%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO224^5 : 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 : n013.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 08:44:02 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 1
% Syntax : Number of formulae : 68 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 58 equ; 0 cnn)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 691 ( 97 ~; 195 |; 29 &; 360 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 11 ^; 36 !; 4 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cJ: $i ).
thf(decl_24,type,
cLIKE: $i > $i > $o ).
thf(decl_25,type,
cWRH: $i > $o ).
thf(decl_26,type,
cW: $i > $o ).
thf(decl_27,type,
cUNIQUE: $i > $o ).
thf(decl_28,type,
cS: $i ).
thf(decl_29,type,
cP: $i ).
thf(decl_30,type,
esk1_1: ( $i > $o ) > $i ).
thf(cLING1,conjecture,
( ( ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ! [X2: $i] :
( ( ( cWRH @ X2 )
& ( cW @ X2 ) )
=> ( X1 = X2 ) ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS ) )
=> ? [X3: $i > $o] :
( ( ( X3 @ cP )
<=> ( cLIKE @ cP @ cS ) )
& ( ( X3 @ cJ )
<=> ? [X1: $i] :
( ( cUNIQUE @ X1 )
& ( cW @ X1 )
& ( cWRH @ X1 )
& ( cLIKE @ cJ @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nr733LacEB/E---3.1_2351021.p',cLING1) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ! [X2: $i] :
( ( ( cWRH @ X2 )
& ( cW @ X2 ) )
=> ( X1 = X2 ) ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS ) )
=> ? [X3: $i > $o] :
( ( ( X3 @ cP )
<=> ( cLIKE @ cP @ cS ) )
& ( ( X3 @ cJ )
<=> ? [X1: $i] :
( ( cUNIQUE @ X1 )
& ( cW @ X1 )
& ( cWRH @ X1 )
& ( cLIKE @ cJ @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cLING1]) ).
thf(c_0_2,negated_conjecture,
! [X8: $i,X9: $i,X10: $i > $o,X11: $i] :
( ( ~ ( cUNIQUE @ X8 )
| ~ ( cWRH @ X9 )
| ~ ( cW @ X9 )
| ( X8 = X9 ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS )
& ( ~ ( X10 @ cJ )
| ~ ( cUNIQUE @ X11 )
| ~ ( cW @ X11 )
| ~ ( cWRH @ X11 )
| ~ ( cLIKE @ cJ @ X11 )
| ~ ( X10 @ cP )
| ~ ( cLIKE @ cP @ cS ) )
& ( ( cUNIQUE @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ~ ( X10 @ cP )
| ~ ( cLIKE @ cP @ cS ) )
& ( ( cW @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ~ ( X10 @ cP )
| ~ ( cLIKE @ cP @ cS ) )
& ( ( cWRH @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ~ ( X10 @ cP )
| ~ ( cLIKE @ cP @ cS ) )
& ( ( cLIKE @ cJ @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ~ ( X10 @ cP )
| ~ ( cLIKE @ cP @ cS ) )
& ( ~ ( X10 @ cJ )
| ~ ( cUNIQUE @ X11 )
| ~ ( cW @ X11 )
| ~ ( cWRH @ X11 )
| ~ ( cLIKE @ cJ @ X11 )
| ( X10 @ cP )
| ( cLIKE @ cP @ cS ) )
& ( ( cUNIQUE @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ( X10 @ cP )
| ( cLIKE @ cP @ cS ) )
& ( ( cW @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ( X10 @ cP )
| ( cLIKE @ cP @ cS ) )
& ( ( cWRH @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ( X10 @ cP )
| ( cLIKE @ cP @ cS ) )
& ( ( cLIKE @ cJ @ ( esk1_1 @ X10 ) )
| ( X10 @ cJ )
| ( X10 @ cP )
| ( cLIKE @ cP @ cS ) ) ),
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_1])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: $i,X3: $i > $o] :
( ~ ( X3 @ cJ )
| ~ ( cUNIQUE @ X1 )
| ~ ( cW @ X1 )
| ~ ( cWRH @ X1 )
| ~ ( cLIKE @ cJ @ X1 )
| ~ ( X3 @ cP )
| ~ ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X3: $i > $o,X1: $i] :
( ( X3 @ cP )
| ( cLIKE @ cP @ cS )
| ~ ( X3 @ cJ )
| ~ ( cUNIQUE @ X1 )
| ~ ( cW @ X1 )
| ~ ( cWRH @ X1 )
