%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO387^5 : 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 : n016.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 08:42:52 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 55 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 357 ( 0 equ; 0 cnn)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 1412 ( 222 ~; 202 |; 100 &; 888 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 68 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 329 ( 0 ^; 329 !; 0 ?; 329 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cQ_5: $i > $i > $i > $o ).
thf(decl_24,type,
f: $i > $i ).
thf(decl_25,type,
cP_4: $i > $i > $o ).
thf(decl_26,type,
cQ_4: $i > $i > $i > $o ).
thf(decl_27,type,
d: $i ).
thf(decl_28,type,
c: $i ).
thf(decl_29,type,
b: $i ).
thf(decl_30,type,
a: $i ).
thf(decl_31,type,
cP_3: $i > $i > $o ).
thf(decl_32,type,
cQ_3: $i > $i > $i > $o ).
thf(decl_33,type,
cP_2: $i > $i > $o ).
thf(decl_34,type,
cQ_2: $i > $i > $i > $o ).
thf(decl_35,type,
cP_1: $i > $i > $o ).
thf(decl_36,type,
cQ_1: $i > $i > $i > $o ).
thf(cTHM409_4,conjecture,
~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [X1: $i] : ( cP_1 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_1 @ X1 @ X2 )
| ( cP_1 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_1 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X3 ) @ X6 )
| ( cQ_2 @ X4 @ X5 @ X6 ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [X1: $i] : ( cP_2 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_2 @ X1 @ X2 )
| ( cP_2 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X3 ) @ X6 )
| ( cQ_3 @ X4 @ X5 @ X6 ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [X1: $i] : ( cP_3 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_3 @ X1 @ X2 )
| ( cP_3 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X3 ) @ X6 )
| ( cQ_4 @ X4 @ X5 @ X6 ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [X1: $i] : ( cP_4 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_4 @ X1 @ X2 )
| ( cP_4 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X3 ) @ X6 )
| ( cQ_5 @ X4 @ X5 @ X6 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_5 @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.etSRRWC7FC/E---3.1_609609.p',cTHM409_4) ).
thf(c_0_1,negated_conjecture,
~ ~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [X1: $i] : ( cP_1 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_1 @ X1 @ X2 )
| ( cP_1 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_1 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X3 ) @ X6 )
| ( cQ_2 @ X4 @ X5 @ X6 ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [X1: $i] : ( cP_2 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_2 @ X1 @ X2 )
| ( cP_2 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X3 ) @ X6 )
| ( cQ_3 @ X4 @ X5 @ X6 ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [X1: $i] : ( cP_3 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_3 @ X1 @ X2 )
| ( cP_3 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X3 ) @ X6 )
| ( cQ_4 @ X4 @ X5 @ X6 ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [X1: $i] : ( cP_4 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_4 @ X1 @ X2 )
| ( cP_4 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X3 ) @ X6 )
| ( cQ_5 @ X4 @ X5 @ X6 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_5 @ X1 @ X2 @ X3 ) ),
inference(assume_negation,[status(cth)],[cTHM409_4]) ).
thf(c_0_2,negated_conjecture,
~ ~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [X1: $i] : ( cP_1 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_1 @ X1 @ X2 )
| ( cP_1 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_1 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X3 ) @ X6 )
| ( cQ_2 @ X4 @ X5 @ X6 ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [X1: $i] : ( cP_2 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_2 @ X1 @ X2 )
