%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO391^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:44:19 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 1
% Syntax : Number of formulae : 79 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 539 ( 0 equ; 0 cnn)
% Maximal formula atoms : 68 ( 6 avg)
% Number of connectives : 2130 ( 332 ~; 312 |; 148 &;1338 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 98 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 489 ( 0 ^; 489 !; 0 ?; 489 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cQ_7: $i > $i > $i > $o ).
thf(decl_24,type,
f: $i > $i ).
thf(decl_25,type,
cP_6: $i > $i > $o ).
thf(decl_26,type,
cQ_6: $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_5: $i > $i > $o ).
thf(decl_32,type,
cQ_5: $i > $i > $i > $o ).
thf(decl_33,type,
cP_4: $i > $i > $o ).
thf(decl_34,type,
cQ_4: $i > $i > $i > $o ).
thf(decl_35,type,
cP_3: $i > $i > $o ).
thf(decl_36,type,
cQ_3: $i > $i > $i > $o ).
thf(decl_37,type,
cP_2: $i > $i > $o ).
thf(decl_38,type,
cQ_2: $i > $i > $i > $o ).
thf(decl_39,type,
cP_1: $i > $i > $o ).
thf(decl_40,type,
cQ_1: $i > $i > $i > $o ).
thf(cTHM409_6,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 ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [X1: $i] : ( cP_5 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_5 @ X1 @ X2 )
| ( cP_5 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X3 ) @ X6 )
| ( cQ_6 @ X4 @ X5 @ X6 ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [X1: $i] : ( cP_6 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_6 @ X1 @ X2 )
| ( cP_6 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cP_6 @ ( f @ X2 ) @ X5 )
| ~ ( cP_6 @ ( f @ X3 ) @ X6 )
| ( cQ_7 @ X4 @ X5 @ X6 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_7 @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.RUboxSNC8q/E---3.1_60082.p',cTHM409_6) ).
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 ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [X1: $i] : ( cP_5 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_5 @ X1 @ X2 )
| ( cP_5 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X3 ) @ X6 )
| ( cQ_6 @ X4 @ X5 @ X6 ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [X1: $i] : ( cP_6 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_6 @ X1 @ X2 )
| ( cP_6 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cP_6 @ ( f @ X2 ) @ X5 )
| ~ ( cP_6 @ ( f @ X3 ) @ X6 )
| ( cQ_7 @ X4 @ X5 @ X6 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_7 @ X1 @ X2 @ X3 ) ),
inference(assume_negation,[status(cth)],[cTHM409_6]) ).
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 ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [X1: $i] : ( cP_5 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_5 @ X1 @ X2 )
| ( cP_5 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X3 ) @ X6 )
| ( cQ_6 @ X4 @ X5 @ X6 ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [X1: $i] : ( cP_6 @ d @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( cP_6 @ X1 @ X2 )
| ( cP_6 @ ( f @ X1 ) @ X2 ) )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cP_6 @ ( f @ X2 ) @ X5 )
| ~ ( cP_6 @ ( f @ X3 ) @ X6 )
