%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO386^5 : 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 : n014.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 08:44:18 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 266 ( 0 equ; 0 cnn)
% Maximal formula atoms : 35 ( 6 avg)
% Number of connectives : 1053 ( 167 ~; 147 |; 76 &; 663 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 249 ( 0 ^; 249 !; 0 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cQ_4: $i > $i > $i > $o ).
thf(decl_24,type,
f: $i > $i ).
thf(decl_25,type,
cP_3: $i > $i > $o ).
thf(decl_26,type,
cQ_3: $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_2: $i > $i > $o ).
thf(decl_32,type,
cQ_2: $i > $i > $i > $o ).
thf(decl_33,type,
cP_1: $i > $i > $o ).
thf(decl_34,type,
cQ_1: $i > $i > $i > $o ).
thf(cTHM409_3,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 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_4 @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.H1Dbng2meA/E---3.1_2918004.p',cTHM409_3) ).
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 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_4 @ X1 @ X2 @ X3 ) ),
inference(assume_negation,[status(cth)],[cTHM409_3]) ).
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 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_4 @ X1 @ X2 @ X3 ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,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] :
( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ( cP_1 @ d @ X37 )
& ( ~ ( cP_1 @ X38 @ X39 )
| ( cP_1 @ ( f @ X38 ) @ X39 ) )
& ( ~ ( cQ_1 @ X40 @ X41 @ X42 )
| ~ ( cP_1 @ ( f @ X40 ) @ X43 )
| ~ ( cP_1 @ ( f @ X41 ) @ X44 )
| ~ ( cP_1 @ ( f @ X42 ) @ X45 )
| ( cQ_2 @ X43 @ X44 @ X45 ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ( cP_2 @ d @ X46 )
& ( ~ ( cP_2 @ X47 @ X48 )
| ( cP_2 @ ( f @ X47 ) @ X48 ) )
& ( ~ ( cQ_2 @ X49 @ X50 @ X51 )
| ~ ( cP_2 @ ( f @ X49 ) @ X52 )
| ~ ( cP_2 @ ( f @ X50 ) @ X53 )
| ~ ( cP_2 @ ( f @ X51 ) @ X54 )
| ( cQ_3 @ X52 @ X53 @ X54 ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ( cP_3 @ d @ X55 )
& ( ~ ( cP_3 @ X56 @ X57 )
| ( cP_3 @ ( f @ X56 ) @ X57 ) )
& ( ~ ( cQ_3 @ X58 @ X59 @ X60 )
| ~ ( cP_3 @ ( f @ X58 ) @ X61 )
| ~ ( cP_3 @ ( f @ X59 ) @ X62 )
| ~ ( cP_3 @ ( f @ X60 ) @ X63 )
| ( cQ_4 @ X61 @ X62 @ X63 ) )
& ~ ( cQ_4 @ X64 @ X65 @ X66 ) ),
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,
! [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_15,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_4 @ X1 @ X2 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_16,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_17,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_18,negated_conjecture,
! [X6: $i,X5: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ ( cP_3 @ ( f @ X1 ) @ X2 )
| ~ ( cP_3 @ ( f @ X3 ) @ X4 )
| ~ ( cP_3 @ ( f @ X5 ) @ X6 )
| ~ ( cQ_3 @ X5 @ X3 @ X1 ) ),
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,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_20,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_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
cP_1 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_3 @ ( f @ X1 ) @ X2 )
| ~ ( cP_3 @ ( f @ X3 ) @ X4 )
| ~ ( cQ_3 @ X3 @ X1 @ X5 )
| ~ ( cP_3 @ X5 @ X6 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,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_20,c_0_21]) ).
thf(c_0_24,negated_conjecture,
cP_1 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_3 @ ( f @ X1 ) @ X2 )
| ~ ( cQ_3 @ X1 @ X3 @ X4 )
| ~ ( cP_3 @ X4 @ X5 )
| ~ ( cP_3 @ X3 @ X6 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
thf(c_0_26,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_23,c_0_24]) ).
