%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO064^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:42:16 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 308 ( 24 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 675 ( 94 ~; 121 |; 14 &; 421 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 6 con; 0-3 aty)
% Number of variables : 167 ( 56 ^; 111 !; 0 ?; 167 :)
% 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,
a: $i > $o ).
thf(decl_44,type,
a1: $i > $o ).
thf(decl_45,type,
a2: $i > $o ).
thf(decl_46,type,
b: $i > $o ).
thf(decl_47,type,
b1: $i > $o ).
thf(decl_48,type,
esk1_1: $i > $i ).
thf(decl_49,type,
esk2_0: $i ).
thf(decl_50,type,
esk3_0: $i ).
thf(decl_51,type,
esk4_0: $i ).
thf(decl_52,type,
esk5_0: $i ).
thf(decl_53,type,
esk6_0: $i ).
thf(ior,axiom,
( ior
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',ior) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',mor) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',mbox_s4) ).
thf(iand,axiom,
( iand
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',iand) ).
thf(mand,axiom,
( mand
= ( ^ [X8: $i > $o,X9: $i > $o,X5: $i] :
( ( X8 @ X5 )
& ( X9 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',mand) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',ivalid) ).
thf(con,conjecture,
ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',con) ).
thf(axiom3,axiom,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',axiom3) ).
thf(trans_axiom,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',trans_axiom) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',mnot) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',iimplies) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',refl_axiom) ).
thf(axiom2,axiom,
ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',axiom2) ).
thf(axiom1,axiom,
ivalid @ ( iatom @ a2 ),
file('/export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p',axiom1) ).
thf(c_0_16,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_17,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_18,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_19,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[iand]) ).
thf(c_0_20,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_21,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_22,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_16,c_0_17]),c_0_18]) ).
thf(c_0_23,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_24,negated_conjecture,
~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_25,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_26,plain,
! [X49: $i] :
( ! [X47: $i] :
( ( irel @ X49 @ X47 )
=> ( ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( b @ X45 ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( a @ X46 ) ) ) )
| ! [X48: $i] :
( ( irel @ X49 @ X48 )
=> ( b @ X48 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom3,c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_27,negated_conjecture,
~ ! [X54: $i] :
( ! [X52: $i] :
( ( irel @ X54 @ X52 )
=> ( a @ X52 ) )
| ! [X53: $i] :
( ( irel @ X54 @ X53 )
=> ( ! [X50: $i] :
( ( irel @ X53 @ X50 )
=> ( ( b @ X50 )
& ( a1 @ X50 ) ) )
| ! [X51: $i] :
( ( irel @ X53 @ X51 )
=> ( ( b1 @ X51 )
& ( a2 @ X51 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_24,c_0_21]),c_0_25]),c_0_22]),c_0_23]) ).
thf(c_0_28,plain,
! [X67: $i,X68: $i,X69: $i,X70: $i,X71: $i] :
( ~ ( irel @ X67 @ X68 )
| ~ ( irel @ X68 @ X69 )
| ( b @ X69 )
| ~ ( irel @ X68 @ X70 )
| ( a @ X70 )
| ~ ( irel @ X67 @ X71 )
| ( b @ X71 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
thf(c_0_29,negated_conjecture,
( ( irel @ esk2_0 @ esk3_0 )
& ~ ( a @ esk3_0 )
& ( irel @ esk2_0 @ esk4_0 )
& ( irel @ esk4_0 @ esk5_0 )
& ( ~ ( b @ esk5_0 )
| ~ ( a1 @ esk5_0 ) )
& ( irel @ esk4_0 @ esk6_0 )
& ( ~ ( b1 @ esk6_0 )
| ~ ( a2 @ esk6_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
thf(c_0_30,plain,
! [X56: $i,X57: $i,X58: $i] :
( ~ ( irel @ X56 @ X57 )
| ~ ( irel @ X57 @ X58 )
| ( irel @ X56 @ X58 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_31,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_32,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_33,plain,
! [X2: $i,X1: $i,X5: $i,X3: $i,X13: $i] :
( ( b @ X3 )
| ( a @ X5 )
| ( b @ X13 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X2 @ X5 )
| ~ ( irel @ X1 @ X13 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_34,negated_conjecture,
irel @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_35,negated_conjecture,
~ ( a @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_36,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_37,negated_conjecture,
irel @ esk4_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_38,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_39,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_31,c_0_32]),c_0_17]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( b @ X1 )
| ( b @ X2 )
| ~ ( irel @ esk2_0 @ X1 )
| ~ ( irel @ X3 @ esk2_0 )
| ~ ( irel @ X3 @ X2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk5_0 )
| ~ ( irel @ X1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_42,negated_conjecture,
irel @ esk2_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_43,plain,
! [X55: $i] : ( irel @ X55 @ X55 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_44,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_38,c_0_39]),c_0_18]) ).
