%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN044^4 : 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 : n009.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 08:40:49 AM UTC 2026
% Result : Theorem 0.86s 0.42s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 351 ( 27 equ; 0 cnn)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 827 ( 100 ~; 148 |; 22 &; 526 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 4 con; 0-3 aty)
% Number of variables : 180 ( 64 ^; 116 !; 0 ?; 180 :)
% 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_37,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
p: $i > $o ).
thf(decl_44,type,
q: $i > $o ).
thf(decl_45,type,
r: $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_0: $i ).
thf(decl_50,type,
esk5_0: $i ).
thf(decl_51,type,
esk6_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',mor) ).
thf(iand,axiom,
( iand
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',iand) ).
thf(mand,axiom,
( mand
= ( ^ [X8: $i > $o,X9: $i > $o,X5: $i] :
( ( X8 @ X5 )
& ( X9 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',mand) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',iimplies) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',mbox_s4) ).
thf(iequiv,axiom,
( iequiv
= ( ^ [X12: $i > $o,X14: $i > $o] : ( iand @ ( iimplies @ X12 @ X14 ) @ ( iimplies @ X14 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',iequiv) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',ivalid) ).
thf(pel10,conjecture,
ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',pel10) ).
thf(pel10_2,axiom,
ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',pel10_2) ).
thf(pel10_1,axiom,
ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',pel10_1) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',refl_axiom) ).
thf(ior,axiom,
( ior
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',ior) ).
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.vXQ2Lticxu/E---3.1_4192713.p',trans_axiom) ).
thf(pel10_3,axiom,
ivalid @ ( iimplies @ ( iatom @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vXQ2Lticxu/E---3.1_4192713.p',pel10_3) ).
thf(c_0_17,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_18,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_19,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
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,
( 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_23,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_17,c_0_18]),c_0_19]) ).
thf(c_0_24,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_25,plain,
( iequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( ~ ! [X28: $i] :
( ( irel @ Z2 @ X28 )
=> ( Z0 @ X28 ) )
| ! [X29: $i] :
( ( irel @ Z2 @ X29 )
=> ( Z1 @ X29 ) ) )
& ( ~ ! [X30: $i] :
( ( irel @ Z2 @ X30 )
=> ( Z1 @ X30 ) )
| ! [X31: $i] :
( ( irel @ Z2 @ X31 )
=> ( Z0 @ X31 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iequiv]) ).
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,
( 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_22,c_0_23]),c_0_24]) ).
thf(c_0_28,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_29,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_30,negated_conjecture,
~ ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) ),
inference(assume_negation,[status(cth)],[pel10]) ).
thf(c_0_31,plain,
( iequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( ~ ! [X28: $i] :
( ( irel @ Z2 @ X28 )
=> ( Z0 @ X28 ) )
| ! [X29: $i] :
( ( irel @ Z2 @ X29 )
=> ( Z1 @ X29 ) ) )
& ( ~ ! [X30: $i] :
( ( irel @ Z2 @ X30 )
=> ( Z1 @ X30 ) )
| ! [X31: $i] :
( ( irel @ Z2 @ X31 )
=> ( Z0 @ X31 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
thf(c_0_32,plain,
! [X42: $i] :
( ~ ! [X40: $i] :
( ( irel @ X42 @ X40 )
=> ( r @ X40 ) )
| ! [X41: $i] :
( ( irel @ X42 @ X41 )
=> ( ( p @ X41 )
& ( q @ X41 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pel10_2,c_0_28]),c_0_26]),c_0_27]),c_0_29]) ).
thf(c_0_33,negated_conjecture,
~ ! [X52: $i] :
( ( ~ ! [X48: $i] :
( ( irel @ X52 @ X48 )
=> ( p @ X48 ) )
| ! [X49: $i] :
( ( irel @ X52 @ X49 )
=> ( q @ X49 ) ) )
& ( ~ ! [X50: $i] :
( ( irel @ X52 @ X50 )
=> ( q @ X50 ) )
| ! [X51: $i] :
( ( irel @ X52 @ X51 )
=> ( p @ X51 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_28]),c_0_31]),c_0_29]) ).
thf(c_0_34,plain,
! [X39: $i] :
( ~ ! [X37: $i] :
( ( irel @ X39 @ X37 )
=> ( q @ X37 ) )
| ! [X38: $i] :
( ( irel @ X39 @ X38 )
=> ( r @ X38 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pel10_1,c_0_28]),c_0_27]),c_0_29]) ).