| ~ ( cLIKE @ cJ @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i] :
( ~ ( cLIKE @ cP @ cS )
| ~ ( cLIKE @ cJ @ X1 )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 )
| ~ ( cUNIQUE @ X1 ) ),
inference(primitive_enumeration,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i] :
( ( cJ = cP )
| ~ ( cLIKE @ cJ @ X1 )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 )
| ~ ( cUNIQUE @ X1 ) ),
inference(csr,[status(thm)],[inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_4]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X3: $i > $o] :
( ( cLIKE @ cJ @ ( esk1_1 @ X3 ) )
| ( X3 @ cJ )
| ( X3 @ cP )
| ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i > $o] :
( ( cUNIQUE @ ( esk1_1 @ X3 ) )
| ( X3 @ cJ )
| ( X3 @ cP )
| ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,negated_conjecture,
! [X3: $i > $o] :
( ( cW @ ( esk1_1 @ X3 ) )
| ( X3 @ cJ )
| ( X3 @ cP )
| ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i > $o] :
( ( cWRH @ ( esk1_1 @ X3 ) )
| ( X3 @ cJ )
| ( X3 @ cP )
| ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( cUNIQUE @ X1 )
| ~ ( cWRH @ X2 )
| ~ ( cW @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i > $o] :
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( X3 @ cJ )
| ( X3 @ cP ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ( cJ = cP )
| ( cJ = X1 )
| ( cLIKE @ cP @ cS )
| ( cUNIQUE @ cP )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
( ( cW
@ ( esk1_1
@ ^ [Z0: $i] : ~ $true ) )
| ( cLIKE @ cP @ cS ) ),
inference(primitive_enumeration,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
( ( cWRH
@ ( esk1_1
@ ^ [Z0: $i] : ~ $true ) )
| ( cLIKE @ cP @ cS ) ),
inference(primitive_enumeration,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
( ( ( esk1_1
@ ^ [Z0: $i] : ~ $true )
= cJ )
| ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cUNIQUE @ cP ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cUNIQUE @ cP )
| ( cW @ cJ ) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
thf(c_0_18,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cUNIQUE @ cP )
| ( cWRH @ cJ ) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( cJ = cP )
| ( cP = X1 )
| ( cLIKE @ cP @ cS )
| ( cW @ cJ )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( cJ = cP )
| ( cP = X1 )
| ( cLIKE @ cP @ cS )
| ( cWRH @ cJ )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cJ @ cP )
| ( cLIKE @ cP @ cS )
| ~ ( cWRH @ cJ )
| ~ ( cW @ cJ )
| ~ ( cUNIQUE @ cJ ) ),
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
thf(c_0_22,negated_conjecture,
( ( ( esk1_1
@ ^ [Z0: $i] : ~ $true )
= cP )
| ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cW @ cJ ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_15]) ).
thf(c_0_23,negated_conjecture,
( ( ( esk1_1
@ ^ [Z0: $i] : ~ $true )
= cP )
| ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cWRH @ cJ ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_15]) ).
thf(c_0_24,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cLIKE @ cJ @ cP )
| ~ ( cWRH @ cJ )
| ~ ( cW @ cJ ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_12]),c_0_11]) ).
thf(c_0_25,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cLIKE @ cJ @ cP )
| ( cW @ cJ ) ),
inference(spm,[status(thm)],[c_0_7,c_0_22]) ).
thf(c_0_26,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cLIKE @ cJ @ cP )
| ( cWRH @ cJ ) ),
inference(spm,[status(thm)],[c_0_7,c_0_23]) ).
