%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO385^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /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 08:47:34 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 1
% Syntax : Number of formulae : 45 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 949 ( 230 equ; 0 cnn)
% Maximal formula atoms : 41 ( 21 avg)
% Number of connectives : 1208 ( 218 ~; 180 |; 78 &; 732 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 265 ( 0 ^; 265 !; 0 ?; 265 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ_3: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_2: $i > $i > $o ).
thf(func_def_3,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_8,type,
cP_1: $i > $i > $o ).
thf(func_def_9,type,
cQ_1: $i > $i > $i > $o ).
thf(f1,conjecture,
~ ( ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X3: $i,X5: $i,X1: $i,X2: $i,X0: $i,X4: $i] :
( ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
& ( cP_2 @ c @ c )
& ! [X1: $i,X0: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [X0: $i,X1: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ! [X2: $i,X1: $i,X0: $i] :
~ ( cQ_3 @ X0 @ X1 @ X2 )
& ( cP_2 @ b @ b )
& ! [X4: $i,X5: $i,X1: $i,X0: $i,X3: $i,X2: $i] :
( ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ( cQ_3 @ X3 @ X4 @ X5 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ a @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM409_2) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X3: $i,X5: $i,X1: $i,X2: $i,X0: $i,X4: $i] :
( ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
& ( cP_2 @ c @ c )
& ! [X1: $i,X0: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ! [X0: $i] : ( cP_2 @ d @ X0 )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [X0: $i,X1: $i] :
( ~ ( cP_2 @ X0 @ X1 )
| ( cP_2 @ ( f @ X0 ) @ X1 ) )
& ! [X2: $i,X1: $i,X0: $i] :
~ ( cQ_3 @ X0 @ X1 @ X2 )
& ( cP_2 @ b @ b )
& ! [X4: $i,X5: $i,X1: $i,X0: $i,X3: $i,X2: $i] :
( ~ ( cQ_2 @ X0 @ X1 @ X2 )
| ~ ( cP_2 @ ( f @ X1 ) @ X4 )
| ~ ( cP_2 @ ( f @ X2 ) @ X5 )
| ~ ( cP_2 @ ( f @ X0 ) @ X3 )
| ( cQ_3 @ X3 @ X4 @ X5 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ a @ a ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( cP_1 @ ( f @ X4 ) @ X2 )
| ~ ( cQ_1 @ X5 @ X3 @ X4 )
| ( cQ_2 @ X1 @ X6 @ X2 )
| ~ ( cP_1 @ ( f @ X5 ) @ X1 )
| ~ ( cP_1 @ ( f @ X3 ) @ X6 ) )
& ( cP_2 @ c @ c )
& ! [X7: $i,X8: $i] :
( ~ ( cP_1 @ X8 @ X7 )
| ( cP_1 @ ( f @ X8 ) @ X7 ) )
& ! [X9: $i] : ( cP_2 @ d @ X9 )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [X10: $i,X11: $i] :
( ~ ( cP_2 @ X10 @ X11 )
| ( cP_2 @ ( f @ X10 ) @ X11 ) )
& ! [X12: $i,X13: $i,X14: $i] :
~ ( cQ_3 @ X14 @ X13 @ X12 )
& ( cP_2 @ b @ b )
& ! [X15: $i,X16: $i,X17: $i,X18: $i,X19: $i,X20: $i] :
( ~ ( cQ_2 @ X18 @ X17 @ X20 )
| ~ ( cP_2 @ ( f @ X17 ) @ X15 )
| ~ ( cP_2 @ ( f @ X20 ) @ X16 )
| ~ ( cP_2 @ ( f @ X18 ) @ X19 )
| ( cQ_3 @ X19 @ X15 @ X16 ) )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_2 @ a @ a ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i] :
( ( cP_1 @ d @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( ( cP_1 @ ( f @ X4 ) @ X2 )
!= $true )
| ( ( cQ_1 @ X5 @ X3 @ X4 )
!= $true )
| ( ( cQ_2 @ X1 @ X6 @ X2 )
= $true )
| ( $true
!= ( cP_1 @ ( f @ X5 ) @ X1 ) )
| ( ( cP_1 @ ( f @ X3 ) @ X6 )
!= $true ) )
& ( ( cP_2 @ c @ c )
= $true )
& ! [X7: $i,X8: $i] :
( ( $true
!= ( cP_1 @ X8 @ X7 ) )
| ( ( cP_1 @ ( f @ X8 ) @ X7 )
= $true ) )
& ! [X9: $i] :
( $true
= ( cP_2 @ d @ X9 ) )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X10: $i,X11: $i] :
( ( ( cP_2 @ X10 @ X11 )
!= $true )
| ( $true
= ( cP_2 @ ( f @ X10 ) @ X11 ) ) )
& ! [X12: $i,X13: $i,X14: $i] :
( ( cQ_3 @ X14 @ X13 @ X12 )
!= $true )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X15: $i,X16: $i,X17: $i,X18: $i,X19: $i,X20: $i] :
( ( ( cQ_2 @ X18 @ X17 @ X20 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X17 ) @ X15 ) )
| ( $true
