%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO064^4.003 : 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 : n010.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 6.00s 1.18s
% Output : CNFRefutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 17
% Syntax : Number of formulae : 134 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 578 ( 24 equ; 0 cnn)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 1428 ( 201 ~; 299 |; 19 &; 876 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 8 con; 0-3 aty)
% Number of variables : 273 ( 56 ^; 217 !; 0 ?; 273 :)
% 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,
a3: $i > $o ).
thf(decl_47,type,
b: $i > $o ).
thf(decl_48,type,
b1: $i > $o ).
thf(decl_49,type,
b2: $i > $o ).
thf(decl_50,type,
esk1_1: $i > $i ).
thf(decl_51,type,
esk2_1: $i > $i ).
thf(decl_52,type,
esk3_0: $i ).
thf(decl_53,type,
esk4_0: $i ).
thf(decl_54,type,
esk5_0: $i ).
thf(decl_55,type,
esk6_0: $i ).
thf(decl_56,type,
esk7_0: $i ).
thf(decl_57,type,
esk8_0: $i ).
thf(decl_58,type,
esk9_0: $i ).
thf(ior,axiom,
( ior
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',ior) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',mor) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',mbox_s4) ).
thf(iand,axiom,
( iand
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',iand) ).
thf(mand,axiom,
( mand
= ( ^ [X8: $i > $o,X9: $i > $o,X5: $i] :
( ( X8 @ X5 )
& ( X9 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',mand) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',ivalid) ).
thf(con,conjecture,
ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( ior @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iand @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',con) ).
thf(axiom4,axiom,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',axiom4) ).
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.4QfQUvSAFY/E---3.1_3085408.p',trans_axiom) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',mnot) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',iimplies) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',refl_axiom) ).
thf(axiom3,axiom,
ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',axiom3) ).
thf(axiom2,axiom,
ivalid @ ( iimplies @ ( iatom @ b1 ) @ ( ior @ ( ior @ ( iatom @ b2 ) @ ( iatom @ a2 ) ) @ ( iatom @ b2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',axiom2) ).
thf(axiom1,axiom,
ivalid @ ( iatom @ a3 ),
file('/export/starexec/sandbox/tmp/tmp.4QfQUvSAFY/E---3.1_3085408.p',axiom1) ).
thf(c_0_17,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_18,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_19,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_20,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[iand]) ).
thf(c_0_21,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_22,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_23,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_17,c_0_18]),c_0_19]) ).
thf(c_0_24,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_25,negated_conjecture,
~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( ior @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iand @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_26,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
! [X56: $i] :
( ! [X54: $i] :
( ( irel @ X56 @ X54 )
=> ( ! [X52: $i] :
( ( irel @ X54 @ X52 )
=> ( b @ X52 ) )
| ! [X53: $i] :
( ( irel @ X54 @ X53 )
=> ( a @ X53 ) ) ) )
| ! [X55: $i] :
( ( irel @ X56 @ X55 )
=> ( b @ X55 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom4,c_0_22]),c_0_23]),c_0_24]) ).
thf(c_0_28,negated_conjecture,
~ ! [X63: $i] :
( ! [X61: $i] :
( ( irel @ X63 @ X61 )
=> ( a @ X61 ) )
| ! [X62: $i] :
( ( irel @ X63 @ X62 )
=> ( ! [X59: $i] :
( ( irel @ X62 @ X59 )
=> ( ( b @ X59 )
& ( a1 @ X59 ) ) )
| ! [X60: $i] :
( ( irel @ X62 @ X60 )
=> ( ! [X57: $i] :
( ( irel @ X60 @ X57 )
=> ( ( b1 @ X57 )
& ( a2 @ X57 ) ) )
| ! [X58: $i] :
( ( irel @ X60 @ X58 )
=> ( ( b2 @ X58 )
& ( a3 @ X58 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_22]),c_0_26]),c_0_23]),c_0_24]) ).
