%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU803^2 : 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 : n002.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 08:31:33 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 76 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 413 ( 24 ~; 15 |; 23 &; 312 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 22 usr; 8 con; 0-4 aty)
% ( 4 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 82 ( 28 ^; 40 !; 14 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
funcSet: $i > $i > $i ).
thf(func_def_2,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_3,type,
surjective: $i > $i > $i > $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
sK2: $i > $i ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(f1,axiom,
( surjective
= ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
thf(f2,conjecture,
! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X1 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X1 @ X0 @ X4 @ ( X2 @ X3 ) )
= X3 ) )
=> ( surjective @ X1 @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leftInvIsSurj) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X1 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X1 @ X0 @ X4 @ ( X2 @ X3 ) )
= X3 ) )
=> ( surjective @ X1 @ X0 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X1 @ X0 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( ap @ X1 @ X0 @ X4 @ ( X2 @ X5 ) )
= X5 ) )
=> ( surjective @ X1 @ X0 @ X4 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ! [X2: $i > $i,X1: $i,X0: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( X2 @ X3 ) @ X1 )
= $true ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( funcSet @ X1 @ X0 ) )
= $true )
=> ( ! [X5: $i] :
( ( $true
= ( in @ X5 @ X0 ) )
=> ( ( ap @ X1 @ X0 @ X4 @ ( X2 @ X5 ) )
= X5 ) )
=> ( ( surjective @ X1 @ X0 @ X4 )
= $true ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( surjective
= ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X2: $i > $i,X1: $i,X0: $i] :
( ? [X4: $i] :
( ( ( surjective @ X1 @ X0 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( ap @ X1 @ X0 @ X4 @ ( X2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ X0 ) ) )
& ( ( in @ X4 @ ( funcSet @ X1 @ X0 ) )
= $true ) )
& ! [X3: $i] :
( ( ( in @ ( X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
? [X1: $i,X0: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ ( X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ? [X4: $i] :
( ( ( surjective @ X1 @ X0 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( ap @ X1 @ X0 @ X4 @ ( X2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ X0 ) ) )
& ( ( in @ X4 @ ( funcSet @ X1 @ X0 ) )
= $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( $true
= ( in @ ( X2 @ X3 ) @ X0 ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ? [X4: $i] :
( ( $true
!= ( surjective @ X0 @ X1 @ X4 ) )
& ! [X5: $i] :
( ( ( ap @ X0 @ X1 @ X4 @ ( X2 @ X5 ) )
= X5 )
| ( ( in @ X5 @ X1 )
!= $true ) )
& ( ( in @ X4 @ ( funcSet @ X0 @ X1 ) )
= $true ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ! [X3: $i] :
( ( $true
= ( in @ ( sK2 @ X3 ) @ sK0 ) )
| ( $true
!= ( in @ X3 @ sK1 ) ) )
& ( ( surjective @ sK0 @ sK1 @ sK3 )
!= $true )
& ! [X5: $i] :
( ( ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ X5 ) )
= X5 )
| ( ( in @ X5 @ sK1 )
!= $true ) )
& ( $true
= ( in @ sK3 @ ( funcSet @ sK0 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3)],[f10]) ).
thf(f12,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
! [X5: $i] :
( ( ( in @ X5 @ sK1 )
!= $true )
| ( ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ X5 ) )
= X5 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( surjective @ sK0 @ sK1 @ sK3 )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
= ( in @ ( sK2 @ X3 ) @ sK0 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) )
@ sK0
@ sK1
@ sK3 ) ),
inference(definition_unfolding,[],[f15,f12]) ).
thf(f20,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y1 )
= Y0 ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( $false
= ( ( in @ sK4 @ sK1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y0 )
= sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y0 )
= sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f25,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y0 )
= sK4 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f26,plain,
! [X1: $i] :
( $false
= ( ( in @ X1 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ X1 )
= sK4 ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X1: $i] :
( ( $false
= ( ( ap @ sK0 @ sK1 @ sK3 @ X1 )
= sK4 ) )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X1: $i] :
( ( ( ap @ sK0 @ sK1 @ sK3 @ X1 )
!= sK4 )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(equality_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK2 @ sK4 ) @ sK0 ) ) ),
inference(constrained_superposition,[],[f16,f24]) ).
thf(f30,plain,
( $true
= ( in @ ( sK2 @ sK4 ) @ sK0 ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
( ( ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ sK4 ) )
= sK4 )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f14,f24]) ).
thf(f32,plain,
( ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ sK4 ) )
= sK4 ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f33,plain,
( ( ( in @ ( sK2 @ sK4 ) @ sK0 )
= $false )
| ( sK4 != sK4 ) ),
inference(constrained_superposition,[],[f28,f32]) ).
thf(f34,plain,
( ( in @ ( sK2 @ sK4 ) @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f36,plain,
$true = $false,
inference(constrained_superposition,[],[f30,f34]) ).
thf(f37,plain,
$false,
inference(trivial_inequality_removal,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU803^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n002.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:34:52 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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
% 0.20/0.28 % (1375546)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1375561)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3920343668:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (1375559)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2506049200:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (1375558)lrs+10_16_si=on:nwc=1.5:random_seed=3826871434:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (1375559)Refutation not found, incomplete strategy
% 0.20/0.28 % (1375559)------------------------------
% 0.20/0.28 % (1375559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1375559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1375559)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1375559)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (1375559)Time elapsed: 0.002 s
% 0.20/0.28 % (1375559)Peak memory usage: 12 MB
% 0.20/0.28 % (1375559)Instructions burned: 2 (million)
% 0.20/0.28 % (1375558) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1375546-1375558"...
% 0.20/0.28 % (1375559)------------------------------
% 0.20/0.28 % (1375559)------------------------------
% 0.20/0.28 % (1375562)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=449225803:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (1375561) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1375546-1375561"...
% 0.20/0.28 % (1375557)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1312474857:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1375558)...printing done.
% 0.20/0.28 % (1375561)...printing done.
% 0.20/0.28 % (1375558)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1375558)------------------------------
% 0.20/0.28 % (1375558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1375558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1375558)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1375558)Termination reason: Refutation
% 0.20/0.28 % (1375558)Time elapsed: 0.004 s
% 0.20/0.28 % (1375558)Peak memory usage: 12 MB
% 0.20/0.28 % (1375558)Instructions burned: 5 (million)
% 0.20/0.28 % (1375546)Success in time 0.042 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------