TSTP Solution File: SEV085^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV085^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.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 16:01:45 EDT 2024
% Result : Theorem 0.15s 0.32s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 519 ( 266 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 511 ( 94 ~; 101 |; 32 &; 273 @)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 399 ( 399 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 365 ( 154 ^ 170 !; 41 ?; 365 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_4,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_5,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_6,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_8,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f228,plain,
$false,
inference(avatar_sat_refutation,[],[f58,f109,f111,f143,f227]) ).
thf(f227,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f226]) ).
thf(f226,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f225,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(beta_eta_normalization,[],[f216]) ).
thf(f216,plain,
( ! [X3: $i] :
( $true
= ( ^ [Y0: $i] : $false
@ X3 ) )
| ~ spl4_1 ),
inference(primitive_instantiation,[],[f188]) ).
thf(f188,plain,
( ! [X3: $i,X1: $i > $o] :
( ( X1 @ X3 )
= $true )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f187]) ).
thf(f187,plain,
( ! [X3: $i,X1: $i > $o] :
( ( $false = $true )
| ( ( X1 @ X3 )
= $true ) )
| ~ spl4_1 ),
inference(beta_eta_normalization,[],[f183]) ).
thf(f183,plain,
( ! [X3: $i,X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] : $true
@ X3 ) )
| ( ( X1 @ X3 )
= $true ) )
| ~ spl4_1 ),
inference(primitive_instantiation,[],[f157]) ).
thf(f157,plain,
( ! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $false
= ( X2 @ X3 ) )
| ( ( X1 @ X3 )
= $true ) )
| ~ spl4_1 ),
inference(binary_proxy_clausification,[],[f144]) ).
thf(f144,plain,
( ! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
| ~ spl4_1 ),
inference(argument_congruence,[],[f50]) ).
thf(f50,plain,
( ! [X2: $i > $o,X1: $i > $o] : ( X1 = X2 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f49,plain,
( spl4_1
<=> ! [X2: $i > $o,X1: $i > $o] : ( X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
thf(f143,plain,
( spl4_3
| spl4_1
| ~ spl4_2
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f142,f106,f52,f49,f56]) ).
thf(f56,plain,
( spl4_3
<=> ! [X4: $i > $o,X3: $i > $o] : ( X3 != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
thf(f52,plain,
( spl4_2
<=> ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
thf(f106,plain,
( spl4_7
<=> ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
thf(f142,plain,
( ! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( X1 = X2 )
| ( X3 != X4 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f141,f54]) ).
thf(f54,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f141,plain,
( ! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( X3 != X4 )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( X1 = X2 ) )
| ~ spl4_7 ),
inference(forward_demodulation,[],[f122,f108]) ).
thf(f108,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f122,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( X3 != X4 )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f121]) ).
thf(f121,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( X3 != X4 )
| ( $true
= ( X1 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f120]) ).
thf(f120,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( X4 = X3 )
!= $true )
| ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( X1 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f119]) ).
thf(f119,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
!= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( X4 = X3 )
!= $true )
| ( $true
= ( X1 = X2 ) ) ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f118,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
!= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( X4 = X3 )
!= $true )
| ( $true != $true )
| ( $true
= ( X1 = X2 ) ) ),
inference(boolean_simplification,[],[f117]) ).
thf(f117,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( X4 = X3 )
!= $true )
| ( $true
= ( X1 = X2 ) )
| ( $true
!= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f112]) ).
thf(f112,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ X3
@ X4 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ X2
@ X1 ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[],[f15]) ).