thf(c_0_29,plain,
! [X83: $i,X84: $i,X85: $i,X86: $i,X87: $i] :
( ~ ( irel @ X83 @ X84 )
| ~ ( irel @ X84 @ X85 )
| ( b @ X85 )
| ~ ( irel @ X84 @ X86 )
| ( a @ X86 )
| ~ ( irel @ X83 @ X87 )
| ( b @ X87 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
thf(c_0_30,negated_conjecture,
( ( irel @ esk3_0 @ esk4_0 )
& ~ ( a @ esk4_0 )
& ( irel @ esk3_0 @ esk5_0 )
& ( irel @ esk5_0 @ esk6_0 )
& ( ~ ( b @ esk6_0 )
| ~ ( a1 @ esk6_0 ) )
& ( irel @ esk5_0 @ esk7_0 )
& ( irel @ esk7_0 @ esk8_0 )
& ( ~ ( b1 @ esk8_0 )
| ~ ( a2 @ esk8_0 ) )
& ( irel @ esk7_0 @ esk9_0 )
& ( ~ ( b2 @ esk9_0 )
| ~ ( a3 @ esk9_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
thf(c_0_31,plain,
! [X65: $i,X66: $i,X67: $i] :
( ~ ( irel @ X65 @ X66 )
| ~ ( irel @ X66 @ X67 )
| ( irel @ X65 @ X67 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_32,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_33,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_34,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_29]) ).
thf(c_0_35,negated_conjecture,
irel @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,negated_conjecture,
~ ( a @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_37,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_38,negated_conjecture,
irel @ esk5_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_39,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_40,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_32,c_0_33]),c_0_18]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( b @ X1 )
| ( b @ X2 )
| ~ ( irel @ esk3_0 @ X1 )
| ~ ( irel @ X3 @ esk3_0 )
| ~ ( irel @ X3 @ X2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk6_0 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_43,negated_conjecture,
irel @ esk3_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_44,plain,
! [X64: $i] : ( irel @ X64 @ X64 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_45,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_39,c_0_40]),c_0_19]) ).
thf(c_0_46,negated_conjecture,
! [X2: $i,X1: $i] :
( ( b @ esk6_0 )
| ( b @ X1 )
| ~ ( irel @ X2 @ esk3_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
thf(c_0_47,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_48,plain,
! [X51: $i] :
( ~ ! [X49: $i] :
( ( irel @ X51 @ X49 )
=> ( b @ X49 ) )
| ! [X50: $i] :
( ( irel @ X51 @ X50 )
=> ( ! [X47: $i] :
( ( irel @ X50 @ X47 )
=> ( ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( b1 @ X45 ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( a1 @ X46 ) ) ) )
| ! [X48: $i] :
( ( irel @ X50 @ X48 )
=> ( b1 @ X48 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom3,c_0_22]),c_0_23]),c_0_45]),c_0_24]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk6_0 )
| ~ ( irel @ X2 @ esk5_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i] :
( ( b @ esk6_0 )
| ( b @ X1 )
| ~ ( irel @ esk3_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_51,negated_conjecture,
irel @ esk7_0 @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_52,plain,
! [X76: $i,X78: $i,X79: $i,X80: $i,X81: $i,X82: $i] :
( ( ( irel @ X76 @ ( esk2_1 @ X76 ) )
| ~ ( irel @ X76 @ X78 )
| ~ ( irel @ X78 @ X79 )
| ~ ( irel @ X79 @ X80 )
| ( b1 @ X80 )
| ~ ( irel @ X79 @ X81 )
| ( a1 @ X81 )
| ~ ( irel @ X78 @ X82 )
| ( b1 @ X82 ) )
& ( ~ ( b @ ( esk2_1 @ X76 ) )
| ~ ( irel @ X76 @ X78 )
| ~ ( irel @ X78 @ X79 )
| ~ ( irel @ X79 @ X80 )
| ( b1 @ X80 )
| ~ ( irel @ X79 @ X81 )
| ( a1 @ X81 )
| ~ ( irel @ X78 @ X82 )
| ( b1 @ X82 ) ) ),
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_48])])])])])]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk6_0 )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_43]) ).