| ( cQ_7 @ X4 @ X5 @ X6 ) )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_7 @ X1 @ X2 @ X3 ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [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,X85: $i,X86: $i,X87: $i,X88: $i,X89: $i,X90: $i,X91: $i,X92: $i,X93: $i,X94: $i,X95: $i,X96: $i,X97: $i,X98: $i,X99: $i,X100: $i,X101: $i,X102: $i,X103: $i,X104: $i,X105: $i,X106: $i,X107: $i,X108: $i,X109: $i,X110: $i,X111: $i,X112: $i,X113: $i,X114: $i,X115: $i,X116: $i,X117: $i,X118: $i,X119: $i,X120: $i] :
( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ( cP_1 @ d @ X64 )
& ( ~ ( cP_1 @ X65 @ X66 )
| ( cP_1 @ ( f @ X65 ) @ X66 ) )
& ( ~ ( cQ_1 @ X67 @ X68 @ X69 )
| ~ ( cP_1 @ ( f @ X67 ) @ X70 )
| ~ ( cP_1 @ ( f @ X68 ) @ X71 )
| ~ ( cP_1 @ ( f @ X69 ) @ X72 )
| ( cQ_2 @ X70 @ X71 @ X72 ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ( cP_2 @ d @ X73 )
& ( ~ ( cP_2 @ X74 @ X75 )
| ( cP_2 @ ( f @ X74 ) @ X75 ) )
& ( ~ ( cQ_2 @ X76 @ X77 @ X78 )
| ~ ( cP_2 @ ( f @ X76 ) @ X79 )
| ~ ( cP_2 @ ( f @ X77 ) @ X80 )
| ~ ( cP_2 @ ( f @ X78 ) @ X81 )
| ( cQ_3 @ X79 @ X80 @ X81 ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ( cP_3 @ d @ X82 )
& ( ~ ( cP_3 @ X83 @ X84 )
| ( cP_3 @ ( f @ X83 ) @ X84 ) )
& ( ~ ( cQ_3 @ X85 @ X86 @ X87 )
| ~ ( cP_3 @ ( f @ X85 ) @ X88 )
| ~ ( cP_3 @ ( f @ X86 ) @ X89 )
| ~ ( cP_3 @ ( f @ X87 ) @ X90 )
| ( cQ_4 @ X88 @ X89 @ X90 ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ( cP_4 @ d @ X91 )
& ( ~ ( cP_4 @ X92 @ X93 )
| ( cP_4 @ ( f @ X92 ) @ X93 ) )
& ( ~ ( cQ_4 @ X94 @ X95 @ X96 )
| ~ ( cP_4 @ ( f @ X94 ) @ X97 )
| ~ ( cP_4 @ ( f @ X95 ) @ X98 )
| ~ ( cP_4 @ ( f @ X96 ) @ X99 )
| ( cQ_5 @ X97 @ X98 @ X99 ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_5 @ d @ X100 )
& ( ~ ( cP_5 @ X101 @ X102 )
| ( cP_5 @ ( f @ X101 ) @ X102 ) )
& ( ~ ( cQ_5 @ X103 @ X104 @ X105 )
| ~ ( cP_5 @ ( f @ X103 ) @ X106 )
| ~ ( cP_5 @ ( f @ X104 ) @ X107 )
| ~ ( cP_5 @ ( f @ X105 ) @ X108 )
| ( cQ_6 @ X106 @ X107 @ X108 ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ( cP_6 @ d @ X109 )
& ( ~ ( cP_6 @ X110 @ X111 )
| ( cP_6 @ ( f @ X110 ) @ X111 ) )
& ( ~ ( cQ_6 @ X112 @ X113 @ X114 )
| ~ ( cP_6 @ ( f @ X112 ) @ X115 )
| ~ ( cP_6 @ ( f @ X113 ) @ X116 )
| ~ ( cP_6 @ ( f @ X114 ) @ X117 )
| ( cQ_7 @ X115 @ X116 @ X117 ) )
& ~ ( cQ_7 @ X118 @ X119 @ X120 ) ),
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,
! [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_27,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_28,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_29,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_30,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_26,c_0_27]) ).
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,X4: $i,X6: $i,X5: $i,X3: $i] :
( ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ ( f @ X4 ) @ X2 )
| ~ ( cP_4 @ ( f @ X5 ) @ X1 )
| ~ ( cQ_4 @ X5 @ X4 @ X6 )
| ~ ( cP_4 @ X6 @ X3 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_33,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_30,c_0_31]) ).
thf(c_0_34,negated_conjecture,
cP_2 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i,X4: $i,X6: $i,X5: $i,X3: $i,X2: $i] :
( ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ ( f @ X4 ) @ X1 )
| ~ ( cQ_4 @ X4 @ X5 @ X6 )
| ~ ( cP_4 @ X6 @ X3 )
| ~ ( cP_4 @ X5 @ X2 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
thf(c_0_36,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_33,c_0_34]) ).