thf(c_0_45,negated_conjecture,
! [X2: $i,X1: $i] :
( ( b @ esk5_0 )
| ( b @ X1 )
| ~ ( irel @ X2 @ esk2_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
thf(c_0_46,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_47,plain,
! [X44: $i] :
( ~ ! [X42: $i] :
( ( irel @ X44 @ X42 )
=> ( b @ X42 ) )
| ! [X43: $i] :
( ( irel @ X44 @ X43 )
=> ( ! [X40: $i] :
( ( irel @ X43 @ X40 )
=> ( ! [X38: $i] :
( ( irel @ X40 @ X38 )
=> ( b1 @ X38 ) )
| ! [X39: $i] :
( ( irel @ X40 @ X39 )
=> ( a1 @ X39 ) ) ) )
| ! [X41: $i] :
( ( irel @ X43 @ X41 )
=> ( b1 @ X41 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom2,c_0_21]),c_0_22]),c_0_44]),c_0_23]) ).
thf(c_0_48,negated_conjecture,
! [X1: $i] :
( ( b @ esk5_0 )
| ( b @ X1 )
| ~ ( irel @ esk2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_49,plain,
! [X37: $i] : ( a2 @ X37 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_21]),c_0_23]) ).
thf(c_0_50,plain,
! [X60: $i,X62: $i,X63: $i,X64: $i,X65: $i,X66: $i] :
( ( ( irel @ X60 @ ( esk1_1 @ X60 ) )
| ~ ( irel @ X60 @ X62 )
| ~ ( irel @ X62 @ X63 )
| ~ ( irel @ X63 @ X64 )
| ( b1 @ X64 )
| ~ ( irel @ X63 @ X65 )
| ( a1 @ X65 )
| ~ ( irel @ X62 @ X66 )
| ( b1 @ X66 ) )
& ( ~ ( b @ ( esk1_1 @ X60 ) )
| ~ ( irel @ X60 @ X62 )
| ~ ( irel @ X62 @ X63 )
| ~ ( irel @ X63 @ X64 )
| ( b1 @ X64 )
| ~ ( irel @ X63 @ X65 )
| ( a1 @ X65 )
| ~ ( irel @ X62 @ X66 )
| ( b1 @ X66 ) ) ),
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_47])])])])])]) ).
thf(c_0_51,negated_conjecture,
( ~ ( b @ esk5_0 )
| ~ ( a1 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_52,negated_conjecture,
b @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_41]),c_0_42])]) ).
thf(c_0_53,plain,
! [X59: $i] : ( a2 @ X59 ),
inference(variable_rename,[status(thm)],[c_0_49]) ).
thf(c_0_54,plain,
! [X1: $i,X3: $i,X2: $i,X13: $i,X5: $i,X16: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( b1 @ X5 )
| ( a1 @ X13 )
| ( b1 @ X16 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X3 @ X5 )
| ~ ( irel @ X3 @ X13 )
| ~ ( irel @ X2 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_55,negated_conjecture,
~ ( a1 @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
thf(c_0_56,negated_conjecture,
irel @ esk4_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_57,negated_conjecture,
( ~ ( b1 @ esk6_0 )
| ~ ( a2 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_58,plain,
! [X1: $i] : ( a2 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_59,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( b1 @ X2 )
| ( b1 @ X3 )
| ~ ( irel @ esk4_0 @ X2 )
| ~ ( irel @ X5 @ esk4_0 )
| ~ ( irel @ X5 @ X3 )
| ~ ( irel @ X1 @ X5 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_37]),c_0_55]) ).
thf(c_0_60,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk6_0 )
| ~ ( irel @ X1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_56]) ).
thf(c_0_61,negated_conjecture,
~ ( b1 @ esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( b1 @ X2 )
| ~ ( irel @ X3 @ esk4_0 )
| ~ ( irel @ X3 @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_46])]),c_0_61]) ).
thf(c_0_63,negated_conjecture,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( b1 @ X2 )
| ~ ( irel @ esk2_0 @ X2 )
| ~ ( irel @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_42]) ).
