%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO001^1 : 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 : n005.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 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 43 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 168 ( 9 ~; 9 |; 12 &; 116 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 6 con; 0-4 aty)
% ( 7 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 63 ( 21 ^; 33 !; 9 ?; 63 :)
% 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_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK3: $i > $i > $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,
! [X2: $i,X0: $i,X1: $i] :
( ( ( leibeq @ X1 @ X2 )
& ( leibeq @ X0 @ X1 ) )
=> ( leibeq @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ! [X2: $i,X0: $i,X1: $i] :
( ( ( leibeq @ X1 @ X2 )
& ( leibeq @ X0 @ X1 ) )
=> ( leibeq @ X0 @ X2 ) ),
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] :
( ( ( leibeq @ X2 @ X0 )
& ( leibeq @ X1 @ X2 ) )
=> ( leibeq @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X1: $i,X0: $i,X2: $i] :
( ( ( $true
= ( leibeq @ X2 @ X0 ) )
& ( ( leibeq @ X1 @ X2 )
= $true ) )
=> ( ( leibeq @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X1: $i,X0: $i,X2: $i] :
( ( ( leibeq @ X1 @ X0 )
!= $true )
& ( $true
= ( leibeq @ X2 @ X0 ) )
& ( ( leibeq @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( leibeq @ X2 @ X0 ) )
& ( ( leibeq @ X1 @ X2 )
= $true )
& ( ( leibeq @ X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( ( leibeq @ X0 @ X1 )
= $true )
& ( $true
= ( leibeq @ X2 @ X0 ) )
& ( ( leibeq @ X2 @ X1 )
!= $true ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( leibeq @ sK0 @ sK1 ) )
& ( $true
= ( leibeq @ sK2 @ sK0 ) )
& ( $true
!= ( leibeq @ sK2 @ sK1 ) ) ),
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,
( $true
!= ( leibeq @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
( $true
= ( leibeq @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( $true
= ( leibeq @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
! [X1: $i] :
( ( leibeq @ X1 )
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f12]) ).
thf(f18,plain,
! [X1: $i] :
( ( leibeq @ X1 )
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ X1 )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( ( leibeq @ X1 @ X2 )
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ X1 )
=> ( Y1 @ Y0 ) ) )
@ X2 ) ),
inference(argument_congruence,[],[f18]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( ( ( leibeq @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ X1 )
=> ( Y1 @ Y0 ) ) )
@ X2 ) ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( ( leibeq @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
=> ( Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( leibeq @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
=> ( Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( leibeq @ X1 @ X2 )
= $false )
| ( ( ( X3 @ X1 )
=> ( X3 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( X3 @ X1 ) )
| ( ( leibeq @ X1 @ X2 )
= $false )
| ( $true
= ( X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f41,plain,
! [X0: $i > $o] :
( ( $false = $true )
| ( $false
= ( X0 @ sK0 ) )
| ( $true
= ( X0 @ sK1 ) ) ),
inference(superposition,[],[f25,f15]) ).
thf(f53,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ sK1 ) )
| ( $false
= ( X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f70,plain,
sK1 = sK0,
inference(leibniz_equality_elimination,[],[f53]) ).
thf(f92,plain,
( $true
!= ( leibeq @ sK2 @ sK0 ) ),
inference(superposition,[],[f13,f70]) ).
thf(f93,plain,
$false,
inference(forward_subsumption_resolution,[],[f92,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO001^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n005.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:20:32 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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 % (1869349)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1869359)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3816615494:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (1869359) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1869349-1869359"...
% 0.22/0.28 % (1869361)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 % (1869359)...printing done.
% 0.22/0.28 % (1869361)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 % (1869359)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 % (1869359)------------------------------
% 0.22/0.28 % (1869359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1869359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1869359)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1869359)Termination reason: Refutation
% 0.22/0.28 % (1869359)Time elapsed: 0.003 s
% 0.22/0.28 % (1869359)Peak memory usage: 12 MB
% 0.22/0.28 % (1869359)Instructions burned: 5 (million)
% 0.22/0.28 % (1869349)Success in time 0.02 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------