%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO007^1 : 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 : n010.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 0.09s 0.29s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 76 ( 9 ~; 0 |; 3 &; 45 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 5 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 29 ( 15 ^; 10 !; 4 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
leibeq: $o > $o > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $o ).
thf(func_def_11,type,
sK1: $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
sK2: $o > $o ).
thf(f1,axiom,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq1) ).
thf(f2,conjecture,
! [X1: $o,X0: $o] :
( ( X1
<=> X0 )
=> ( leibeq @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ! [X1: $o,X0: $o] :
( ( X1
<=> X0 )
=> ( leibeq @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $o,X1: $o] :
( ( X0
<=> X1 )
=> ( leibeq @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ! [X1: $o,X0: $o] :
( ( X0 = X1 )
=> ( $true
= ( leibeq @ X1 @ X0 ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X1: $o,X0: $o] :
( ( $true
!= ( leibeq @ X1 @ X0 ) )
& ( X0 = X1 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
? [X0: $o,X1: $o] :
( ( ( leibeq @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( ( leibeq @ sK0 @ sK1 )
!= $true )
& ( sK0 = sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
thf(f11,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( ( leibeq @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
( ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK1 )
!= $true ),
inference(definition_unfolding,[],[f13,f11,f12]) ).
thf(f17,plain,
( ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK1 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( ( ^ [Y0: $o > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK1 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK2 @ sK1 )
=> ( sK2 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( sK2 @ sK1 )
= $false ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( sK2 @ sK1 )
= $true ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
$true = $false,
inference(backward_demodulation,[],[f21,f20]) ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO007^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n010.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:21:18 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.09/0.26 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
% 0.09/0.29 % (3070558)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.29 % (3070568)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3808620468:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.29 % (3070568) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3070558-3070568"...
% 0.09/0.29 % (3070568)...printing done.
% 0.09/0.29 % (3070569)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.29 % (3070569)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.09/0.29 % (3070568)Refutation found. Thanks to Tanya!
% 0.09/0.29 % SZS status Theorem for theBenchmark
% 0.09/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.29 % (3070568)------------------------------
% 0.09/0.29 % (3070568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.29 % (3070568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.29 % (3070568)CaDiCaL version: 2.1.3
% 0.09/0.29 % (3070568)Termination reason: Refutation
% 0.09/0.29 % (3070568)Time elapsed: 0.001 s
% 0.09/0.29 % (3070568)Peak memory usage: 12 MB
% 0.09/0.29 % (3070568)Instructions burned: 1 (million)
% 0.09/0.29 % (3070558)Success in time 0.019 s
% 0.09/0.29 % Vampire exiting
%------------------------------------------------------------------------------