%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO038^1.003.003 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:46:20 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 23
% Syntax : Number of formulae : 165 ( 33 unt; 0 typ; 17 def)
% Number of atoms : 715 ( 121 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1206 ( 145 ~; 123 |; 0 &; 918 @)
% ( 17 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 20 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
f: $i > $i > $i ).
thf(func_def_3,type,
d: $i > $o ).
thf(f1,axiom,
! [X0: $i] :
( ( f @ X0 @ one )
= ( s @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f2,axiom,
! [X0: $i] :
( ( f @ one @ ( s @ X0 ) )
= ( s @ ( s @ ( f @ one @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( f @ ( s @ X0 ) @ ( s @ X1 ) )
= ( f @ X0 @ ( f @ ( s @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(f4,axiom,
d @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(f5,axiom,
! [X0: $i] :
( ( d @ X0 )
=> ( d @ ( s @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(f6,conjecture,
d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f7,negated_conjecture,
~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
d @ one,
inference(rectify,[],[f4]) ).
thf(f9,plain,
( ( d @ one )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f11,plain,
( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
!= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $i] :
( ( d @ X0 )
=> ( d @ ( s @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( d @ X0 )
= $true )
=> ( ( d @ ( s @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
!= $true ),
inference(flattening,[],[f11]) ).
thf(f15,plain,
! [X0: $i] :
( ( ( d @ X0 )
!= $true )
| ( ( d @ ( s @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f16,plain,
! [X0: $i] :
( ( f @ one @ ( s @ X0 ) )
= ( s @ ( s @ ( f @ one @ X0 ) ) ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f17,plain,
! [X0: $i] :
( ( f @ X0 @ one )
= ( s @ one ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f18,plain,
( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
! [X0: $i] :
( ( ( d @ ( s @ X0 ) )
= $true )
| ( ( d @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
( ( d @ one )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( f @ ( s @ X0 ) @ ( s @ X1 ) )
= ( f @ X0 @ ( f @ ( s @ X0 ) @ X1 ) ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f24,definition,
( spl0_1
<=> ( ( d @ one )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f26,plain,
( ( ( d @ one )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
spl0_1,
inference(avatar_split_clause,[],[f20,f24]) ).
thf(f29,definition,
( spl0_2
<=> ( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f31,plain,
( ( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f18,f29]) ).
thf(f33,plain,
( ( $true
!= ( d @ ( f @ ( s @ one ) @ ( f @ ( s @ ( s @ one ) ) @ ( s @ one ) ) ) ) )
| spl0_2 ),
inference(superposition,[],[f31,f21]) ).
thf(f34,plain,
( ( ( d @ ( f @ ( s @ one ) @ ( f @ ( s @ one ) @ ( f @ ( s @ ( s @ one ) ) @ one ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f33,f21]) ).
thf(f35,plain,
( ( ( d @ ( f @ ( s @ one ) @ ( f @ ( s @ one ) @ ( s @ one ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f34,f17]) ).
thf(f36,plain,
( ( ( d @ ( f @ ( s @ one ) @ ( f @ one @ ( f @ ( s @ one ) @ one ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f35,f21]) ).
thf(f37,plain,
( ( ( d @ ( f @ ( s @ one ) @ ( f @ one @ ( s @ one ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f36,f17]) ).
thf(f38,plain,
( ( ( d @ ( f @ ( s @ one ) @ ( s @ ( s @ ( f @ one @ one ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f37,f16]) ).
thf(f39,plain,
( ( ( d @ ( f @ one @ ( f @ ( s @ one ) @ ( s @ ( f @ one @ one ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f38,f21]) ).
thf(f40,plain,
( ( ( d @ ( f @ one @ ( f @ one @ ( f @ ( s @ one ) @ ( f @ one @ one ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f39,f21]) ).
thf(f41,plain,
( ( $true
!= ( d @ ( f @ one @ ( f @ one @ ( f @ ( s @ one ) @ ( s @ one ) ) ) ) ) )
| spl0_2 ),
inference(forward_demodulation,[],[f40,f17]) ).
thf(f42,plain,
( ( ( d @ ( f @ one @ ( f @ one @ ( f @ one @ ( f @ ( s @ one ) @ one ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f41,f21]) ).
thf(f43,plain,
( ( ( d @ ( f @ one @ ( f @ one @ ( f @ one @ ( s @ one ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f42,f17]) ).
thf(f44,plain,
( ( ( d @ ( f @ one @ ( f @ one @ ( s @ ( s @ ( f @ one @ one ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f43,f16]) ).
thf(f45,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( s @ ( f @ one @ ( s @ ( f @ one @ one ) ) ) ) ) ) ) )
| spl0_2 ),
inference(forward_demodulation,[],[f44,f16]) ).
thf(f46,plain,
( ( ( d @ ( s @ ( s @ ( f @ one @ ( s @ ( f @ one @ ( s @ ( f @ one @ one ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f45,f16]) ).
thf(f47,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( f @ one @ ( s @ ( f @ one @ one ) ) ) ) ) ) ) ) ) )
| spl0_2 ),
inference(forward_demodulation,[],[f46,f16]) ).
