%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV426^2 : TPTP v9.3.1. Released v3.6.0.
% 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 08:39:42 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 25 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 515 ( 60 ~; 78 |; 10 &; 345 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 6 con; 0-3 aty)
% Number of variables : 131 ( 52 ^; 79 !; 0 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_29,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_42,type,
rel: $i > $i > $o ).
thf(decl_43,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(decl_44,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(decl_47,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_51,type,
iclval: ( $i > $o ) > $o ).
thf(decl_52,type,
s: $i > $o ).
thf(decl_53,type,
t: $i > $o ).
thf(decl_54,type,
a: $i > $o ).
thf(decl_55,type,
esk1_2: ( $i > $o ) > $i > $i ).
thf(decl_56,type,
esk2_2: ( $i > $o ) > $i > $i ).
thf(decl_57,type,
esk3_0: $i ).
thf(decl_58,type,
esk4_0: $i ).
thf(decl_59,type,
esk5_2: $i > $i > $i ).
thf(decl_60,type,
esk6_0: $i ).
thf(decl_61,type,
esk7_0: $i ).
thf(decl_62,type,
esk8_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',mor) ).
thf(icl_atom,axiom,
( icl_atom
= ( ^ [X11: $i > $o] : ( mbox @ rel @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',icl_atom) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',mbox) ).
thf(icl_impl,axiom,
( icl_impl
= ( ^ [X19: $i > $o,X20: $i > $o] : ( mbox @ rel @ ( mimpl @ X19 @ X20 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',icl_impl) ).
thf(icl_says,axiom,
( icl_says
= ( ^ [X19: $i > $o,X21: $i > $o] : ( mbox @ rel @ ( mor @ X19 @ X21 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',icl_says) ).
thf(icl_s4_valid,axiom,
( iclval
= ( ^ [X22: $i > $o] : ( mvalid @ X22 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',icl_s4_valid) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',mvalid) ).
thf(cuc,conjecture,
iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_atom @ t ) ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ t ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',cuc) ).
thf(icl_princ,axiom,
( icl_princ
= ( ^ [X11: $i > $o] : X11 ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',icl_princ) ).
thf(trans_axiom,axiom,
! [X20: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X20 ) @ ( mbox @ rel @ ( mbox @ rel @ X20 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',trans_axiom) ).
thf(refl_axiom,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X19 ) @ X19 ) ),
file('/export/starexec/sandbox/tmp/tmp.fBg8mD3uR8/E---3.1_3042509.p',refl_axiom) ).
thf(c_0_13,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_14,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_15,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_16,plain,
( icl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X25: $i] :
( ( rel @ Z1 @ X25 )
=> ( Z0 @ X25 ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_atom]) ).
thf(c_0_17,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X12: $i] :
( ( Z0 @ Z2 @ X12 )
=> ( Z1 @ X12 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_18,plain,
( icl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X26: $i] :
( ( rel @ Z2 @ X26 )
=> ( ~ ( Z0 @ X26 )
| ( Z1 @ X26 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_impl]) ).
thf(c_0_19,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_20,plain,
( icl_says
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X27: $i] :
( ( rel @ Z2 @ X27 )
=> ( ( Z0 @ X27 )
| ( Z1 @ X27 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_says]) ).
thf(c_0_21,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(fof_simplification,[status(thm)],[icl_s4_valid]) ).
thf(c_0_22,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_23,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_atom @ t ) ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ t ) ) ) ) ),
inference(assume_negation,[status(cth)],[cuc]) ).
thf(c_0_24,plain,
( icl_atom
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X25: $i] :
( ( rel @ Z1 @ X25 )
=> ( Z0 @ X25 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_25,plain,
( icl_princ
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[icl_princ]) ).
thf(c_0_26,plain,
( icl_impl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X26: $i] :
( ( rel @ Z2 @ X26 )
=> ( ~ ( Z0 @ X26 )
| ( Z1 @ X26 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_17]) ).
thf(c_0_27,plain,
( icl_says
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X27: $i] :
( ( rel @ Z2 @ X27 )
=> ( ( Z0 @ X27 )
| ( Z1 @ X27 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_15]),c_0_17]) ).
thf(c_0_28,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_29,plain,
! [X20: $i > $o,X34: $i] :
( ~ ! [X31: $i] :
( ( rel @ X34 @ X31 )
=> ( X20 @ X31 ) )
| ! [X33: $i] :
( ( rel @ X34 @ X33 )
=> ! [X32: $i] :
( ( rel @ X33 @ X32 )
=> ( X20 @ X32 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[trans_axiom,c_0_19]),c_0_17]),c_0_22]) ).
