1 @ ( esk4_1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
thf(c_0_54,plain,
! [X1: $i] :
( ( irel @ ( esk4_1 @ X1 ) @ ( esk1_1 @ ( esk4_1 @ X1 ) ) )
| ( f @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_42]),c_0_43]) ).
thf(c_0_55,plain,
! [X1: $i] :
( ( irel @ ( esk6_1 @ ( esk4_1 @ X1 ) ) @ ( esk2_1 @ ( esk7_1 @ ( esk4_1 @ X1 ) ) ) )
| ( f @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
thf(c_0_56,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk6_1 @ ( esk4_1 @ X2 ) ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ ( esk3_1 @ ( esk4_1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_52]) ).
thf(c_0_57,plain,
! [X1: $i] :
( ( irel @ ( esk4_1 @ X1 ) @ ( esk3_1 @ ( esk4_1 @ X1 ) ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_58,negated_conjecture,
~ ( ivalid @ ( iatom @ f ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_59,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( p1 @ X2 )
| ( f @ X3 )
| ~ ( irel @ ( esk4_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_60,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk2_1 @ ( esk7_1 @ ( esk4_1 @ X2 ) ) ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ ( esk6_1 @ ( esk4_1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
thf(c_0_61,plain,
! [X1: $i] :
( ( irel @ ( esk4_1 @ X1 ) @ ( esk6_1 @ ( esk4_1 @ X1 ) ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_62,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( p2 @ X2 )
| ( f @ X3 )
| ~ ( irel @ ( esk6_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_63,negated_conjecture,
~ ! [X48: $i] : ( f @ X48 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_58,c_0_23]),c_0_27]) ).
thf(c_0_64,plain,
! [X1: $i,X2: $i] :
( ( f @ X2 )
| ~ ( p1 @ ( esk2_1 @ X1 ) )
| ~ ( p2 @ ( esk2_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_65,plain,
! [X1: $i,X2: $i] :
( ( f @ X1 )
| ( p1 @ X2 )
| ~ ( irel @ ( esk4_1 @ X1 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_33]) ).
thf(c_0_66,plain,
! [X1: $i] :
( ( irel @ ( esk4_1 @ X1 ) @ ( esk2_1 @ ( esk7_1 @ ( esk4_1 @ X1 ) ) ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_67,plain,
! [X1: $i,X2: $i] :
( ( f @ X1 )
| ( p2 @ X2 )
| ~ ( irel @ ( esk6_1 @ ( esk4_1 @ X1 ) ) @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_42]),c_0_43]) ).
thf(c_0_68,negated_conjecture,
~ ( f @ esk8_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])]) ).
thf(c_0_69,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( p1 @ ( esk2_1 @ X1 ) )
| ~ ( p2 @ ( esk2_1 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_64,c_0_33]) ).
thf(c_0_70,plain,
! [X1: $i] :
( ( p1 @ ( esk2_1 @ ( esk7_1 @ ( esk4_1 @ X1 ) ) ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_71,plain,
! [X1: $i] :
( ( p2 @ ( esk2_1 @ ( esk7_1 @ ( esk4_1 @ X1 ) ) ) )
| ( f @ X1 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_55]) ).
thf(c_0_72,negated_conjecture,
~ ( f @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_73,plain,
! [X1: $i] : ( f @ X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_51]) ).
thf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO067^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:29:24 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.21/0.26 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.RPil1cMl9Z/E---3.1_1004271.p
% 23.62/3.74 % Version: 3.5.1-ho
% 23.62/3.74 % Preprocessing class: HSMSSMSSMLSNHSN.
% 23.62/3.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.62/3.74 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 23.62/3.74 % Starting post_as_ho3 with 300s (1) cores
% 23.62/3.74 % Starting post_as_ho11 with 300s (1) cores
% 23.62/3.74 % Starting full_lambda_8 with 300s (1) cores
% 23.62/3.74 % new_ho_10_cnf2 with pid 1004284 completed with status 0
% 23.62/3.74 % Result found by new_ho_10_cnf2
% 23.62/3.74 % Preprocessing class: HSMSSMSSMLSNHSN.
% 23.62/3.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.62/3.74 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 23.62/3.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.62/3.74 % No SInE strategy applied
% 23.62/3.74 % Search class: HGUNF-FFSF11-SHSSMFNN
% 23.62/3.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 23.62/3.74 % Starting SubtermCWHack with 136s (1) cores
% 23.62/3.74 % Starting new_ho_10_cnf2 with 151s (1) cores
% 23.62/3.74 % Starting post_as_ho11 with 136s (1) cores
% 23.62/3.74 % Starting post_as_ho1 with 136s (1) cores
% 23.62/3.74 % Starting lpo5_fix with 136s (1) cores
% 23.62/3.74 % lpo5_fix with pid 1004295 completed with status 0
% 23.62/3.74 % Result found by lpo5_fix
% 23.62/3.74 % Preprocessing class: HSMSSMSSMLSNHSN.
