%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV239^5 : 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 : n002.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 08:38:06 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 406 ( 147 equ; 24 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 390 ( 60 ~; 88 |; 38 &; 174 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 12 con; 0-4 aty)
% ( 0 !!; 24 ??; 0 @@+; 0 @@-)
% Number of variables : 76 ( 0 sgn 20 !; 6 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
y: a > $o ).
thf(func_def_2,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
sK0: a ).
thf(func_def_12,type,
sK1: a > $o ).
thf(func_def_13,type,
sK2: a ).
thf(func_def_15,type,
sK4: ( a > $o ) > a > a ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( y @ X2 )
& ( X1
= ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 ) ) ) ) )
= y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5211_pme) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( y @ X2 )
& ( X1
= ( ^ [X0: a,X3: a] : ( X0 = X3 )
@ X2 ) ) ) ) )
!= y ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a] :
( ( y @ X2 )
& ( X1
= ( ^ [X3: a,X4: a] : ( X3 = X4 )
@ X2 ) ) ) ) )
!= y ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
@ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( y
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( (=) @ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( (=) @ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
!= ( y @ sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f11,plain,
( ( ( y @ sK0 )
= $true )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( (=) @ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( ( y @ sK0 )
= $false )
| ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] :
( ( Y1
= ( (=) @ Y2 ) )
& ( y @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK0 ) ) )
= $false )
| ( ( y @ sK0 )
= $false ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
! [X1: a > $o] :
( ( ( ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK0 ) )
@ X1 )
= $false )
| ( ( y @ sK0 )
= $false ) ),
inference(pi_proxy_clausification,[],[f13]) ).
thf(f15,plain,
! [X1: a > $o] :
( ( ( y @ sK0 )
= $false )
| ( $false
= ( ( ?? @ a
@ ^ [Y0: a] :
( ( X1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) )
& ( X1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
! [X1: a > $o] :
( ( $false
= ( X1 @ sK0 ) )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( X1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) )
= $false )
| ( ( y @ sK0 )
= $false ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( X1 @ sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( ( X1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) )
@ X2 ) )
| ( ( y @ sK0 )
= $false ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X2: a,X1: a > $o] :
( ( $false
= ( X1 @ sK0 ) )
| ( ( y @ sK0 )
= $false )
| ( ( ( X1
= ( (=) @ X2 ) )
& ( y @ X2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: a,X1: a > $o] :
( ( ( y @ sK0 )
= $false )
| ( ( y @ X2 )
= $false )
| ( $false
= ( X1 @ sK0 ) )
| ( ( X1
= ( (=) @ X2 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X2: a,X1: a > $o] :
( ( ( y @ sK0 )
= $false )
| ( ( (=) @ X2 )
!= X1 )
| ( $false
= ( X1 @ sK0 ) )
| ( ( y @ X2 )
= $false ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( ( y @ sK0 )
= $true )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f22,plain,
( ( ( ^ [Y0: a > $o] :
( ( ?? @ a
@ ^ [Y1: a] :
( ( Y0
= ( (=) @ Y1 ) )
& ( y @ Y1 ) ) )
& ( Y0 @ sK0 ) )
@ sK1 )
= $true )
| ( ( y @ sK0 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( ( y @ sK0 )
= $true )
| ( ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) )
& ( sK1 @ sK0 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( ( sK1 @ sK0 )
= $true )
| ( ( y @ sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) ) )
= $true )
| ( ( y @ sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( ( y @ sK0 )
= $true )
| ( ( ^ [Y0: a] :
( ( sK1
= ( (=) @ Y0 ) )
& ( y @ Y0 ) )
@ sK2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( ( ( sK1
= ( (=) @ sK2 ) )
& ( y @ sK2 ) )
= $true )
| ( ( y @ sK0 )
= $true ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
( ( ( y @ sK0 )
= $true )
| ( ( y @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( ( y @ sK0 )
= $true )
| ( ( sK1
= ( (=) @ sK2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f30,plain,
( ( ( y @ sK0 )
= $true )
| ( ( (=) @ sK2 )
= sK1 ) ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f32,definition,
( spl3_1
<=> ! [X2: a,X1: a > $o] :
( ( ( (=) @ X2 )
!= X1 )
| ( ( y @ X2 )
= $false )
| ( $false
= ( X1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f33,plain,
( ! [X2: a,X1: a > $o] :
( ( ( (=) @ X2 )
!= X1 )
| ( $false
= ( X1 @ sK0 ) )
| ( ( y @ X2 )
= $false ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,definition,
( spl3_2
<=> ( ( y @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f37,plain,
( ( ( y @ sK0 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f20,f35,f32]) ).