thf(c_0_54,negated_conjecture,
( ~ ( b @ esk6_0 )
| ~ ( a1 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_55,negated_conjecture,
b @ esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_43])]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk8_0 )
| ~ ( irel @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
thf(c_0_57,plain,
! [X1: $i,X3: $i,X2: $i,X13: $i,X5: $i,X16: $i] :
( ( irel @ X1 @ ( esk2_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_52]) ).
thf(c_0_58,negated_conjecture,
irel @ esk3_0 @ esk6_0,
inference(spm,[status(thm)],[c_0_53,c_0_47]) ).
thf(c_0_59,negated_conjecture,
~ ( a1 @ esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
thf(c_0_60,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk8_0 )
| ~ ( irel @ X2 @ esk7_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_56]) ).
thf(c_0_61,negated_conjecture,
irel @ esk5_0 @ esk7_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( b1 @ X2 )
| ( b1 @ X3 )
| ~ ( irel @ esk3_0 @ X2 )
| ~ ( irel @ X5 @ esk3_0 )
| ~ ( irel @ X5 @ X3 )
| ~ ( irel @ X1 @ X5 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
thf(c_0_63,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk8_0 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_64,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( b1 @ esk8_0 )
| ( b1 @ X2 )
| ~ ( irel @ X3 @ esk3_0 )
| ~ ( irel @ X3 @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_43])]) ).
thf(c_0_65,negated_conjecture,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( b1 @ esk8_0 )
| ( b1 @ X2 )
| ~ ( irel @ esk3_0 @ X2 )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_47]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( b1 @ esk8_0 )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_63]),c_0_43])]) ).
thf(c_0_67,negated_conjecture,
( ( irel @ esk3_0 @ ( esk2_1 @ esk3_0 ) )
| ( b1 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_47]) ).
thf(c_0_68,negated_conjecture,
! [X2: $i,X1: $i] :
( ( b @ ( esk2_1 @ esk3_0 ) )
| ( b1 @ esk8_0 )
| ( b @ X1 )
| ~ ( irel @ X2 @ esk3_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_67]) ).
thf(c_0_69,negated_conjecture,
! [X1: $i] :
( ( b @ ( esk2_1 @ esk3_0 ) )
| ( b1 @ esk8_0 )
| ( b @ X1 )
| ~ ( irel @ esk3_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_47]) ).
thf(c_0_70,plain,
! [X44: $i] :
( ~ ! [X42: $i] :
( ( irel @ X44 @ X42 )
=> ( b1 @ X42 ) )
| ! [X43: $i] :
( ( irel @ X44 @ X43 )
=> ( ! [X40: $i] :
( ( irel @ X43 @ X40 )
=> ( ! [X38: $i] :
( ( irel @ X40 @ X38 )
=> ( b2 @ X38 ) )
| ! [X39: $i] :
( ( irel @ X40 @ X39 )
=> ( a2 @ X39 ) ) ) )
| ! [X41: $i] :
( ( irel @ X43 @ X41 )
=> ( b2 @ X41 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom2,c_0_22]),c_0_23]),c_0_45]),c_0_24]) ).
thf(c_0_71,plain,
! [X37: $i] : ( a3 @ X37 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_22]),c_0_24]) ).
thf(c_0_72,plain,
! [X1: $i,X3: $i,X2: $i,X13: $i,X5: $i,X16: $i] :
( ( b1 @ X5 )
| ( a1 @ X13 )
| ( b1 @ X16 )
| ~ ( b @ ( esk2_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X3 @ X5 )
| ~ ( irel @ X3 @ X13 )
| ~ ( irel @ X2 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_73,negated_conjecture,
( ( b @ ( esk2_1 @ esk3_0 ) )
| ( b1 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_67]) ).
