%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET619^5 : 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 : n008.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 08:23:23 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 337 ( 92 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 395 ( 44 ~; 97 |; 53 &; 201 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 30 ( 20 ^; 8 !; 2 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_95_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= ( ^ [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ( X0 @ X3 )
& ( X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f10,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f11,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f12,plain,
( ( $false
= ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
| ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) )
| ( $false
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) )
| ( $false
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( ( $false
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $false
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) )
| ( $false
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f18,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f19]) ).
thf(f23,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) )
| ( $false
= ( ~ ( sK0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f25,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ~ ( sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f26]) ).
thf(f29,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f13]) ).
thf(f33,plain,
( ( $false
= ( ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f34,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f34]) ).
thf(f36,plain,
( ( $true
= ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
| ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) )
| ( $true
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f37,plain,
( ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) )
| ( $true
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) )
| ( $true
= ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f36]) ).
thf(f39,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) )
| ( $true
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f40,plain,
( ( $true
= ( ( sK1 @ sK2 )
| ( sK0 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
| ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f40]) ).
thf(f43,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f45,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f46,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f45]) ).
thf(f70,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(superposition,[],[f20,f27]) ).
thf(f74,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f70]) ).
thf(f75,plain,
( $false
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f78,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f46,f75]) ).
thf(f79,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f83,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $false = $true ) ),
inference(superposition,[],[f35,f79]) ).
thf(f84,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f88,plain,
$false = $true,
inference(forward_demodulation,[],[f84,f75]) ).
thf(f89,plain,
$false,
inference(trivial_inequality_removal,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET619^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:40:09 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.29 % (3164803)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3164812)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1569344721:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (3164812) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3164803-3164812"...
% 0.22/0.29 % (3164812)...printing done.
% 0.22/0.29 % (3164812)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (3164812)------------------------------
% 0.22/0.29 % (3164812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3164812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3164812)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3164812)Termination reason: Refutation
% 0.22/0.29 % (3164812)Time elapsed: 0.002 s
% 0.22/0.29 % (3164812)Peak memory usage: 12 MB
% 0.22/0.29 % (3164812)Instructions burned: 5 (million)
% 0.22/0.29 % (3164803)Success in time 0.027 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------