%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO006^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:46:16 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 20 unt; 0 typ; 4 def)
% Number of atoms : 205 ( 52 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 138 ( 31 ~; 34 |; 3 &; 47 @)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 9 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 0 sgn 13 !; 4 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
leibeq: $o > $o > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $o ).
thf(func_def_11,type,
sK1: $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq1) ).
thf(f2,conjecture,
! [X1: $o,X0: $o] :
( ( leibeq @ X0 @ X1 )
=> ( X0
<=> X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ! [X1: $o,X0: $o] :
( ( leibeq @ X0 @ X1 )
=> ( X0
<=> X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $o,X1: $o] :
( ( leibeq @ X1 @ X0 )
=> ( X1
<=> X0 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $o,X1: $o] :
( ( ( leibeq @ X1 @ X0 )
= $true )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X1: $o,X0: $o] :
( ( X0 != X1 )
& ( ( leibeq @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
? [X0: $o,X1: $o] :
( ( X0 != X1 )
& ( ( leibeq @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( sK0 != sK1 )
& ( ( leibeq @ sK0 @ sK1 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
thf(f11,plain,
( ( leibeq @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f12,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f11,f13]) ).
thf(f17,plain,
( $true
= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X1: $o > $o] :
( $true
= ( ^ [Y0: $o > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: $o > $o] :
( $true
= ( ( X1 @ sK0 )
=> ( X1 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X1: $o > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( ( X1 @ sK0 )
= $false ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( sK0 = $true )
| ( sK1 = $true ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f22,plain,
( ( sK0 = $false )
| ( sK1 = $false ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f24,definition,
( spl2_1
<=> ( sK1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f26,plain,
( ( sK1 = $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f28,definition,
( spl2_2
<=> ( sK0 = $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f30,plain,
( ( sK0 = $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f31,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f22,f28,f24]) ).
thf(f33,definition,
( spl2_3
<=> ( sK1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f35,plain,
( ( sK1 = $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f37,definition,
( spl2_4
<=> ( sK0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f39,plain,
( ( sK0 = $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f21,f37,f33]) ).
thf(f41,plain,
sK0 = sK1,
inference(leibniz_equality_elimination,[],[f20]) ).
thf(f42,plain,
sK0 = sK1,
inference(leibniz_equality_elimination,[],[f20]) ).
thf(f43,plain,
( ( ( ^ [Y0: $o] : Y0
@ sK1 )
= $true )
| ( ( ^ [Y0: $o] : Y0
@ sK0 )
= $false ) ),
inference(primitive_instantiation,[],[f20]) ).
thf(f61,plain,
( ( sK1 = $false )
| ( sK0 = $true ) ),
inference(iff_proxy_clausification,[],[f41]) ).
thf(f66,plain,
( ( sK1 = $false )
| ( sK0 = $true ) ),
inference(iff_proxy_clausification,[],[f42]) ).
thf(f68,plain,
( ( sK0 = $false )
| ( sK1 = $true ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f72,plain,
( ( $true = $false )
| ( sK0 = $true )
| ~ spl2_3 ),
inference(forward_demodulation,[],[f61,f35]) ).
thf(f73,plain,
( ( sK0 = $true )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f77,plain,
( ( sK1 = $false )
| ( $true = $false )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f66,f30]) ).
thf(f78,plain,
( ( sK1 = $false )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f85,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f78,f28,f24]) ).
thf(f88,plain,
( spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f73,f33,f37]) ).
thf(f116,plain,
( ( $true = $false )
| ( sK1 = $true )
| ~ spl2_4 ),
inference(forward_demodulation,[],[f68,f39]) ).
thf(f117,plain,
( ( sK1 = $true )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f123,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_demodulation,[],[f117,f26]) ).
thf(f124,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f125,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f124]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f85]) ).
cnf(s5,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f88]) ).
cnf(s11,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
spl2_1,
inference(rat,[],[s1,s4]) ).
cnf(s13,plain,
~ spl2_4,
inference(rat,[],[s11,s12]) ).
cnf(s15,plain,
~ spl2_3,
inference(rat,[],[s5,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s13,s15]) ).
thf(f127,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO006^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n010.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:21:18 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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
% 0.23/0.30 % (3070513)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (3070522)lrs+10_16_si=on:nwc=1.5:random_seed=3127530821:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (3070522) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3070513-3070522"...
% 0.23/0.30 % (3070522)...printing done.
% 0.23/0.30 % (3070522)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (3070522)------------------------------
% 0.23/0.30 % (3070522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (3070522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (3070522)CaDiCaL version: 2.1.3
% 0.23/0.30 % (3070522)Termination reason: Refutation
% 0.23/0.30 % (3070522)Time elapsed: 0.003 s
% 0.23/0.30 % (3070522)Peak memory usage: 13 MB
% 0.23/0.30 % (3070522)Instructions burned: 4 (million)
% 0.23/0.30 % (3070513)Success in time 0.03 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------