thf(c_0_27,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cJ @ cP )
| ( cLIKE @ cP @ cS ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_28,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cLIKE @ cJ @ cJ )
| ( cUNIQUE @ cP ) ),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
thf(c_0_29,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ~ ( cWRH @ cP )
| ~ ( cW @ cP )
| ~ ( cUNIQUE @ cP ) ),
inference(spm,[status(thm)],[c_0_6,c_0_27]) ).
thf(c_0_30,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cW @ cJ )
| ( cWRH @ cP ) ),
inference(spm,[status(thm)],[c_0_10,c_0_22]) ).
thf(c_0_31,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cWRH @ cJ )
| ( cW @ cP ) ),
inference(spm,[status(thm)],[c_0_9,c_0_23]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( cJ = cP )
| ( cP = X1 )
| ( cLIKE @ cJ @ cJ )
| ( cLIKE @ cP @ cS )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_28]) ).
thf(c_0_33,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cW @ cJ ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_17]),c_0_12]),c_0_30]) ).
thf(c_0_34,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cWRH @ cJ ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_18]),c_0_31]),c_0_12]) ).
thf(c_0_35,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cLIKE @ cJ @ cJ ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_36,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ~ ( cUNIQUE @ cJ ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_35]),c_0_33]),c_0_34]) ).
thf(c_0_37,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cUNIQUE @ cP ) ),
inference(spm,[status(thm)],[c_0_36,c_0_12]) ).
thf(c_0_38,negated_conjecture,
! [X3: $i > $o] :
( ( cW @ ( esk1_1 @ X3 ) )
| ( X3 @ cJ )
| ~ ( X3 @ cP )
| ~ ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i] :
( ( cJ = cP )
| ( cP = X1 )
| ( cLIKE @ cP @ cS )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_37]) ).
thf(c_0_40,negated_conjecture,
! [X3: $i > $o] :
( ( cWRH @ ( esk1_1 @ X3 ) )
| ( X3 @ cJ )
| ~ ( X3 @ cP )
| ~ ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_41,negated_conjecture,
cUNIQUE @ cS,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_42,negated_conjecture,
( ( cJ = cP )
| ( cW
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 != cJ ) ) )
| ~ ( cLIKE @ cP @ cS ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_38]) ).
thf(c_0_43,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cP @ cS ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_34]) ).
thf(c_0_44,negated_conjecture,
( ( cJ = cP )
| ( cWRH
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 != cJ ) ) )
| ~ ( cLIKE @ cP @ cS ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_40]) ).
thf(c_0_45,negated_conjecture,
! [X3: $i > $o] :
( ( cLIKE @ cJ @ ( esk1_1 @ X3 ) )
| ( X3 @ cJ )
| ~ ( X3 @ cP )
| ~ ( cLIKE @ cP @ cS ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i] :
( ( cS = X1 )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_41]) ).
thf(c_0_47,negated_conjecture,
( ( cJ = cP )
| ( cW
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 != cJ ) ) ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_48,negated_conjecture,
( ( cJ = cP )
| ( cWRH
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 != cJ ) ) ) ),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
thf(c_0_49,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cJ
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 != cJ ) ) ) ),
inference(csr,[status(thm)],[inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_45]),c_0_43]) ).
thf(c_0_50,negated_conjecture,
( ( ( esk1_1
@ ^ [Z0: $i] : ( Z0 != cJ ) )
= cS )
| ( cJ = cP ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
thf(c_0_51,negated_conjecture,
! [X3: $i > $o] :
( ( ( esk1_1 @ X3 )
= cS )
| ( cLIKE @ cP @ cS )
| ( X3 @ cJ )
| ( X3 @ cP ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_9]),c_0_10]) ).
thf(c_0_52,negated_conjecture,
( ( cJ = cP )
| ( cLIKE @ cJ @ cS ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_53,negated_conjecture,
cWRH @ cS,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_54,negated_conjecture,
cW @ cS,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i > $o] :
( ( cLIKE @ cP @ cS )
| ( cLIKE @ cJ @ cS )
| ( X3 @ cJ )
| ( X3 @ cP ) ),
inference(spm,[status(thm)],[c_0_7,c_0_51]) ).
