%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO002^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:46:15 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 133 ( 8 ~; 1 |; 2 &; 100 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 5 con; 0-4 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 40 ( 20 ^; 17 !; 3 ?; 40 :)
% 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_12,type,
sK2: $i > $i ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK3: $i > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( leibeq
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq) ).
thf(f2,conjecture,
! [X1: $i,X0: $i,X2: $i > $i] :
( ( leibeq @ X0 @ X1 )
=> ( leibeq @ ( X2 @ X0 ) @ ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i,X2: $i > $i] :
( ( leibeq @ X0 @ X1 )
=> ( leibeq @ ( X2 @ X0 ) @ ( X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( leibeq
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
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 > $i] :
( ( leibeq @ X1 @ X0 )
=> ( leibeq @ ( X2 @ X1 ) @ ( X2 @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X2: $i > $i,X0: $i,X1: $i] :
( ( $true
= ( leibeq @ X1 @ X0 ) )
=> ( $true
= ( leibeq @ ( X2 @ X1 ) @ ( X2 @ X0 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i,X2: $i > $i] :
( ( $true
= ( leibeq @ X1 @ X0 ) )
& ( $true
!= ( leibeq @ ( X2 @ X1 ) @ ( X2 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
= ( leibeq @ sK1 @ sK0 ) )
& ( $true
!= ( leibeq @ ( sK2 @ sK1 ) @ ( sK2 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
( $true
!= ( leibeq @ ( sK2 @ sK1 ) @ ( sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( $true
= ( leibeq @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f15,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[],[f11,f12]) ).
thf(f16,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( sK2 @ sK1 )
@ ( sK2 @ sK0 ) ) ),
inference(definition_unfolding,[],[f10,f12]) ).
thf(f17,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( sK2 @ sK1 ) )
=> ( Y0 @ ( sK2 @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( ( ^ [Y0: $i > $o] :
( ( Y0 @ ( sK2 @ sK1 ) )
=> ( Y0 @ ( sK2 @ sK0 ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK3 @ ( sK2 @ sK1 ) )
=> ( sK3 @ ( sK2 @ sK0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( $false
= ( sK3 @ ( sK2 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( $true
= ( sK3 @ ( sK2 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f23,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X1: $i > $o] :
( $true
= ( ( X1 @ sK1 )
=> ( X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ sK1 ) )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f27,plain,
sK0 = sK1,
inference(leibniz_equality_elimination,[],[f25]) ).
thf(f37,plain,
( $true
= ( sK3 @ ( sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f21,f27]) ).
thf(f38,plain,
$true = $false,
inference(forward_demodulation,[],[f37,f20]) ).
thf(f39,plain,
$false,
inference(trivial_inequality_removal,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO002^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:18:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.08/0.26 % (3573557)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (3573566)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=514731404:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.26 % (3573566) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3573557-3573566"...
% 0.08/0.26 % (3573566)...printing done.
% 0.08/0.26 % (3573566)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (3573566)------------------------------
% 0.08/0.26 % (3573566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3573566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3573566)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3573566)Termination reason: Refutation
% 0.08/0.26 % (3573566)Time elapsed: 0.001 s
% 0.08/0.26 % (3573566)Peak memory usage: 12 MB
% 0.08/0.26 % (3573566)Instructions burned: 2 (million)
% 0.08/0.26 % (3573557)Success in time 0.015 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------