%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV400^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 : Wed Feb 25 09:41:10 AM UTC 2026
% Result : Theorem 1.62s 1.65s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 3 unt; 0 typ; 3 def)
% Number of atoms : 711 ( 223 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 932 ( 107 ~; 124 |; 150 &; 520 @)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 215 ( 92 ^; 95 !; 28 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_5,type,
sP0: ( $i > $o ) > $o ).
thf(func_def_6,type,
sK1: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_8,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_9,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_12,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f205,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f176,f187,f195,f204]) ).
thf(f204,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f203]) ).
thf(f203,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f199,f169]) ).
thf(f169,plain,
( ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f167]) ).
thf(f167,definition,
( spl5_1
<=> ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f199,plain,
( ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
!= $true )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false = $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
!= $true )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f186,f43]) ).
thf(f43,plain,
! [X0: $i > $o] :
( ( ( cQ @ ( sK2 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $i > $o] :
( ( ( cQ @ ( sK2 @ X0 ) )
= $true )
| ( $true != $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i > $o] :
( ( $true != $true )
| ( ( cQ @ ( sK2 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f22,f19]) ).
thf(f19,plain,
! [X0: $i > $o] :
( ( ( sK1 @ X0 @ ( sK2 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i > $o] :
( ( ! [X2: $i] :
( ( ( cQ @ X2 )
= $true )
| ( ( sK1 @ X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( cP @ X3 )
= $true )
| ( ( sK1 @ X0 @ X3 )
!= $true ) )
& ( ( X0 @ ( sK2 @ X0 ) )
!= $true )
& ( ( sK1 @ X0 @ ( sK2 @ X0 ) )
= $true ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f13,f12]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ? [X1: $i > $o] :
( ! [X2: $i] :
( ( ( cQ @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( cP @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ? [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true ) ) )
=> ( ! [X2: $i] :
( ( ( cQ @ X2 )
= $true )
| ( ( sK1 @ X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( cP @ X3 )
= $true )
| ( ( sK1 @ X0 @ X3 )
!= $true ) )
& ? [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
& ( ( sK1 @ X0 @ X4 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: $i > $o] :
( ? [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
& ( ( sK1 @ X0 @ X4 )
= $true ) )
=> ( ( ( X0 @ ( sK2 @ X0 ) )
!= $true )
& ( ( sK1 @ X0 @ ( sK2 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ? [X1: $i > $o] :
( ! [X2: $i] :
( ( ( cQ @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( cP @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ? [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ? [X2: $i > $o] :
( ! [X3: $i] :
( ( ( cQ @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( ( cP @ X4 )
= $true )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X5: $i] :
( ( ( X0 @ X5 )
!= $true )
& ( ( X2 @ X5 )
= $true ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X2: $i > $o] :
( ! [X3: $i] :
( ( ( cQ @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( ( cP @ X4 )
= $true )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X5: $i] :
( ( ( X0 @ X5 )
!= $true )
& ( ( X2 @ X5 )
= $true ) ) )
| ( ( sP0 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X2: $i,X0: $i > $o] :
( ( ( sK1 @ X0 @ X2 )
!= $true )
| ( ( sP0 @ X0 )
!= $true )
| ( ( cQ @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f186,plain,
( ( $false
= ( cQ
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f184]) ).
thf(f184,definition,
( spl5_4
<=> ( $false
= ( cQ
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f195,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f194]) ).
thf(f194,plain,
( $false
| ~ spl5_1
| ~ spl5_3 ),
inference(subsumption_resolution,[status(thm)],[f190,f169]) ).
thf(f190,plain,
( ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
!= $true )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
!= $true )
| ( $false = $true )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f182,f37]) ).
thf(f37,plain,
! [X0: $i > $o] :
( ( ( cP @ ( sK2 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i > $o] :
( ( ( cP @ ( sK2 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $i > $o] :
( ( $true != $true )
| ( ( sP0 @ X0 )
!= $true )
| ( ( cP @ ( sK2 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f21,f19]) ).
thf(f21,plain,
! [X3: $i,X0: $i > $o] :
( ( ( sK1 @ X0 @ X3 )
!= $true )
| ( ( cP @ X3 )
= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f182,plain,
( ( $false
= ( cP
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f180]) ).
thf(f180,definition,
( spl5_3
<=> ( $false
= ( cP
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f187,plain,
( spl5_3
| spl5_4
| ~ spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f178,f167,f184,f180]) ).
thf(f178,plain,
( ( $false
= ( cP
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) )
| ( $false
= ( cQ
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ( $false
= ( cP
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) )
| ( $false
= ( cQ
@ ( sK2
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) ) )
| ( $true != $true )
| ~ spl5_1 ),
inference(superposition,[status(thm)],[f31,f169]) ).