thf(f48,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( s @ ( s @ ( f @ one @ ( f @ one @ one ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f47,f16]) ).
thf(f49,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( s @ ( f @ one @ ( f @ one @ one ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f48,f16]) ).
thf(f50,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( f @ one @ ( f @ one @ one ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f49,f16]) ).
thf(f51,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( f @ one @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f50,f17]) ).
thf(f52,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( s @ ( s @ ( f @ one @ one ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f51,f16]) ).
thf(f53,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( s @ ( f @ one @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f52,f16]) ).
thf(f54,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( f @ one @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f53,f16]) ).
thf(f55,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| spl0_2 ),
inference(forward_demodulation,[],[f54,f17]) ).
thf(f56,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( f @ one @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f55,f16]) ).
thf(f57,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f56,f17]) ).
thf(f59,definition,
( spl0_3
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f61,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_3 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f57,f29,f59]) ).
thf(f63,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_3 ),
inference(superposition,[],[f61,f19]) ).
thf(f64,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_3 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f66,definition,
( spl0_4
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f68,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f69,plain,
( ~ spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f64,f59,f66]) ).
thf(f70,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| ( $true != $true )
| spl0_4 ),
inference(superposition,[],[f68,f19]) ).
thf(f71,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_4 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f73,definition,
( spl0_5
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f75,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_5 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f76,plain,
( ~ spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f71,f66,f73]) ).
thf(f77,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_5 ),
inference(superposition,[],[f75,f19]) ).
thf(f78,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_5 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f80,definition,
( spl0_6
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f82,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_6 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f83,plain,
( ~ spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f78,f73,f80]) ).
thf(f84,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| ( $true != $true )
| spl0_6 ),
inference(superposition,[],[f82,f19]) ).
thf(f85,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_6 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f87,definition,
( spl0_7
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f89,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f90,plain,
( ~ spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f85,f80,f87]) ).
thf(f91,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_7 ),
inference(superposition,[],[f89,f19]) ).
thf(f92,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_7 ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f94,definition,
( spl0_8
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f96,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) )
!= $true )
| spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f97,plain,
( ~ spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f92,f87,f94]) ).
thf(f98,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) )
| ( $true != $true )
| spl0_8 ),
inference(superposition,[],[f96,f19]) ).
thf(f99,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) )
| spl0_8 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f101,definition,
( spl0_9
<=> ( $true
= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f103,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) )
| spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f104,plain,
( ~ spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f99,f94,f101]) ).
thf(f105,plain,
( ( $true != $true )
| ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) )
| spl0_9 ),
inference(superposition,[],[f103,f19]) ).
thf(f106,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) )
| spl0_9 ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f108,definition,
( spl0_10
<=> ( $true
= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f110,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ) )
| spl0_10 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f111,plain,
( ~ spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f106,f101,f108]) ).
thf(f112,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
!= $true )
| spl0_10 ),
inference(superposition,[],[f110,f19]) ).
thf(f113,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
!= $true )
| spl0_10 ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f115,definition,
( spl0_11
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
thf(f117,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
!= $true )
| spl0_11 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f118,plain,
( ~ spl0_11
| spl0_10 ),
inference(avatar_split_clause,[],[f113,f108,f115]) ).
thf(f119,plain,
( ( $true != $true )
| ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
| spl0_11 ),
inference(superposition,[],[f117,f19]) ).
thf(f120,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
| spl0_11 ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f122,definition,
( spl0_12
<=> ( $true
= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
thf(f124,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
| spl0_12 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f125,plain,
( ~ spl0_12
| spl0_11 ),
inference(avatar_split_clause,[],[f120,f115,f122]) ).
thf(f126,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) )
!= $true )
| spl0_12 ),
inference(superposition,[],[f124,f19]) ).
thf(f127,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) )
!= $true )
| spl0_12 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f129,definition,
( spl0_13
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
thf(f131,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) )
!= $true )
| spl0_13 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f132,plain,
( ~ spl0_13
| spl0_12 ),
inference(avatar_split_clause,[],[f127,f122,f129]) ).
thf(f133,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) )
!= $true )
| spl0_13 ),
inference(superposition,[],[f131,f19]) ).
thf(f134,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) )
!= $true )
| spl0_13 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f136,definition,
( spl0_14
<=> ( ( d @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
thf(f138,plain,
( ( ( d @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) )
!= $true )
| spl0_14 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f139,plain,
( ~ spl0_14
| spl0_13 ),
inference(avatar_split_clause,[],[f134,f129,f136]) ).
thf(f140,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ ( s @ one ) ) ) )
!= $true )
| spl0_14 ),
inference(superposition,[],[f138,f19]) ).
thf(f141,plain,
( ( ( d @ ( s @ ( s @ ( s @ one ) ) ) )
!= $true )
| spl0_14 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f143,definition,
( spl0_15
<=> ( ( d @ ( s @ ( s @ ( s @ one ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
thf(f145,plain,
( ( ( d @ ( s @ ( s @ ( s @ one ) ) ) )
!= $true )
| spl0_15 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f146,plain,
( ~ spl0_15
| spl0_14 ),
inference(avatar_split_clause,[],[f141,f136,f143]) ).