thf(c_0_64,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ~ ( irel @ X1 @ esk2_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_60]),c_0_42])]),c_0_61]) ).
thf(c_0_65,negated_conjecture,
! [X2: $i,X1: $i] :
( ( b @ ( esk1_1 @ esk2_0 ) )
| ( b @ X1 )
| ~ ( irel @ X2 @ esk2_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_64]),c_0_46])]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i] :
( ( b @ ( esk1_1 @ esk2_0 ) )
| ( b @ X1 )
| ~ ( irel @ esk2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_46]) ).
thf(c_0_67,plain,
! [X1: $i,X3: $i,X2: $i,X13: $i,X5: $i,X16: $i] :
( ( b1 @ X5 )
| ( a1 @ X13 )
| ( b1 @ X16 )
| ~ ( b @ ( esk1_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X3 @ X5 )
| ~ ( irel @ X3 @ X13 )
| ~ ( irel @ X2 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_68,negated_conjecture,
b @ ( esk1_1 @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_64]),c_0_46])]) ).
thf(c_0_69,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i,X13: $i] :
( ( b1 @ X1 )
| ( b1 @ X2 )
| ( a1 @ X3 )
| ~ ( irel @ esk2_0 @ X5 )
| ~ ( irel @ X13 @ X3 )
| ~ ( irel @ X13 @ X1 )
| ~ ( irel @ X5 @ X2 )
| ~ ( irel @ X5 @ X13 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_70,negated_conjecture,
! [X2: $i,X1: $i,X5: $i,X3: $i] :
( ( a1 @ X1 )
| ( b1 @ X2 )
| ( b1 @ X3 )
| ~ ( irel @ esk2_0 @ X2 )
| ~ ( irel @ esk2_0 @ X5 )
| ~ ( irel @ X5 @ X1 )
| ~ ( irel @ X5 @ X3 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_46]) ).
thf(c_0_71,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( b1 @ X1 )
| ( a1 @ X2 )
| ~ ( irel @ esk2_0 @ X3 )
| ~ ( irel @ X3 @ X2 )
| ~ ( irel @ X3 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_60]),c_0_42])]),c_0_61]) ).
thf(c_0_72,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk6_0 )
| ~ ( irel @ X2 @ esk4_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_60]) ).
thf(c_0_73,negated_conjecture,
! [X1: $i,X2: $i] :
( ( a1 @ X1 )
| ( b1 @ X2 )
| ~ ( irel @ esk2_0 @ X1 )
| ~ ( irel @ esk2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_46]) ).
thf(c_0_74,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk6_0 )
| ~ ( irel @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_42]) ).
thf(c_0_75,negated_conjecture,
! [X1: $i] :
( ( b1 @ X1 )
| ~ ( irel @ esk2_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_41]),c_0_42])]),c_0_55]) ).
thf(c_0_76,negated_conjecture,
irel @ esk2_0 @ esk6_0,
inference(spm,[status(thm)],[c_0_74,c_0_46]) ).
thf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_75]),c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO064^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:26:15 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.47Lnm4EFjg/E---3.1_2881853.p
% 0.21/0.30 % Version: 3.5.1-ho
% 0.21/0.30 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.30 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.30 % Starting post_as_ho11 with 300s (1) cores
% 0.21/0.30 % Starting full_lambda_8 with 300s (1) cores
% 0.21/0.30 % new_ho_10_cnf2 with pid 2881883 completed with status 0
% 0.21/0.30 % Result found by new_ho_10_cnf2
% 0.21/0.30 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.30 % No SInE strategy applied
% 0.21/0.30 % Search class: HGHNS-FFSS11-SHSSMFNN
% 0.21/0.30 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 0.21/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.30 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.21/0.30 % Starting sh5l with 136s (1) cores
% 0.21/0.30 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.21/0.30 % Starting lpo1_def_fix with 136s (1) cores
% 0.21/0.30 % ehoh_best_sine_rwall with pid 2881895 completed with status 0
% 0.21/0.30 % Result found by ehoh_best_sine_rwall
% 0.21/0.30 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.30 % No SInE strategy applied
% 0.21/0.30 % Search class: HGHNS-FFSS11-SHSSMFNN
% 0.21/0.30 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 0.21/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.30 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.21/0.30 % Starting sh5l with 136s (1) cores
% 0.21/0.30 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.21/0.30 % Preprocessing time : 0.002 s
% 0.21/0.30 % Presaturation interreduction done
% 0.21/0.30
% 0.21/0.30 % Proof found!