thf(c_0_35,plain,
! [X60: $i,X62: $i] :
( ( ( p @ X62 )
| ~ ( irel @ X60 @ X62 )
| ( irel @ X60 @ ( esk2_1 @ X60 ) ) )
& ( ( q @ X62 )
| ~ ( irel @ X60 @ X62 )
| ( irel @ X60 @ ( esk2_1 @ X60 ) ) )
& ( ( p @ X62 )
| ~ ( irel @ X60 @ X62 )
| ~ ( r @ ( esk2_1 @ X60 ) ) )
& ( ( q @ X62 )
| ~ ( irel @ X60 @ X62 )
| ~ ( r @ ( esk2_1 @ X60 ) ) ) ),
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_32])])])])])]) ).
thf(c_0_36,negated_conjecture,
! [X69: $i,X71: $i] :
( ( ~ ( irel @ esk4_0 @ X71 )
| ( q @ X71 )
| ~ ( irel @ esk4_0 @ X69 )
| ( p @ X69 ) )
& ( ( irel @ esk4_0 @ esk6_0 )
| ~ ( irel @ esk4_0 @ X69 )
| ( p @ X69 ) )
& ( ~ ( p @ esk6_0 )
| ~ ( irel @ esk4_0 @ X69 )
| ( p @ X69 ) )
& ( ~ ( irel @ esk4_0 @ X71 )
| ( q @ X71 )
| ( irel @ esk4_0 @ esk5_0 ) )
& ( ( irel @ esk4_0 @ esk6_0 )
| ( irel @ esk4_0 @ esk5_0 ) )
& ( ~ ( p @ esk6_0 )
| ( irel @ esk4_0 @ esk5_0 ) )
& ( ~ ( irel @ esk4_0 @ X71 )
| ( q @ X71 )
| ~ ( q @ esk5_0 ) )
& ( ( irel @ esk4_0 @ esk6_0 )
| ~ ( q @ esk5_0 ) )
& ( ~ ( p @ esk6_0 )
| ~ ( q @ esk5_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_33])])])])])]) ).
thf(c_0_37,plain,
! [X57: $i,X59: $i] :
( ( ( irel @ X57 @ ( esk1_1 @ X57 ) )
| ~ ( irel @ X57 @ X59 )
| ( r @ X59 ) )
& ( ~ ( q @ ( esk1_1 @ X57 ) )
| ~ ( irel @ X57 @ X59 )
| ( r @ X59 ) ) ),
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_34])])])])])]) ).
thf(c_0_38,plain,
! [X2: $i,X1: $i] :
( ( p @ X1 )
| ( irel @ X2 @ ( esk2_1 @ X2 ) )
| ~ ( irel @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_39,negated_conjecture,
( ( irel @ esk4_0 @ esk6_0 )
| ( irel @ esk4_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_40,negated_conjecture,
( ( irel @ esk4_0 @ esk5_0 )
| ~ ( p @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_41,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( r @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,negated_conjecture,
( ( irel @ esk4_0 @ ( esk2_1 @ esk4_0 ) )
| ( irel @ esk4_0 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
thf(c_0_43,plain,
! [X1: $i,X2: $i] :
( ( p @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( r @ ( esk2_1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_44,negated_conjecture,
( ( irel @ esk4_0 @ ( esk1_1 @ esk4_0 ) )
| ( irel @ esk4_0 @ esk5_0 )
| ( r @ ( esk2_1 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_45,plain,
! [X53: $i] : ( irel @ X53 @ X53 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_46,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_47,negated_conjecture,
! [X1: $i] :
( ( irel @ esk4_0 @ ( esk1_1 @ esk4_0 ) )
| ( irel @ esk4_0 @ esk5_0 )
| ( p @ X1 )
| ~ ( irel @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_48,plain,
! [X54: $i,X55: $i,X56: $i] :
( ~ ( irel @ X54 @ X55 )
| ~ ( irel @ X55 @ X56 )
| ( irel @ X54 @ X56 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_49,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_50,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_46,c_0_19]),c_0_24]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i] :
( ( q @ X1 )
| ( irel @ esk4_0 @ esk5_0 )
| ~ ( irel @ esk4_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_52,negated_conjecture,
( ( irel @ esk4_0 @ ( esk1_1 @ esk4_0 ) )
| ( irel @ esk4_0 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_39]),c_0_40]) ).
