%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV417^5 : 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 : 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 08:38:36 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 56 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 367 ( 110 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 326 ( 37 ~; 60 |; 64 &; 148 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 117 ( 42 sgn 40 !; 9 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: ( a > $o ) > $o ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a > $o ).
thf(func_def_11,type,
sK4: a ).
thf(func_def_12,type,
sK5: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ( cP
@ ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) ) )
=> ( ( cP
@ ^ [X3: a] : $false )
& ( X0
= ( ^ [X3: a] : $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM502_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ( cP
@ ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) ) )
=> ( ( cP
@ ^ [X3: a] : $false )
& ( X0
= ( ^ [X3: a] : $false ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ( cP
@ ^ [X4: a] :
( ( X1 @ X4 )
& ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( X0 @ X5 )
=> ( X1 @ X5 ) )
& ( ( ^ [X6: a] :
( ( X2 @ X6 )
& ( X1 @ X6 ) ) )
= ( ^ [X7: a] : $false ) ) )
=> ( ( cP
@ ^ [X8: a] : $false )
& ( X0
= ( ^ [X9: a] : $false ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ( ( cP
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= $true )
& ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
=> ( $true
= ( X1 @ X5 ) ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ) )
=> ( ( ( ^ [Y0: a] : $false )
= X0 )
& ( $true
= ( cP
@ ^ [Y0: a] : $false ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ( ( cP
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= $true )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
=> ( ( X1 @ X4 )
= $true ) ) )
=> ( ( ( ^ [Y0: a] : $false )
= X0 )
& ( $true
= ( cP
@ ^ [Y0: a] : $false ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( cP
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= $true )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
= $true ) )
& ( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) )
& ( ( cP
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= $true )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
= ( X2 @ X4 ) ) )
& ( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) )
& ( ( cP
@ ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= $true )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( ( sK2 @ X4 )
= $true ) )
& ( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| ( sK0
!= ( ^ [Y0: a] : $false ) ) )
& ( $true
= ( cP
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( $true
= ( cP
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( sK0
!= ( ^ [Y0: a] : $false ) )
| ( $true
!= ( cP
@ ^ [Y0: a] : $false ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
| ( ( sK2 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X3: a] :
( ( ( sK0 @ X3 )
!= $true )
| ( $true
= ( sK1 @ X3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,definition,
( spl3_1
<=> ( $true
= ( cP
@ ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f19,plain,
( ( $true
!= ( cP
@ ^ [Y0: a] : $false ) )
| spl3_1 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,definition,
( spl3_2
<=> ( sK0
= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f22,plain,
( ( sK0
!= ( ^ [Y0: a] : $false ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f23,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f12,f21,f18]) ).
thf(f24,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) ),
inference(argument_congruence,[],[f10]) ).
thf(f26,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 )
= $false )
| ( ( ^ [Y0: a] : $false
@ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f24]) ).
thf(f27,plain,
! [X1: a] :
( ( $false
= ( ( sK2 @ X1 )
& ( sK1 @ X1 ) ) )
| ( $true = $false ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true = $false )
| ( ( sK2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f34,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( $true != $true )
| spl3_1 ),
inference(constrained_superposition,[],[f19,f11]) ).
thf(f35,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f38,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ sK4 )
!= ( ^ [Y0: a] : $false
@ sK4 ) )
| spl3_1 ),
inference(negative_extensionality,[],[f35]) ).
thf(f41,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ sK4 )
= $true )
| ( $true
= ( ^ [Y0: a] : $false
@ sK4 ) )
| spl3_1 ),
inference(xor_proxy_clausification,[],[f38]) ).
thf(f45,plain,
( ( ( ( sK1 @ sK4 )
& ( sK2 @ sK4 ) )
= $true )
| ( $true = $false )
| spl3_1 ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f46,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ( $true = $false )
| spl3_1 ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $true = $false )
| spl3_1 ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f48,plain,
( ( ( sK1 @ sK4 )
= $true )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f49,plain,
( ( $true
= ( sK2 @ sK4 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f52,plain,
( ( $false
= ( sK2 @ sK4 ) )
| ( $true = $false )
| spl3_1 ),
inference(constrained_superposition,[],[f29,f48]) ).
thf(f53,plain,
( ( $false
= ( sK2 @ sK4 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f55,plain,
( ( $true = $false )
| spl3_1 ),
inference(backward_demodulation,[],[f49,f53]) ).
thf(f56,plain,
( $false
| spl3_1 ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f57,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f56]) ).
thf(f64,plain,
( ( ( ^ [Y0: a] : $false
@ sK5 )
!= ( sK0 @ sK5 ) )
| spl3_2 ),
inference(negative_extensionality,[],[f22]) ).
thf(f67,plain,
( ( ( ^ [Y0: a] : $false
@ sK5 )
= $true )
| ( $true
= ( sK0 @ sK5 ) )
| spl3_2 ),
inference(xor_proxy_clausification,[],[f64]) ).
thf(f70,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true = $false )
| spl3_2 ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f71,plain,
( ( $true
= ( sK0 @ sK5 ) )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f73,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(constrained_superposition,[],[f14,f71]) ).
thf(f74,plain,
( ( $true != $true )
| ( ( sK2 @ sK5 )
= $true )
| spl3_2 ),
inference(constrained_superposition,[],[f13,f71]) ).
thf(f75,plain,
( ( ( sK2 @ sK5 )
= $true )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( ( $true
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f77,plain,
( ( $true = $false )
| ( ( sK2 @ sK5 )
= $false )
| spl3_2 ),
inference(constrained_superposition,[],[f76,f29]) ).
thf(f79,plain,
( ( ( sK2 @ sK5 )
= $false )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f81,plain,
( ( $true = $false )
| spl3_2 ),
inference(backward_demodulation,[],[f75,f79]) ).
thf(f82,plain,
( $false
| spl3_2 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f83,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f82]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f57]) ).
cnf(s4,plain,
spl3_2,
inference(sat_conversion,[],[f83]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
thf(f84,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV417^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n002.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 15:48:22 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.20 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
% 0.08/0.24 % (1453386)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.24 % (1453396)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2608608945:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.24 % (1453396) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1453386-1453396"...
% 0.08/0.24 % (1453396)...printing done.
% 0.08/0.24 % (1453396)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (1453396)------------------------------
% 0.08/0.25 % (1453396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (1453396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (1453396)CaDiCaL version: 2.1.3
% 0.08/0.25 % (1453396)Termination reason: Refutation
% 0.08/0.25 % (1453396)Time elapsed: 0.003 s
% 0.08/0.25 % (1453396)Peak memory usage: 13 MB
% 0.08/0.25 % (1453396)Instructions burned: 6 (million)
% 0.08/0.25 % (1453386)Success in time 0.03 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------