thf(c_0_37,negated_conjecture,
cP_2 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_38,negated_conjecture,
! [X2: $i,X6: $i,X5: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cQ_4 @ X4 @ X5 @ X6 )
| ~ ( cP_4 @ X6 @ X3 )
| ~ ( cP_4 @ X5 @ X2 )
| ~ ( cP_4 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
thf(c_0_39,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_36,c_0_37]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
( ( cQ_6 @ X4 @ X5 @ X6 )
| ~ ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_5 @ ( f @ X1 ) @ X4 )
| ~ ( cP_5 @ ( f @ X2 ) @ X5 )
| ~ ( cP_5 @ ( f @ X3 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP_5 @ ( f @ X1 ) @ X2 )
| ~ ( cP_5 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_42,negated_conjecture,
! [X3: $i,X2: $i,X5: $i,X6: $i,X4: $i,X1: $i] :
( ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ c @ X4 )
| ~ ( cP_3 @ b @ X5 )
| ~ ( cP_3 @ a @ X6 )
| ~ ( cP_4 @ X4 @ X3 )
| ~ ( cP_4 @ X5 @ X2 )
| ~ ( cP_4 @ X6 @ X1 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
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,X4: $i,X6: $i,X5: $i,X3: $i] :
( ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_5 @ ( f @ X4 ) @ X2 )
| ~ ( cP_5 @ ( f @ X5 ) @ X1 )
| ~ ( cQ_5 @ X5 @ X4 @ X6 )
| ~ ( cP_5 @ X6 @ X3 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_45,negated_conjecture,
! [X2: $i,X4: $i,X5: $i,X3: $i,X1: $i] :
( ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ b @ X4 )
| ~ ( cP_3 @ a @ X5 )
| ~ ( cP_4 @ c @ X3 )
| ~ ( cP_4 @ X4 @ X2 )
| ~ ( cP_4 @ X5 @ X1 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_46,negated_conjecture,
cP_3 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i,X4: $i,X6: $i,X5: $i,X3: $i,X2: $i] :
( ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_5 @ ( f @ X4 ) @ X1 )
| ~ ( cQ_5 @ X4 @ X5 @ X6 )
| ~ ( cP_5 @ X6 @ X3 )
| ~ ( cP_5 @ X5 @ X2 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
thf(c_0_48,negated_conjecture,
! [X2: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_3 @ a @ X4 )
| ~ ( cP_4 @ c @ X3 )
| ~ ( cP_4 @ b @ X2 )
| ~ ( cP_4 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_49,negated_conjecture,
cP_3 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
( ( cQ_7 @ X4 @ X5 @ X6 )
| ~ ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_6 @ ( f @ X1 ) @ X4 )
| ~ ( cP_6 @ ( f @ X2 ) @ X5 )
| ~ ( cP_6 @ ( f @ X3 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_7 @ X1 @ X2 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_52,negated_conjecture,
! [X2: $i,X6: $i,X5: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cQ_5 @ X4 @ X5 @ X6 )
| ~ ( cP_5 @ X6 @ X3 )
| ~ ( cP_5 @ X5 @ X2 )
| ~ ( cP_5 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
thf(c_0_53,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( cQ_5 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ c @ X3 )
| ~ ( cP_4 @ b @ X2 )
| ~ ( cP_4 @ a @ X1 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_54,negated_conjecture,
! [X6: $i,X5: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ ( cP_6 @ ( f @ X1 ) @ X2 )
| ~ ( cP_6 @ ( f @ X3 ) @ X4 )
| ~ ( cP_6 @ ( f @ X5 ) @ X6 )
| ~ ( cQ_6 @ X5 @ X3 @ X1 ) ),
inference(sr,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP_6 @ ( f @ X1 ) @ X2 )
| ~ ( cP_6 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_56,negated_conjecture,
! [X3: $i,X2: $i,X5: $i,X6: $i,X4: $i,X1: $i] :
( ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ c @ X4 )
| ~ ( cP_4 @ b @ X5 )
| ~ ( cP_4 @ a @ X6 )
| ~ ( cP_5 @ X4 @ X3 )
| ~ ( cP_5 @ X5 @ X2 )
| ~ ( cP_5 @ X6 @ X1 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_57,negated_conjecture,
cP_4 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_58,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_6 @ ( f @ X1 ) @ X2 )
| ~ ( cP_6 @ ( f @ X3 ) @ X4 )
| ~ ( cQ_6 @ X3 @ X1 @ X5 )
| ~ ( cP_6 @ X5 @ X6 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_59,negated_conjecture,
! [X2: $i,X4: $i,X5: $i,X3: $i,X1: $i] :
( ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ b @ X4 )
| ~ ( cP_4 @ a @ X5 )
| ~ ( cP_5 @ c @ X3 )
| ~ ( cP_5 @ X4 @ X2 )
| ~ ( cP_5 @ X5 @ X1 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_60,negated_conjecture,
cP_4 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_61,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_6 @ ( f @ X1 ) @ X2 )
| ~ ( cQ_6 @ X1 @ X3 @ X4 )
| ~ ( cP_6 @ X4 @ X5 )
| ~ ( cP_6 @ X3 @ X6 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_55]) ).
