%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO003^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:46:16 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 111 ( 9 ~; 2 |; 12 &; 72 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 5 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 45 ( 19 ^; 17 !; 9 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $i > $o ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq) ).
thf(f2,conjecture,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
& ( leibeq @ X0 @ X1 ) )
=> ( X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
& ( leibeq @ X0 @ X1 ) )
=> ( X2 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
& ( leibeq @ X0 @ X1 ) )
=> ( X2 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X1: $i,X2: $i > $o,X0: $i] :
( ( ( ( X2 @ X0 )
= $true )
& ( ( leibeq @ X0 @ X1 )
= $true ) )
=> ( ( X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X1: $i,X2: $i > $o,X0: $i] :
( ( ( X2 @ X1 )
!= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( leibeq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
? [X2: $i > $o,X1: $i,X0: $i] :
( ( ( X2 @ X1 )
!= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( leibeq @ X0 @ X1 )
= $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( X0 @ X1 ) )
& ( ( X0 @ X2 )
= $true )
& ( $true
= ( leibeq @ X2 @ X1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( $true
!= ( sK0 @ sK1 ) )
& ( ( sK0 @ sK2 )
= $true )
& ( ( leibeq @ sK2 @ sK1 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
thf(f12,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
( ( leibeq @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
( ( sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( $true
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK2
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f13,f12]) ).
thf(f19,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK2 )
=> ( X1 @ sK1 ) )
= $true ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( ( X1 @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f21]) ).
thf(f28,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f15,f22]) ).
thf(f41,plain,
( ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f42,plain,
( ( sK0 @ sK2 )
= $false ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f48,plain,
$false = $true,
inference(backward_demodulation,[],[f14,f42]) ).
thf(f49,plain,
$false,
inference(trivial_inequality_removal,[],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO003^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.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 16:18:41 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.29 % (3573310)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3573320)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2771900348:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (3573320) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3573310-3573320"...
% 0.21/0.29 % (3573320)...printing done.
% 0.21/0.29 % (3573320)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (3573320)------------------------------
% 0.21/0.29 % (3573320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3573320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3573320)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3573320)Termination reason: Refutation
% 0.21/0.29 % (3573320)Time elapsed: 0.002 s
% 0.21/0.29 % (3573320)Peak memory usage: 12 MB
% 0.21/0.29 % (3573320)Instructions burned: 3 (million)
% 0.21/0.29 % (3573310)Success in time 0.039 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------