thf(f31,plain,
! [X3: $i > $o,X4: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) )
!= $true )
| ( $false
= ( X4
@ ( sK2
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) ) )
| ( ( X3
@ ( sK2
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X3: $i > $o,X4: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) )
!= $true )
| ( ( ( X4
@ ( sK2
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
& ( X3
@ ( sK2
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: $i > $o,X4: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
!= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( sK2 @ X0 ) )
!= $true )
| ( ( sP0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f176,plain,
spl5_1,
inference(avatar_split_clause,[status(thm)],[f175,f167]) ).
thf(f175,plain,
( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f158,f138]) ).
thf(f138,plain,
! [X0: $i > $o] :
( ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f137]) ).
thf(f137,plain,
! [X0: $i > $o] :
( ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true )
| ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X0: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true )
| ( ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
& ( cP
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
! [X0: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) )
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
! [X0: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( $true != $true )
| ( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) )
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true )
| ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X0: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) )
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( $true != $true )
| ( ( X0
@ ( sK4
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
& ( cP @ Y0 ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f25,f55]) ).
thf(f55,plain,
! [X3: $i > $o,X4: $i > $o] :
( ( ( X3
@ ( sK3
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
= $true )
| ( ( X4
@ ( sK4
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X3: $i > $o,X4: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) )
= $true )
| ( ( ( X4
@ ( sK3
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
& ( X3
@ ( sK3
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) ) )
= $true )
| ( ( X4
@ ( sK4
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X3: $i > $o,X4: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) )
= $true )
| ( ( ( X4
@ ( sK4
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
& ( X3
@ ( sK4
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) ) )
= $true )
| ( ( ( X4
@ ( sK3
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
& ( X3
@ ( sK3
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X3: $i > $o,X4: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) )
@ ( sK4
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) )
@ ( sK3
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
& ( X3 @ Y0 ) ) )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( sK4 @ X0 ) )
= $true )
| ( ( X0 @ ( sK3 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i > $o] :
( ( ( sP0 @ X0 )
= $true )
| ( ( ( cP @ ( sK3 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK3 @ X0 ) )
= $true ) )
| ( ( ( cQ @ ( sK4 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK4 @ X0 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f15,f17,f16]) ).
thf(f16,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
=> ( ( ( cP @ ( sK3 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK3 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: $i > $o] :
( ? [X2: $i] :
( ( ( cQ @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
=> ( ( ( cQ @ ( sK4 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK4 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: $i > $o] :
( ( ( sP0 @ X0 )
= $true )
| ? [X1: $i] :
( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
| ? [X2: $i] :
( ( ( cQ @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ( ( sP0 @ X0 )
= $true )
| ? [X1: $i] :
( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
| ? [X6: $i] :
( ( ( cQ @ X6 )
!= $true )
& ( ( X0 @ X6 )
= $true ) ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ? [X2: $i > $o] :
( ! [X3: $i] :
( ( ( cQ @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: $i] :
( ( ( cP @ X4 )
= $true )
| ( ( X2 @ X4 )
!= $true ) )
& ? [X5: $i] :
( ( ( X0 @ X5 )
!= $true )
& ( ( X2 @ X5 )
= $true ) ) )
| ? [X1: $i] :
( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
| ? [X6: $i] :
( ( ( cQ @ X6 )
!= $true )
& ( ( X0 @ X6 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
| ? [X6: $i] :
( ( ( cQ @ X6 )
!= $true )
& ( ( X0 @ X6 )
= $true ) )
| ? [X2: $i > $o] :
( ? [X5: $i] :
( ( ( X0 @ X5 )
!= $true )
& ( ( X2 @ X5 )
= $true ) )
& ! [X4: $i] :
( ( ( cP @ X4 )
= $true )
| ( ( X2 @ X4 )
!= $true ) )
& ! [X3: $i] :
( ( ( cQ @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $o] :
( ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( cP @ X1 )
= $true ) )
& ! [X6: $i] :
( ( ( X0 @ X6 )
= $true )
=> ( ( cQ @ X6 )
= $true ) )
& ! [X2: $i > $o] :
( ( ! [X4: $i] :
( ( ( X2 @ X4 )
= $true )
=> ( ( cP @ X4 )
= $true ) )
& ! [X3: $i] :
( ( ( X2 @ X3 )
= $true )
=> ( ( cQ @ X3 )
= $true ) ) )
=> ! [X5: $i] :
( ( ( X2 @ X5 )
= $true )
=> ( ( X0 @ X5 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
& ! [X2: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( cQ @ X3 ) )
& ! [X4: $i] :
( ( X2 @ X4 )
=> ( cP @ X4 ) ) )
=> ! [X5: $i] :
( ( X2 @ X5 )
=> ( X0 @ X5 ) ) )
& ! [X6: $i] :
( ( X0 @ X6 )
=> ( cQ @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
& ! [X2: $i > $o] :
( ( ! [X1: $i] :
( ( X2 @ X1 )
=> ( cQ @ X1 ) )
& ! [X1: $i] :
( ( X2 @ X1 )
=> ( cP @ X1 ) ) )
=> ! [X1: $i] :
( ( X2 @ X1 )
=> ( X0 @ X1 ) ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cQ @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cP @ X1 ) )
& ! [X2: $i > $o] :
( ( ! [X1: $i] :
( ( X2 @ X1 )
=> ( cQ @ X1 ) )
& ! [X1: $i] :
( ( X2 @ X1 )
=> ( cP @ X1 ) ) )
=> ! [X1: $i] :
( ( X2 @ X1 )
=> ( X0 @ X1 ) ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cQ @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Z7iZWmoUqd/DTF2THF_30570.p',cTHM590_pme) ).
