%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO068^4.005 : 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 : n001.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 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 64 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 297 ( 16 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 752 ( 115 ~; 131 |; 15 &; 465 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 2 con; 0-3 aty)
% Number of variables : 134 ( 34 ^; 100 !; 0 ?; 134 :)
% 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_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_35,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
p0: $i > $o ).
thf(decl_44,type,
p1: $i > $o ).
thf(decl_45,type,
p2: $i > $o ).
thf(decl_46,type,
p3: $i > $o ).
thf(decl_47,type,
p4: $i > $o ).
thf(decl_48,type,
p5: $i > $o ).
thf(decl_49,type,
esk1_1: $i > $i ).
thf(decl_50,type,
esk2_2: $i > $i > $i ).
thf(decl_51,type,
esk3_1: $i > $i ).
thf(decl_52,type,
esk4_2: $i > $i > $i ).
thf(decl_53,type,
esk5_1: $i > $i ).
thf(decl_54,type,
esk6_2: $i > $i > $i ).
thf(decl_55,type,
esk7_1: $i > $i ).
thf(decl_56,type,
esk8_2: $i > $i > $i ).
thf(decl_57,type,
esk9_1: $i > $i ).
thf(decl_58,type,
esk10_2: $i > $i > $i ).
thf(decl_59,type,
esk11_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',mor) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.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.LvAo5wYrBP/E---3.1_1457143.p',mbox_s4) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',ivalid) ).
thf(axiom6,axiom,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',axiom6) ).
thf(axiom1,axiom,
ivalid @ ( iatom @ p5 ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',axiom1) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',refl_axiom) ).
thf(axiom5,axiom,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',axiom5) ).
thf(axiom4,axiom,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',axiom4) ).
thf(axiom3,axiom,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',axiom3) ).
thf(axiom2,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',axiom2) ).
thf(con,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p',con) ).
thf(c_0_15,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_16,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
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,
( 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_19,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_15,c_0_16]),c_0_17]) ).
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,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
thf(c_0_23,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_24,plain,
! [X62: $i] :
( ~ ! [X60: $i] :
( ( irel @ X62 @ X60 )
=> ( p5 @ X60 ) )
| ! [X61: $i] :
( ( irel @ X62 @ X61 )
=> ( ~ ! [X58: $i] :
( ( irel @ X61 @ X58 )
=> ( p5 @ X58 ) )
| ! [X59: $i] :
( ( irel @ X61 @ X59 )
=> ( p4 @ X59 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom6,c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_25,plain,
! [X37: $i] : ( p5 @ X37 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_21]),c_0_23]) ).
thf(c_0_26,plain,
! [X89: $i,X91: $i,X93: $i] :
( ( ( irel @ X91 @ ( esk10_2 @ X89 @ X91 ) )
| ~ ( irel @ X91 @ X93 )
| ( p4 @ X93 )
| ~ ( irel @ X89 @ X91 )
| ( irel @ X89 @ ( esk9_1 @ X89 ) ) )
& ( ~ ( p5 @ ( esk10_2 @ X89 @ X91 ) )
| ~ ( irel @ X91 @ X93 )
| ( p4 @ X93 )
| ~ ( irel @ X89 @ X91 )
| ( irel @ X89 @ ( esk9_1 @ X89 ) ) )
& ( ( irel @ X91 @ ( esk10_2 @ X89 @ X91 ) )
| ~ ( irel @ X91 @ X93 )
| ( p4 @ X93 )
| ~ ( irel @ X89 @ X91 )
| ~ ( p5 @ ( esk9_1 @ X89 ) ) )
& ( ~ ( p5 @ ( esk10_2 @ X89 @ X91 ) )
| ~ ( irel @ X91 @ X93 )
| ( p4 @ X93 )
| ~ ( irel @ X89 @ X91 )
| ~ ( p5 @ ( esk9_1 @ X89 ) ) ) ),
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_24])])])])])]) ).
thf(c_0_27,plain,
! [X68: $i] : ( p5 @ X68 ),
inference(variable_rename,[status(thm)],[c_0_25]) ).