thf(f40,definition,
( spl3_3
<=> ( ( (=) @ sK2 )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f42,plain,
( ( ( (=) @ sK2 )
= sK1 )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f44,definition,
( spl3_4
<=> ( ( y @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f45,plain,
( ( ( y @ sK0 )
!= $true )
| spl3_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f46,plain,
( ( ( y @ sK0 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f47,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f30,f44,f40]) ).
thf(f49,definition,
( spl3_5
<=> ( ( y @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f51,plain,
( ( ( y @ sK2 )
= $true )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f52,plain,
( spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f28,f49,f44]) ).
thf(f54,definition,
( spl3_6
<=> ( ( sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f56,plain,
( ( ( sK1 @ sK0 )
= $true )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f57,plain,
( spl3_6
| spl3_4 ),
inference(avatar_split_clause,[],[f24,f44,f54]) ).
thf(f58,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f37,f46]) ).
thf(f59,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f60,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f59]) ).
thf(f64,plain,
( ! [X0: a] :
( ( ( X0 = sK0 )
= $false )
| ( ( y @ X0 )
= $false ) )
| ~ spl3_1 ),
inference(equality_resolution,[],[f33]) ).
thf(f65,plain,
( ! [X0: a] :
( ( sK0 != X0 )
| ( ( y @ X0 )
= $false ) )
| ~ spl3_1 ),
inference(equality_proxy_clausification,[],[f64]) ).
thf(f72,plain,
( ( sK0 != sK0 )
| ( ( y @ sK0 )
= $false )
| ~ spl3_1 ),
inference(imitation,[],[f65]) ).
thf(f74,plain,
( ( ( y @ sK0 )
= $false )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f78,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[],[f74,f46]) ).
thf(f79,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f79]) ).
thf(f82,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( sK2 = X1 ) )
| ~ spl3_3 ),
inference(argument_congruence,[],[f42]) ).
thf(f84,plain,
( ! [X1: a] :
( ( $true
= ( sK2 = X1 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl3_3 ),
inference(iff_proxy_clausification,[],[f82]) ).
thf(f85,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( sK2 = X1 ) )
| ~ spl3_3 ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f87,plain,
( ( sK2 = sK0 )
| ( $false = $true )
| ~ spl3_3
| ~ spl3_6 ),
inference(constrained_superposition,[],[f85,f56]) ).
thf(f89,plain,
( ( sK2 = sK0 )
| ~ spl3_3
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f92,plain,
( ( ( y @ sK0 )
= $true )
| ~ spl3_3
| ~ spl3_5
| ~ spl3_6 ),
inference(constrained_superposition,[],[f51,f89]) ).
thf(f93,plain,
( $false
| ~ spl3_3
| spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f92,f45]) ).
thf(f94,plain,
( ~ spl3_3
| spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f93]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( spl3_4
| spl3_6 ),
inference(sat_conversion,[],[f57]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s7,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f80]) ).
cnf(s8,plain,
( ~ spl3_3
| spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f94]) ).
cnf(s9,plain,
spl3_4,
inference(rat,[],[s8,s2,s3,s4]) ).
cnf(s10,plain,
~ spl3_1,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
~ spl3_2,
inference(rat,[],[s5,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s10]) ).
thf(f95,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV239^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 15:29:23 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.22 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
% 0.20/0.26 % (1427685)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (1427690)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3097347472:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.26 % (1427690) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1427685-1427690"...
% 0.20/0.26 % (1427690)...printing done.
% 0.20/0.26 % (1427690)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (1427690)------------------------------
% 0.20/0.26 % (1427690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (1427690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (1427690)CaDiCaL version: 2.1.3
% 0.20/0.26 % (1427690)Termination reason: Refutation
% 0.20/0.26 % (1427690)Time elapsed: 0.003 s
% 0.20/0.26 % (1427690)Peak memory usage: 13 MB
% 0.20/0.26 % (1427690)Instructions burned: 6 (million)
% 0.20/0.26 % (1427685)Success in time 0.032 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------