thf(c_0_74,plain,
! [X69: $i,X71: $i,X72: $i,X73: $i,X74: $i,X75: $i] :
( ( ( irel @ X69 @ ( esk1_1 @ X69 ) )
| ~ ( irel @ X69 @ X71 )
| ~ ( irel @ X71 @ X72 )
| ~ ( irel @ X72 @ X73 )
| ( b2 @ X73 )
| ~ ( irel @ X72 @ X74 )
| ( a2 @ X74 )
| ~ ( irel @ X71 @ X75 )
| ( b2 @ X75 ) )
& ( ~ ( b1 @ ( esk1_1 @ X69 ) )
| ~ ( irel @ X69 @ X71 )
| ~ ( irel @ X71 @ X72 )
| ~ ( irel @ X72 @ X73 )
| ( b2 @ X73 )
| ~ ( irel @ X72 @ X74 )
| ( a2 @ X74 )
| ~ ( irel @ X71 @ X75 )
| ( b2 @ X75 ) ) ),
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_70])])])])])]) ).
thf(c_0_75,plain,
! [X68: $i] : ( a3 @ X68 ),
inference(variable_rename,[status(thm)],[c_0_71]) ).
thf(c_0_76,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i,X13: $i] :
( ( b1 @ esk8_0 )
| ( b1 @ X1 )
| ( b1 @ X2 )
| ( a1 @ X3 )
| ~ ( irel @ esk3_0 @ X5 )
| ~ ( irel @ X13 @ X3 )
| ~ ( irel @ X13 @ X1 )
| ~ ( irel @ X5 @ X2 )
| ~ ( irel @ X5 @ X13 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_77,plain,
! [X1: $i,X3: $i,X2: $i,X13: $i,X5: $i,X16: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( b2 @ X5 )
| ( a2 @ X13 )
| ( b2 @ X16 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X3 @ X5 )
| ~ ( irel @ X3 @ X13 )
| ~ ( irel @ X2 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
thf(c_0_78,negated_conjecture,
irel @ esk7_0 @ esk9_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_79,negated_conjecture,
( ~ ( b2 @ esk9_0 )
| ~ ( a3 @ esk9_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_80,plain,
! [X1: $i] : ( a3 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_81,negated_conjecture,
! [X2: $i,X1: $i,X5: $i,X3: $i] :
( ( b1 @ esk8_0 )
| ( a1 @ X1 )
| ( b1 @ X2 )
| ( b1 @ X3 )
| ~ ( irel @ esk3_0 @ X2 )
| ~ ( irel @ esk3_0 @ X5 )
| ~ ( irel @ X5 @ X1 )
| ~ ( irel @ X5 @ X3 ) ),
inference(spm,[status(thm)],[c_0_76,c_0_47]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( a2 @ esk8_0 )
| ( b2 @ X2 )
| ( b2 @ X3 )
| ~ ( irel @ esk7_0 @ X2 )
| ~ ( irel @ X5 @ esk7_0 )
| ~ ( irel @ X5 @ X3 )
| ~ ( irel @ X1 @ X5 ) ),
inference(spm,[status(thm)],[c_0_77,c_0_51]) ).
thf(c_0_83,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk9_0 )
| ~ ( irel @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_78]) ).
thf(c_0_84,negated_conjecture,
~ ( b2 @ esk9_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( b1 @ esk8_0 )
| ( b1 @ X1 )
| ( a1 @ X2 )
| ~ ( irel @ esk3_0 @ X3 )
| ~ ( irel @ X3 @ X2 )
| ~ ( irel @ X3 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_63]),c_0_43])]) ).
thf(c_0_86,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( a2 @ esk8_0 )
| ( b2 @ X2 )
| ~ ( irel @ X3 @ esk7_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_82,c_0_83]),c_0_47])]),c_0_84]) ).
thf(c_0_87,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk9_0 )
| ~ ( irel @ X2 @ esk7_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_83]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i,X2: $i] :
( ( b1 @ esk8_0 )
| ( a1 @ X1 )
| ( b1 @ X2 )
| ~ ( irel @ esk3_0 @ X1 )
| ~ ( irel @ esk3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_47]) ).
thf(c_0_89,negated_conjecture,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( a2 @ esk8_0 )
| ( b2 @ X2 )
| ~ ( irel @ esk5_0 @ X2 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_86,c_0_61]) ).
thf(c_0_90,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk9_0 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_87,c_0_61]) ).
thf(c_0_91,negated_conjecture,
! [X1: $i] :
( ( b1 @ esk8_0 )
| ( b1 @ X1 )
| ~ ( irel @ esk3_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_42]),c_0_43])]),c_0_59]) ).