thf(c_0_28,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p4 @ X3 )
| ~ ( p5 @ ( esk10_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p5 @ ( esk9_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_29,plain,
! [X1: $i] : ( p5 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,plain,
! [X64: $i] : ( irel @ X64 @ X64 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_31,plain,
! [X57: $i] :
( ~ ! [X55: $i] :
( ( irel @ X57 @ X55 )
=> ( p4 @ X55 ) )
| ! [X56: $i] :
( ( irel @ X57 @ X56 )
=> ( ~ ! [X53: $i] :
( ( irel @ X56 @ X53 )
=> ( p4 @ X53 ) )
| ! [X54: $i] :
( ( irel @ X56 @ X54 )
=> ( p3 @ X54 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom5,c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_32,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p4 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),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,
! [X84: $i,X86: $i,X88: $i] :
( ( ( irel @ X86 @ ( esk8_2 @ X84 @ X86 ) )
| ~ ( irel @ X86 @ X88 )
| ( p3 @ X88 )
| ~ ( irel @ X84 @ X86 )
| ( irel @ X84 @ ( esk7_1 @ X84 ) ) )
& ( ~ ( p4 @ ( esk8_2 @ X84 @ X86 ) )
| ~ ( irel @ X86 @ X88 )
| ( p3 @ X88 )
| ~ ( irel @ X84 @ X86 )
| ( irel @ X84 @ ( esk7_1 @ X84 ) ) )
& ( ( irel @ X86 @ ( esk8_2 @ X84 @ X86 ) )
| ~ ( irel @ X86 @ X88 )
| ( p3 @ X88 )
| ~ ( irel @ X84 @ X86 )
| ~ ( p4 @ ( esk7_1 @ X84 ) ) )
& ( ~ ( p4 @ ( esk8_2 @ X84 @ X86 ) )
| ~ ( irel @ X86 @ X88 )
| ( p3 @ X88 )
| ~ ( irel @ X84 @ X86 )
| ~ ( p4 @ ( esk7_1 @ X84 ) ) ) ),
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_31])])])])])]) ).
thf(c_0_35,plain,
! [X2: $i,X1: $i] :
( ( p4 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p3 @ X3 )
| ~ ( p4 @ ( esk8_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p4 @ ( esk7_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_37,plain,
! [X1: $i] : ( p4 @ X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
thf(c_0_38,plain,
! [X52: $i] :
( ~ ! [X50: $i] :
( ( irel @ X52 @ X50 )
=> ( p3 @ X50 ) )
| ! [X51: $i] :
( ( irel @ X52 @ X51 )
=> ( ~ ! [X48: $i] :
( ( irel @ X51 @ X48 )
=> ( p3 @ X48 ) )
| ! [X49: $i] :
( ( irel @ X51 @ X49 )
=> ( p2 @ X49 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom4,c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_39,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p3 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37])]) ).
thf(c_0_40,plain,
! [X79: $i,X81: $i,X83: $i] :
( ( ( irel @ X81 @ ( esk6_2 @ X79 @ X81 ) )
| ~ ( irel @ X81 @ X83 )
| ( p2 @ X83 )
| ~ ( irel @ X79 @ X81 )
| ( irel @ X79 @ ( esk5_1 @ X79 ) ) )
& ( ~ ( p3 @ ( esk6_2 @ X79 @ X81 ) )
| ~ ( irel @ X81 @ X83 )
| ( p2 @ X83 )
| ~ ( irel @ X79 @ X81 )
| ( irel @ X79 @ ( esk5_1 @ X79 ) ) )
& ( ( irel @ X81 @ ( esk6_2 @ X79 @ X81 ) )
| ~ ( irel @ X81 @ X83 )
| ( p2 @ X83 )
| ~ ( irel @ X79 @ X81 )
| ~ ( p3 @ ( esk5_1 @ X79 ) ) )
& ( ~ ( p3 @ ( esk6_2 @ X79 @ X81 ) )
| ~ ( irel @ X81 @ X83 )
| ( p2 @ X83 )
| ~ ( irel @ X79 @ X81 )
| ~ ( p3 @ ( esk5_1 @ X79 ) ) ) ),
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_38])])])])])]) ).
thf(c_0_41,plain,
! [X2: $i,X1: $i] :
( ( p3 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
thf(c_0_42,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p2 @ X3 )
| ~ ( p3 @ ( esk6_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p3 @ ( esk5_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_43,plain,
! [X1: $i] : ( p3 @ X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
thf(c_0_44,plain,
! [X47: $i] :
( ~ ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( p2 @ X45 ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( ~ ! [X43: $i] :
( ( irel @ X46 @ X43 )
=> ( p2 @ X43 ) )
| ! [X44: $i] :
( ( irel @ X46 @ X44 )
=> ( p1 @ X44 ) ) ) ) ),
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_45,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p2 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43])]) ).