thf(c_0_62,negated_conjecture,
! [X2: $i,X4: $i,X3: $i,X1: $i] :
( ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_4 @ a @ X4 )
| ~ ( cP_5 @ c @ X3 )
| ~ ( cP_5 @ b @ X2 )
| ~ ( cP_5 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_63,negated_conjecture,
cP_4 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_64,negated_conjecture,
! [X3: $i,X2: $i,X1: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_6 @ X3 @ X4 )
| ~ ( cP_6 @ X2 @ X5 )
| ~ ( cP_6 @ X1 @ X6 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_55]) ).
thf(c_0_65,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( cQ_6 @ X1 @ X2 @ X3 )
| ~ ( cP_5 @ c @ X3 )
| ~ ( cP_5 @ b @ X2 )
| ~ ( cP_5 @ a @ X1 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_5 @ c @ X1 )
| ~ ( cP_5 @ b @ X2 )
| ~ ( cP_5 @ a @ X3 )
| ~ ( cP_6 @ X1 @ X4 )
| ~ ( cP_6 @ X2 @ X5 )
| ~ ( cP_6 @ X3 @ X6 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_67,negated_conjecture,
cP_5 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( cP_5 @ b @ X1 )
| ~ ( cP_5 @ a @ X2 )
| ~ ( cP_6 @ c @ X3 )
| ~ ( cP_6 @ X1 @ X4 )
| ~ ( cP_6 @ X2 @ X5 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_69,negated_conjecture,
cP_5 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_70,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( cP_5 @ a @ X1 )
| ~ ( cP_6 @ c @ X2 )
| ~ ( cP_6 @ b @ X3 )
| ~ ( cP_6 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_71,negated_conjecture,
cP_5 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_72,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( cP_6 @ c @ X1 )
| ~ ( cP_6 @ b @ X2 )
| ~ ( cP_6 @ a @ X3 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_73,negated_conjecture,
cP_6 @ c @ c,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_74,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( cP_6 @ b @ X1 )
| ~ ( cP_6 @ a @ X2 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_75,negated_conjecture,
cP_6 @ b @ b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_76,negated_conjecture,
cP_6 @ a @ a,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_77,negated_conjecture,
! [X1: $i] :
~ ( cP_6 @ a @ X1 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
thf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_76,c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO391^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.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 16:50:30 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.RUboxSNC8q/E---3.1_60082.p
% 0.22/0.28 % Version: 3.5.1-ho
% 0.22/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.22/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.22/0.28 % Starting new_ho_10_unif with 300s (1) cores
% 0.22/0.28 % new_bool_1 with pid 60096 completed with status 0
% 0.22/0.28 % Result found by new_bool_1
% 0.22/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.22/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.28 % Search class: HHUNM-FFMM11-SFFFFFNN
% 0.22/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.28 % SubtermCWHack with pid 60101 completed with status 0
% 0.22/0.28 % Result found by SubtermCWHack
% 0.22/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.22/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.28 % Search class: HHUNM-FFMM11-SFFFFFNN
% 0.22/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.28 % Preprocessing time : 0.001 s
% 0.22/0.28
% 0.22/0.28 % Proof found!