thf(c_0_56,negated_conjecture,
cJ = cP,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_52]),c_0_53]),c_0_54]),c_0_41])]) ).
thf(c_0_57,negated_conjecture,
! [X3: $i > $o] :
( ( cLIKE @ cP @ cS )
| ( X3 @ cP ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56])]) ).
thf(c_0_58,negated_conjecture,
! [X1: $i] :
( ~ ( cLIKE @ cP @ cS )
| ~ ( cLIKE @ cP @ X1 )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 )
| ~ ( cUNIQUE @ X1 ) ),
inference(rw,[status(thm)],[c_0_5,c_0_56]) ).
thf(c_0_59,negated_conjecture,
( ( cS = cP )
| ( cLIKE @ cP @ cS ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_57]),c_0_57]) ).
thf(c_0_60,negated_conjecture,
cS = cP,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_53]),c_0_54]),c_0_41])]),c_0_59]) ).
thf(c_0_61,negated_conjecture,
! [X3: $i > $o] :
( ( cLIKE @ cP @ cP )
| ( X3 @ cP ) ),
inference(rw,[status(thm)],[c_0_57,c_0_60]) ).
thf(c_0_62,negated_conjecture,
cLIKE @ cP @ cP,
inference(ef,[status(thm)],[c_0_61]) ).
thf(c_0_63,negated_conjecture,
! [X1: $i] :
( ~ ( cLIKE @ cP @ X1 )
| ~ ( cWRH @ X1 )
| ~ ( cW @ X1 )
| ~ ( cUNIQUE @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_60]),c_0_62])]) ).
thf(c_0_64,negated_conjecture,
cWRH @ cP,
inference(rw,[status(thm)],[c_0_53,c_0_60]) ).
thf(c_0_65,negated_conjecture,
cW @ cP,
inference(rw,[status(thm)],[c_0_54,c_0_60]) ).
thf(c_0_66,negated_conjecture,
cUNIQUE @ cP,
inference(rw,[status(thm)],[c_0_41,c_0_60]) ).
thf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_62]),c_0_64]),c_0_65]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO224^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:39:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.nr733LacEB/E---3.1_2351021.p
% 0.23/0.31 % Version: 3.5.1-ho
% 0.23/0.31 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting post_as_ho12 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_9 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho4 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.31 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.31 % Starting full_lambda_10 with 300s (1) cores
% 0.23/0.31 % Starting new_ho_8 with 300s (1) cores
% 0.23/0.31 % ehoh_best2_full_lfho with pid 2351057 completed with status 0
% 0.23/0.31 % Result found by ehoh_best2_full_lfho
% 0.23/0.31 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting post_as_ho12 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_9 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho4 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.31 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.31 % No SInE strategy applied
% 0.23/0.31 % Search class: HGHSF-FFSS11-SSSFFMBN
% 0.23/0.31 % partial match(1): HGHSF-FFSF11-SSSFFMBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % SubtermCWHack with pid 2351062 completed with status 10
% 0.23/0.31 % Starting ehoh_best2_full_lfho with 31s (1) cores
% 0.23/0.31 % ehoh_best2_full_lfho with pid 2351075 completed with status 0
% 0.23/0.31 % Result found by ehoh_best2_full_lfho
% 0.23/0.31 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.23/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting post_as_ho12 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_9 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho4 with 300s (1) cores
% 0.23/0.31 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.31 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.31 % No SInE strategy applied
% 0.23/0.31 % Search class: HGHSF-FFSS11-SSSFFMBN
% 0.23/0.31 % partial match(1): HGHSF-FFSF11-SSSFFMBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % SubtermCWHack with pid 2351062 completed with status 10
% 0.23/0.31 % Starting ehoh_best2_full_lfho with 31s (1) cores
% 0.23/0.31 % Preprocessing time : 0.001 s
% 0.23/0.31
% 0.23/0.31 % Proof found!