thf(c_0_92,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( a2 @ esk8_0 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_47])]),c_0_84]) ).
thf(c_0_93,negated_conjecture,
( ~ ( b1 @ esk8_0 )
| ~ ( a2 @ esk8_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_94,negated_conjecture,
b1 @ esk8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_63]),c_0_43])]) ).
thf(c_0_95,negated_conjecture,
( ( irel @ esk3_0 @ ( esk1_1 @ esk3_0 ) )
| ( a2 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_92,c_0_43]) ).
thf(c_0_96,negated_conjecture,
~ ( a2 @ esk8_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
thf(c_0_97,negated_conjecture,
irel @ esk3_0 @ ( esk1_1 @ esk3_0 ),
inference(sr,[status(thm)],[c_0_95,c_0_96]) ).
thf(c_0_98,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( b1 @ ( esk1_1 @ esk3_0 ) )
| ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( b1 @ X2 )
| ~ ( irel @ X3 @ esk3_0 )
| ~ ( irel @ X3 @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_97]) ).
thf(c_0_99,negated_conjecture,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( b1 @ ( esk1_1 @ esk3_0 ) )
| ( b1 @ X2 )
| ~ ( irel @ esk3_0 @ X2 )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_98,c_0_47]) ).
thf(c_0_100,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ esk3_0 ) )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_97]) ).
thf(c_0_101,negated_conjecture,
! [X1: $i] :
( ( b1 @ ( esk1_1 @ esk3_0 ) )
| ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_47])]) ).
thf(c_0_102,plain,
! [X1: $i,X3: $i,X2: $i,X13: $i,X5: $i,X16: $i] :
( ( b2 @ X5 )
| ( a2 @ X13 )
| ( b2 @ X16 )
| ~ ( b1 @ ( 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_74]) ).
thf(c_0_103,negated_conjecture,
( ( irel @ esk3_0 @ ( esk2_1 @ esk3_0 ) )
| ( b1 @ ( esk1_1 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_101,c_0_47]) ).
thf(c_0_104,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i,X13: $i] :
( ( irel @ esk3_0 @ ( esk2_1 @ esk3_0 ) )
| ( b2 @ X1 )
| ( b2 @ X2 )
| ( a2 @ X3 )
| ~ ( irel @ esk3_0 @ X5 )
| ~ ( irel @ X13 @ X3 )
| ~ ( irel @ X13 @ X1 )
| ~ ( irel @ X5 @ X2 )
| ~ ( irel @ X5 @ X13 ) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
thf(c_0_105,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk7_0 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_61]) ).
thf(c_0_106,negated_conjecture,
! [X2: $i,X1: $i,X5: $i,X3: $i] :
( ( irel @ esk3_0 @ ( esk2_1 @ esk3_0 ) )
| ( a2 @ X1 )
| ( b2 @ X2 )
| ( b2 @ X3 )
| ~ ( irel @ esk7_0 @ X2 )
| ~ ( irel @ esk7_0 @ X5 )
| ~ ( irel @ X5 @ X1 )
| ~ ( irel @ X5 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_43])]) ).
thf(c_0_107,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ esk3_0 @ ( esk2_1 @ esk3_0 ) )
| ( b2 @ X1 )
| ( a2 @ X2 )
| ~ ( irel @ esk7_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_106,c_0_83]),c_0_47])]),c_0_84]) ).
thf(c_0_108,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ esk3_0 @ ( esk2_1 @ esk3_0 ) )
| ( a2 @ X1 )
| ( b2 @ X2 )
| ~ ( irel @ esk7_0 @ X1 )
| ~ ( irel @ esk7_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_107,c_0_47]) ).
thf(c_0_109,negated_conjecture,
! [X1: $i] :
( ( irel @ esk3_0 @ ( esk2_1 @ esk3_0 ) )
| ( b2 @ X1 )
| ~ ( irel @ esk7_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_56]),c_0_47])]),c_0_96]) ).