thf(c_0_30,negated_conjecture,
~ ! [X45: $i,X44: $i] :
( ( rel @ X45 @ X44 )
=> ( ~ ! [X38: $i] :
( ( rel @ X44 @ X38 )
=> ( ( a @ X38 )
| ! [X37: $i] :
( ( rel @ X38 @ X37 )
=> ( ~ ! [X35: $i] :
( ( rel @ X37 @ X35 )
=> ( s @ X35 ) )
| ! [X36: $i] :
( ( rel @ X37 @ X36 )
=> ( t @ X36 ) ) ) ) ) )
| ! [X43: $i] :
( ( rel @ X44 @ X43 )
=> ( ~ ! [X40: $i] :
( ( rel @ X43 @ X40 )
=> ( ( a @ X40 )
| ! [X39: $i] :
( ( rel @ X40 @ X39 )
=> ( s @ X39 ) ) ) )
| ! [X42: $i] :
( ( rel @ X43 @ X42 )
=> ( ( a @ X42 )
| ! [X41: $i] :
( ( rel @ X42 @ X41 )
=> ( t @ X41 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]) ).
thf(c_0_31,plain,
! [X49: $i > $o,X50: $i,X52: $i,X53: $i] :
( ( ( rel @ X50 @ ( esk2_2 @ X49 @ X50 ) )
| ~ ( rel @ X50 @ X52 )
| ~ ( rel @ X52 @ X53 )
| ( X49 @ X53 ) )
& ( ~ ( X49 @ ( esk2_2 @ X49 @ X50 ) )
| ~ ( rel @ X50 @ X52 )
| ~ ( rel @ X52 @ X53 )
| ( X49 @ X53 ) ) ),
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_29])])])])])]) ).
thf(c_0_32,negated_conjecture,
! [X56: $i,X57: $i,X59: $i,X61: $i,X62: $i] :
( ( rel @ esk3_0 @ esk4_0 )
& ( ( rel @ X57 @ ( esk5_2 @ X56 @ X57 ) )
| ~ ( rel @ X57 @ X59 )
| ( t @ X59 )
| ~ ( rel @ X56 @ X57 )
| ( a @ X56 )
| ~ ( rel @ esk4_0 @ X56 ) )
& ( ~ ( s @ ( esk5_2 @ X56 @ X57 ) )
| ~ ( rel @ X57 @ X59 )
| ( t @ X59 )
| ~ ( rel @ X56 @ X57 )
| ( a @ X56 )
| ~ ( rel @ esk4_0 @ X56 ) )
& ( rel @ esk4_0 @ esk6_0 )
& ( ~ ( rel @ esk6_0 @ X61 )
| ( a @ X61 )
| ~ ( rel @ X61 @ X62 )
| ( s @ X62 ) )
& ( rel @ esk6_0 @ esk7_0 )
& ~ ( a @ esk7_0 )
& ( rel @ esk7_0 @ esk8_0 )
& ~ ( t @ esk8_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_30])])])])])]) ).
thf(c_0_33,plain,
! [X1: $i,X2: $i > $o,X3: $i,X12: $i] :
( ( rel @ X1 @ ( esk2_2 @ X2 @ X1 ) )
| ( X2 @ X12 )
| ~ ( rel @ X1 @ X3 )
| ~ ( rel @ X3 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_34,negated_conjecture,
rel @ esk6_0 @ esk7_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_35,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( rel @ X1 @ ( esk2_2 @ X2 @ X1 ) )
| ( X2 @ esk7_0 )
| ~ ( rel @ X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_36,negated_conjecture,
rel @ esk4_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
! [X1: $i,X2: $i > $o,X3: $i,X12: $i] :
( ( X2 @ X12 )
| ~ ( X2 @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( rel @ X1 @ X3 )
| ~ ( rel @ X3 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_38,negated_conjecture,
! [X2: $i > $o] :
( ( rel @ esk4_0 @ ( esk2_2 @ X2 @ esk4_0 ) )
| ( X2 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X3: $i,X1: $i] :
( ( rel @ esk4_0 @ esk7_0 )
| ( rel @ esk4_0 @ X1 )
| ~ ( rel @ esk4_0 @ X3 )
| ~ ( rel @ X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_40,plain,
! [X19: $i > $o,X30: $i] :
( ~ ! [X29: $i] :
( ( rel @ X30 @ X29 )
=> ( X19 @ X29 ) )
| ( X19 @ X30 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom,c_0_19]),c_0_17]),c_0_22]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i] :
( ( rel @ esk4_0 @ esk7_0 )
| ( rel @ esk4_0 @ X1 )
| ~ ( rel @ esk6_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
thf(c_0_42,plain,
! [X46: $i > $o,X47: $i] :
( ( ( rel @ X47 @ ( esk1_2 @ X46 @ X47 ) )
| ( X46 @ X47 ) )
& ( ~ ( X46 @ ( esk1_2 @ X46 @ X47 ) )
| ( X46 @ X47 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i,X12: $i,X3: $i] :
( ( rel @ X1 @ ( esk5_2 @ X3 @ X1 ) )
| ( t @ X12 )
| ( a @ X3 )
| ~ ( rel @ X1 @ X12 )
| ~ ( rel @ X3 @ X1 )
| ~ ( rel @ esk4_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_44,negated_conjecture,
rel @ esk4_0 @ esk7_0,
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
thf(c_0_45,negated_conjecture,
~ ( a @ esk7_0 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_46,plain,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_47,plain,
