%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO530^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:48:21 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 67 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 289 ( 34 ~; 21 |; 2 &; 215 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 5 con; 0-4 aty)
% ( 0 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 114 ( 41 ^; 57 !; 16 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epsa: ( $i > $i > $o ) > $i ).
thf(func_def_3,type,
epsb: ( $i > $i > $o ) > $i ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
sK0: $i > $i > $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
sK3: ( $i > $i > $o ) > $i ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax) ).
thf(f2,axiom,
( epsa
= ( ^ [X0: $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsad) ).
thf(f3,axiom,
( epsb
= ( ^ [X0: $i > $i > $o] :
( eps
@ ^ [X1: $i] : ( X0 @ ( epsa @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsbd) ).
thf(f4,conjecture,
! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f5,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( epsb
= ( ^ [X0: $i > $i > $o] :
( eps
@ ^ [X1: $i] : ( X0 @ ( epsa @ X0 ) @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( epsb
= ( ^ [Y0: $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
~ ! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
= $true )
=> ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( epsa
= ( ^ [X0: $i > $i > $o] :
( eps
@ ^ [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( epsa
= ( ^ [Y0: $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f15,plain,
? [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f16,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
& ( $true
!= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
thf(f17,plain,
( epsa
= ( ^ [Y0: $i > $i > $o] :
( eps
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
!= ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f19,plain,
( $true
= ( sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f20,plain,
( epsb
= ( ^ [Y0: $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f21,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
( epsb
= ( ^ [Y0: $i > $i > $o] : ( eps @ ( Y0 @ ( epsa @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f24,plain,
( epsa
= ( ^ [Y0: $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( ?? @ $i @ ( Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f28,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
!= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) ),
inference(primitive_instantiation,[],[f21]) ).
thf(f31,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
!= ( ~ ( X2 @ X1 ) ) )
| ( $true
= ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f32,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( X2 @ X1 ) )
| ( ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f38,plain,
! [X1: $i > $i > $o] :
( ( epsa @ X1 )
= ( ^ [Y0: $i > $i > $o] :
( eps
@ ^ [Y1: $i] : ( ?? @ $i @ ( Y0 @ Y1 ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f24]) ).
thf(f39,plain,
! [X1: $i > $i > $o] :
( ( epsa @ X1 )
= ( eps
@ ^ [Y0: $i] : ( ?? @ $i @ ( X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f46,plain,
! [X3: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ X1 ) )
| ( ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
~ ( X3 @ Y1 )
@ Y0 ) ) )
= $false ) ),
inference(primitive_instantiation,[],[f33]) ).
thf(f54,plain,
! [X3: $i > $o,X1: $i] :
( ( $true
= ( ~ ( X3 @ X1 ) ) )
| ( ( ~ ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f55,plain,
! [X3: $i > $o,X1: $i] :
( ( ( ~ ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) ) )
= $false )
| ( ( X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X3: $i > $o,X1: $i] :
( ( ( X3 @ X1 )
= $false )
| ( $true
= ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X3: $i > $o,X1: $i] :
( ( $true
= ( X3
@ ( eps
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( ( X3 @ X1 )
= $false ) ),
inference(boolean_simplification,[],[f56]) ).
thf(f58,plain,
! [X3: $i > $o,X1: $i] :
( ( $true
= ( X3 @ ( eps @ X3 ) ) )
| ( ( X3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f100,plain,
! [X1: $i > $i > $o] :
( ( epsb @ X1 )
= ( ^ [Y0: $i > $i > $o] : ( eps @ ( Y0 @ ( epsa @ Y0 ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f23]) ).
thf(f101,plain,
! [X1: $i > $i > $o] :
( ( eps @ ( X1 @ ( epsa @ X1 ) ) )
= ( epsb @ X1 ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f105,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( X0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( X0 @ Y0 ) )
@ ( epsa @ X0 ) ) ) ),
inference(superposition,[],[f58,f39]) ).
thf(f106,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true
= ( ?? @ $i @ ( X0 @ ( epsa @ X0 ) ) ) )
| ( ( ?? @ $i @ ( X0 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( epsa @ X0 ) @ ( sK3 @ X0 ) ) )
| ( ( ?? @ $i @ ( X0 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( epsa @ X0 ) @ ( sK3 @ X0 ) ) )
| ( ( X0 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f107]) ).
thf(f121,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ ( epsa @ X0 ) @ ( eps @ ( X0 @ ( epsa @ X0 ) ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f21,f108]) ).
thf(f126,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ ( epsa @ X0 ) @ ( eps @ ( X0 @ ( epsa @ X0 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f157,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) )
= $true ) ),
inference(forward_demodulation,[],[f126,f101]) ).
thf(f179,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[],[f18,f157]) ).
thf(f198,plain,
! [X0: $i,X1: $i] :
( $false
= ( sK0 @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f219,plain,
$true = $false,
inference(superposition,[],[f198,f19]) ).
thf(f233,plain,
$false,
inference(trivial_inequality_removal,[],[f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO530^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n007.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 17:10:57 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running higher-order theorem proving
% 0.06/0.21 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
% 0.21/0.26 % (3664821)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.26 % (3664826)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2259525573:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.26 % (3664826)Refutation not found, incomplete strategy
% 0.21/0.26 % (3664826)------------------------------
% 0.21/0.26 % (3664826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (3664826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (3664826)CaDiCaL version: 2.1.3
% 0.21/0.26 % (3664826)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.26 % (3664826)Time elapsed: 0.002 s
% 0.21/0.26 % (3664826)Peak memory usage: 12 MB
% 0.21/0.26 % (3664826)Instructions burned: 5 (million)
% 0.21/0.26 % (3664826)------------------------------
% 0.21/0.26 % (3664826)------------------------------
% 0.21/0.26 % (3664827)lrs+10_16_si=on:nwc=1.5:random_seed=2005149179:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.26 % (3664828)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3747434594:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.26 % (3664830)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2586308593:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.26 % (3664829)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=2911402203: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)
% 0.21/0.26 % (3664828)Refutation not found, incomplete strategy
% 0.21/0.26 % (3664828)------------------------------
% 0.21/0.26 % (3664828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (3664828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (3664828)CaDiCaL version: 2.1.3
% 0.21/0.26 % (3664828)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.26 % (3664828)Time elapsed: 0.002 s
% 0.21/0.26 % (3664828)Peak memory usage: 12 MB
% 0.21/0.26 % (3664828)Instructions burned: 2 (million)
% 0.21/0.26 % (3664828)------------------------------
% 0.21/0.26 % (3664828)------------------------------
% 0.21/0.26 % (3664831)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1033265226:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.26 % (3664830) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3664821-3664830"...
% 0.21/0.26 % (3664829) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3664821-3664829"...
% 0.21/0.26 % (3664830)...printing done.
% 0.21/0.26 % (3664829)...printing done.
% 0.21/0.26 % (3664827)Instruction limit reached!
% 0.21/0.26 % (3664827)------------------------------
% 0.21/0.26 % (3664827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (3664827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (3664830)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (3664830)------------------------------
% 0.21/0.27 % (3664830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (3664830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (3664830)CaDiCaL version: 2.1.3
% 0.21/0.27 % (3664830)Termination reason: Refutation
% 0.21/0.27 % (3664830)Time elapsed: 0.008 s
% 0.21/0.27 % (3664830)Peak memory usage: 12 MB
% 0.21/0.27 % (3664830)Instructions burned: 13 (million)
% 0.21/0.27 % (3664821)Success in time 0.047 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------