%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO148^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:46:43 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 78 ( 9 unt; 0 typ; 5 def)
% Number of atoms : 420 ( 109 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 344 ( 94 ~; 99 |; 3 &; 126 @)
% ( 17 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn 13 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cZ: a > $o ).
thf(func_def_1,type,
cY: a > $o ).
thf(func_def_2,type,
cX: a > $o ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vIFF: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: a ).
thf(f1,conjecture,
( ! [X0: a] :
( ( ( cZ @ X0 )
<=> ( cY @ X0 ) )
<=> ~ ( cX @ X0 ) )
=> ( cX
= ( ^ [X0: a] :
~ ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL25) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a] :
( ( ( cZ @ X0 )
<=> ( cY @ X0 ) )
<=> ~ ( cX @ X0 ) )
=> ( cX
= ( ^ [X0: a] :
~ ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: a] :
( ( ( cZ @ X0 )
<=> ( cY @ X0 ) )
<=> ~ ( cX @ X0 ) )
=> ( cX
= ( ^ [X1: a] :
~ ( ( cY @ X1 )
<=> ( cZ @ X1 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: a] :
( ( ( cY @ X0 )
= ( cZ @ X0 ) )
<=> ( ( cX @ X0 )
!= $true ) )
=> ( cX
= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: a] :
( ( ( cX @ X0 )
!= $true )
<=> ( ( cY @ X0 )
= ( cZ @ X0 ) ) )
=> ( cX
= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( cX
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) )
& ! [X0: a] :
( ( ( cX @ X0 )
!= $true )
<=> ( ( cY @ X0 )
= ( cZ @ X0 ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( cX
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) )
& ! [X0: a] :
( ( ( ( cX @ X0 )
!= $true )
| ( ( cY @ X0 )
!= ( cZ @ X0 ) ) )
& ( ( ( cY @ X0 )
= ( cZ @ X0 ) )
| ( ( cX @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X0: a] :
( ( ( cY @ X0 )
= ( cZ @ X0 ) )
| ( ( cX @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X0: a] :
( ( ( cY @ X0 )
!= ( cZ @ X0 ) )
| ( ( cX @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( cX
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: a] :
( ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $false )
| ( ( cX @ X0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f8]) ).
thf(f14,plain,
! [X0: a] :
( ( ( cY @ X0 )
= $false )
| ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f8]) ).
thf(f15,plain,
! [X0: a] :
( ( ( cX @ X0 )
!= $true )
| ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f16,plain,
! [X0: a] :
( ( ( cX @ X0 )
!= $true )
| ( ( cZ @ X0 )
= $false )
| ( ( cY @ X0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) )
@ sK0 )
!= ( cX @ sK0 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) )
@ sK0 ) )
| ( $true
= ( cX @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) )
@ sK0 )
= $false )
| ( ( cX @ sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( ( cX @ sK0 )
= $false )
| ( ( ( cY @ sK0 )
!= ( cZ @ sK0 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( ( cX @ sK0 )
= $false )
| ( $true
= ( ( cY @ sK0 )
= ( cZ @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( ( cY @ sK0 )
= ( cZ @ sK0 ) )
| ( ( cX @ sK0 )
= $false ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( ( cZ @ sK0 )
= $false )
| ( ( cY @ sK0 )
= $true )
| ( ( cX @ sK0 )
= $false ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( ( cY @ sK0 )
= $false )
| ( $true
= ( cZ @ sK0 ) )
| ( ( cX @ sK0 )
= $false ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $true
= ( ( cY @ sK0 )
!= ( cZ @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f26,plain,
( ( ( ( cY @ sK0 )
= ( cZ @ sK0 ) )
= $false )
| ( $true
= ( cX @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( ( cY @ sK0 )
!= ( cZ @ sK0 ) )
| ( $true
= ( cX @ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( cX @ sK0 ) )
| ( ( cY @ sK0 )
= $true )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( cX @ sK0 ) )
| ( ( cZ @ sK0 )
= $false )
| ( ( cY @ sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f27]) ).
thf(f31,definition,
( spl1_1
<=> ( ( cY @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f32,plain,
( ( ( cY @ sK0 )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,definition,
( spl1_2
<=> ( $true
= ( cZ @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f35,plain,
( ( $true
= ( cZ @ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f37,definition,
( spl1_3
<=> ( ( cX @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f38,plain,
( ( ( cX @ sK0 )
= $false )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f39,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f24,f37,f34,f31]) ).