! [X2: $i > $o,X1: $i] :
( ( rel @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_48,negated_conjecture,
! [X1: $i,X3: $i] :
( ( a @ X1 )
| ( s @ X3 )
| ~ ( rel @ esk6_0 @ X1 )
| ~ ( rel @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i,X3: $i] :
( ( rel @ X1 @ ( esk5_2 @ esk7_0 @ X1 ) )
| ( t @ X3 )
| ~ ( rel @ esk7_0 @ X1 )
| ~ ( rel @ X1 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
thf(c_0_50,plain,
! [X1: $i] : ( rel @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_51,negated_conjecture,
! [X12: $i,X3: $i,X1: $i] :
( ( t @ X12 )
| ( a @ X1 )
| ~ ( s @ ( esk5_2 @ X1 @ X3 ) )
| ~ ( rel @ X3 @ X12 )
| ~ ( rel @ X1 @ X3 )
| ~ ( rel @ esk4_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i] :
( ( s @ X1 )
| ~ ( rel @ esk7_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_34]),c_0_45]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
( ( rel @ esk7_0 @ ( esk5_2 @ esk7_0 @ esk7_0 ) )
| ( t @ X1 )
| ~ ( rel @ esk7_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_54,negated_conjecture,
rel @ esk7_0 @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_55,negated_conjecture,
~ ( t @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( a @ X1 )
| ( t @ X3 )
| ~ ( rel @ esk7_0 @ ( esk5_2 @ X1 @ X12 ) )
| ~ ( rel @ esk4_0 @ X1 )
| ~ ( rel @ X12 @ X3 )
| ~ ( rel @ X1 @ X12 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_57,negated_conjecture,
rel @ esk7_0 @ ( esk5_2 @ esk7_0 @ esk7_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
thf(c_0_58,negated_conjecture,
! [X1: $i] :
( ( t @ X1 )
| ~ ( rel @ esk7_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_44]),c_0_50])]),c_0_45]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_58]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV426^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n010.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 16:01:18 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.30 Running higher-order theorem proving
% 0.25/0.31 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.fBg8mD3uR8/E---3.1_3042509.p
% 0.25/0.36 % Version: 3.5.1-ho
% 0.25/0.36 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.25/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.36 % Starting post_as_ho3 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho11 with 300s (1) cores
% 0.25/0.36 % Starting full_lambda_8 with 300s (1) cores
% 0.25/0.36 % new_ho_10_cnf2 with pid 3042522 completed with status 0
% 0.25/0.36 % Result found by new_ho_10_cnf2
% 0.25/0.36 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.25/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.36 % No SInE strategy applied
% 0.25/0.36 % Search class: HGUNF-FFSS22-SHSSMSBN
% 0.25/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.36 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.25/0.36 % Starting sh5l with 136s (1) cores
% 0.25/0.36 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.25/0.36 % Starting lpo1_def_fix with 136s (1) cores
% 0.25/0.36 % ehoh_best_sine_rwall with pid 3042529 completed with status 0
% 0.25/0.36 % Result found by ehoh_best_sine_rwall
% 0.25/0.36 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.25/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.36 % No SInE strategy applied
% 0.25/0.36 % Search class: HGUNF-FFSS22-SHSSMSBN
% 0.25/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.36 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.25/0.36 % Starting sh5l with 136s (1) cores
% 0.25/0.36 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.25/0.36 % Preprocessing time : 0.002 s
% 0.25/0.36 % Presaturation interreduction done
% 0.25/0.36
% 0.25/0.36 % Proof found!