% 0.22/0.28 % SZS status Theorem
% 0.22/0.28 % SZS output start CNFRefutation
% See solution above
% 0.22/0.28 % Parsed axioms : 19
% 0.22/0.28 % Removed by relevancy pruning/SinE : 18
% 0.22/0.28 % Initial clauses : 38
% 0.22/0.28 % Removed in clause preprocessing : 0
% 0.22/0.28 % Initial clauses in saturation : 38
% 0.22/0.28 % Processed clauses : 79
% 0.22/0.28 % ...of these trivial : 0
% 0.22/0.28 % ...subsumed : 0
% 0.22/0.28 % ...remaining for further processing : 79
% 0.22/0.28 % Other redundant clauses eliminated : 0
% 0.22/0.28 % Clauses deleted for lack of memory : 0
% 0.22/0.28 % Backward-subsumed : 2
% 0.22/0.28 % Backward-rewritten : 0
% 0.22/0.28 % Generated clauses : 42
% 0.22/0.28 % ...of the previous two non-redundant : 41
% 0.22/0.28 % ...aggressively subsumed : 0
% 0.22/0.28 % Contextual simplify-reflections : 0
% 0.22/0.28 % Paramodulations : 41
% 0.22/0.28 % Factorizations : 0
% 0.22/0.28 % NegExts : 0
% 0.22/0.28 % Equation resolutions : 0
% 0.22/0.28 % Disequality decompositions : 0
% 0.22/0.28 % Total rewrite steps : 0
% 0.22/0.28 % ...of those cached : 0
% 0.22/0.28 % Propositional unsat checks : 0
% 0.22/0.28 % Propositional check models : 0
% 0.22/0.28 % Propositional check unsatisfiable : 0
% 0.22/0.28 % Propositional clauses : 0
% 0.22/0.28 % Propositional clauses after purity: 0
% 0.22/0.28 % Propositional unsat core size : 0
% 0.22/0.28 % Propositional preprocessing time : 0.000
% 0.22/0.28 % Propositional encoding time : 0.000
% 0.22/0.28 % Propositional solver time : 0.000
% 0.22/0.28 % Success case prop preproc time : 0.000
% 0.22/0.28 % Success case prop encoding time : 0.000
% 0.22/0.28 % Success case prop solver time : 0.000
% 0.22/0.28 % Current number of processed clauses : 76
% 0.22/0.28 % Positive orientable unit clauses : 24
% 0.22/0.28 % Positive unorientable unit clauses: 0
% 0.22/0.28 % Negative unit clauses : 2
% 0.22/0.28 % Non-unit-clauses : 50
% 0.22/0.28 % Current number of unprocessed clauses: 0
% 0.22/0.28 % ...number of literals in the above : 0
% 0.22/0.28 % Current number of archived formulas : 0
% 0.22/0.28 % Current number of archived clauses : 3
% 0.22/0.28 % Clause-clause subsumption calls (NU) : 256
% 0.22/0.28 % Rec. Clause-clause subsumption calls : 73
% 0.22/0.28 % Non-unit clause-clause subsumptions : 1
% 0.22/0.28 % Unit Clause-clause subsumption calls : 9
% 0.22/0.28 % Rewrite failures with RHS unbound : 0
% 0.22/0.28 % BW rewrite match attempts : 0
% 0.22/0.28 % BW rewrite match successes : 0
% 0.22/0.28 % Condensation attempts : 0
% 0.22/0.28 % Condensation successes : 0
% 0.22/0.28 % Termbank termtop insertions : 5207
% 0.22/0.28 % Search garbage collected termcells : 564
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.010 s
% 0.22/0.28 % System time : 0.001 s
% 0.22/0.28 % Total time : 0.011 s
% 0.22/0.28 % Maximum resident set size: 3676 pages
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.012 s
% 0.22/0.28 % System time : 0.005 s
% 0.22/0.28 % Total time : 0.018 s
% 0.22/0.28 % Maximum resident set size: 4608 pages
% 0.22/0.28 % E exiting
%------------------------------------------------------------------------------