!= ( cP_2 @ ( f @ X20 ) @ X16 ) )
| ( ( cP_2 @ ( f @ X18 ) @ X19 )
!= $true )
| ( ( cQ_3 @ X19 @ X15 @ X16 )
= $true ) )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_2 @ a @ a )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X7: $i,X8: $i] :
( ( ( cP_1 @ ( f @ X8 ) @ X7 )
= $true )
| ( $true
!= ( cP_1 @ X8 @ X7 ) ) )
& ! [X2: $i,X3: $i,X5: $i,X1: $i,X4: $i,X6: $i] :
( ( ( cQ_2 @ X1 @ X6 @ X2 )
= $true )
| ( $true
!= ( cP_1 @ ( f @ X5 ) @ X1 ) )
| ( ( cP_1 @ ( f @ X3 ) @ X6 )
!= $true )
| ( ( cP_1 @ ( f @ X4 ) @ X2 )
!= $true )
| ( ( cQ_1 @ X5 @ X3 @ X4 )
!= $true ) )
& ! [X13: $i,X12: $i,X14: $i] :
( ( cQ_3 @ X14 @ X13 @ X12 )
!= $true )
& ! [X11: $i,X10: $i] :
( ( $true
= ( cP_2 @ ( f @ X10 ) @ X11 ) )
| ( ( cP_2 @ X10 @ X11 )
!= $true ) )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X0: $i] :
( ( cP_1 @ d @ X0 )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X9: $i] :
( $true
= ( cP_2 @ d @ X9 ) )
& ! [X15: $i,X17: $i,X16: $i,X20: $i,X19: $i,X18: $i] :
( ( $true
!= ( cP_2 @ ( f @ X17 ) @ X15 ) )
| ( ( cP_2 @ ( f @ X18 ) @ X19 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X20 ) @ X16 ) )
| ( ( cQ_2 @ X18 @ X17 @ X20 )
!= $true )
| ( ( cQ_3 @ X19 @ X15 @ X16 )
= $true ) )
& ( ( cP_1 @ a @ a )
= $true ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ( cP_2 @ c @ c )
= $true )
& ( ( cP_2 @ a @ a )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ X1 ) @ X0 )
= $true )
| ( $true
!= ( cP_1 @ X1 @ X0 ) ) )
& ! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( $true
= ( cQ_2 @ X5 @ X7 @ X2 ) )
| ( ( cP_1 @ ( f @ X4 ) @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ X3 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ X6 ) @ X2 )
!= $true )
| ( ( cQ_1 @ X4 @ X3 @ X6 )
!= $true ) )
& ! [X8: $i,X9: $i,X10: $i] :
( ( cQ_3 @ X10 @ X8 @ X9 )
!= $true )
& ! [X11: $i,X12: $i] :
( ( ( cP_2 @ ( f @ X12 ) @ X11 )
= $true )
| ( ( cP_2 @ X12 @ X11 )
!= $true ) )
& ( ( cP_2 @ b @ b )
= $true )
& ! [X13: $i] :
( ( cP_1 @ d @ X13 )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X14: $i] :
( ( cP_2 @ d @ X14 )
= $true )
& ! [X15: $i,X16: $i,X17: $i,X18: $i,X19: $i,X20: $i] :
( ( ( cP_2 @ ( f @ X16 ) @ X15 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X20 ) @ X19 ) )
| ( ( cP_2 @ ( f @ X18 ) @ X17 )
!= $true )
| ( ( cQ_2 @ X20 @ X16 @ X18 )
!= $true )
| ( $true
= ( cQ_3 @ X19 @ X15 @ X17 ) ) )
& ( ( cP_1 @ a @ a )
= $true ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X18: $i,X19: $i,X16: $i,X17: $i,X15: $i,X20: $i] :
( ( ( cP_2 @ ( f @ X16 ) @ X15 )
!= $true )
| ( ( cP_2 @ ( f @ X18 ) @ X17 )
!= $true )
| ( ( cQ_2 @ X20 @ X16 @ X18 )
!= $true )
| ( $true
= ( cQ_3 @ X19 @ X15 @ X17 ) )
| ( $true
!= ( cP_2 @ ( f @ X20 ) @ X19 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
! [X11: $i,X12: $i] :
( ( ( cP_2 @ ( f @ X12 ) @ X11 )
= $true )
| ( ( cP_2 @ X12 @ X11 )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
! [X10: $i,X8: $i,X9: $i] :
( ( cQ_3 @ X10 @ X8 @ X9 )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
! [X2: $i,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_1 @ X4 @ X3 @ X6 )
!= $true )
| ( ( cP_1 @ ( f @ X6 ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ X3 ) @ X7 )
!= $true )
| ( $true
= ( cQ_2 @ X5 @ X7 @ X2 ) )
| ( ( cP_1 @ ( f @ X4 ) @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ X1 ) @ X0 )
= $true )
| ( $true
!= ( cP_1 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f18,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f19,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f20,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f22,plain,
! [X18: $i,X19: $i,X16: $i,X17: $i,X15: $i,X20: $i] :
( ( ( cQ_2 @ X20 @ X16 @ X18 )
!= $true )
| ( ( cP_2 @ ( f @ X18 ) @ X17 )
!= $true )
| ( ( cP_2 @ ( f @ X16 ) @ X15 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X20 ) @ X19 ) ) ),
inference(forward_subsumption_resolution,[],[f8,f14]) ).
