%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV288^5 : 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 : n014.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 08:38:11 AM UTC 2026
% Result : Theorem 0.28s 0.41s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 162 ( 63 equ; 3 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 212 ( 42 ~; 44 |; 0 &; 89 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 16 usr; 10 con; 0-4 aty)
% ( 13 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 57 ( 0 sgn 8 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
sK0: a ).
thf(func_def_12,type,
sK1: a ).
thf(func_def_13,type,
sK2: a > $o ).
thf(f1,conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 ) )
= ( ^ [X0: a,X1: a] :
! [X2: a > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE1_eq__pme) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 ) )
!= ( ^ [X0: a,X1: a] :
! [X2: a > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a,X1: a] : ( X0 = X1 ) )
!= ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( (=)
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0 )
!= ( (=) @ sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) ) )
!= ( (=) @ sK0 ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 )
!= ( sK0 = sK1 ) ),
inference(negative_extensionality,[],[f11]) ).
thf(f13,plain,
( ( $true
= ( sK0 = sK1 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) )
| ( $false
= ( sK0 = sK1 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( ( sK1 != sK0 )
| ( $false
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( sK1 != sK0 )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( sK1 != sK0 )
| ( $false
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( sK1 != sK0 )
| ( $false
= ( ( sK2 @ sK0 )
=> ( sK2 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( sK1 != sK0 )
| ( $false
= ( sK2 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( sK1 != sK0 )
| ( ( sK2 @ sK0 )
= $true ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK0 )
=> ( Y1 @ Y0 ) ) )
@ sK1 ) )
| ( sK1 = sK0 ) ),
inference(equality_proxy_clausification,[],[f13]) ).
thf(f22,plain,
( ( sK1 = sK0 )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X1: a > $o] :
( ( sK1 = sK0 )
| ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X1: a > $o] :
( ( ( ( X1 @ sK0 )
=> ( X1 @ sK1 ) )
= $true )
| ( sK1 = sK0 ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( ( X1 @ sK0 )
= $false )
| ( sK1 = sK0 ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f27,definition,
( spl3_1
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f28,plain,
( ( sK1 = sK0 )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( ( sK1 != sK0 )
| spl3_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl3_2
<=> ( ( sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f33,plain,
( ( ( sK2 @ sK0 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f20,f31,f27]) ).
thf(f36,definition,
( spl3_3
<=> ( $false
= ( sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f38,plain,
( ( $false
= ( sK2 @ sK1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( spl3_3
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f19,f27,f36]) ).
thf(f41,definition,
( spl3_4
<=> ! [X1: a > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( ( X1 @ sK0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f42,plain,
( ! [X1: a > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( ( X1 @ sK0 )
= $false ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f43,plain,
( spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f25,f27,f41]) ).
thf(f44,plain,
( ( sK1 = sK0 )
| ~ spl3_4 ),
inference(leibniz_equality_elimination,[],[f42]) ).
thf(f56,plain,
( $false
| spl3_1
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f44,f29]) ).
thf(f57,plain,
( spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f56]) ).
thf(f58,plain,
( ( ( sK2 @ sK0 )
= $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(constrained_superposition,[],[f38,f28]) ).
thf(f59,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f58,f33]) ).
thf(f60,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f61,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
( spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s6,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s7,plain,
spl3_1,
inference(rat,[],[s3,s5]) ).
cnf(s8,plain,
spl3_3,
inference(rat,[],[s2,s7]) ).
cnf(s9,plain,
spl3_2,
inference(rat,[],[s1,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s7,s8,s9]) ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV288^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.28 % Computer : n014.cluster.edu
% 0.14/0.28 % Model : x86_64 x86_64
% 0.14/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.28 % Memory : 8046.5625MB
% 0.14/0.28 % OS : Linux 6.8.0-71-generic
% 0.14/0.28 % CPULimit : 300
% 0.14/0.28 % WCLimit : 300
% 0.14/0.28 % DateTime : Tue Sep 29 15:31:00 UTC 2026
% 0.14/0.28 % CPUTime :
% 0.14/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.34 Running higher-order theorem proving
% 0.28/0.35 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
% 0.28/0.41 % (2808360)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.41 % (2808365)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3523990449:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.41 % (2808365) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2808360-2808365"...
% 0.28/0.41 % (2808365)...printing done.
% 0.28/0.41 % (2808365)Refutation found. Thanks to Tanya!
% 0.28/0.41 % SZS status Theorem for theBenchmark
% 0.28/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.52/0.41 % (2808365)------------------------------
% 0.52/0.41 % (2808365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.41 % (2808365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.41 % (2808365)CaDiCaL version: 2.1.3
% 0.52/0.41 % (2808365)Termination reason: Refutation
% 0.52/0.41 % (2808365)Time elapsed: 0.003 s
% 0.52/0.41 % (2808365)Peak memory usage: 13 MB
% 0.52/0.41 % (2808365)Instructions burned: 3 (million)
% 0.52/0.41 % (2808360)Success in time 0.038 s
% 0.52/0.41 % Vampire exiting
%------------------------------------------------------------------------------