| ( cP_2 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X3 ) @ X6 )
| ( cQ_3 @ X4 @ X5 @ X6 ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [X1: $i] : ( cP_3 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_3 @ X1 @ X2 )
| ( cP_3 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X3 ) @ X6 )
| ( cQ_4 @ X4 @ X5 @ X6 ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [X1: $i] : ( cP_4 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_4 @ X1 @ X2 )
| ( cP_4 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X3 ) @ X6 )
| ( cQ_5 @ X4 @ X5 @ X6 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_5 @ X1 @ X2 @ X3 ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X46: $i,X47: $i,X48: $i,X49: $i,X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i,X60: $i,X61: $i,X62: $i,X63: $i,X64: $i,X65: $i,X66: $i,X67: $i,X68: $i,X69: $i,X70: $i,X71: $i,X72: $i,X73: $i,X74: $i,X75: $i,X76: $i,X77: $i,X78: $i,X79: $i,X80: $i,X81: $i,X82: $i,X83: $i,X84: $i] :
( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ( cP_1 @ d @ X46 )
& ( ~ ( cP_1 @ X47 @ X48 )
| ( cP_1 @ ( f @ X47 ) @ X48 ) )
& ( ~ ( cQ_1 @ X49 @ X50 @ X51 )
| ~ ( cP_1 @ ( f @ X49 ) @ X52 )
| ~ ( cP_1 @ ( f @ X50 ) @ X53 )
| ~ ( cP_1 @ ( f @ X51 ) @ X54 )
| ( cQ_2 @ X52 @ X53 @ X54 ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ( cP_2 @ d @ X55 )
& ( ~ ( cP_2 @ X56 @ X57 )
| ( cP_2 @ ( f @ X56 ) @ X57 ) )
& ( ~ ( cQ_2 @ X58 @ X59 @ X60 )
| ~ ( cP_2 @ ( f @ X58 ) @ X61 )
| ~ ( cP_2 @ ( f @ X59 ) @ X62 )
| ~ ( cP_2 @ ( f @ X60 ) @ X63 )
| ( cQ_3 @ X61 @ X62 @ X63 ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ( cP_3 @ d @ X64 )
& ( ~ ( cP_3 @ X65 @ X66 )
| ( cP_3 @ ( f @ X65 ) @ X66 ) )
& ( ~ ( cQ_3 @ X67 @ X68 @ X69 )
| ~ ( cP_3 @ ( f @ X67 ) @ X70 )
| ~ ( cP_3 @ ( f @ X68 ) @ X71 )
| ~ ( cP_3 @ ( f @ X69 ) @ X72 )
| ( cQ_4 @ X70 @ X71 @ X72 ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ( cP_4 @ d @ X73 )
& ( ~ ( cP_4 @ X74 @ X75 )
| ( cP_4 @ ( f @ X74 ) @ X75 ) )
& ( ~ ( cQ_4 @ X76 @ X77 @ X78 )
| ~ ( cP_4 @ ( f @ X76 ) @ X79 )
| ~ ( cP_4 @ ( f @ X77 ) @ X80 )
| ~ ( cP_4 @ ( f @ X78 ) @ X81 )
| ( cQ_5 @ X79 @ X80 @ X81 ) )
& ~ ( cQ_5 @ X82 @ X83 @ X84 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
thf(c_0_4,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
( ( cQ_2 @ X4 @ X5 @ X6 )
| ~ ( cQ_1 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X3 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP_1 @ ( f @ X1 ) @ X2 )
| ~ ( cP_1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
( ( cQ_3 @ X4 @ X5 @ X6 )
| ~ ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X3 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP_2 @ ( f @ X1 ) @ X2 )
| ~ ( cP_2 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X6: $i,X5: $i,X3: $i] :
( ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ ( f @ X4 ) @ X2 )
| ~ ( cP_1 @ ( f @ X5 ) @ X1 )
| ~ ( cQ_1 @ X5 @ X4 @ X6 )
| ~ ( cP_1 @ X6 @ X3 ) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X6: $i,X5: $i,X3: $i] :
( ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ ( f @ X4 ) @ X2 )
| ~ ( cP_2 @ ( f @ X5 ) @ X1 )
| ~ ( cQ_2 @ X5 @ X4 @ X6 )
| ~ ( cP_2 @ X6 @ X3 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X4: $i,X6: $i,X5: $i,X3: $i,X2: $i] :
( ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ ( f @ X4 ) @ X1 )
| ~ ( cQ_1 @ X4 @ X5 @ X6 )
| ~ ( cP_1 @ X6 @ X3 )
| ~ ( cP_1 @ X5 @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X4: $i,X6: $i,X5: $i,X3: $i,X2: $i] :
( ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ ( f @ X4 ) @ X1 )
| ~ ( cQ_2 @ X4 @ X5 @ X6 )
| ~ ( cP_2 @ X6 @ X3 )
| ~ ( cP_2 @ X5 @ X2 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X2: $i,X6: $i,X5: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cQ_1 @ X4 @ X5 @ X6 )
| ~ ( cP_1 @ X6 @ X3 )
| ~ ( cP_1 @ X5 @ X2 )
| ~ ( cP_1 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_5]) ).
