%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO033^1 : 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 : n009.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 08:46:19 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 17 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 90 ( 6 ~; 0 |; 0 &; 62 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 10 usr; 4 con; 0-4 aty)
% ( 15 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 28 ( 14 ^; 11 !; 3 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vIFF: $o > $o > $o ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
sK0: ( ( $i > $o ) > $o ) > $i > $o ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > $o] :
! [X1: $i > $o] :
( ! [X2: $i] : ( X1 @ X2 )
<=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > $o] :
! [X1: $i > $o] :
( ! [X2: $i] : ( X1 @ X2 )
<=> ( X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ? [X0: ( $i > $o ) > $o] :
! [X1: $i > $o] :
( ! [X2: $i] : ( X1 @ X2 )
<=> ( X0 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
= ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
= ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i @ Y1 )
= ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5]) ).
thf(f9,plain,
( $false
= ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i @ Y1 )
= ( Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f8]) ).
thf(f10,plain,
! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i @ Y1 )
= ( Y0 @ Y1 ) ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f9]) ).
thf(f13,plain,
! [X1: ( $i > $o ) > $o] :
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i @ Y0 )
= ( X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f14,plain,
! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: $i > $o] :
( ( !! @ $i @ Y0 )
= ( X1 @ Y0 ) )
@ ( sK0 @ X1 ) )
= $false ),
inference(sigma_proxy_clausification,[],[f13]) ).
thf(f15,plain,
! [X1: ( $i > $o ) > $o] :
( ( ( !! @ $i @ ( sK0 @ X1 ) )
= ( X1 @ ( sK0 @ X1 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
! [X1: ( $i > $o ) > $o] :
( ( X1 @ ( sK0 @ X1 ) )
!= ( !! @ $i @ ( sK0 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f23,plain,
$false,
inference(equality_resolution,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO033^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:23:24 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.23/0.30 % (9489)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (9498)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3104732649:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (9498)Refutation not found, incomplete strategy
% 0.23/0.30 % (9498)------------------------------
% 0.23/0.30 % (9498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9498)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9498)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (9498)Time elapsed: 0.001 s
% 0.23/0.30 % (9498)Peak memory usage: 12 MB
% 0.23/0.30 % (9498)Instructions burned: 2 (million)
% 0.23/0.30 % (9498)------------------------------
% 0.23/0.30 % (9498)------------------------------
% 0.23/0.30 % (9504)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (9504)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
% 0.23/0.30 % (9499)lrs+10_16_si=on:nwc=1.5:random_seed=733303591:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (9500)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=503848541:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (9501)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1419416328:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.30 % (9504)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=187346774:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (9503)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=752858573:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (9502)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1598269671:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (9500)Refutation not found, incomplete strategy
% 0.23/0.30 % (9500)------------------------------
% 0.23/0.30 % (9500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9500)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9500)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (9500)Time elapsed: 0.002 s
% 0.23/0.30 % (9500)Peak memory usage: 12 MB
% 0.23/0.30 % (9500)Instructions burned: 1 (million)
% 0.23/0.30 % (9501)Refutation not found, incomplete strategy
% 0.23/0.30 % (9501)------------------------------
% 0.23/0.30 % (9501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9501)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9501)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (9501)Time elapsed: 0.002 s
% 0.23/0.30 % (9501)Peak memory usage: 12 MB
% 0.23/0.30 % (9501)Instructions burned: 1 (million)
% 0.23/0.30 % (9500)------------------------------
% 0.23/0.30 % (9500)------------------------------
% 0.23/0.30 % (9502)Refutation not found, incomplete strategy
% 0.23/0.30 % (9502)------------------------------
% 0.23/0.30 % (9502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9502)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9502)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (9502)Time elapsed: 0.002 s
% 0.23/0.30 % (9502)Peak memory usage: 12 MB
% 0.23/0.30 % (9502)Instructions burned: 3 (million)
% 0.23/0.30 % (9501)------------------------------
% 0.23/0.30 % (9501)------------------------------
% 0.23/0.30 % (9504)Refutation not found, incomplete strategy
% 0.23/0.30 % (9504)------------------------------
% 0.23/0.30 % (9504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9504)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9504)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (9504)Time elapsed: 0.003 s
% 0.23/0.30 % (9504)Peak memory usage: 12 MB
% 0.23/0.30 % (9504)Instructions burned: 4 (million)
% 0.23/0.30 % (9502)------------------------------
% 0.23/0.30 % (9502)------------------------------
% 0.23/0.30 % (9504)------------------------------
% 0.23/0.30 % (9504)------------------------------
% 0.23/0.30 % (9508)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1453172867:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.30 % (9508)Instruction limit reached!
% 0.23/0.30 % (9508)------------------------------
% 0.23/0.30 % (9508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9508)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9508)Termination reason: Instruction limit
% 0.23/0.30 % (9508)Termination phase: Saturation
% 0.23/0.30 % (9508)Time elapsed: 0.001 s
% 0.23/0.30 % (9508)Peak memory usage: 12 MB
% 0.23/0.30 % (9508)Instructions burned: 2 (million)
% 0.23/0.30 % (9499)Instruction limit reached!
% 0.23/0.30 % (9499)------------------------------
% 0.23/0.30 % (9499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9499)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9499)Termination reason: Instruction limit
% 0.23/0.30 % (9499)Termination phase: Saturation
% 0.23/0.30 % (9499)Time elapsed: 0.011 s
% 0.23/0.30 % (9499)Peak memory usage: 12 MB
% 0.23/0.30 % (9499)Instructions burned: 19 (million)
% 0.23/0.30 % (9523)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2751724238:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.23/0.30 % (9523) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-9489-9523"...
% 0.23/0.30 % (9523)...printing done.
% 0.23/0.30 % (9523)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (9523)------------------------------
% 0.23/0.30 % (9523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (9523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (9523)CaDiCaL version: 2.1.3
% 0.23/0.30 % (9523)Termination reason: Refutation
% 0.23/0.30 % (9523)Time elapsed: 0.001 s
% 0.23/0.30 % (9523)Peak memory usage: 12 MB
% 0.23/0.30 % (9523)Instructions burned: 2 (million)
% 0.23/0.30 % (9489)Success in time 0.042 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------