thf(c_0_46,plain,
! [X74: $i,X76: $i,X78: $i] :
( ( ( irel @ X76 @ ( esk4_2 @ X74 @ X76 ) )
| ~ ( irel @ X76 @ X78 )
| ( p1 @ X78 )
| ~ ( irel @ X74 @ X76 )
| ( irel @ X74 @ ( esk3_1 @ X74 ) ) )
& ( ~ ( p2 @ ( esk4_2 @ X74 @ X76 ) )
| ~ ( irel @ X76 @ X78 )
| ( p1 @ X78 )
| ~ ( irel @ X74 @ X76 )
| ( irel @ X74 @ ( esk3_1 @ X74 ) ) )
& ( ( irel @ X76 @ ( esk4_2 @ X74 @ X76 ) )
| ~ ( irel @ X76 @ X78 )
| ( p1 @ X78 )
| ~ ( irel @ X74 @ X76 )
| ~ ( p2 @ ( esk3_1 @ X74 ) ) )
& ( ~ ( p2 @ ( esk4_2 @ X74 @ X76 ) )
| ~ ( irel @ X76 @ X78 )
| ( p1 @ X78 )
| ~ ( irel @ X74 @ X76 )
| ~ ( p2 @ ( esk3_1 @ X74 ) ) ) ),
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_44])])])])])]) ).
thf(c_0_47,plain,
! [X2: $i,X1: $i] :
( ( p2 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_33]) ).
thf(c_0_48,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p1 @ X3 )
| ~ ( p2 @ ( esk4_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p2 @ ( esk3_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_49,plain,
! [X1: $i] : ( p2 @ X1 ),
inference(spm,[status(thm)],[c_0_47,c_0_33]) ).
thf(c_0_50,plain,
! [X42: $i] :
( ~ ! [X40: $i] :
( ( irel @ X42 @ X40 )
=> ( p1 @ X40 ) )
| ! [X41: $i] :
( ( irel @ X42 @ X41 )
=> ( ~ ! [X38: $i] :
( ( irel @ X41 @ X38 )
=> ( p1 @ X38 ) )
| ! [X39: $i] :
( ( irel @ X41 @ X39 )
=> ( p0 @ X39 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom2,c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_51,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p1 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_49])]) ).
thf(c_0_52,plain,
! [X69: $i,X71: $i,X73: $i] :
( ( ( irel @ X71 @ ( esk2_2 @ X69 @ X71 ) )
| ~ ( irel @ X71 @ X73 )
| ( p0 @ X73 )
| ~ ( irel @ X69 @ X71 )
| ( irel @ X69 @ ( esk1_1 @ X69 ) ) )
& ( ~ ( p1 @ ( esk2_2 @ X69 @ X71 ) )
| ~ ( irel @ X71 @ X73 )
| ( p0 @ X73 )
| ~ ( irel @ X69 @ X71 )
| ( irel @ X69 @ ( esk1_1 @ X69 ) ) )
& ( ( irel @ X71 @ ( esk2_2 @ X69 @ X71 ) )
| ~ ( irel @ X71 @ X73 )
| ( p0 @ X73 )
| ~ ( irel @ X69 @ X71 )
| ~ ( p1 @ ( esk1_1 @ X69 ) ) )
& ( ~ ( p1 @ ( esk2_2 @ X69 @ X71 ) )
| ~ ( irel @ X71 @ X73 )
| ( p0 @ X73 )
| ~ ( irel @ X69 @ X71 )
| ~ ( p1 @ ( esk1_1 @ X69 ) ) ) ),
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_50])])])])])]) ).
thf(c_0_53,plain,
! [X2: $i,X1: $i] :
( ( p1 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_33]) ).
thf(c_0_54,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_55,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p0 @ X3 )
| ~ ( p1 @ ( esk2_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p1 @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_56,plain,
! [X1: $i] : ( p1 @ X1 ),
inference(spm,[status(thm)],[c_0_53,c_0_33]) ).
thf(c_0_57,negated_conjecture,
~ ! [X63: $i] : ( p0 @ X63 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_54,c_0_21]),c_0_23]) ).
thf(c_0_58,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p0 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56])]) ).
thf(c_0_59,negated_conjecture,
~ ( p0 @ esk11_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
thf(c_0_60,plain,
! [X2: $i,X1: $i] :
( ( p0 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_33]) ).
thf(c_0_61,negated_conjecture,
~ ( p0 @ esk11_0 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_62,plain,
! [X1: $i] : ( p0 @ X1 ),
inference(spm,[status(thm)],[c_0_60,c_0_33]) ).
thf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO068^4.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:35:20 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.LvAo5wYrBP/E---3.1_1457143.p
% 0.08/0.27 % Version: 3.5.1-ho
% 0.08/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.27 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.27 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.27 % post_as_ho3 with pid 1457157 completed with status 0
% 0.08/0.27 % Result found by post_as_ho3
% 0.08/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.27 % No SInE strategy applied
% 0.08/0.27 % Search class: HGUNS-FFMF21-SHSSMFNN
% 0.08/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.27 % SubtermCWHack with pid 1457160 completed with status 0
% 0.08/0.27 % Result found by SubtermCWHack
% 0.08/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.27 % No SInE strategy applied
% 0.08/0.27 % Search class: HGUNS-FFMF21-SHSSMFNN
% 0.08/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.27 % Preprocessing time : 0.002 s
% 0.08/0.27
% 0.08/0.27 % Proof found!