thf(c_0_13,negated_conjecture,
cQ_1 @ a @ b @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i,X6: $i,X5: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cQ_2 @ X4 @ X5 @ X6 )
| ~ ( cP_2 @ X6 @ X3 )
| ~ ( cP_2 @ X5 @ X2 )
| ~ ( cP_2 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( cQ_2 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ c @ X3 )
| ~ ( cP_1 @ b @ X2 )
| ~ ( cP_1 @ a @ X1 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
( ( cQ_4 @ X4 @ X5 @ X6 )
| ~ ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ ( f @ X1 ) @ X4 )
| ~ ( cP_3 @ ( f @ X2 ) @ X5 )
| ~ ( cP_3 @ ( f @ X3 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP_3 @ ( f @ X1 ) @ X2 )
| ~ ( cP_3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_18,negated_conjecture,
! [X3: $i,X2: $i,X5: $i,X6: $i,X4: $i,X1: $i] :
( ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ c @ X4 )
| ~ ( cP_1 @ b @ X5 )
| ~ ( cP_1 @ a @ X6 )
| ~ ( cP_2 @ X4 @ X3 )
| ~ ( cP_2 @ X5 @ X2 )
| ~ ( cP_2 @ X6 @ X1 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,negated_conjecture,
cP_1 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X6: $i,X5: $i,X3: $i] :
( ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ ( f @ X4 ) @ X2 )
| ~ ( cP_3 @ ( f @ X5 ) @ X1 )
| ~ ( cQ_3 @ X5 @ X4 @ X6 )
| ~ ( cP_3 @ X6 @ X3 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i,X4: $i,X5: $i,X3: $i,X1: $i] :
( ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ b @ X4 )
| ~ ( cP_1 @ a @ X5 )
| ~ ( cP_2 @ c @ X3 )
| ~ ( cP_2 @ X4 @ X2 )
| ~ ( cP_2 @ X5 @ X1 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,negated_conjecture,
cP_1 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X4: $i,X6: $i,X5: $i,X3: $i,X2: $i] :
( ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ ( f @ X4 ) @ X1 )
| ~ ( cQ_3 @ X4 @ X5 @ X6 )
| ~ ( cP_3 @ X6 @ X3 )
| ~ ( cP_3 @ X5 @ X2 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_1 @ a @ X4 )
| ~ ( cP_2 @ c @ X3 )
| ~ ( cP_2 @ b @ X2 )
| ~ ( cP_2 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,negated_conjecture,
cP_1 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
( ( cQ_5 @ X4 @ X5 @ X6 )
| ~ ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ ( f @ X1 ) @ X4 )
| ~ ( cP_4 @ ( f @ X2 ) @ X5 )
| ~ ( cP_4 @ ( f @ X3 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_5 @ X1 @ X2 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i,X6: $i,X5: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cQ_3 @ X4 @ X5 @ X6 )
| ~ ( cP_3 @ X6 @ X3 )
| ~ ( cP_3 @ X5 @ X2 )
| ~ ( cP_3 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ c @ X3 )
| ~ ( cP_2 @ b @ X2 )
| ~ ( cP_2 @ a @ X1 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_30,negated_conjecture,
! [X6: $i,X5: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ ( cP_4 @ ( f @ X1 ) @ X2 )
| ~ ( cP_4 @ ( f @ X3 ) @ X4 )
| ~ ( cP_4 @ ( f @ X5 ) @ X6 )
| ~ ( cQ_4 @ X5 @ X3 @ X1 ) ),
inference(sr,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP_4 @ ( f @ X1 ) @ X2 )
| ~ ( cP_4 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_32,negated_conjecture,
! [X3: $i,X2: $i,X5: $i,X6: $i,X4: $i,X1: $i] :
( ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ c @ X4 )
| ~ ( cP_2 @ b @ X5 )
| ~ ( cP_2 @ a @ X6 )
| ~ ( cP_3 @ X4 @ X3 )
| ~ ( cP_3 @ X5 @ X2 )
| ~ ( cP_3 @ X6 @ X1 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_33,negated_conjecture,
cP_2 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_4 @ ( f @ X1 ) @ X2 )
| ~ ( cP_4 @ ( f @ X3 ) @ X4 )
| ~ ( cQ_4 @ X3 @ X1 @ X5 )
| ~ ( cP_4 @ X5 @ X6 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_35,negated_conjecture,
! [X2: $i,X4: $i,X5: $i,X3: $i,X1: $i] :
( ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ b @ X4 )
| ~ ( cP_2 @ a @ X5 )
| ~ ( cP_3 @ c @ X3 )
| ~ ( cP_3 @ X4 @ X2 )
| ~ ( cP_3 @ X5 @ X1 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,negated_conjecture,
cP_2 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_4 @ ( f @ X1 ) @ X2 )
| ~ ( cQ_4 @ X1 @ X3 @ X4 )
| ~ ( cP_4 @ X4 @ X5 )
| ~ ( cP_4 @ X3 @ X6 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
thf(c_0_38,negated_conjecture,
! [X2: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_2 @ a @ X4 )
| ~ ( cP_3 @ c @ X3 )
| ~ ( cP_3 @ b @ X2 )
| ~ ( cP_3 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_39,negated_conjecture,
cP_2 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_40,negated_conjecture,