thf(c_0_27,negated_conjecture,
cP_1 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i,X2: $i,X1: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_3 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ X3 @ X4 )
| ~ ( cP_3 @ X2 @ X5 )
| ~ ( cP_3 @ X1 @ X6 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
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_26,c_0_27]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_2 @ c @ X1 )
| ~ ( cP_2 @ b @ X2 )
| ~ ( cP_2 @ a @ X3 )
| ~ ( cP_3 @ X1 @ X4 )
| ~ ( cP_3 @ X2 @ X5 )
| ~ ( cP_3 @ X3 @ X6 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_31,negated_conjecture,
cP_2 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( cP_2 @ b @ X1 )
| ~ ( cP_2 @ a @ X2 )
| ~ ( cP_3 @ c @ X3 )
| ~ ( cP_3 @ X1 @ X4 )
| ~ ( cP_3 @ X2 @ X5 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_33,negated_conjecture,
cP_2 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( cP_2 @ a @ X1 )
| ~ ( cP_3 @ c @ X2 )
| ~ ( cP_3 @ b @ X3 )
| ~ ( cP_3 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_35,negated_conjecture,
cP_2 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( cP_3 @ c @ X1 )
| ~ ( cP_3 @ b @ X2 )
| ~ ( cP_3 @ a @ X3 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_37,negated_conjecture,
cP_3 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( cP_3 @ b @ X1 )
| ~ ( cP_3 @ a @ X2 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_39,negated_conjecture,
cP_3 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_40,negated_conjecture,
cP_3 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i] :
~ ( cP_3 @ a @ X1 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_40,c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO386^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n014.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:50:00 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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.H1Dbng2meA/E---3.1_2918004.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.24 % Starting full_lambda_5 with 300s (1) cores
% 0.09/0.24 % Starting new_ho_10_unif with 300s (1) cores
% 0.09/0.24 % new_bool_1 with pid 2918037 completed with status 0
% 0.09/0.24 % Result found by new_bool_1
% 0.09/0.24 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.24 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.24 % Search class: HHUNS-FFSM11-SFFFFFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 2918046 completed with status 0
% 0.09/0.24 % Result found by SubtermCWHack
% 0.09/0.24 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.24 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.24 % Search class: HHUNS-FFSM11-SFFFFFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 13
% 0.09/0.24 % Removed by relevancy pruning/SinE : 12
% 0.09/0.24 % Initial clauses : 20
% 0.09/0.24 % Removed in clause preprocessing : 0
% 0.09/0.24 % Initial clauses in saturation : 20
% 0.09/0.24 % Processed clauses : 40
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 40
% 0.09/0.24 % Other redundant clauses eliminated : 0
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 2
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 21
% 0.09/0.24 % ...of the previous two non-redundant : 20
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 20
% 0.09/0.24 % Factorizations : 0
% 0.09/0.24 % NegExts : 0
% 0.09/0.24 % Equation resolutions : 0
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 0
% 0.09/0.24 % ...of those cached : 0
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 37
% 0.09/0.24 % Positive orientable unit clauses : 12
% 0.09/0.24 % Positive unorientable unit clauses: 0
% 0.09/0.24 % Negative unit clauses : 2
% 0.09/0.24 % Non-unit-clauses : 23
% 0.09/0.24 % Current number of unprocessed clauses: 0
% 0.09/0.24 % ...number of literals in the above : 0
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 3
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 98
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 37
% 0.09/0.24 % Non-unit clause-clause subsumptions : 1
% 0.09/0.24 % Unit Clause-clause subsumption calls : 9
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 0
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 0
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 2570
% 0.09/0.24 % Search garbage collected termcells : 288
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.005 s
% 0.09/0.24 % System time : 0.004 s
% 0.09/0.24 % Total time : 0.009 s
% 0.09/0.24 % Maximum resident set size: 3600 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.008 s
% 0.09/0.24 % System time : 0.009 s
% 0.09/0.24 % Total time : 0.016 s
% 0.09/0.24 % Maximum resident set size: 4608 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------