% 0.25/0.36 % SZS status Theorem
% 0.25/0.36 % SZS output start CNFRefutation
% See solution above
% 0.25/0.36 % Parsed axioms : 60
% 0.25/0.36 % Removed by relevancy pruning/SinE : 0
% 0.25/0.36 % Initial clauses : 46
% 0.25/0.36 % Removed in clause preprocessing : 33
% 0.25/0.36 % Initial clauses in saturation : 13
% 0.25/0.36 % Processed clauses : 77
% 0.25/0.36 % ...of these trivial : 0
% 0.25/0.36 % ...subsumed : 6
% 0.25/0.36 % ...remaining for further processing : 71
% 0.25/0.36 % Other redundant clauses eliminated : 2
% 0.25/0.36 % Clauses deleted for lack of memory : 0
% 0.25/0.36 % Backward-subsumed : 2
% 0.25/0.36 % Backward-rewritten : 9
% 0.25/0.36 % Generated clauses : 233
% 0.25/0.36 % ...of the previous two non-redundant : 208
% 0.25/0.36 % ...aggressively subsumed : 0
% 0.25/0.36 % Contextual simplify-reflections : 0
% 0.25/0.36 % Paramodulations : 218
% 0.25/0.36 % Factorizations : 0
% 0.25/0.36 % NegExts : 0
% 0.25/0.36 % Equation resolutions : 2
% 0.25/0.36 % Disequality decompositions : 0
% 0.25/0.36 % Total rewrite steps : 24
% 0.25/0.36 % ...of those cached : 10
% 0.25/0.36 % Propositional unsat checks : 0
% 0.25/0.36 % Propositional check models : 0
% 0.25/0.36 % Propositional check unsatisfiable : 0
% 0.25/0.36 % Propositional clauses : 0
% 0.25/0.36 % Propositional clauses after purity: 0
% 0.25/0.36 % Propositional unsat core size : 0
% 0.25/0.36 % Propositional preprocessing time : 0.000
% 0.25/0.36 % Propositional encoding time : 0.000
% 0.25/0.36 % Propositional solver time : 0.000
% 0.25/0.36 % Success case prop preproc time : 0.000
% 0.25/0.36 % Success case prop encoding time : 0.000
% 0.25/0.36 % Success case prop solver time : 0.000
% 0.25/0.36 % Current number of processed clauses : 47
% 0.25/0.36 % Positive orientable unit clauses : 13
% 0.25/0.36 % Positive unorientable unit clauses: 0
% 0.25/0.36 % Negative unit clauses : 2
% 0.25/0.36 % Non-unit-clauses : 32
% 0.25/0.36 % Current number of unprocessed clauses: 144
% 0.25/0.36 % ...number of literals in the above : 412
% 0.25/0.36 % Current number of archived formulas : 0
% 0.25/0.36 % Current number of archived clauses : 24
% 0.25/0.36 % Clause-clause subsumption calls (NU) : 355
% 0.25/0.36 % Rec. Clause-clause subsumption calls : 157
% 0.25/0.36 % Non-unit clause-clause subsumptions : 7
% 0.25/0.36 % Unit Clause-clause subsumption calls : 9
% 0.25/0.36 % Rewrite failures with RHS unbound : 0
% 0.25/0.36 % BW rewrite match attempts : 17
% 0.25/0.36 % BW rewrite match successes : 7
% 0.25/0.36 % Condensation attempts : 0
% 0.25/0.36 % Condensation successes : 0
% 0.25/0.36 % Termbank termtop insertions : 10715
% 0.25/0.36 % Search garbage collected termcells : 944
% 0.25/0.36
% 0.25/0.36 % -------------------------------------------------
% 0.25/0.36 % User time : 0.020 s
% 0.25/0.36 % System time : 0.005 s
% 0.25/0.36 % Total time : 0.025 s
% 0.25/0.36 % Maximum resident set size: 3680 pages
% 0.25/0.36
% 0.25/0.36 % -------------------------------------------------
% 0.25/0.36 % User time : 0.101 s
% 0.25/0.36 % System time : 0.015 s
% 0.25/0.36 % Total time : 0.115 s
% 0.25/0.36 % Maximum resident set size: 4864 pages
% 0.25/0.36 % E exiting
%------------------------------------------------------------------------------