%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU548^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:30:01 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 33 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 82 ( 8 ~; 2 |; 9 &; 48 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 16 !; 8 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
inCongP: $o ).
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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f2,conjecture,
( inCongP
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
<=> ( in @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(f3,negated_conjecture,
~ ( inCongP
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
<=> ( in @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ( inCongP
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X3 @ X1 )
<=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ( ( inCongP = $true )
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
= ( in @ X3 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f8,plain,
( ( inCongP = $true )
& ? [X1: $i,X0: $i] :
( ( X0 = X1 )
& ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( in @ X2 @ X0 )
!= ( in @ X3 @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
( ( inCongP = $true )
& ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( in @ X3 @ X0 )
!= ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( inCongP = $true )
& ( sK1 = sK0 )
& ( sK2 = sK3 )
& ( ( in @ sK3 @ sK0 )
!= ( in @ sK2 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f9]) ).
thf(f11,plain,
( ( in @ sK3 @ sK0 )
!= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f12,plain,
sK2 = sK3,
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
sK1 = sK0,
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
( ( in @ sK3 @ sK0 )
!= ( in @ sK3 @ sK0 ) ),
inference(definition_unfolding,[],[f11,f12,f13]) ).
thf(f20,plain,
( ( ( in @ sK3 @ sK0 )
= $true )
| ( ( in @ sK3 @ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f18]) ).
thf(f22,plain,
( ( in @ sK3 @ sK0 )
= $false ),
inference(duplicate_literal_removal,[],[f21]) ).
thf(f23,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(duplicate_literal_removal,[],[f20]) ).
thf(f37,plain,
$false = $true,
inference(forward_demodulation,[],[f23,f22]) ).
thf(f38,plain,
$false,
inference(trivial_inequality_removal,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU548^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:50:09 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.19/0.27 % (3183938)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (3183952)lrs+10_16_si=on:nwc=1.5:random_seed=750529329:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (3183952) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3183938-3183952"...
% 0.19/0.27 % (3183952)...printing done.
% 0.19/0.27 % (3183952)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (3183952)------------------------------
% 0.19/0.27 % (3183952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3183952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3183952)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3183952)Termination reason: Refutation
% 0.19/0.27 % (3183952)Time elapsed: 0.001 s
% 0.19/0.27 % (3183952)Peak memory usage: 12 MB
% 0.19/0.27 % (3183952)Instructions burned: 2 (million)
% 0.19/0.27 % (3183938)Success in time 0.031 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------