%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO066^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:43:44 AM UTC 2026
% Result : Theorem 1.06s 0.38s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 111 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 368 ( 16 equ; 0 cnn)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 737 ( 95 ~; 111 |; 26 &; 482 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 12 con; 0-3 aty)
% Number of variables : 132 ( 36 ^; 96 !; 0 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
irel: $i > $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_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_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
o11: $i > $o ).
thf(decl_44,type,
o12: $i > $o ).
thf(decl_45,type,
o21: $i > $o ).
thf(decl_46,type,
o22: $i > $o ).
thf(decl_47,type,
o31: $i > $o ).
thf(decl_48,type,
o32: $i > $o ).
thf(decl_49,type,
esk1_0: $i ).
thf(decl_50,type,
esk2_0: $i ).
thf(decl_51,type,
esk3_0: $i ).
thf(decl_52,type,
esk4_0: $i ).
thf(decl_53,type,
esk5_0: $i ).
thf(decl_54,type,
esk6_0: $i ).
thf(decl_55,type,
esk7_0: $i ).
thf(decl_56,type,
esk8_0: $i ).
thf(decl_57,type,
esk9_0: $i ).
thf(decl_58,type,
esk10_0: $i ).
thf(decl_59,type,
esk11_0: $i ).
thf(iand,axiom,
( iand
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',iand) ).
thf(mand,axiom,
( mand
= ( ^ [X8: $i > $o,X9: $i > $o,X5: $i] :
( ( X8 @ X5 )
& ( X9 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',mand) ).
thf(ior,axiom,
( ior
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',ior) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.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.cEiWVqt1OW/E---3.1_1257650.p',mbox_s4) ).
thf(con,conjecture,
ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',con) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',ivalid) ).
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.cEiWVqt1OW/E---3.1_1257650.p',trans_axiom) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',refl_axiom) ).
thf(axiom3,axiom,
ivalid @ ( ior @ ( iatom @ o31 ) @ ( iatom @ o32 ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',axiom3) ).
thf(axiom2,axiom,
ivalid @ ( ior @ ( iatom @ o21 ) @ ( iatom @ o22 ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',axiom2) ).
thf(axiom1,axiom,
ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o12 ) ),
file('/export/starexec/sandbox/tmp/tmp.cEiWVqt1OW/E---3.1_1257650.p',axiom1) ).
thf(c_0_13,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[iand]) ).
thf(c_0_14,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_15,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_16,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_17,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X2: $i] :
( ( irel @ Z1 @ X2 )
=> ( Z0 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_18,negated_conjecture,
~ ( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_19,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_20,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_21,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_15,c_0_16]),c_0_17]) ).
thf(c_0_22,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_23,negated_conjecture,
~ ! [X56: $i] :
( ! [X54: $i] :
( ( irel @ X56 @ X54 )
=> ( ( o11 @ X54 )
& ( o21 @ X54 ) ) )
| ! [X55: $i] :
( ( irel @ X56 @ X55 )
=> ( ! [X52: $i] :
( ( irel @ X55 @ X52 )
=> ( ( o11 @ X52 )
& ( o31 @ X52 ) ) )
| ! [X53: $i] :
( ( irel @ X55 @ X53 )
=> ( ! [X50: $i] :
( ( irel @ X53 @ X50 )
=> ( ( o21 @ X50 )
& ( o31 @ X50 ) ) )
| ! [X51: $i] :
( ( irel @ X53 @ X51 )
=> ( ! [X48: $i] :
( ( irel @ X51 @ X48 )
=> ( ( o12 @ X48 )
& ( o22 @ X48 ) ) )
| ! [X49: $i] :
( ( irel @ X51 @ X49 )
=> ( ! [X46: $i] :
( ( irel @ X49 @ X46 )
=> ( ( o12 @ X46 )
& ( o32 @ X46 ) ) )
| ! [X47: $i] :
( ( irel @ X49 @ X47 )
=> ( ( o22 @ X47 )
& ( o32 @ X47 ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22]) ).