! [X3: $i,X2: $i,X1: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ X3 @ X4 )
| ~ ( cP_4 @ X2 @ X5 )
| ~ ( cP_4 @ X1 @ X6 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
thf(c_0_41,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( cQ_4 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ c @ X3 )
| ~ ( cP_3 @ b @ X2 )
| ~ ( cP_3 @ a @ X1 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_3 @ c @ X1 )
| ~ ( cP_3 @ b @ X2 )
| ~ ( cP_3 @ a @ X3 )
| ~ ( cP_4 @ X1 @ X4 )
| ~ ( cP_4 @ X2 @ X5 )
| ~ ( cP_4 @ X3 @ X6 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_43,negated_conjecture,
cP_3 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( cP_3 @ b @ X1 )
| ~ ( cP_3 @ a @ X2 )
| ~ ( cP_4 @ c @ X3 )
| ~ ( cP_4 @ X1 @ X4 )
| ~ ( cP_4 @ X2 @ X5 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_45,negated_conjecture,
cP_3 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( cP_3 @ a @ X1 )
| ~ ( cP_4 @ c @ X2 )
| ~ ( cP_4 @ b @ X3 )
| ~ ( cP_4 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_47,negated_conjecture,
cP_3 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_48,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( cP_4 @ c @ X1 )
| ~ ( cP_4 @ b @ X2 )
| ~ ( cP_4 @ a @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_49,negated_conjecture,
cP_4 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( cP_4 @ b @ X1 )
| ~ ( cP_4 @ a @ X2 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_51,negated_conjecture,
cP_4 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_52,negated_conjecture,
cP_4 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
~ ( cP_4 @ a @ X1 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_52,c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO387^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n016.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 16:55:04 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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.etSRRWC7FC/E---3.1_609609.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.25 % Starting full_lambda_5 with 300s (1) cores
% 0.08/0.25 % Starting new_ho_10_unif with 300s (1) cores
% 0.08/0.25 % new_bool_1 with pid 609623 completed with status 0
% 0.08/0.25 % Result found by new_bool_1
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.25 % Search class: HHUNM-FFSM11-SFFFFFNN
% 0.08/0.25 % partial match(1): HHUNS-FFSM11-SFFFFFNN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 609628 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.25 % Search class: HHUNM-FFSM11-SFFFFFNN
% 0.08/0.25 % partial match(1): HHUNS-FFSM11-SFFFFFNN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 15
% 0.08/0.25 % Removed by relevancy pruning/SinE : 14
% 0.08/0.25 % Initial clauses : 26
% 0.08/0.25 % Removed in clause preprocessing : 0
% 0.08/0.25 % Initial clauses in saturation : 26
% 0.08/0.25 % Processed clauses : 53
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 53
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 2
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 28
% 0.08/0.25 % ...of the previous two non-redundant : 27
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 27
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 0
% 0.08/0.25 % ...of those cached : 0
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 50
% 0.08/0.25 % Positive orientable unit clauses : 16
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 2
% 0.08/0.25 % Non-unit-clauses : 32
% 0.08/0.25 % Current number of unprocessed clauses: 0
% 0.08/0.25 % ...number of literals in the above : 0
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 3
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 144
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 49
% 0.08/0.25 % Non-unit clause-clause subsumptions : 1
% 0.08/0.25 % Unit Clause-clause subsumption calls : 9
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 3449
% 0.08/0.25 % Search garbage collected termcells : 380
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.007 s
% 0.08/0.25 % System time : 0.001 s
% 0.08/0.25 % Total time : 0.008 s
% 0.08/0.25 % Maximum resident set size: 3660 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.007 s
% 0.08/0.25 % System time : 0.007 s
% 0.08/0.25 % Total time : 0.014 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------