thf(f23,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ c ) @ X0 )
!= $true )
| ( ( cQ_2 @ X2 @ X1 @ X0 )
= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true ) ),
inference(superposition,[],[f15,f17]) ).
thf(f24,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cQ_2 @ X2 @ X1 @ X0 )
= $true )
| ( ( cP_1 @ ( f @ c ) @ X0 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ c ) @ X2 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X0 ) ) ),
inference(superposition,[],[f22,f24]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ c ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X0 ) )
| ( ( cP_2 @ ( f @ X2 ) @ X3 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) ) ),
inference(superposition,[],[f26,f16]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ a ) @ X2 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X3 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X2 ) @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ a @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X2 ) )
| ( $true != $true )
| ( ( cP_1 @ c @ X3 )
!= $true ) ),
inference(superposition,[],[f28,f16]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( ( cP_1 @ c @ X3 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X1 ) @ X2 ) )
| ( ( cP_2 @ ( f @ X3 ) @ X4 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ c @ X3 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X5 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X4 ) ) ),
inference(superposition,[],[f30,f13]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ b ) @ X2 )
!= $true )
| ( ( cP_1 @ c @ X3 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( ( cP_2 @ ( f @ X3 ) @ X5 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_2 @ ( f @ X2 ) @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_1 @ c @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true ) ),
inference(superposition,[],[f32,f16]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X1 ) @ X3 )
!= $true )
| ( ( cP_2 @ X2 @ X4 )
!= $true )
| ( ( cP_2 @ ( f @ X0 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_1 @ c @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( $true != $true )
| ( ( cP_2 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X4 )
!= $true ) ),
inference(superposition,[],[f34,f13]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ ( f @ X4 ) @ X5 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X0 ) )
| ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_1 @ b @ X4 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true
!= ( cP_1 @ c @ X2 ) )
| ( ( cP_2 @ X2 @ X5 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cP_1 @ a @ X3 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_2 @ X3 @ X4 )
!= $true ) ),
inference(superposition,[],[f36,f13]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( cP_1 @ c @ X2 ) )
| ( $true
!= ( cP_1 @ a @ X3 ) )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X5 )
!= $true )
| ( ( cP_2 @ X3 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_2 @ X1 @ X2 )
!= $true )
| ( ( cP_1 @ a @ X0 )
!= $true )
| ( $true
!= ( cP_2 @ X0 @ X4 ) )
| ( ( cP_1 @ b @ X1 )
!= $true )
| ( ( cP_2 @ c @ X3 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f38,f10]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( cP_2 @ c @ X3 )
!= $true )
| ( ( cP_1 @ b @ X1 )
!= $true )
| ( ( cP_2 @ X1 @ X2 )
!= $true )
| ( $true
!= ( cP_2 @ X0 @ X4 ) )
| ( ( cP_1 @ a @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( $true != $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_2 @ X2 @ X3 )
!= $true ) ),
inference(superposition,[],[f40,f20]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP_2 @ X2 @ X3 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true )
| ( $true
!= ( cP_1 @ a @ X2 ) )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( ( cP_1 @ a @ a )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) ),
inference(superposition,[],[f42,f19]) ).