thf(c_0_24,plain,
! [X58: $i,X59: $i,X60: $i] :
( ~ ( irel @ X58 @ X59 )
| ~ ( irel @ X59 @ X60 )
| ( irel @ X58 @ X60 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_25,negated_conjecture,
( ( irel @ esk1_0 @ esk2_0 )
& ( ~ ( o11 @ esk2_0 )
| ~ ( o21 @ esk2_0 ) )
& ( irel @ esk1_0 @ esk3_0 )
& ( irel @ esk3_0 @ esk4_0 )
& ( ~ ( o11 @ esk4_0 )
| ~ ( o31 @ esk4_0 ) )
& ( irel @ esk3_0 @ esk5_0 )
& ( irel @ esk5_0 @ esk6_0 )
& ( ~ ( o21 @ esk6_0 )
| ~ ( o31 @ esk6_0 ) )
& ( irel @ esk5_0 @ esk7_0 )
& ( irel @ esk7_0 @ esk8_0 )
& ( ~ ( o12 @ esk8_0 )
| ~ ( o22 @ esk8_0 ) )
& ( irel @ esk7_0 @ esk9_0 )
& ( irel @ esk9_0 @ esk10_0 )
& ( ~ ( o12 @ esk10_0 )
| ~ ( o32 @ esk10_0 ) )
& ( irel @ esk9_0 @ esk11_0 )
& ( ~ ( o22 @ esk11_0 )
| ~ ( o32 @ esk11_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
thf(c_0_26,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_27,negated_conjecture,
irel @ esk3_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk5_0 )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_29,negated_conjecture,
irel @ esk5_0 @ esk7_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk5_0 )
| ~ ( irel @ X2 @ esk3_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
thf(c_0_31,negated_conjecture,
irel @ esk1_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_32,plain,
! [X57: $i] : ( irel @ X57 @ X57 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk7_0 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk5_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_35,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_36,negated_conjecture,
irel @ esk7_0 @ esk9_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk7_0 )
| ~ ( irel @ X2 @ esk5_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
thf(c_0_38,negated_conjecture,
irel @ esk1_0 @ esk5_0,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk9_0 )
| ~ ( irel @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk7_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_41,negated_conjecture,
irel @ esk9_0 @ esk11_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk9_0 )
| ~ ( irel @ X2 @ esk7_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
thf(c_0_43,negated_conjecture,
irel @ esk1_0 @ esk7_0,
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
thf(c_0_44,negated_conjecture,
irel @ esk7_0 @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk11_0 )
| ~ ( irel @ X1 @ esk9_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_41]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk9_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk8_0 )
| ~ ( irel @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
thf(c_0_48,negated_conjecture,
irel @ esk9_0 @ esk10_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_49,plain,
! [X45: $i] :
( ! [X43: $i] :
( ( irel @ X45 @ X43 )
=> ( o31 @ X43 ) )
| ! [X44: $i] :
( ( irel @ X45 @ X44 )
=> ( o32 @ X44 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom3,c_0_19]),c_0_21]),c_0_22]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk11_0 )
| ~ ( irel @ X2 @ esk9_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
thf(c_0_51,negated_conjecture,
irel @ esk1_0 @ esk9_0,
inference(spm,[status(thm)],[c_0_46,c_0_35]) ).
thf(c_0_52,plain,
! [X42: $i] :
( ! [X40: $i] :
( ( irel @ X42 @ X40 )
=> ( o21 @ X40 ) )
| ! [X41: $i] :
( ( irel @ X42 @ X41 )
=> ( o22 @ X41 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom2,c_0_19]),c_0_21]),c_0_22]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk8_0 )
| ~ ( irel @ X2 @ esk7_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk10_0 )
| ~ ( irel @ X1 @ esk9_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_48]) ).
thf(c_0_55,plain,
! [X67: $i,X68: $i,X69: $i] :
( ~ ( irel @ X67 @ X68 )
| ( o31 @ X68 )
| ~ ( irel @ X67 @ X69 )
| ( o32 @ X69 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk11_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_57,plain,
! [X64: $i,X65: $i,X66: $i] :
( ~ ( irel @ X64 @ X65 )
| ( o21 @ X65 )
| ~ ( irel @ X64 @ X66 )
| ( o22 @ X66 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
thf(c_0_58,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk8_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_43]) ).