thf(f15,plain,
! [X2: $i > $o,X3: $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
!= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X3 @ X4 )
!= $true )
| ( $true
= ( X0 @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( $true
= ( X0 @ X2 @ X1 ) )
| ! [X3: $i > $o,X4: $i > $o] :
( ( X0 @ X3 @ X4 )
!= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( $true
!= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X5: $i > $o] :
( ( X0 @ X5 @ X5 )
!= $true )
=> ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ( X0 @ X7 @ X8 )
!= $true )
& ( ( X0 @ X7 @ X6 )
= $true )
& ( $true
= ( X0 @ X6 @ X8 ) ) )
=> ( ( $true
!= ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( $true
= ( X0 @ X2 @ X1 ) )
| ! [X3: $i > $o,X4: $i > $o] :
( ( X0 @ X3 @ X4 )
!= $true )
| ? [X5: $i > $o] :
( ( X0 @ X5 @ X5 )
!= $true )
| ? [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ( X0 @ X7 @ X8 )
!= $true )
& ( ( X0 @ X7 @ X6 )
= $true )
& ( $true
= ( X0 @ X6 @ X8 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X5: $i > $o,X4: $i > $o] :
( $true
= ( X0 @ X4 @ X5 ) )
| ! [X1: $i > $o,X2: $i > $o] :
( ( X0 @ X1 @ X2 )
!= $true )
| ? [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
!= $true )
| ? [X6: $i > $o,X8: $i > $o,X7: $i > $o] :
( ( ( X0 @ X8 @ X7 )
!= $true )
& ( $true
= ( X0 @ X8 @ X6 ) )
& ( ( X0 @ X6 @ X7 )
= $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
!= $true )
| ? [X7: $i > $o,X6: $i > $o,X8: $i > $o] :
( ( ( X0 @ X8 @ X7 )
!= $true )
& ( $true
= ( X0 @ X8 @ X6 ) )
& ( ( X0 @ X6 @ X7 )
= $true ) )
| ! [X5: $i > $o,X4: $i > $o] :
( $true
= ( X0 @ X4 @ X5 ) )
| ! [X1: $i > $o,X2: $i > $o] :
( ( X0 @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
= $true )
& ! [X7: $i > $o,X6: $i > $o,X8: $i > $o] :
( ( ( $true
= ( X0 @ X8 @ X6 ) )
& ( ( X0 @ X6 @ X7 )
= $true ) )
=> ( ( X0 @ X8 @ X7 )
= $true ) )
& ? [X4: $i > $o,X5: $i > $o] :
( $true
!= ( X0 @ X4 @ X5 ) )
& ? [X2: $i > $o,X1: $i > $o] :
( ( X0 @ X1 @ X2 )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] :
( ( X0 @ X1 @ X2 )
= $true )
& ! [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
= $true )
& ? [X4: $i > $o,X5: $i > $o] :
( $true
!= ( X0 @ X4 @ X5 ) )
& ! [X7: $i > $o,X6: $i > $o,X8: $i > $o] :
( ( ( $true
= ( X0 @ X8 @ X6 ) )
& ( ( X0 @ X6 @ X7 )
= $true ) )
=> ( ( X0 @ X8 @ X7 )
= $true ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] : ( X0 @ X1 @ X2 )
& ! [X3: $i > $o] : ( X0 @ X3 @ X3 )
& ? [X4: $i > $o,X5: $i > $o] :
~ ( X0 @ X4 @ X5 )
& ! [X6: $i > $o,X7: $i > $o,X8: $i > $o] :
( ( ( X0 @ X8 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X0 @ X8 @ X7 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] : ( X0 @ X1 @ X2 )
& ! [X5: $i > $o] : ( X0 @ X5 @ X5 )
& ? [X3: $i > $o,X4: $i > $o] :
~ ( X0 @ X3 @ X4 )
& ! [X6: $i > $o,X7: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X0 @ X5 @ X7 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] : ( X0 @ X1 @ X2 )
& ! [X5: $i > $o] : ( X0 @ X5 @ X5 )
& ? [X3: $i > $o,X4: $i > $o] :
~ ( X0 @ X3 @ X4 )
& ! [X6: $i > $o,X7: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X0 @ X5 @ X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_2_pme) ).
thf(f111,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f110]) ).
thf(f110,plain,
( $false
| ~ spl4_3 ),
inference(flex-flex_simplify,[],[f57]) ).
thf(f57,plain,
( ! [X3: $i > $o,X4: $i > $o] : ( X3 != X4 )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f109,plain,
( spl4_3
| spl4_1
| spl4_7 ),
inference(avatar_split_clause,[],[f79,f106,f49,f56]) ).
thf(f79,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( X3 != X4 )
| ( X1 = X2 )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f78]) ).
thf(f78,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( X3 != X4 )
| ( $true
= ( X1 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f77]) ).
thf(f77,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( X4 = X3 )
!= $true )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( $true
= ( X1 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f76]) ).
thf(f76,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( X4 = X3 )
!= $true )
| ( $true
= ( X1 = X2 ) ) ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f75,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( X4 = X3 )
!= $true )
| ( $true != $true )
| ( $true
= ( X1 = X2 ) ) ),
inference(boolean_simplification,[],[f74]) ).
thf(f74,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( X4 = X3 )
!= $true )
| ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( X1 = X2 ) ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ X3
@ X4 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ X2
@ X1 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[],[f14]) ).
thf(f14,plain,
! [X2: $i > $o,X3: $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
= ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) ) )
| ( $true
= ( X0 @ X2 @ X1 ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f58,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f38,f56,f52,f49]) ).
thf(f38,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( X3 != X4 )
| ( X1 = X2 )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f37]) ).
