%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET594^5 : 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 : n017.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 08:23:19 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 48 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 184 ( 13 ~; 28 |; 36 &; 97 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 45 ( 11 ^; 26 !; 8 ?; 45 :)
% 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,
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_10,type,
sK3: a ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X0 @ X3 )
& ( X2 @ X3 ) ) ) )
= X0 )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_53_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X0 @ X3 )
& ( X2 @ X3 ) ) ) )
= X0 )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) )
= X2 )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ( ( X0 @ X4 )
| ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X2 )
=> ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
=> ( ( ( X0 @ X4 )
= $true )
| ( ( X1 @ X4 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X2 )
=> ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
!= $true )
& ( ( X2 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X2 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= X2 )
& ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
!= $true )
& ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( sK2
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
& ( ( sK0 @ sK3 )
!= $true )
& ( $true
!= ( sK1 @ sK3 ) )
& ( $true
= ( sK2 @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
!= ( sK1 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( sK0 @ sK3 )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( sK2
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ X1 )
= ( sK2 @ X1 ) ),
inference(argument_congruence,[],[f12]) ).
thf(f16,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ X1 )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f23,plain,
! [X1: a] :
( ( ( ( ( sK0 @ X1 )
& ( sK2 @ X1 ) )
| ( ( sK2 @ X1 )
& ( sK1 @ X1 ) ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f24,plain,
! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ( sK0 @ X1 )
& ( sK2 @ X1 ) ) )
| ( $true
= ( ( sK2 @ X1 )
& ( sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f23]) ).
thf(f26,plain,
! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ( sK2 @ X1 )
& ( sK1 @ X1 ) ) )
| ( ( sK0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f27,plain,
! [X1: a] :
( ( ( sK0 @ X1 )
= $true )
| ( $false
= ( sK2 @ X1 ) )
| ( ( sK1 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f32,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true != $true )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f11,f27]) ).
thf(f33,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f33,f10]) ).
thf(f35,plain,
$false = $true,
inference(backward_demodulation,[],[f9,f34]) ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:33:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.08/0.28 % (341019)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.28 % (341031)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2377845664:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.28 % (341031) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-341019-341031"...
% 0.08/0.28 % (341031)...printing done.
% 0.08/0.28 % (341031)Refutation found. Thanks to Tanya!
% 0.08/0.28 % SZS status Theorem for theBenchmark
% 0.08/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.28 % (341031)------------------------------
% 0.08/0.28 % (341031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.28 % (341031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.28 % (341031)CaDiCaL version: 2.1.3
% 0.08/0.28 % (341031)Termination reason: Refutation
% 0.08/0.28 % (341031)Time elapsed: 0.002 s
% 0.08/0.28 % (341031)Peak memory usage: 12 MB
% 0.08/0.28 % (341031)Instructions burned: 2 (million)
% 0.08/0.28 % (341019)Success in time 0.018 s
% 0.08/0.28 % Vampire exiting
%------------------------------------------------------------------------------