thf(c_0_59,plain,
! [X39: $i] :
( ! [X37: $i] :
( ( irel @ X39 @ X37 )
=> ( o11 @ X37 ) )
| ! [X38: $i] :
( ( irel @ X39 @ X38 )
=> ( o12 @ X38 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_19]),c_0_21]),c_0_22]) ).
thf(c_0_60,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ esk10_0 )
| ~ ( irel @ X2 @ esk9_0 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_54]) ).
thf(c_0_61,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( o31 @ X2 )
| ( o32 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_62,negated_conjecture,
irel @ esk1_0 @ esk11_0,
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
thf(c_0_63,negated_conjecture,
irel @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_64,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( o21 @ X2 )
| ( o22 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_65,negated_conjecture,
irel @ esk1_0 @ esk8_0,
inference(spm,[status(thm)],[c_0_58,c_0_35]) ).
thf(c_0_66,plain,
! [X61: $i,X62: $i,X63: $i] :
( ~ ( irel @ X61 @ X62 )
| ( o11 @ X62 )
| ~ ( irel @ X61 @ X63 )
| ( o12 @ X63 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk10_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_51]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i] :
( ( o32 @ esk11_0 )
| ( o31 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_69,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk4_0 )
| ~ ( irel @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
thf(c_0_70,negated_conjecture,
! [X1: $i] :
( ( o22 @ esk8_0 )
| ( o21 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_71,negated_conjecture,
irel @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_72,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( o11 @ X2 )
| ( o12 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_73,negated_conjecture,
irel @ esk1_0 @ esk10_0,
inference(spm,[status(thm)],[c_0_67,c_0_35]) ).
thf(c_0_74,negated_conjecture,
irel @ esk5_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_75,negated_conjecture,
( ~ ( o22 @ esk11_0 )
| ~ ( o32 @ esk11_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_76,negated_conjecture,
( ( o31 @ esk4_0 )
| ( o32 @ esk11_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_31])]) ).
thf(c_0_77,negated_conjecture,
! [X2: $i,X1: $i] :
( ( o22 @ esk11_0 )
| ( o21 @ X1 )
| ~ ( irel @ X2 @ esk9_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_45]) ).
thf(c_0_78,negated_conjecture,
( ~ ( o12 @ esk8_0 )
| ~ ( o22 @ esk8_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_79,negated_conjecture,
( ( o21 @ esk2_0 )
| ( o22 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_80,negated_conjecture,
! [X2: $i,X1: $i] :
( ( o12 @ esk8_0 )
| ( o11 @ X1 )
| ~ ( irel @ X2 @ esk7_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_47]) ).
thf(c_0_81,negated_conjecture,
! [X1: $i] :
( ( o32 @ esk10_0 )
| ( o31 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_73]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk6_0 )
| ~ ( irel @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_74]) ).
thf(c_0_83,negated_conjecture,
( ~ ( o11 @ esk4_0 )
| ~ ( o31 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_84,negated_conjecture,
( ( o31 @ esk4_0 )
| ~ ( o22 @ esk11_0 ) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
thf(c_0_85,negated_conjecture,
! [X1: $i] :
( ( o22 @ esk11_0 )
| ( o21 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_77,c_0_51]) ).
thf(c_0_86,negated_conjecture,
( ~ ( o11 @ esk2_0 )
| ~ ( o21 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_87,negated_conjecture,
( ( o21 @ esk2_0 )
| ~ ( o12 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i] :
( ( o12 @ esk8_0 )
| ( o11 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_80,c_0_43]) ).
thf(c_0_89,negated_conjecture,
( ~ ( o12 @ esk10_0 )
| ~ ( o32 @ esk10_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_90,negated_conjecture,
( ( o31 @ esk6_0 )
| ( o32 @ esk10_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_38])]) ).
thf(c_0_91,negated_conjecture,
( ~ ( o11 @ esk4_0 )
| ~ ( o22 @ esk11_0 ) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
thf(c_0_92,negated_conjecture,
( ( o21 @ esk2_0 )
| ( o22 @ esk11_0 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_71]) ).
