TSTP Solution File: SEV177^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV177^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:02:08 EDT 2024
% Result : Theorem 0.22s 0.38s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 304 ( 46 ~; 4 |; 34 &; 192 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 3 con; 0-2 aty)
% ( 0 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 70 ( 49 ^ 14 !; 7 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
sK0: $i > $o ).
thf(func_def_11,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK4: $i > $o ).
thf(func_def_15,type,
sK5: $i > $o ).
thf(func_def_16,type,
sK6: $i > $o ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f46]) ).
thf(f46,plain,
$true = $false,
inference(forward_demodulation,[],[f37,f25]) ).
thf(f25,plain,
( ( sK4 @ ( sK1 @ sK4 ) )
= $false ),
inference(not_proxy_clausification,[],[f22]) ).
thf(f22,plain,
( $true
= ( ~ ( sK4 @ ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( $true
= ( ( ( sK1 @ sK4 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) )
& ~ ( sK4 @ ( sK1 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[],[f20]) ).
thf(f20,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( sK1 @ Y2 )
= Y1 )
& ~ ( Y2 @ ( sK1 @ Y2 ) ) ) ) ) )
& ~ ( Y0 @ ( sK1 @ Y0 ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f19]) ).
thf(f19,plain,
( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( sK1 @ Y2 )
= Y1 )
& ~ ( Y2 @ ( sK1 @ Y2 ) ) ) ) ) )
& ~ ( Y0 @ ( sK1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) )
@ ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) )
= $true ),
inference(equality_resolution,[],[f17]) ).
thf(f17,plain,
! [X1: $i > $o] :
( ( ( sK1 @ X1 )
!= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) )
| ( $true
= ( X1 @ ( sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f16]) ).
thf(f16,plain,
! [X1: $i > $o] :
( ( ( sK1 @ X1 )
!= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) )
| ( ( ~ ( X1 @ ( sK1 @ X1 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f15]) ).
thf(f15,plain,
! [X1: $i > $o] :
( ( ( ( sK1 @ X1 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) )
= $false )
| ( ( ~ ( X1 @ ( sK1 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f14]) ).
thf(f14,plain,
! [X1: $i > $o] :
( ( ( ( sK1 @ X1 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) )
& ~ ( X1 @ ( sK1 @ X1 ) ) )
= $false ),
inference(beta_eta_normalization,[],[f13]) ).
thf(f13,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( sK1 @ Y2 )
= Y1 )
& ~ ( Y2 @ ( sK1 @ Y2 ) ) ) ) ) )
& ~ ( Y0 @ ( sK1 @ Y0 ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[],[f12]) ).
thf(f12,plain,
( $true
!= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( sK1 @ Y0 )
= ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( sK1 @ Y2 )
= Y1 )
& ~ ( Y2 @ ( sK1 @ Y2 ) ) ) ) ) )
& ~ ( Y0 @ ( sK1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) )
@ ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f9,f10,f10]) ).
thf(f10,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
= sK0 ),
inference(cnf_transformation,[],[f8]) ).
thf(f8,plain,
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
= sK0 )
& ( $true
!= ( sK0 @ ( sK1 @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X1 @ Y1 ) ) ) ) )
= X0 )
& ( $true
!= ( X0 @ ( X1 @ X0 ) ) ) )
=> ( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
= sK0 )
& ( $true
!= ( sK0 @ ( sK1 @ sK0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f6,plain,
? [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X1 @ Y1 ) ) ) ) )
= X0 )
& ( $true
!= ( X0 @ ( X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X1 @ Y1 ) ) ) ) )
= X0 )
=> ( $true
= ( X0 @ ( X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
& ( ( X1 @ X3 )
= X2 ) ) )
= X0 )
=> ( X0 @ ( X1 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i > $o,X0: ( $i > $o ) > $i] :
( ( ( ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= X2 ) ) )
= X1 )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: $i > $o,X0: ( $i > $o ) > $i] :
( ( ( ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( ( X0 @ X3 )
= X2 ) ) )
= X1 )
=> ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM144_pme) ).
thf(f9,plain,
( $true
!= ( sK0 @ ( sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f37,plain,
( $true
= ( sK4 @ ( sK1 @ sK4 ) ) ),
inference(equality_resolution,[],[f27]) ).
thf(f27,plain,
! [X0: $i > $o] :
( ( ( sK1 @ X0 )
!= ( sK1 @ sK4 ) )
| ( $true
= ( X0 @ ( sK1 @ X0 ) ) ) ),
inference(superposition,[],[f17,f24]) ).
thf(f24,plain,
( ( sK1 @ sK4 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( $true
= ( ( sK1 @ sK4 )
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV177^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_vampire %s %d THM
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 19:29:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.22/0.35 This is a TH0_THM_EQU_NAR problem
% 0.22/0.36 Running higher-order theorem proving
% 0.22/0.36 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.22/0.37 % (30854)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.22/0.37 % (30854)First to succeed.
% 0.22/0.38 % (30854)Refutation found. Thanks to Tanya!
% 0.22/0.38 % SZS status Theorem for theBenchmark
% 0.22/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38 % (30854)------------------------------
% 0.22/0.38 % (30854)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (30854)Termination reason: Refutation
% 0.22/0.38
% 0.22/0.38 % (30854)Memory used [KB]: 5500
% 0.22/0.38 % (30854)Time elapsed: 0.005 s
% 0.22/0.38 % (30854)Instructions burned: 3 (million)
% 0.22/0.38 % (30854)------------------------------
% 0.22/0.38 % (30854)------------------------------
% 0.22/0.38 % (30846)Success in time 0.016 s
%------------------------------------------------------------------------------