thf(c_0_53,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_54,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( p @ X1 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
thf(c_0_55,plain,
! [X47: $i] :
( ~ ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( p @ X45 ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( ! [X43: $i] :
( ( irel @ X46 @ X43 )
=> ( q @ X43 ) )
| ! [X44: $i] :
( ( irel @ X46 @ X44 )
=> ( r @ X44 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pel10_3,c_0_28]),c_0_50]),c_0_27]),c_0_29]) ).
thf(c_0_56,plain,
! [X1: $i,X2: $i] :
( ( r @ X2 )
| ~ ( q @ ( esk1_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_57,negated_conjecture,
( ( q @ ( esk1_1 @ esk4_0 ) )
| ( irel @ esk4_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_58,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk2_1 @ X2 ) )
| ( p @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_59,plain,
! [X63: $i,X65: $i,X66: $i,X67: $i] :
( ( ( irel @ X63 @ ( esk3_1 @ X63 ) )
| ~ ( irel @ X63 @ X65 )
| ~ ( irel @ X65 @ X66 )
| ( q @ X66 )
| ~ ( irel @ X65 @ X67 )
| ( r @ X67 ) )
& ( ~ ( p @ ( esk3_1 @ X63 ) )
| ~ ( irel @ X63 @ X65 )
| ~ ( irel @ X65 @ X66 )
| ( q @ X66 )
| ~ ( irel @ X65 @ X67 )
| ( r @ X67 ) ) ),
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_55])])])])])]) ).
thf(c_0_60,plain,
! [X2: $i,X1: $i] :
( ( q @ X1 )
| ( irel @ X2 @ ( esk2_1 @ X2 ) )
| ~ ( irel @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_61,negated_conjecture,
! [X1: $i] :
( ( irel @ esk4_0 @ esk5_0 )
| ( r @ X1 )
| ~ ( irel @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_62,negated_conjecture,
( ( irel @ esk4_0 @ ( esk2_1 @ esk6_0 ) )
| ( irel @ esk4_0 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_39]),c_0_40]) ).
thf(c_0_63,plain,
! [X1: $i,X2: $i,X3: $i,X5: $i] :
( ( irel @ X1 @ ( esk3_1 @ X1 ) )
| ( q @ X3 )
| ( r @ X5 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X2 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_64,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ( q @ X1 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
thf(c_0_65,plain,
! [X1: $i,X2: $i] :
( ( q @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( r @ ( esk2_1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_66,negated_conjecture,
( ( r @ ( esk2_1 @ esk6_0 ) )
| ( irel @ esk4_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_67,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( irel @ X1 @ ( esk3_1 @ X1 ) )
| ( q @ X2 )
| ( q @ X3 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i] :
( ( irel @ esk4_0 @ esk5_0 )
| ( p @ X1 )
| ~ ( irel @ esk6_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_66]) ).
thf(c_0_69,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk3_1 @ X1 ) )
| ( q @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_49]) ).
thf(c_0_70,negated_conjecture,
irel @ esk4_0 @ esk5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_49]),c_0_40]) ).
thf(c_0_71,negated_conjecture,
! [X1: $i,X2: $i] :
( ( q @ X1 )
| ( p @ X2 )
| ~ ( irel @ esk4_0 @ X1 )
| ~ ( irel @ esk4_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_72,negated_conjecture,
( ( irel @ esk4_0 @ ( esk3_1 @ esk4_0 ) )
| ( q @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_73,negated_conjecture,
! [X1: $i] :
( ( q @ X1 )
| ~ ( irel @ esk4_0 @ X1 )
| ~ ( q @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_74,negated_conjecture,
! [X1: $i] :
( ( p @ ( esk3_1 @ esk4_0 ) )
| ( q @ X1 )
| ~ ( irel @ esk4_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
thf(c_0_75,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk5_0 )
| ~ ( irel @ X1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_70]) ).
thf(c_0_76,plain,
! [X1: $i,X2: $i,X3: $i,X5: $i] :
( ( q @ X3 )
| ( r @ X5 )
| ~ ( p @ ( esk3_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X2 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_77,negated_conjecture,
( ( p @ ( esk3_1 @ esk4_0 ) )
| ( q @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_49])]) ).