thf(f52,plain,
! [X0: $i,X1: $i] :
( ( ( cP_1 @ b @ X0 )
!= $true )
| ( ( cP_1 @ a @ a )
!= $true )
| ( ( cP_2 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( ( cP_2 @ X0 @ X1 )
!= $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f52,f7]) ).
thf(f56,plain,
( ( ( cP_1 @ b @ b )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f53,f12]) ).
thf(f61,plain,
( ( cP_1 @ b @ b )
!= $true ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f64,plain,
$false,
inference(forward_subsumption_resolution,[],[f61,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO385^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n013.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 16:49:21 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (2365867)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2365884)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2542658368:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2365890)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (2365890)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.29 % (2365885)lrs+10_16_si=on:nwc=1.5:random_seed=3607431571:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (2365886)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3239214986:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (2365887)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=116210162:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29 % (2365889)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1064851598:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (2365888)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3753664296:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2365890)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3653912385:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (2365886)Instruction limit reached!
% 0.21/0.29 % (2365886)------------------------------
% 0.21/0.29 % (2365886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2365886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2365886)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2365886)Termination reason: Instruction limit
% 0.21/0.29 % (2365886)Termination phase: Saturation
% 0.21/0.29 % (2365886)Time elapsed: 0.002 s
% 0.21/0.29 % (2365886)Peak memory usage: 12 MB
% 0.21/0.29 % (2365886)Instructions burned: 3 (million)
% 0.21/0.29 % (2365888) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2365867-2365888"...
% 0.21/0.29 % (2365887) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2365867-2365887"...
% 0.21/0.29 % (2365884) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2365867-2365884"...
% 0.21/0.29 % (2365888)...printing done.
% 0.21/0.29 % (2365887)...printing done.
% 0.21/0.29 % (2365885)Instruction limit reached!
% 0.21/0.29 % (2365885)------------------------------
% 0.21/0.29 % (2365885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2365885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2365885)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2365885)Termination reason: Instruction limit
% 0.21/0.29 % (2365885)Termination phase: Saturation
% 0.21/0.29 % (2365885)Time elapsed: 0.010 s
% 0.21/0.29 % (2365885)Peak memory usage: 12 MB
% 0.21/0.29 % (2365885)Instructions burned: 19 (million)
% 0.21/0.29 % (2365884)...printing done.
% 0.21/0.29 % (2365888)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (2365888)------------------------------
% 0.21/0.29 % (2365888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2365888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2365888)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2365888)Termination reason: Refutation
% 0.21/0.29 % (2365888)Time elapsed: 0.008 s
% 0.21/0.29 % (2365888)Peak memory usage: 12 MB
% 0.21/0.29 % (2365888)Instructions burned: 14 (million)
% 0.21/0.29 % (2365867)Success in time 0.052 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------