% 0.08/0.27 % SZS status Theorem
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27 % Parsed axioms : 54
% 0.08/0.27 % Removed by relevancy pruning/SinE : 0
% 0.08/0.27 % Initial clauses : 50
% 0.08/0.27 % Removed in clause preprocessing : 26
% 0.08/0.27 % Initial clauses in saturation : 24
% 0.08/0.27 % Processed clauses : 25
% 0.08/0.27 % ...of these trivial : 1
% 0.08/0.27 % ...subsumed : 0
% 0.08/0.27 % ...remaining for further processing : 24
% 0.08/0.27 % Other redundant clauses eliminated : 0
% 0.08/0.27 % Clauses deleted for lack of memory : 0
% 0.08/0.27 % Backward-subsumed : 5
% 0.08/0.27 % Backward-rewritten : 11
% 0.08/0.27 % Generated clauses : 12
% 0.08/0.27 % ...of the previous two non-redundant : 16
% 0.08/0.27 % ...aggressively subsumed : 0
% 0.08/0.27 % Contextual simplify-reflections : 0
% 0.08/0.27 % Paramodulations : 12
% 0.08/0.27 % Factorizations : 0
% 0.08/0.27 % NegExts : 0
% 0.08/0.27 % Equation resolutions : 0
% 0.08/0.27 % Disequality decompositions : 0
% 0.08/0.27 % Total rewrite steps : 19
% 0.08/0.27 % ...of those cached : 2
% 0.08/0.27 % Propositional unsat checks : 0
% 0.08/0.27 % Propositional check models : 0
% 0.08/0.27 % Propositional check unsatisfiable : 0
% 0.08/0.27 % Propositional clauses : 0
% 0.08/0.27 % Propositional clauses after purity: 0
% 0.08/0.27 % Propositional unsat core size : 0
% 0.08/0.27 % Propositional preprocessing time : 0.000
% 0.08/0.27 % Propositional encoding time : 0.000
% 0.08/0.27 % Propositional solver time : 0.000
% 0.08/0.27 % Success case prop preproc time : 0.000
% 0.08/0.27 % Success case prop encoding time : 0.000
% 0.08/0.27 % Success case prop solver time : 0.000
% 0.08/0.27 % Current number of processed clauses : 8
% 0.08/0.27 % Positive orientable unit clauses : 7
% 0.08/0.27 % Positive unorientable unit clauses: 0
% 0.08/0.27 % Negative unit clauses : 0
% 0.08/0.27 % Non-unit-clauses : 1
% 0.08/0.27 % Current number of unprocessed clauses: 15
% 0.08/0.27 % ...number of literals in the above : 73
% 0.08/0.27 % Current number of archived formulas : 0
% 0.08/0.27 % Current number of archived clauses : 16
% 0.08/0.27 % Clause-clause subsumption calls (NU) : 8
% 0.08/0.27 % Rec. Clause-clause subsumption calls : 8
% 0.08/0.27 % Non-unit clause-clause subsumptions : 5
% 0.08/0.27 % Unit Clause-clause subsumption calls : 0
% 0.08/0.27 % Rewrite failures with RHS unbound : 0
% 0.08/0.27 % BW rewrite match attempts : 14
% 0.08/0.27 % BW rewrite match successes : 14
% 0.08/0.27 % Condensation attempts : 0
% 0.08/0.27 % Condensation successes : 0
% 0.08/0.27 % Termbank termtop insertions : 4121
% 0.08/0.27 % Search garbage collected termcells : 1297
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.006 s
% 0.08/0.27 % System time : 0.003 s
% 0.08/0.27 % Total time : 0.009 s
% 0.08/0.27 % Maximum resident set size: 3924 pages
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.008 s
% 0.08/0.27 % System time : 0.008 s
% 0.08/0.27 % Total time : 0.016 s
% 0.08/0.27 % Maximum resident set size: 4864 pages
% 0.08/0.27 % E exiting
%------------------------------------------------------------------------------