thf(f25,plain,
! [X0: $i > $o] :
( ( ( cP @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK4 @ X0 ) )
= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f158,plain,
( ( ( cQ
@ ( sK4
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) )
!= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( $true != $true )
| ( ( cQ
@ ( sK4
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( $true != $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) )
= $true )
| ( ( cQ
@ ( sK4
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( cP @ Y0 ) ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f26,f116]) ).
thf(f116,plain,
! [X0: $i > $o] :
( ( ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: $i > $o] :
( ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) )
= $true )
| ( ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X0: $i > $o] :
( ( ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( ( cQ
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
& ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f112]) ).
thf(f112,plain,
! [X0: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) )
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: $i > $o] :
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) )
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f108]) ).
thf(f108,plain,
! [X0: $i > $o] :
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) )
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) )
= $true )
| ( ( X0
@ ( sK3
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) ) )
= $true )
| ( ( sP0
@ ^ [Y0: $i] :
( ( cQ @ Y0 )
& ( X0 @ Y0 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f24,f55]) ).
thf(f24,plain,
! [X0: $i > $o] :
( ( ( cQ @ ( sK4 @ X0 ) )
!= $true )
| ( ( sP0 @ X0 )
= $true )
| ( ( X0 @ ( sK3 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f26,plain,
! [X0: $i > $o] :
( ( ( cP @ ( sK3 @ X0 ) )
!= $true )
| ( ( cQ @ ( sK4 @ X0 ) )
!= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV400^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n004.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:46:11 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEV400^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : TPS problem THM590
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : A simple theorem about existence of intersection.
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0451 [Bro09]
% 0.19/0.46 % : THM590 [TPS]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.50 v9.1.0, 0.62 v9.0.0, 0.67 v8.2.0, 0.64 v8.1.0, 0.75 v7.4.0, 0.67 v7.3.0, 0.70 v7.2.0, 0.62 v7.1.0, 0.57 v7.0.0, 0.75 v6.4.0, 0.71 v6.3.0, 0.67 v5.5.0, 0.80 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.19/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.46 % Number of connectives : 19 ( 0 ~; 0 |; 3 &; 10 @)
% 0.19/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.19/0.46 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % : Polymorphic definitions expanded.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(cQ,type,
% 0.19/0.46 cQ: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cP,type,
% 0.19/0.46 cP: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM590_pme,conjecture,
% 0.19/0.46 ? [S: $i > $o] :
% 0.19/0.46 ( ! [Xx: $i] :
% 0.19/0.46 ( ( S @ Xx )
% 0.19/0.46 => ( cP @ Xx ) )
% 0.19/0.46 & ! [Xx: $i] :
% 0.19/0.46 ( ( S @ Xx )
% 0.19/0.46 => ( cQ @ Xx ) )
% 0.19/0.46 & ! [R: $i > $o] :
% 0.19/0.46 ( ( ! [Xx: $i] :
% 0.19/0.46 ( ( R @ Xx )
% 0.19/0.46 => ( cP @ Xx ) )
% 0.19/0.46 & ! [Xx: $i] :
% 0.19/0.46 ( ( R @ Xx )
% 0.19/0.46 => ( cQ @ Xx ) ) )
% 0.19/0.46 => ! [Xx: $i] :
% 0.19/0.46 ( ( R @ Xx )
% 0.19/0.46 => ( S @ Xx ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.54/1.25 ---- Embedded in THF ---
% 1.54/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.25 %%% Generated on Tue Feb 24 12:46:12 EST 2026
% 1.54/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.25 %%% Logic specification used:
% 1.54/1.25 %%% thf(spec, logic, $$dhol).