thf(f147,plain,
( ( $true != $true )
| ( ( d @ ( s @ ( s @ one ) ) )
!= $true )
| spl0_15 ),
inference(superposition,[],[f145,f19]) ).
thf(f148,plain,
( ( ( d @ ( s @ ( s @ one ) ) )
!= $true )
| spl0_15 ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f150,definition,
( spl0_16
<=> ( ( d @ ( s @ ( s @ one ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
thf(f152,plain,
( ( ( d @ ( s @ ( s @ one ) ) )
!= $true )
| spl0_16 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f153,plain,
( ~ spl0_16
| spl0_15 ),
inference(avatar_split_clause,[],[f148,f143,f150]) ).
thf(f154,plain,
( ( $true != $true )
| ( ( d @ ( s @ one ) )
!= $true )
| spl0_16 ),
inference(superposition,[],[f152,f19]) ).
thf(f155,plain,
( ( ( d @ ( s @ one ) )
!= $true )
| spl0_16 ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f157,definition,
( spl0_17
<=> ( ( d @ ( s @ one ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
thf(f159,plain,
( ( ( d @ ( s @ one ) )
!= $true )
| spl0_17 ),
inference(avatar_component_clause,[],[f157]) ).
thf(f160,plain,
( ~ spl0_17
| spl0_16 ),
inference(avatar_split_clause,[],[f155,f150,f157]) ).
thf(f161,plain,
( ( $true != $true )
| ( ( d @ one )
!= $true )
| spl0_17 ),
inference(superposition,[],[f159,f19]) ).
thf(f162,plain,
( ( ( d @ one )
!= $true )
| spl0_17 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f163,plain,
( $false
| ~ spl0_1
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f162,f26]) ).
thf(f164,plain,
( ~ spl0_1
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f163]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
( spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f83]) ).
cnf(s7,plain,
( spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f90]) ).
cnf(s8,plain,
( spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s9,plain,
( spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f104]) ).
cnf(s10,plain,
( spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s11,plain,
( spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f118]) ).
cnf(s12,plain,
( spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f125]) ).
cnf(s13,plain,
( spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s14,plain,
( spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s15,plain,
( spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s16,plain,
( spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f153]) ).
cnf(s17,plain,
( spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f160]) ).
cnf(s18,plain,
( ~ spl0_1
| spl0_17 ),
inference(sat_conversion,[],[f164]) ).
cnf(s19,plain,
~ spl0_3,
inference(rat,[],[s3,s2]) ).
cnf(s20,plain,
~ spl0_4,
inference(rat,[],[s4,s19]) ).
cnf(s21,plain,
~ spl0_5,
inference(rat,[],[s5,s20]) ).
cnf(s22,plain,
~ spl0_6,
inference(rat,[],[s6,s21]) ).
cnf(s23,plain,
~ spl0_7,
inference(rat,[],[s7,s22]) ).
cnf(s24,plain,
~ spl0_8,
inference(rat,[],[s8,s23]) ).
cnf(s25,plain,
~ spl0_9,
inference(rat,[],[s9,s24]) ).
cnf(s26,plain,
~ spl0_10,
inference(rat,[],[s10,s25]) ).
cnf(s27,plain,
~ spl0_11,
inference(rat,[],[s11,s26]) ).
cnf(s28,plain,
~ spl0_12,
inference(rat,[],[s12,s27]) ).
cnf(s29,plain,
~ spl0_13,
inference(rat,[],[s13,s28]) ).
cnf(s30,plain,
~ spl0_14,
inference(rat,[],[s14,s29]) ).
cnf(s31,plain,
~ spl0_15,
inference(rat,[],[s15,s30]) ).
cnf(s32,plain,
~ spl0_16,
inference(rat,[],[s16,s31]) ).
cnf(s33,plain,
~ spl0_17,
inference(rat,[],[s17,s32]) ).
cnf(s34,plain,
~ spl0_1,
inference(rat,[],[s18,s33]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s1,s34]) ).
thf(f165,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO038^1.003.003 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:23:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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 % (291117)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (291125)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=103829992: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 % (291128)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 % (291128)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 % (291125) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-291117-291125"...
% 0.21/0.29 % (291125)...printing done.
% 0.21/0.29 % (291124)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4074701925:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (291122)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3433171861:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (291123)lrs+10_16_si=on:nwc=1.5:random_seed=2960699196:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (291125)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 % (291125)------------------------------
% 0.21/0.29 % (291125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (291125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (291125)CaDiCaL version: 2.1.3
% 0.21/0.29 % (291125)Termination reason: Refutation
% 0.21/0.29 % (291125)Time elapsed: 0.006 s
% 0.21/0.29 % (291125)Peak memory usage: 13 MB
% 0.21/0.29 % (291125)Instructions burned: 19 (million)
% 0.21/0.29 % (291117)Success in time 0.038 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------