%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO010^1 : 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 : n019.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 08:46:17 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 120 ( 13 ~; 2 |; 8 &; 81 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 4 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 50 ( 32 ^; 18 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_2,type,
p: ( $i > $i ) > $o ).
thf(func_def_3,type,
f: $i > $i ).
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_12,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/sandbox2/benchmark/theBenchmark.p',leibeq) ).
thf(f2,conjecture,
( ( ! [X0: $i] : ( leibeq @ ( f @ X0 ) @ X0 )
& ( p
@ ^ [X0: $i] : X0 ) )
=> ( p
@ ^ [X0: $i] : ( f @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ( ( ! [X0: $i] : ( leibeq @ ( f @ X0 ) @ X0 )
& ( p
@ ^ [X0: $i] : X0 ) )
=> ( p
@ ^ [X0: $i] : ( f @ X0 ) ) ),
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] : ( leibeq @ ( f @ X0 ) @ X0 )
& ( p
@ ^ [X1: $i] : X1 ) )
=> ( p
@ ^ [X2: $i] : ( f @ X2 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( ! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true )
& ( ( p
@ ^ [Y0: $i] : Y0 )
= $true ) )
=> ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
!= $true )
& ! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true )
& ( ( p
@ ^ [Y0: $i] : Y0 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true )
& ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
!= $true )
& ( ( p
@ ^ [Y0: $i] : Y0 )
= $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ( p
@ ^ [Y0: $i] : Y0 )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f16,plain,
! [X0: $i] :
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( f @ X0 )
@ X0 )
= $true ),
inference(definition_unfolding,[],[f12,f13]) ).
thf(f17,plain,
! [X0: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( f @ X0 ) )
=> ( Y0 @ X0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ ( f @ X0 ) )
=> ( Y0 @ X0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X0: $i,X1: $i > $o] :
( ( ( X1 @ ( f @ X0 ) )
=> ( X1 @ X0 ) )
= $true ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X0: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( f @ X0 ) ) )
| ( ( X1 @ X0 )
= $true ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( p @ f )
!= $true ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f22,plain,
( ( f
!= ( ^ [Y0: $i] : Y0 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f21,f10]) ).
thf(f23,plain,
( f
!= ( ^ [Y0: $i] : Y0 ) ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
( ( f @ sK0 )
!= ( ^ [Y0: $i] : Y0
@ sK0 ) ),
inference(negative_extensionality,[],[f23]) ).
thf(f25,plain,
( ( f @ sK0 )
!= sK0 ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X0: $i] :
( ( f @ X0 )
= X0 ),
inference(leibniz_equality_elimination,[],[f20]) ).
thf(f52,plain,
sK0 != sK0,
inference(backward_demodulation,[],[f25,f26]) ).
thf(f53,plain,
$false,
inference(trivial_inequality_removal,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO010^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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 16:21:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.28 % (995155)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (995174)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2085335964:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.28 % (995174) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-995155-995174"...
% 0.22/0.28 % (995174)...printing done.
% 0.22/0.28 % (995175)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (995175)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
% 0.22/0.28 % (995174)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (995174)------------------------------
% 0.22/0.28 % (995174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (995174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (995174)CaDiCaL version: 2.1.3
% 0.22/0.28 % (995174)Termination reason: Refutation
% 0.22/0.28 % (995174)Time elapsed: 0.002 s
% 0.22/0.28 % (995174)Peak memory usage: 12 MB
% 0.22/0.28 % (995174)Instructions burned: 3 (million)
% 0.22/0.28 % (995155)Success in time 0.034 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------