% 0.23/0.31 % SZS status Theorem
% 0.23/0.31 % SZS output start CNFRefutation
% See solution above
% 0.23/0.31 % Parsed axioms : 8
% 0.23/0.31 % Removed by relevancy pruning/SinE : 0
% 0.23/0.31 % Initial clauses : 21
% 0.23/0.31 % Removed in clause preprocessing : 7
% 0.23/0.31 % Initial clauses in saturation : 14
% 0.23/0.31 % Processed clauses : 156
% 0.23/0.31 % ...of these trivial : 2
% 0.23/0.31 % ...subsumed : 37
% 0.23/0.31 % ...remaining for further processing : 117
% 0.23/0.31 % Other redundant clauses eliminated : 16
% 0.23/0.31 % Clauses deleted for lack of memory : 0
% 0.23/0.31 % Backward-subsumed : 56
% 0.23/0.31 % Backward-rewritten : 48
% 0.23/0.31 % Generated clauses : 454
% 0.23/0.31 % ...of the previous two non-redundant : 356
% 0.23/0.31 % ...aggressively subsumed : 0
% 0.23/0.31 % Contextual simplify-reflections : 33
% 0.23/0.31 % Paramodulations : 340
% 0.23/0.31 % Factorizations : 2
% 0.23/0.31 % NegExts : 0
% 0.23/0.31 % Equation resolutions : 18
% 0.23/0.31 % Disequality decompositions : 0
% 0.23/0.31 % Total rewrite steps : 150
% 0.23/0.31 % ...of those cached : 141
% 0.23/0.31 % Propositional unsat checks : 0
% 0.23/0.31 % Propositional check models : 0
% 0.23/0.31 % Propositional check unsatisfiable : 0
% 0.23/0.31 % Propositional clauses : 0
% 0.23/0.31 % Propositional clauses after purity: 0
% 0.23/0.31 % Propositional unsat core size : 0
% 0.23/0.31 % Propositional preprocessing time : 0.000
% 0.23/0.31 % Propositional encoding time : 0.000
% 0.23/0.31 % Propositional solver time : 0.000
% 0.23/0.31 % Success case prop preproc time : 0.000
% 0.23/0.31 % Success case prop encoding time : 0.000
% 0.23/0.31 % Success case prop solver time : 0.000
% 0.23/0.31 % Current number of processed clauses : 9
% 0.23/0.31 % Positive orientable unit clauses : 6
% 0.23/0.31 % Positive unorientable unit clauses: 0
% 0.23/0.31 % Negative unit clauses : 0
% 0.23/0.31 % Non-unit-clauses : 3
% 0.23/0.31 % Current number of unprocessed clauses: 163
% 0.23/0.31 % ...number of literals in the above : 870
% 0.23/0.31 % Current number of archived formulas : 0
% 0.23/0.31 % Current number of archived clauses : 108
% 0.23/0.31 % Clause-clause subsumption calls (NU) : 539
% 0.23/0.31 % Rec. Clause-clause subsumption calls : 217
% 0.23/0.31 % Non-unit clause-clause subsumptions : 125
% 0.23/0.31 % Unit Clause-clause subsumption calls : 1
% 0.23/0.31 % Rewrite failures with RHS unbound : 0
% 0.23/0.31 % BW rewrite match attempts : 3
% 0.23/0.31 % BW rewrite match successes : 3
% 0.23/0.31 % Condensation attempts : 0
% 0.23/0.31 % Condensation successes : 0
% 0.23/0.31 % Termbank termtop insertions : 10522
% 0.23/0.31 % Search garbage collected termcells : 298
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.030 s
% 0.23/0.31 % System time : 0.003 s
% 0.23/0.31 % Total time : 0.033 s
% 0.23/0.31 % Maximum resident set size: 3636 pages
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.032 s
% 0.23/0.31 % System time : 0.006 s
% 0.23/0.31 % Total time : 0.038 s
% 0.23/0.31 % Maximum resident set size: 4864 pages
% 0.23/0.31 % E exiting
%------------------------------------------------------------------------------