thf(c_0_78,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( q @ esk5_0 )
| ( r @ X1 )
| ( q @ X2 )
| ~ ( irel @ esk4_0 @ X3 )
| ~ ( irel @ X3 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_79,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( r @ ( esk2_1 @ X1 ) )
| ( p @ X1 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_54]) ).
thf(c_0_80,negated_conjecture,
! [X2: $i,X1: $i] :
( ( q @ esk5_0 )
| ( q @ X1 )
| ( r @ X2 )
| ~ ( irel @ esk5_0 @ X2 )
| ~ ( irel @ esk5_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_75]),c_0_49])]) ).
thf(c_0_81,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( p @ X1 )
| ( p @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_79]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i] :
( ( q @ esk5_0 )
| ( q @ X1 )
| ~ ( irel @ esk5_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_64]),c_0_65]) ).
thf(c_0_83,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( p @ X1 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_49]) ).
thf(c_0_84,negated_conjecture,
( ( irel @ esk4_0 @ esk6_0 )
| ~ ( q @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_85,negated_conjecture,
q @ esk5_0,
inference(spm,[status(thm)],[c_0_82,c_0_49]) ).
thf(c_0_86,negated_conjecture,
( ~ ( p @ esk6_0 )
| ~ ( q @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_87,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk1_1 @ X2 ) )
| ( p @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_83]) ).
thf(c_0_88,negated_conjecture,
irel @ esk4_0 @ esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
thf(c_0_89,negated_conjecture,
~ ( p @ esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_85])]) ).
thf(c_0_90,negated_conjecture,
! [X1: $i] :
( ( q @ X1 )
| ~ ( irel @ esk4_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_85])]) ).
thf(c_0_91,negated_conjecture,
irel @ esk4_0 @ ( esk1_1 @ esk6_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
thf(c_0_92,negated_conjecture,
! [X2: $i,X1: $i] :
( ( r @ X1 )
| ~ ( irel @ esk4_0 @ ( esk1_1 @ X2 ) )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_90]) ).
thf(c_0_93,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk1_1 @ esk6_0 ) )
| ~ ( irel @ X1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_91]) ).
thf(c_0_94,negated_conjecture,
! [X1: $i] :
( ( r @ X1 )
| ~ ( irel @ esk6_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_49])]) ).
thf(c_0_95,negated_conjecture,
! [X2: $i,X1: $i] :
( ( p @ X1 )
| ~ ( irel @ esk6_0 @ ( esk2_1 @ X2 ) )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_94]) ).
thf(c_0_96,negated_conjecture,
! [X1: $i] :
( ( p @ X1 )
| ~ ( irel @ esk6_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_54]),c_0_89]) ).
thf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_96]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN044^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n009.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:14:30 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.28 Running higher-order theorem proving
% 0.26/0.30 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.vXQ2Lticxu/E---3.1_4192713.p
% 0.86/0.42 % Version: 3.5.1-ho
% 0.86/0.42 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.86/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.42 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.86/0.42 % Starting post_as_ho3 with 300s (1) cores
% 0.86/0.42 % Starting post_as_ho11 with 300s (1) cores
% 0.86/0.42 % Starting full_lambda_8 with 300s (1) cores
% 0.86/0.42 % new_ho_10_cnf2 with pid 4192726 completed with status 0
% 0.86/0.42 % Result found by new_ho_10_cnf2
% 0.86/0.42 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.86/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.42 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.86/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.86/0.42 % No SInE strategy applied
% 0.86/0.42 % Search class: HGHNF-FFSF11-SHSSMFNN
% 0.86/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.86/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.86/0.42 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.86/0.42 % Starting sh5l with 136s (1) cores
% 0.86/0.42 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.86/0.42 % Starting lpo1_def_fix with 136s (1) cores
% 0.86/0.42 % ehoh_best_sine_rwall with pid 4192736 completed with status 0
% 0.86/0.42 % Result found by ehoh_best_sine_rwall
% 0.86/0.42 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.86/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.42 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.86/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.86/0.42 % No SInE strategy applied
% 0.86/0.42 % Search class: HGHNF-FFSF11-SHSSMFNN
% 0.86/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.86/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.86/0.42 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.86/0.42 % Starting sh5l with 136s (1) cores
% 0.86/0.42 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.86/0.42 % Preprocessing time : 0.001 s
% 0.86/0.42 % Presaturation interreduction done
% 0.86/0.42
% 0.86/0.42 % Proof found!
