%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV220^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:38:03 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 145 ( 14 ~; 7 |; 27 &; 79 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 5 con; 0-4 aty)
% ( 0 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 49 ( 15 ^; 19 !; 15 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: b > a ).
thf(func_def_1,type,
w: ( b > $o ) > $o ).
thf(func_def_5,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK0: a ).
thf(func_def_12,type,
sK1: b ).
thf(func_def_13,type,
sK2: a > $o ).
thf(func_def_14,type,
sK3: b > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ? [X1: b > $o] :
( ( ( ^ [X3: a] :
? [X4: b] :
( ( X1 @ X4 )
& ( X3
= ( f @ X4 ) ) ) )
= X2 )
& ( w @ X1 ) )
=> ( X2 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5205_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ? [X1: b > $o] :
( ( ( ^ [X3: a] :
? [X4: b] :
( ( X1 @ X4 )
& ( X3
= ( f @ X4 ) ) ) )
= X2 )
& ( w @ X1 ) )
=> ( X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) ) )
=> ! [X3: a > $o] :
( ? [X4: b > $o] :
( ( ( ^ [X5: a] :
? [X6: b] :
( ( X4 @ X6 )
& ( ( f @ X6 )
= X5 ) ) )
= X3 )
& ( w @ X4 ) )
=> ( X3 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ! [X2: b > $o] :
( ( ( w @ X2 )
= $true )
=> ( ( X2 @ X1 )
= $true ) ) )
=> ! [X3: a > $o] :
( ? [X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( X4 @ Y1 ) ) ) )
= X3 )
& ( ( w @ X4 )
= $true ) )
=> ( ( X3 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ! [X2: b > $o] :
( ( ( X2 @ X1 )
= $true )
| ( ( w @ X2 )
!= $true ) ) )
& ? [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
& ? [X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( X4 @ Y1 ) ) ) )
= X3 )
& ( ( w @ X4 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( sK0
= ( f @ sK1 ) )
& ! [X2: b > $o] :
( ( $true
= ( X2 @ sK1 ) )
| ( ( w @ X2 )
!= $true ) )
& ( ( sK2 @ sK0 )
!= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( sK3 @ Y1 ) ) ) )
= sK2 )
& ( $true
= ( w @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2),skolemize(X4,sK3)],[f5]) ).
thf(f7,plain,
( $true
= ( w @ sK3 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( sK3 @ Y1 ) ) ) )
= sK2 ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
! [X2: b > $o] :
( ( ( w @ X2 )
!= $true )
| ( $true
= ( X2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( sK0
= ( f @ sK1 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( sK3 @ Y1 ) ) )
@ sK0 )
!= $true ),
inference(definition_unfolding,[],[f9,f8]) ).
thf(f15,plain,
( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK0 )
& ( sK3 @ Y0 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
! [X1: b] :
( ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK0 )
& ( sK3 @ Y0 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X1: b] :
( ( ( ( f @ X1 )
= sK0 )
& ( sK3 @ X1 ) )
= $false ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X1: b] :
( ( ( sK3 @ X1 )
= $false )
| ( $false
= ( ( f @ X1 )
= sK0 ) ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( sK3 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ( sK3 @ sK1 )
= $false )
| ( sK0 != sK0 ) ),
inference(constrained_superposition,[],[f19,f11]) ).
thf(f21,plain,
( ( sK3 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
( ( ( sK3 @ sK1 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f10,f7]) ).
thf(f23,plain,
( ( sK3 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
$true = $false,
inference(forward_demodulation,[],[f23,f21]) ).
thf(f25,plain,
$false,
inference(trivial_inequality_removal,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV220^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n010.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 15:23:03 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.22 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
% 0.20/0.27 % (2989225)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2989232)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=776364048:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (2989232)Refutation not found, incomplete strategy
% 0.20/0.27 % (2989232)------------------------------
% 0.20/0.27 % (2989232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2989232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2989232)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2989232)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (2989232)Time elapsed: 0.001 s
% 0.20/0.27 % (2989232)Peak memory usage: 12 MB
% 0.20/0.27 % (2989232)Instructions burned: 1 (million)
% 0.20/0.27 % (2989232)------------------------------
% 0.20/0.27 % (2989232)------------------------------
% 0.20/0.27 % (2989231)lrs+10_16_si=on:nwc=1.5:random_seed=2502931253:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (2989230)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3682110854:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (2989233)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=544182312: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 % (2989230) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2989225-2989230"...
% 0.20/0.27 % (2989231) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2989225-2989231"...
% 0.20/0.27 % (2989233) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2989225-2989233"...
% 0.20/0.27 % (2989231)...printing done.
% 0.20/0.27 % (2989230)...printing done.
% 0.20/0.27 % (2989238)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2677105378:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.27 % (2989231)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 % (2989231)------------------------------
% 0.20/0.27 % (2989231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2989231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2989231)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2989231)Termination reason: Refutation
% 0.20/0.27 % (2989231)Time elapsed: 0.002 s
% 0.20/0.27 % (2989231)Peak memory usage: 12 MB
% 0.20/0.27 % (2989231)Instructions burned: 2 (million)
% 0.20/0.27 % (2989225)Success in time 0.038 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------