thf(c_0_110,negated_conjecture,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( a2 @ esk8_0 )
| ( b2 @ X2 )
| ~ ( irel @ esk7_0 @ X2 )
| ~ ( irel @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_86,c_0_47]) ).
thf(c_0_111,negated_conjecture,
irel @ esk3_0 @ ( esk2_1 @ esk3_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_83]),c_0_47])]),c_0_84]) ).
thf(c_0_112,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( a2 @ esk8_0 )
| ~ ( irel @ X1 @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_83]),c_0_47])]),c_0_84]) ).
thf(c_0_113,negated_conjecture,
! [X2: $i,X1: $i] :
( ( b @ ( esk2_1 @ esk3_0 ) )
| ( b @ X1 )
| ~ ( irel @ X2 @ esk3_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_111]) ).
thf(c_0_114,negated_conjecture,
( ( irel @ esk7_0 @ ( esk1_1 @ esk7_0 ) )
| ( a2 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_112,c_0_47]) ).
thf(c_0_115,negated_conjecture,
! [X1: $i] :
( ( b @ ( esk2_1 @ esk3_0 ) )
| ( b @ X1 )
| ~ ( irel @ esk3_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_113,c_0_47]) ).
thf(c_0_116,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ esk3_0 ) )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_111]) ).
thf(c_0_117,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ esk7_0 ) )
| ( a2 @ esk8_0 )
| ~ ( irel @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_114]) ).
thf(c_0_118,negated_conjecture,
b @ ( esk2_1 @ esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_47])]) ).
thf(c_0_119,negated_conjecture,
( ( irel @ esk5_0 @ ( esk1_1 @ esk7_0 ) )
| ( a2 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_117,c_0_61]) ).
thf(c_0_120,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i,X13: $i] :
( ( b1 @ X1 )
| ( b1 @ X2 )
| ( a1 @ X3 )
| ~ ( irel @ esk3_0 @ X5 )
| ~ ( irel @ X13 @ X3 )
| ~ ( irel @ X13 @ X1 )
| ~ ( irel @ X5 @ X2 )
| ~ ( irel @ X5 @ X13 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_118]) ).
thf(c_0_121,negated_conjecture,
irel @ esk5_0 @ ( esk1_1 @ esk7_0 ),
inference(sr,[status(thm)],[c_0_119,c_0_96]) ).
thf(c_0_122,negated_conjecture,
! [X2: $i,X1: $i,X5: $i,X3: $i] :
( ( a1 @ X1 )
| ( b1 @ X2 )
| ( b1 @ X3 )
| ~ ( irel @ esk3_0 @ X2 )
| ~ ( irel @ esk3_0 @ X5 )
| ~ ( irel @ X5 @ X1 )
| ~ ( irel @ X5 @ X3 ) ),
inference(spm,[status(thm)],[c_0_120,c_0_47]) ).
thf(c_0_123,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ esk7_0 ) )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_121]) ).
thf(c_0_124,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( b1 @ ( esk1_1 @ esk7_0 ) )
| ( b1 @ X1 )
| ( a1 @ X2 )
| ~ ( irel @ esk3_0 @ X3 )
| ~ ( irel @ X3 @ X2 )
| ~ ( irel @ X3 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_43])]) ).
thf(c_0_125,negated_conjecture,
! [X1: $i,X2: $i] :
( ( b1 @ ( esk1_1 @ esk7_0 ) )
| ( a1 @ X1 )
| ( b1 @ X2 )
| ~ ( irel @ esk3_0 @ X1 )
| ~ ( irel @ esk3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_124,c_0_47]) ).
thf(c_0_126,negated_conjecture,
! [X1: $i] :
( ( b1 @ ( esk1_1 @ esk7_0 ) )
| ( b1 @ X1 )
| ~ ( irel @ esk3_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_42]),c_0_43])]),c_0_59]) ).
thf(c_0_127,negated_conjecture,
b1 @ ( esk1_1 @ esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_123]),c_0_43])]) ).