thf(f37,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( X3 != X4 )
| ( $true
= ( X1 = X2 ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f36,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( X4 = X3 )
!= $true )
| ( $true
= ( X1 = X2 ) )
| ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f35,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( X4 = X3 )
!= $true )
| ( $true
= ( X1 = X2 ) ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f34,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( X4 = X3 )
!= $true )
| ( $true
= ( X1 = X2 ) )
| ( $true != $true ) ),
inference(boolean_simplification,[],[f33]) ).
thf(f33,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( ( X4 = X3 )
!= $true )
| ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
!= ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( X1 = X2 ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ X3
@ X4 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ X2
@ X1 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[],[f13]) ).
thf(f13,plain,
! [X2: $i > $o,X3: $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $o,X1: $i > $o,X4: $i > $o] :
( ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) ) )
| ( $true
= ( X0 @ X2 @ X1 ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV085^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire %s %d THM
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Jun 21 19:08:53 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.14/0.30 This is a TH0_THM_NEQ_NAR problem
% 0.14/0.30 Running higher-order theorem proving
% 0.14/0.30 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.15/0.31 % (14096)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.31 % (14098)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)
% 0.15/0.31 % (14096)Instruction limit reached!
% 0.15/0.31 % (14096)------------------------------
% 0.15/0.31 % (14096)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.31 % (14096)Termination reason: Unknown
% 0.15/0.31 % (14096)Termination phase: Saturation
% 0.15/0.31
% 0.15/0.31 % (14096)Memory used [KB]: 5373
% 0.15/0.31 % (14096)Time elapsed: 0.002 s
% 0.15/0.31 % (14096)Instructions burned: 2 (million)
% 0.15/0.31 % (14096)------------------------------
% 0.15/0.31 % (14096)------------------------------
% 0.15/0.32 % (14095)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.32 % (14094)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.32 % (14095)Refutation not found, incomplete strategy
% 0.15/0.32 % (14095)------------------------------
% 0.15/0.32 % (14095)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (14095)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32
% 0.15/0.32
% 0.15/0.32 % (14095)Memory used [KB]: 5500
% 0.15/0.32 % (14095)Time elapsed: 0.003 s
% 0.15/0.32 % (14095)Instructions burned: 1 (million)
% 0.15/0.32 % (14095)------------------------------
% 0.15/0.32 % (14095)------------------------------
% 0.15/0.32 % (14097)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.32 % (14099)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.32 % (14093)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.32 % (14094)Instruction limit reached!
% 0.15/0.32 % (14094)------------------------------
% 0.15/0.32 % (14094)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (14094)Termination reason: Unknown
% 0.15/0.32 % (14094)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (14094)Memory used [KB]: 5500
% 0.15/0.32 % (14094)Time elapsed: 0.004 s
% 0.15/0.32 % (14094)Instructions burned: 4 (million)
% 0.15/0.32 % (14094)------------------------------
% 0.15/0.32 % (14094)------------------------------
% 0.15/0.32 % (14097)Instruction limit reached!
% 0.15/0.32 % (14097)------------------------------
% 0.15/0.32 % (14097)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (14097)Termination reason: Unknown
% 0.15/0.32 % (14097)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (14097)Memory used [KB]: 5500
% 0.15/0.32 % (14097)Time elapsed: 0.003 s
% 0.15/0.32 % (14097)Instructions burned: 2 (million)
% 0.15/0.32 % (14097)------------------------------
% 0.15/0.32 % (14097)------------------------------
% 0.15/0.32 % (14098)First to succeed.
% 0.15/0.32 % (14100)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.32 % (14100)Instruction limit reached!
% 0.15/0.32 % (14100)------------------------------
% 0.15/0.32 % (14100)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (14100)Termination reason: Unknown
% 0.15/0.32 % (14100)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (14100)Memory used [KB]: 5500
% 0.15/0.32 % (14100)Time elapsed: 0.002 s
% 0.15/0.32 % (14100)Instructions burned: 3 (million)
% 0.15/0.32 % (14100)------------------------------
% 0.15/0.32 % (14100)------------------------------
% 0.15/0.32 % (14098)Refutation found. Thanks to Tanya!
% 0.15/0.32 % SZS status Theorem for theBenchmark
% 0.15/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.32 % (14098)------------------------------
% 0.15/0.32 % (14098)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (14098)Termination reason: Refutation
% 0.15/0.32
% 0.15/0.32 % (14098)Memory used [KB]: 5628
% 0.15/0.32 % (14098)Time elapsed: 0.011 s
% 0.15/0.32 % (14098)Instructions burned: 19 (million)
% 0.15/0.32 % (14098)------------------------------
% 0.15/0.32 % (14098)------------------------------
% 0.15/0.32 % (14092)Success in time 0.018 s
%------------------------------------------------------------------------------