% 0.21/0.30 % SZS status Theorem
% 0.21/0.30 % SZS output start CNFRefutation
% See solution above
% 0.21/0.31 % Parsed axioms : 50
% 0.21/0.31 % Removed by relevancy pruning/SinE : 0
% 0.21/0.31 % Initial clauses : 38
% 0.21/0.31 % Removed in clause preprocessing : 25
% 0.21/0.31 % Initial clauses in saturation : 13
% 0.21/0.31 % Processed clauses : 262
% 0.21/0.31 % ...of these trivial : 15
% 0.21/0.31 % ...subsumed : 48
% 0.21/0.31 % ...remaining for further processing : 199
% 0.21/0.31 % Other redundant clauses eliminated : 0
% 0.21/0.31 % Clauses deleted for lack of memory : 0
% 0.21/0.31 % Backward-subsumed : 40
% 0.21/0.31 % Backward-rewritten : 23
% 0.21/0.31 % Generated clauses : 733
% 0.21/0.31 % ...of the previous two non-redundant : 570
% 0.21/0.31 % ...aggressively subsumed : 0
% 0.21/0.31 % Contextual simplify-reflections : 1
% 0.21/0.31 % Paramodulations : 733
% 0.21/0.31 % Factorizations : 0
% 0.21/0.31 % NegExts : 0
% 0.21/0.31 % Equation resolutions : 0
% 0.21/0.31 % Disequality decompositions : 0
% 0.21/0.31 % Total rewrite steps : 341
% 0.21/0.31 % ...of those cached : 326
% 0.21/0.31 % Propositional unsat checks : 0
% 0.21/0.31 % Propositional check models : 0
% 0.21/0.31 % Propositional check unsatisfiable : 0
% 0.21/0.31 % Propositional clauses : 0
% 0.21/0.31 % Propositional clauses after purity: 0
% 0.21/0.31 % Propositional unsat core size : 0
% 0.21/0.31 % Propositional preprocessing time : 0.000
% 0.21/0.31 % Propositional encoding time : 0.000
% 0.21/0.31 % Propositional solver time : 0.000
% 0.21/0.31 % Success case prop preproc time : 0.000
% 0.21/0.31 % Success case prop encoding time : 0.000
% 0.21/0.31 % Success case prop solver time : 0.000
% 0.21/0.31 % Current number of processed clauses : 123
% 0.21/0.31 % Positive orientable unit clauses : 17
% 0.21/0.31 % Positive unorientable unit clauses: 0
% 0.21/0.31 % Negative unit clauses : 7
% 0.21/0.31 % Non-unit-clauses : 99
% 0.21/0.31 % Current number of unprocessed clauses: 205
% 0.21/0.31 % ...number of literals in the above : 1353
% 0.21/0.31 % Current number of archived formulas : 0
% 0.21/0.31 % Current number of archived clauses : 76
% 0.21/0.31 % Clause-clause subsumption calls (NU) : 6928
% 0.21/0.31 % Rec. Clause-clause subsumption calls : 1703
% 0.21/0.31 % Non-unit clause-clause subsumptions : 74
% 0.21/0.31 % Unit Clause-clause subsumption calls : 237
% 0.21/0.31 % Rewrite failures with RHS unbound : 0
% 0.21/0.31 % BW rewrite match attempts : 15
% 0.21/0.31 % BW rewrite match successes : 10
% 0.21/0.31 % Condensation attempts : 0
% 0.21/0.31 % Condensation successes : 0
% 0.21/0.31 % Termbank termtop insertions : 26956
% 0.21/0.31 % Search garbage collected termcells : 931
% 0.21/0.31
% 0.21/0.31 % -------------------------------------------------
% 0.21/0.31 % User time : 0.041 s
% 0.21/0.31 % System time : 0.004 s
% 0.21/0.31 % Total time : 0.045 s
% 0.21/0.31 % Maximum resident set size: 3668 pages
% 0.21/0.31
% 0.21/0.31 % -------------------------------------------------
% 0.21/0.31 % User time : 0.199 s
% 0.21/0.31 % System time : 0.020 s
% 0.21/0.31 % Total time : 0.219 s
% 0.21/0.31 % Maximum resident set size: 4864 pages
% 0.21/0.31 % E exiting
%------------------------------------------------------------------------------