thf(c_0_128,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X5: $i,X13: $i] :
( ( b2 @ X1 )
| ( b2 @ X2 )
| ( a2 @ X3 )
| ~ ( irel @ esk7_0 @ X5 )
| ~ ( irel @ X13 @ X3 )
| ~ ( irel @ X13 @ X1 )
| ~ ( irel @ X5 @ X2 )
| ~ ( irel @ X5 @ X13 ) ),
inference(spm,[status(thm)],[c_0_102,c_0_127]) ).
thf(c_0_129,negated_conjecture,
! [X2: $i,X1: $i,X5: $i,X3: $i] :
( ( a2 @ X1 )
| ( b2 @ X2 )
| ( b2 @ X3 )
| ~ ( irel @ esk7_0 @ X2 )
| ~ ( irel @ esk7_0 @ X5 )
| ~ ( irel @ X5 @ X1 )
| ~ ( irel @ X5 @ X3 ) ),
inference(spm,[status(thm)],[c_0_128,c_0_47]) ).
thf(c_0_130,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( b2 @ X1 )
| ( a2 @ X2 )
| ~ ( irel @ esk7_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_129,c_0_83]),c_0_47])]),c_0_84]) ).
thf(c_0_131,negated_conjecture,
! [X1: $i,X2: $i] :
( ( a2 @ X1 )
| ( b2 @ X2 )
| ~ ( irel @ esk7_0 @ X1 )
| ~ ( irel @ esk7_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_130,c_0_47]) ).
thf(c_0_132,negated_conjecture,
! [X1: $i] :
( ( b2 @ X1 )
| ~ ( irel @ esk7_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_56]),c_0_47])]),c_0_96]) ).
thf(c_0_133,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_132]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO064^4.003 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n010.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 16:26:48 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.24 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.4QfQUvSAFY/E---3.1_3085408.p
% 6.00/1.18 % Version: 3.5.1-ho
% 6.00/1.18 % Preprocessing class: HSMSSMSSMLSNHSN.
% 6.00/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.00/1.18 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 6.00/1.18 % Starting post_as_ho3 with 300s (1) cores
% 6.00/1.18 % Starting post_as_ho11 with 300s (1) cores
% 6.00/1.18 % Starting full_lambda_8 with 300s (1) cores
% 6.00/1.18 % new_ho_10_cnf2 with pid 3085421 completed with status 0
% 6.00/1.18 % Result found by new_ho_10_cnf2
% 6.00/1.18 % Preprocessing class: HSMSSMSSMLSNHSN.
% 6.00/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.00/1.18 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 6.00/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.00/1.18 % No SInE strategy applied
% 6.00/1.18 % Search class: HGHNS-FFSM11-SHSSMFNN
% 6.00/1.18 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 6.00/1.18 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.00/1.18 % Starting SubtermCWHack with 136s (1) cores
% 6.00/1.18 % Starting new_ho_10_cnf2 with 151s (1) cores
% 6.00/1.18 % Starting sh5l with 136s (1) cores
% 6.00/1.18 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 6.00/1.18 % Starting lpo1_def_fix with 136s (1) cores
% 6.00/1.18 % ehoh_best_sine_rwall with pid 3085427 completed with status 0
% 6.00/1.18 % Result found by ehoh_best_sine_rwall
% 6.00/1.18 % Preprocessing class: HSMSSMSSMLSNHSN.
% 6.00/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.00/1.18 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 6.00/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.00/1.18 % No SInE strategy applied
% 6.00/1.18 % Search class: HGHNS-FFSM11-SHSSMFNN
% 6.00/1.18 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 6.00/1.18 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.00/1.18 % Starting SubtermCWHack with 136s (1) cores
% 6.00/1.18 % Starting new_ho_10_cnf2 with 151s (1) cores
% 6.00/1.18 % Starting sh5l with 136s (1) cores
% 6.00/1.18 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 6.00/1.18 % Preprocessing time : 0.001 s
% 6.00/1.18 % Presaturation interreduction done
% 6.00/1.18
% 6.00/1.18 % Proof found!