thf(f41,definition,
( spl1_4
<=> ( ( cZ @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f42,plain,
( ( ( cZ @ sK0 )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,definition,
( spl1_5
<=> ( ( cY @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f45,plain,
( ( ( cY @ sK0 )
= $true )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f46,plain,
( spl1_4
| spl1_5
| spl1_3 ),
inference(avatar_split_clause,[],[f23,f37,f44,f41]) ).
thf(f47,plain,
( ( ( cZ @ sK0 )
= $false )
| ( ( cY @ sK0 )
= $false ) ),
inference(forward_subsumption_resolution,[],[f29,f16]) ).
thf(f48,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( ( cY @ sK0 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f28,f15]) ).
thf(f49,plain,
( spl1_1
| spl1_4 ),
inference(avatar_split_clause,[],[f47,f41,f31]) ).
thf(f50,plain,
( spl1_5
| spl1_2 ),
inference(avatar_split_clause,[],[f48,f34,f44]) ).
thf(f51,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_4 ),
inference(backward_demodulation,[],[f35,f42]) ).
thf(f52,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f53,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f52]) ).
thf(f54,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_5 ),
inference(forward_demodulation,[],[f45,f32]) ).
thf(f55,plain,
( $false
| ~ spl1_1
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f55]) ).
thf(f65,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( $true
= ( cX @ sK0 ) )
| ( $true = $false )
| ~ spl1_5 ),
inference(constrained_superposition,[],[f14,f45]) ).
thf(f67,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( $true
= ( cX @ sK0 ) )
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f70,plain,
( ( $true = $false )
| ( $true
= ( cX @ sK0 ) )
| ~ spl1_4
| ~ spl1_5 ),
inference(forward_demodulation,[],[f67,f42]) ).
thf(f71,plain,
( ( $true
= ( cX @ sK0 ) )
| ~ spl1_4
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f75,plain,
( ( $true = $false )
| ~ spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(forward_demodulation,[],[f71,f38]) ).
thf(f76,plain,
( $false
| ~ spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f77,plain,
( ~ spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f76]) ).
thf(f79,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $true = $false )
| ( ( cZ @ sK0 )
= $false )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f32,f13]) ).
thf(f82,plain,
( ( ( cZ @ sK0 )
= $false )
| ( $true
= ( cX @ sK0 ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f85,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $true = $false )
| ~ spl1_1
| ~ spl1_2 ),
inference(forward_demodulation,[],[f82,f35]) ).
thf(f86,plain,
( ( $true
= ( cX @ sK0 ) )
| ~ spl1_1
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f90,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f86,f38]) ).
thf(f91,plain,
( $false
| ~ spl1_1
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
( ~ spl1_1
| ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f91]) ).
cnf(s1,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
( spl1_3
| spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f49]) ).
cnf(s4,plain,
( spl1_2
| spl1_5 ),
inference(sat_conversion,[],[f50]) ).
cnf(s5,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s6,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s8,plain,
( ~ spl1_3
| ~ spl1_4
| ~ spl1_5 ),
inference(sat_conversion,[],[f77]) ).
cnf(s10,plain,
( ~ spl1_1
| ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f92]) ).
cnf(s11,plain,
spl1_1,
inference(rat,[],[s8,s1,s4,s5,s3]) ).
cnf(s12,plain,
~ spl1_5,
inference(rat,[],[s6,s11]) ).
cnf(s13,plain,
spl1_2,
inference(rat,[],[s4,s12]) ).
cnf(s14,plain,
~ spl1_4,
inference(rat,[],[s5,s13]) ).
cnf(s15,plain,
~ spl1_3,
inference(rat,[],[s10,s11,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s12,s15,s14]) ).
thf(f93,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO148^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:35:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.27 % (311704)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (311714)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3999643667:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (311714) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-311704-311714"...
% 0.21/0.27 % (311714)...printing done.
% 0.21/0.27 % (311714)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (311714)------------------------------
% 0.21/0.27 % (311714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (311714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (311714)CaDiCaL version: 2.1.3
% 0.21/0.27 % (311714)Termination reason: Refutation
% 0.21/0.27 % (311714)Time elapsed: 0.002 s
% 0.21/0.27 % (311714)Peak memory usage: 13 MB
% 0.21/0.27 % (311714)Instructions burned: 5 (million)
% 0.21/0.27 % (311704)Success in time 0.025 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------