%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO008^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 33 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 157 ( 11 ~; 2 |; 2 &; 114 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 4 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 60 ( 30 ^; 28 !; 2 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
leibeq1: $i > $i > $o ).
thf(func_def_2,type,
leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
thf(func_def_3,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK0: $i > $i ).
thf(func_def_12,type,
sK1: $i > $i ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK2: ( $i > $i ) > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( leibeq1
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq1) ).
thf(f2,axiom,
( ( ^ [X0: $i > $i,X1: $i > $i] :
! [X2: ( $i > $i ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq2) ).
thf(f3,conjecture,
! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] : ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
=> ( leibeq2 @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f4,negated_conjecture,
~ ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] : ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
=> ( leibeq2 @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( leibeq1
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] : ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
=> ( leibeq2 @ X0 @ X1 ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ! [X1: $i > $i,X0: $i > $i] :
( ! [X2: $i] :
( ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
= $true )
=> ( ( leibeq2 @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( ( ^ [X0: $i > $i,X1: $i > $i] :
! [X2: ( $i > $i ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq2 ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( leibeq2
= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
= $true )
& ( ( leibeq2 @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ! [X2: $i] :
( $true
= ( leibeq1 @ ( sK0 @ X2 ) @ ( sK1 @ X2 ) ) )
& ( ( leibeq2 @ sK0 @ sK1 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
thf(f13,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( ( leibeq2 @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f15,plain,
! [X2: $i] :
( $true
= ( leibeq1 @ ( sK0 @ X2 ) @ ( sK1 @ X2 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( leibeq2
= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
! [X2: $i] :
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( sK0 @ X2 )
@ ( sK1 @ X2 ) )
= $true ),
inference(definition_unfolding,[],[f15,f13]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f21,plain,
( $true
!= ( !! @ ( ( $i > $i ) > $o )
@ ^ [Y0: ( $i > $i ) > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( ^ [Y0: ( $i > $i ) > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( ( sK2 @ sK0 )
=> ( sK2 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( sK2 @ sK1 )
= $false ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( $true
= ( sK2 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f26,plain,
! [X2: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( sK0 @ X2 ) )
=> ( Y0 @ ( sK1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f27,plain,
! [X2: $i,X3: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ ( sK0 @ X2 ) )
=> ( Y0 @ ( sK1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i > $o] :
( ( ( X3 @ ( sK0 @ X2 ) )
=> ( X3 @ ( sK1 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i > $o] :
( ( $true
= ( X3 @ ( sK1 @ X2 ) ) )
| ( ( X3 @ ( sK0 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
! [X0: $i] :
( ( sK0 @ X0 )
= ( sK1 @ X0 ) ),
inference(leibniz_equality_elimination,[],[f29]) ).
thf(f59,plain,
( ( $true = $false )
| ( sK1 != sK0 ) ),
inference(constrained_superposition,[],[f25,f24]) ).
thf(f61,plain,
sK1 != sK0,
inference(trivial_inequality_removal,[],[f59]) ).
thf(f63,plain,
( ( sK0 @ sK3 )
!= ( sK1 @ sK3 ) ),
inference(negative_extensionality,[],[f61]) ).
thf(f64,plain,
$false,
inference(forward_subsumption_resolution,[],[f63,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO008^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:21:00 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (2870506)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2870511)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2251759246:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (2870511)Refutation not found, incomplete strategy
% 0.20/0.27 % (2870511)------------------------------
% 0.20/0.27 % (2870511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2870511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2870511)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2870511)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (2870511)Time elapsed: 0.001 s
% 0.20/0.27 % (2870511)Peak memory usage: 12 MB
% 0.20/0.27 % (2870511)Instructions burned: 2 (million)
% 0.20/0.27 % (2870511)------------------------------
% 0.20/0.27 % (2870511)------------------------------
% 0.20/0.27 % (2870517)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (2870517)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
% 0.20/0.27 % (2870512)lrs+10_16_si=on:nwc=1.5:random_seed=2938525711:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (2870513)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4025435138:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (2870514)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=133250368: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)
% 0.20/0.27 % (2870515)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1559928141:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (2870516)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1255859208:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (2870517)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=3479956261:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.27 % (2870513)Refutation not found, incomplete strategy
% 0.20/0.27 % (2870513)------------------------------
% 0.20/0.27 % (2870513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2870513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2870513)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2870513)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (2870513)Time elapsed: 0.001 s
% 0.20/0.27 % (2870513)Peak memory usage: 12 MB
% 0.20/0.27 % (2870513)Instructions burned: 1 (million)
% 0.20/0.27 % (2870513)------------------------------
% 0.20/0.27 % (2870513)------------------------------
% 0.20/0.27 % (2870512) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2870506-2870512"...
% 0.20/0.27 % (2870517)Refutation not found, incomplete strategy
% 0.20/0.27 % (2870517)------------------------------
% 0.20/0.27 % (2870517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2870517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2870517)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2870517)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (2870517)Time elapsed: 0.002 s
% 0.20/0.27 % (2870517)Peak memory usage: 12 MB
% 0.20/0.27 % (2870517)Instructions burned: 3 (million)
% 0.20/0.27 % (2870516) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2870506-2870516"...
% 0.20/0.27 % (2870519)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2361729954:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.27 % (2870517)------------------------------
% 0.20/0.27 % (2870517)------------------------------
% 0.20/0.27 % (2870512)...printing done.
% 0.20/0.27 % (2870514)Refutation not found, incomplete strategy
% 0.20/0.27 % (2870514)------------------------------
% 0.20/0.27 % (2870514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2870514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2870514)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2870514)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (2870514)Time elapsed: 0.004 s
% 0.20/0.27 % (2870514)Peak memory usage: 12 MB
% 0.20/0.27 % (2870514)Instructions burned: 6 (million)
% 0.20/0.27 % (2870519)Instruction limit reached!
% 0.20/0.27 % (2870519)------------------------------
% 0.20/0.27 % (2870519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2870519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2870519)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2870519)Termination reason: Instruction limit
% 0.20/0.27 % (2870519)Termination phase: Saturation
% 0.20/0.27 % (2870519)Time elapsed: 0.001 s
% 0.20/0.27 % (2870519)Peak memory usage: 12 MB
% 0.20/0.27 % (2870519)Instructions burned: 2 (million)
% 0.20/0.27 % (2870516)...printing done.
% 0.20/0.27 % (2870512)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2870512)------------------------------
% 0.20/0.27 % (2870512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2870512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2870512)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2870512)Termination reason: Refutation
% 0.20/0.27 % (2870512)Time elapsed: 0.003 s
% 0.20/0.27 % (2870512)Peak memory usage: 12 MB
% 0.20/0.27 % (2870512)Instructions burned: 4 (million)
% 0.20/0.27 % (2870506)Success in time 0.035 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------