% 6.00/1.18 % SZS status Theorem
% 6.00/1.18 % SZS output start CNFRefutation
% See solution above
% 6.00/1.18 % Parsed axioms : 53
% 6.00/1.18 % Removed by relevancy pruning/SinE : 0
% 6.00/1.18 % Initial clauses : 45
% 6.00/1.18 % Removed in clause preprocessing : 27
% 6.00/1.18 % Initial clauses in saturation : 18
% 6.00/1.18 % Processed clauses : 5695
% 6.00/1.18 % ...of these trivial : 84
% 6.00/1.18 % ...subsumed : 2952
% 6.00/1.18 % ...remaining for further processing : 2659
% 6.00/1.18 % Other redundant clauses eliminated : 0
% 6.00/1.18 % Clauses deleted for lack of memory : 0
% 6.00/1.18 % Backward-subsumed : 1174
% 6.00/1.18 % Backward-rewritten : 941
% 6.00/1.18 % Generated clauses : 25643
% 6.00/1.18 % ...of the previous two non-redundant : 19072
% 6.00/1.18 % ...aggressively subsumed : 0
% 6.00/1.18 % Contextual simplify-reflections : 0
% 6.00/1.18 % Paramodulations : 25634
% 6.00/1.18 % Factorizations : 0
% 6.00/1.18 % NegExts : 0
% 6.00/1.18 % Equation resolutions : 0
% 6.00/1.18 % Disequality decompositions : 0
% 6.00/1.18 % Total rewrite steps : 11009
% 6.00/1.18 % ...of those cached : 10969
% 6.00/1.18 % Propositional unsat checks : 0
% 6.00/1.18 % Propositional check models : 0
% 6.00/1.18 % Propositional check unsatisfiable : 0
% 6.00/1.18 % Propositional clauses : 0
% 6.00/1.18 % Propositional clauses after purity: 0
% 6.00/1.18 % Propositional unsat core size : 0
% 6.00/1.18 % Propositional preprocessing time : 0.000
% 6.00/1.18 % Propositional encoding time : 0.000
% 6.00/1.18 % Propositional solver time : 0.000
% 6.00/1.18 % Success case prop preproc time : 0.000
% 6.00/1.18 % Success case prop encoding time : 0.000
% 6.00/1.18 % Success case prop solver time : 0.000
% 6.00/1.18 % Current number of processed clauses : 517
% 6.00/1.18 % Positive orientable unit clauses : 43
% 6.00/1.18 % Positive unorientable unit clauses: 0
% 6.00/1.18 % Negative unit clauses : 9
% 6.00/1.18 % Non-unit-clauses : 465
% 6.00/1.18 % Current number of unprocessed clauses: 4360
% 6.00/1.18 % ...number of literals in the above : 38979
% 6.00/1.18 % Current number of archived formulas : 0
% 6.00/1.18 % Current number of archived clauses : 2142
% 6.00/1.18 % Clause-clause subsumption calls (NU) : 385967
% 6.00/1.18 % Rec. Clause-clause subsumption calls : 37925
% 6.00/1.18 % Non-unit clause-clause subsumptions : 4041
% 6.00/1.18 % Unit Clause-clause subsumption calls : 2712
% 6.00/1.18 % Rewrite failures with RHS unbound : 0
% 6.00/1.18 % BW rewrite match attempts : 37
% 6.00/1.18 % BW rewrite match successes : 32
% 6.00/1.18 % Condensation attempts : 0
% 6.00/1.18 % Condensation successes : 0
% 6.00/1.18 % Termbank termtop insertions : 813963
% 6.00/1.18 % Search garbage collected termcells : 1274
% 6.00/1.18
% 6.00/1.18 % -------------------------------------------------
% 6.00/1.18 % User time : 0.747 s
% 6.00/1.18 % System time : 0.010 s
% 6.00/1.18 % Total time : 0.757 s
% 6.00/1.18 % Maximum resident set size: 3924 pages
% 6.00/1.18
% 6.00/1.18 % -------------------------------------------------
% 6.00/1.18 % User time : 3.930 s
% 6.00/1.18 % System time : 0.101 s
% 6.00/1.18 % Total time : 4.032 s
% 6.00/1.18 % Maximum resident set size: 4864 pages
% 6.00/1.18 % E exiting
%------------------------------------------------------------------------------