% 0.86/0.42 % SZS status Theorem
% 0.86/0.42 % SZS output start CNFRefutation
% See solution above
% 0.86/0.42 % Parsed axioms : 48
% 0.86/0.42 % Removed by relevancy pruning/SinE : 0
% 0.86/0.42 % Initial clauses : 42
% 0.86/0.42 % Removed in clause preprocessing : 23
% 0.86/0.42 % Initial clauses in saturation : 19
% 0.86/0.42 % Processed clauses : 812
% 0.86/0.42 % ...of these trivial : 19
% 0.86/0.42 % ...subsumed : 320
% 0.86/0.42 % ...remaining for further processing : 473
% 0.86/0.42 % Other redundant clauses eliminated : 0
% 0.86/0.42 % Clauses deleted for lack of memory : 0
% 0.86/0.42 % Backward-subsumed : 149
% 0.86/0.42 % Backward-rewritten : 133
% 0.86/0.42 % Generated clauses : 4159
% 0.86/0.42 % ...of the previous two non-redundant : 3331
% 0.86/0.42 % ...aggressively subsumed : 0
% 0.86/0.42 % Contextual simplify-reflections : 20
% 0.86/0.42 % Paramodulations : 4159
% 0.86/0.42 % Factorizations : 0
% 0.86/0.42 % NegExts : 0
% 0.86/0.42 % Equation resolutions : 0
% 0.86/0.42 % Disequality decompositions : 0
% 0.86/0.42 % Total rewrite steps : 1024
% 0.86/0.42 % ...of those cached : 1009
% 0.86/0.42 % Propositional unsat checks : 0
% 0.86/0.42 % Propositional check models : 0
% 0.86/0.42 % Propositional check unsatisfiable : 0
% 0.86/0.42 % Propositional clauses : 0
% 0.86/0.42 % Propositional clauses after purity: 0
% 0.86/0.42 % Propositional unsat core size : 0
% 0.86/0.42 % Propositional preprocessing time : 0.000
% 0.86/0.42 % Propositional encoding time : 0.000
% 0.86/0.42 % Propositional solver time : 0.000
% 0.86/0.42 % Success case prop preproc time : 0.000
% 0.86/0.42 % Success case prop encoding time : 0.000
% 0.86/0.42 % Success case prop solver time : 0.000
% 0.86/0.42 % Current number of processed clauses : 172
% 0.86/0.42 % Positive orientable unit clauses : 14
% 0.86/0.42 % Positive unorientable unit clauses: 0
% 0.86/0.42 % Negative unit clauses : 1
% 0.86/0.42 % Non-unit-clauses : 157
% 0.86/0.42 % Current number of unprocessed clauses: 1847
% 0.86/0.42 % ...number of literals in the above : 7592
% 0.86/0.42 % Current number of archived formulas : 0
% 0.86/0.42 % Current number of archived clauses : 301
% 0.86/0.42 % Clause-clause subsumption calls (NU) : 8660
% 0.86/0.42 % Rec. Clause-clause subsumption calls : 4146
% 0.86/0.42 % Non-unit clause-clause subsumptions : 477
% 0.86/0.42 % Unit Clause-clause subsumption calls : 108
% 0.86/0.42 % Rewrite failures with RHS unbound : 0
% 0.86/0.42 % BW rewrite match attempts : 13
% 0.86/0.42 % BW rewrite match successes : 10
% 0.86/0.42 % Condensation attempts : 0
% 0.86/0.42 % Condensation successes : 0
% 0.86/0.42 % Termbank termtop insertions : 89239
% 0.86/0.42 % Search garbage collected termcells : 897
% 0.86/0.42
% 0.86/0.42 % -------------------------------------------------
% 0.86/0.42 % User time : 0.085 s
% 0.86/0.42 % System time : 0.009 s
% 0.86/0.42 % Total time : 0.094 s
% 0.86/0.42 % Maximum resident set size: 3664 pages
% 0.86/0.42
% 0.86/0.42 % -------------------------------------------------
% 0.86/0.42 % User time : 0.421 s
% 0.86/0.42 % System time : 0.030 s
% 0.86/0.42 % Total time : 0.451 s
% 0.86/0.42 % Maximum resident set size: 4864 pages
% 0.86/0.42 % E exiting
%------------------------------------------------------------------------------