%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n003.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 08:49:02 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 9 unt; 0 typ; 5 def)
% Number of atoms : 406 ( 107 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 318 ( 76 ~; 90 |; 3 &; 127 @)
% ( 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] :
( ~ ( cX @ X0 )
<=> ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) )
=> ( cX
= ( ^ [X0: a] :
~ ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL25) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a] :
( ~ ( cX @ X0 )
<=> ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) )
=> ( cX
= ( ^ [X0: a] :
~ ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: a] :
( ~ ( cX @ X0 )
<=> ( ( cY @ X0 )
<=> ( cZ @ X0 ) ) )
=> ( cX
= ( ^ [X1: a] :
~ ( ( cY @ X1 )
<=> ( cZ @ X1 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: a] :
( ( ( cX @ X0 )
!= $true )
<=> ( ( cY @ X0 )
= ( cZ @ X0 ) ) )
=> ( 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] :
( ( ( cX @ X0 )
!= $true )
| ( ( cY @ X0 )
!= ( cZ @ X0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( cX
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: a] :
( ( ( cX @ X0 )
= $true )
| ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $false ) ),
inference(iff_proxy_clausification,[],[f8]) ).
thf(f14,plain,
! [X0: a] :
( ( ( cX @ X0 )
= $true )
| ( ( cY @ X0 )
= $false )
| ( ( 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 )
| ( ( cY @ X0 )
= $false )
| ( ( cZ @ X0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f17,plain,
( ( cX @ sK0 )
!= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f18,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $true
= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( cX @ sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( ( cY @ Y0 )
!= ( cZ @ Y0 ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( cX @ sK0 ) )
| ( $false
= ( ( cY @ sK0 )
!= ( cZ @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( cX @ sK0 ) )
| ( $true
= ( ( cY @ sK0 )
= ( cZ @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( cX @ sK0 ) )
| ( ( cY @ sK0 )
= ( cZ @ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $false
= ( cX @ sK0 ) )
| ( $true
= ( cY @ sK0 ) )
| ( $false
= ( cZ @ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( cX @ sK0 ) )
| ( $false
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $true
= ( ( cY @ sK0 )
!= ( cZ @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f26,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $false
= ( ( cY @ sK0 )
= ( cZ @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $true
= ( cX @ sK0 ) )
| ( ( cY @ sK0 )
!= ( cZ @ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $true
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( cX @ sK0 ) )
| ( $false
= ( cY @ sK0 ) )
| ( $false
= ( cZ @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f27]) ).
thf(f31,definition,
( spl1_1
<=> ( $true
= ( cZ @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
!= ( cZ @ sK0 ) )
| spl1_1 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f33,plain,
( ( $true
= ( cZ @ sK0 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f35,definition,
( spl1_2
<=> ( $false
= ( cY @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f36,plain,
( ( $false
!= ( cY @ sK0 ) )
| spl1_2 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( ( $false
= ( cY @ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f39,definition,
( spl1_3
<=> ( $false
= ( cX @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f41,plain,
( ( $false
= ( cX @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f24,f39,f35,f31]) ).
thf(f44,definition,
( spl1_4
<=> ( $false
= ( cZ @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f46,plain,
( ( $false
= ( cZ @ sK0 ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f48,definition,
( spl1_5
<=> ( $true
= ( cY @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( cY @ sK0 ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
( spl1_4
| spl1_5
| spl1_3 ),
inference(avatar_split_clause,[],[f23,f39,f48,f44]) ).
thf(f52,plain,
( ( $false
= ( cY @ sK0 ) )
| ( $false
= ( cZ @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f29,f16]) ).
thf(f53,plain,
( ( $true
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f28,f15]) ).
thf(f54,plain,
( spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f52,f35,f44]) ).
thf(f55,plain,
( spl1_1
| spl1_5 ),
inference(avatar_split_clause,[],[f53,f48,f31]) ).
thf(f56,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_5 ),
inference(forward_demodulation,[],[f50,f37]) ).
thf(f57,plain,
( $false
| ~ spl1_2
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f58,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f57]) ).
thf(f77,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[],[f46,f33]) ).
thf(f83,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f84,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f83]) ).
thf(f94,plain,
( ( $true = $false )
| ( $false
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f41,f14]) ).
thf(f100,plain,
( ( $true = $false )
| ( $true
= ( cY @ sK0 ) )
| ( $false
= ( cZ @ sK0 ) )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f13,f41]) ).
thf(f101,plain,
( ( $true
= ( cY @ sK0 ) )
| ( $false
= ( cZ @ sK0 ) )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f105,plain,
( ( $false
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f106,plain,
( ( $true = $false )
| ( $false
= ( cZ @ sK0 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f101,f37]) ).
thf(f107,plain,
( ( $false
= ( cZ @ sK0 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f110,plain,
( spl1_4
| ~ spl1_2
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f107,f39,f35,f44]) ).
thf(f112,plain,
( ( $true
= ( cZ @ sK0 ) )
| spl1_2
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f105,f36]) ).
thf(f115,plain,
( $false
| spl1_1
| spl1_2
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f112,f32]) ).
thf(f116,plain,
( spl1_1
| spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl1_3
| spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
( spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f54]) ).
cnf(s4,plain,
( spl1_1
| spl1_5 ),
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(sat_conversion,[],[f58]) ).
cnf(s7,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f84]) ).
cnf(s8,plain,
( ~ spl1_2
| ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
( spl1_1
| spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f116]) ).
cnf(s12,plain,
( spl1_2
| spl1_1 ),
inference(rat,[],[s11,s1]) ).
cnf(s13,plain,
spl1_1,
inference(rat,[],[s12,s5,s4]) ).
cnf(s14,plain,
~ spl1_4,
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
spl1_2,
inference(rat,[],[s3,s14]) ).
cnf(s16,plain,
~ spl1_3,
inference(rat,[],[s8,s14,s15]) ).
cnf(s17,plain,
~ spl1_5,
inference(rat,[],[s5,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s14,s16,s17]) ).
thf(f117,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:37:14 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (2718586)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (2718591)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1295032910_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (2718592)% WARNING: option uhcvi not known.
% 0.20/0.28 % (2718594)dis+10_1_sil=32000:sp=arity:random_seed=3083993625:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (2718592)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=343872470:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (2718592)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (2718592)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (2718595)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3140440985:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (2718595)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (2718599)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1833425477:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (2718595) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2718586-2718595"...
% 0.20/0.28 % (2718594) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2718586-2718594"...
% 0.20/0.28 % (2718592) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2718586-2718592"...
% 0.20/0.28 % (2718595)...printing done.
% 0.20/0.28 % (2718594)...printing done.
% 0.20/0.28 % (2718592)...printing done.
% 0.20/0.28 % (2718595)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2718595)------------------------------
% 0.20/0.28 % (2718595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2718595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2718595)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2718595)Termination reason: Refutation
% 0.20/0.28 % (2718595)Time elapsed: 0.004 s
% 0.20/0.28 % (2718595)Peak memory usage: 13 MB
% 0.20/0.28 % (2718595)Instructions burned: 5 (million)
% 0.20/0.28 % (2718586)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------