% 23.62/3.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.62/3.74 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 23.62/3.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.62/3.74 % No SInE strategy applied
% 23.62/3.74 % Search class: HGUNF-FFSF11-SHSSMFNN
% 23.62/3.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 23.62/3.74 % Starting SubtermCWHack with 136s (1) cores
% 23.62/3.74 % Starting new_ho_10_cnf2 with 151s (1) cores
% 23.62/3.74 % Starting post_as_ho11 with 136s (1) cores
% 23.62/3.74 % Starting post_as_ho1 with 136s (1) cores
% 23.62/3.74 % Starting lpo5_fix with 136s (1) cores
% 23.62/3.74 % Preprocessing time : 0.001 s
% 23.62/3.74
% 23.62/3.74 % Proof found!
% 23.62/3.74 % SZS status Theorem
% 23.62/3.74 % SZS output start CNFRefutation
% See solution above
% 23.62/3.74 % Parsed axioms : 46
% 23.62/3.74 % Removed by relevancy pruning/SinE : 0
% 23.62/3.74 % Initial clauses : 38
% 23.62/3.74 % Removed in clause preprocessing : 23
% 23.62/3.74 % Initial clauses in saturation : 15
% 23.62/3.74 % Processed clauses : 5021
% 23.62/3.74 % ...of these trivial : 0
% 23.62/3.74 % ...subsumed : 3441
% 23.62/3.74 % ...remaining for further processing : 1580
% 23.62/3.74 % Other redundant clauses eliminated : 0
% 23.62/3.74 % Clauses deleted for lack of memory : 0
% 23.62/3.74 % Backward-subsumed : 341
% 23.62/3.74 % Backward-rewritten : 1236
% 23.62/3.74 % Generated clauses : 134924
% 23.62/3.74 % ...of the previous two non-redundant : 134913
% 23.62/3.74 % ...aggressively subsumed : 0
% 23.62/3.74 % Contextual simplify-reflections : 281
% 23.62/3.74 % Paramodulations : 134924
% 23.62/3.74 % Factorizations : 0
% 23.62/3.74 % NegExts : 0
% 23.62/3.74 % Equation resolutions : 0
% 23.62/3.74 % Disequality decompositions : 0
% 23.62/3.74 % Total rewrite steps : 1772
% 23.62/3.74 % ...of those cached : 1664
% 23.62/3.74 % Propositional unsat checks : 0
% 23.62/3.74 % Propositional check models : 0
% 23.62/3.74 % Propositional check unsatisfiable : 0
% 23.62/3.74 % Propositional clauses : 0
% 23.62/3.74 % Propositional clauses after purity: 0
% 23.62/3.74 % Propositional unsat core size : 0
% 23.62/3.74 % Propositional preprocessing time : 0.000
% 23.62/3.74 % Propositional encoding time : 0.000
% 23.62/3.74 % Propositional solver time : 0.000
% 23.62/3.74 % Success case prop preproc time : 0.000
% 23.62/3.74 % Success case prop encoding time : 0.000
% 23.62/3.74 % Success case prop solver time : 0.000
% 23.62/3.74 % Current number of processed clauses : 3
% 23.62/3.74 % Positive orientable unit clauses : 2
% 23.62/3.74 % Positive unorientable unit clauses: 0
% 23.62/3.74 % Negative unit clauses : 0
% 23.62/3.74 % Non-unit-clauses : 1
% 23.62/3.74 % Current number of unprocessed clauses: 127213
% 23.62/3.74 % ...number of literals in the above : 489908
% 23.62/3.74 % Current number of archived formulas : 0
% 23.62/3.74 % Current number of archived clauses : 1577
% 23.62/3.74 % Clause-clause subsumption calls (NU) : 166245
% 23.62/3.74 % Rec. Clause-clause subsumption calls : 84650
% 23.62/3.74 % Non-unit clause-clause subsumptions : 4063
% 23.62/3.74 % Unit Clause-clause subsumption calls : 0
% 23.62/3.74 % Rewrite failures with RHS unbound : 0
% 23.62/3.74 % BW rewrite match attempts : 108
% 23.62/3.74 % BW rewrite match successes : 108
% 23.62/3.74 % Condensation attempts : 5021
% 23.62/3.74 % Condensation successes : 0
% 23.62/3.74 % Termbank termtop insertions : 2485038
% 23.62/3.74 % Search garbage collected termcells : 865
% 23.62/3.74
% 23.62/3.74 % -------------------------------------------------
% 23.62/3.74 % User time : 3.119 s
% 23.62/3.74 % System time : 0.159 s
% 23.62/3.74 % Total time : 3.278 s
% 23.62/3.74 % Maximum resident set size: 3612 pages
% 23.62/3.74
% 23.62/3.74 % -------------------------------------------------
% 23.62/3.74 % User time : 15.899 s
% 23.62/3.74 % System time : 0.663 s
% 23.62/3.74 % Total time : 16.562 s
% 23.62/3.74 % Maximum resident set size: 4864 pages
% 23.62/3.74 % E exiting
%------------------------------------------------------------------------------