thf(c_0_93,negated_conjecture,
( ~ ( o11 @ esk2_0 )
| ~ ( o12 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
thf(c_0_94,negated_conjecture,
( ( o11 @ esk4_0 )
| ( o12 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_69]),c_0_31])]) ).
thf(c_0_95,negated_conjecture,
! [X2: $i,X1: $i] :
( ( o12 @ esk10_0 )
| ( o11 @ X1 )
| ~ ( irel @ X2 @ esk9_0 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_54]) ).
thf(c_0_96,negated_conjecture,
( ~ ( o21 @ esk6_0 )
| ~ ( o31 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_97,negated_conjecture,
( ( o31 @ esk6_0 )
| ~ ( o12 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_98,negated_conjecture,
( ( o21 @ esk6_0 )
| ( o22 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_82]),c_0_38])]) ).
thf(c_0_99,negated_conjecture,
( ( o21 @ esk2_0 )
| ~ ( o11 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
thf(c_0_100,negated_conjecture,
( ( o11 @ esk4_0 )
| ~ ( o11 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
thf(c_0_101,negated_conjecture,
! [X1: $i] :
( ( o12 @ esk10_0 )
| ( o11 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_51]) ).
thf(c_0_102,negated_conjecture,
( ~ ( o21 @ esk6_0 )
| ~ ( o12 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
thf(c_0_103,negated_conjecture,
( ( o21 @ esk6_0 )
| ~ ( o12 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_98]) ).
thf(c_0_104,negated_conjecture,
( ( o11 @ esk2_0 )
| ( o12 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_88,c_0_71]) ).
thf(c_0_105,negated_conjecture,
~ ( o11 @ esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_99]),c_0_100]) ).
thf(c_0_106,negated_conjecture,
( ( o11 @ esk2_0 )
| ( o12 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_101,c_0_71]) ).
thf(c_0_107,negated_conjecture,
( ~ ( o12 @ esk10_0 )
| ~ ( o12 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
thf(c_0_108,negated_conjecture,
o12 @ esk8_0,
inference(sr,[status(thm)],[c_0_104,c_0_105]) ).
thf(c_0_109,negated_conjecture,
o12 @ esk10_0,
inference(sr,[status(thm)],[c_0_106,c_0_105]) ).
thf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]),c_0_109])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO066^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:28:58 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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.cEiWVqt1OW/E---3.1_1257650.p
% 1.06/0.38 % Version: 3.5.1-ho
% 1.06/0.38 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.06/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.06/0.38 % Starting post_as_ho3 with 300s (1) cores
% 1.06/0.38 % Starting post_as_ho11 with 300s (1) cores
% 1.06/0.38 % Starting full_lambda_8 with 300s (1) cores
% 1.06/0.38 % post_as_ho11 with pid 1257665 completed with status 0
% 1.06/0.38 % Result found by post_as_ho11
% 1.06/0.38 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.06/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.06/0.38 % Starting post_as_ho3 with 300s (1) cores
% 1.06/0.38 % Starting post_as_ho11 with 300s (1) cores
% 1.06/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.06/0.38 % No SInE strategy applied
% 1.06/0.38 % Search class: HGHNF-FFSM00-SHSSMFNN
% 1.06/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.06/0.38 % Starting SubtermCWHack with 28s (1) cores
% 1.06/0.38 % SubtermCWHack with pid 1257667 completed with status 0
% 1.06/0.38 % Result found by SubtermCWHack
% 1.06/0.38 % Preprocessing class: HSMSSMSSMLSNHSN.
% 1.06/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.06/0.38 % Starting post_as_ho3 with 300s (1) cores
% 1.06/0.38 % Starting post_as_ho11 with 300s (1) cores
% 1.06/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.06/0.38 % No SInE strategy applied
% 1.06/0.38 % Search class: HGHNF-FFSM00-SHSSMFNN
% 1.06/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.06/0.38 % Starting SubtermCWHack with 28s (1) cores
% 1.06/0.38 % Preprocessing time : 0.002 s
% 1.06/0.38
% 1.06/0.38 % Proof found!
% 1.06/0.38 % SZS status Theorem
% 1.06/0.38 % SZS output start CNFRefutation
% See solution above
% 1.06/0.38 % Parsed axioms : 51
% 1.06/0.38 % Removed by relevancy pruning/SinE : 0
% 1.06/0.38 % Initial clauses : 47
% 1.06/0.38 % Removed in clause preprocessing : 26
% 1.06/0.38 % Initial clauses in saturation : 21
% 1.06/0.38 % Processed clauses : 1950
% 1.06/0.38 % ...of these trivial : 1
% 1.06/0.38 % ...subsumed : 1216
% 1.06/0.38 % ...remaining for further processing : 732
% 1.06/0.38 % Other redundant clauses eliminated : 0
% 1.06/0.38 % Clauses deleted for lack of memory : 0
% 1.06/0.38 % Backward-subsumed : 188
% 1.06/0.38 % Backward-rewritten : 142
% 1.06/0.38 % Generated clauses : 2502
% 1.06/0.38 % ...of the previous two non-redundant : 2528
% 1.06/0.38 % ...aggressively subsumed : 0
% 1.06/0.38 % Contextual simplify-reflections : 1
% 1.06/0.38 % Paramodulations : 2492
% 1.06/0.38 % Factorizations : 0
% 1.06/0.38 % NegExts : 0
% 1.06/0.38 % Equation resolutions : 0
% 1.06/0.38 % Disequality decompositions : 0
% 1.06/0.38 % Total rewrite steps : 1058
% 1.06/0.38 % ...of those cached : 1030
% 1.06/0.38 % Propositional unsat checks : 0
% 1.06/0.38 % Propositional check models : 0
% 1.06/0.38 % Propositional check unsatisfiable : 0
% 1.06/0.38 % Propositional clauses : 0
% 1.06/0.38 % Propositional clauses after purity: 0
% 1.06/0.38 % Propositional unsat core size : 0
% 1.06/0.38 % Propositional preprocessing time : 0.000
% 1.06/0.38 % Propositional encoding time : 0.000
% 1.06/0.38 % Propositional solver time : 0.000
% 1.06/0.38 % Success case prop preproc time : 0.000
% 1.06/0.38 % Success case prop encoding time : 0.000
% 1.06/0.38 % Success case prop solver time : 0.000
% 1.06/0.38 % Current number of processed clauses : 392
% 1.06/0.38 % Positive orientable unit clauses : 35
% 1.06/0.38 % Positive unorientable unit clauses: 0
% 1.06/0.38 % Negative unit clauses : 1
% 1.06/0.38 % Non-unit-clauses : 356
% 1.06/0.38 % Current number of unprocessed clauses: 599
% 1.06/0.38 % ...number of literals in the above : 1783
% 1.06/0.38 % Current number of archived formulas : 0
% 1.06/0.38 % Current number of archived clauses : 340
% 1.06/0.38 % Clause-clause subsumption calls (NU) : 160574
% 1.06/0.38 % Rec. Clause-clause subsumption calls : 131514
% 1.06/0.38 % Non-unit clause-clause subsumptions : 1297
% 1.06/0.38 % Unit Clause-clause subsumption calls : 3934
% 1.06/0.38 % Rewrite failures with RHS unbound : 0
% 1.06/0.38 % BW rewrite match attempts : 26
% 1.06/0.38 % BW rewrite match successes : 16
% 1.06/0.38 % Condensation attempts : 0
% 1.06/0.38 % Condensation successes : 0
% 1.06/0.38 % Termbank termtop insertions : 26936
% 1.06/0.38 % Search garbage collected termcells : 1128
% 1.06/0.38
% 1.06/0.38 % -------------------------------------------------
% 1.06/0.38 % User time : 0.107 s
% 1.06/0.38 % System time : 0.000 s
% 1.06/0.38 % Total time : 0.108 s
% 1.06/0.38 % Maximum resident set size: 3668 pages
% 1.06/0.38
% 1.06/0.38 % -------------------------------------------------
% 1.06/0.38 % User time : 0.109 s
% 1.06/0.38 % System time : 0.005 s
% 1.06/0.38 % Total time : 0.115 s
% 1.06/0.38 % Maximum resident set size: 4864 pages
% 1.06/0.38 % E exiting
%------------------------------------------------------------------------------