% 1.54/1.25
% 1.54/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Z7iZWmoUqd/DTF2DTF30570.p
% See solution above
% 1.54/1.25 ------------------------
% 1.54/1.26 ---- Cleaned THF ---
% 1.54/1.26 thf(cQ,type,
% 1.54/1.26 cQ: $i > $o ).
% 1.54/1.26
% 1.54/1.26 thf(cP,type,
% 1.54/1.26 cP: $i > $o ).
% 1.54/1.26
% 1.54/1.26 thf(cTHM590_pme,conjecture,
% 1.54/1.26 ? [S: $i > $o] :
% 1.54/1.26 ( ! [Xx: $i] :
% 1.54/1.26 ( ( S @ Xx )
% 1.54/1.26 => ( cP @ Xx ) )
% 1.54/1.26 & ! [Xx: $i] :
% 1.54/1.26 ( ( S @ Xx )
% 1.54/1.26 => ( cQ @ Xx ) )
% 1.54/1.26 & ! [R: $i > $o] :
% 1.54/1.26 ( ( ! [Xx: $i] :
% 1.54/1.26 ( ( R @ Xx )
% 1.54/1.26 => ( cP @ Xx ) )
% 1.54/1.26 & ! [Xx: $i] :
% 1.54/1.26 ( ( R @ Xx )
% 1.54/1.26 => ( cQ @ Xx ) ) )
% 1.54/1.26 => ! [Xx: $i] :
% 1.54/1.26 ( ( R @ Xx )
% 1.54/1.26 => ( S @ Xx ) ) ) ) ).
% 1.54/1.26 ------------------------
% 1.54/1.27 % (30764)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/275Mi)
% 1.54/1.27 % (30759)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/183Mi)
% 1.54/1.27 % (30763)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/2Mi)
% 1.54/1.27 % (30763)Instruction limit reached!
% 1.54/1.27 % (30763)------------------------------
% 1.54/1.27 % (30763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.27 % (30763)Termination reason: Unknown
% 1.54/1.27 % (30763)Termination phase: Saturation
% 1.54/1.27
% 1.54/1.27 % (30763)Memory used [KB]: 5500
% 1.54/1.27 % (30763)Time elapsed: 0.002 s
% 1.54/1.27 % (30763)Instructions burned: 2 (million)
% 1.54/1.27 % (30763)------------------------------
% 1.54/1.27 % (30763)------------------------------
% 1.54/1.28 % (30764)Refutation not found, incomplete strategy
% 1.54/1.28 % (30764)------------------------------
% 1.54/1.28 % (30764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (30764)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.28
% 1.54/1.28
% 1.54/1.28 % (30764)Memory used [KB]: 5500
% 1.54/1.28 % (30764)Time elapsed: 0.007 s
% 1.54/1.28 % (30764)Instructions burned: 16 (million)
% 1.54/1.28 % (30764)------------------------------
% 1.54/1.28 % (30764)------------------------------
% 1.54/1.28 % (30760)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 DTF2THF_30570 for (2999ds/4Mi)
% 1.54/1.28 % (30761)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 DTF2THF_30570 for (2999ds/27Mi)
% 1.54/1.28 % (30762)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/2Mi)
% 1.54/1.28 % (30762)Instruction limit reached!
% 1.54/1.28 % (30762)------------------------------
% 1.54/1.28 % (30762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (30762)Termination reason: Unknown
% 1.54/1.28 % (30762)Termination phase: Property scanning
% 1.54/1.28
% 1.54/1.28 % (30762)Memory used [KB]: 895
% 1.54/1.28 % (30762)Time elapsed: 0.003 s
% 1.54/1.28 % (30762)Instructions burned: 2 (million)
% 1.54/1.28 % (30762)------------------------------
% 1.54/1.28 % (30762)------------------------------
% 1.54/1.28 % (30765)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/18Mi)
% 1.54/1.28 % (30760)Instruction limit reached!
% 1.54/1.28 % (30760)------------------------------
% 1.54/1.28 % (30760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (30760)Termination reason: Unknown
% 1.54/1.28 % (30760)Termination phase: Saturation
% 1.54/1.28
% 1.54/1.28 % (30760)Memory used [KB]: 5500
% 1.54/1.28 % (30760)Time elapsed: 0.005 s
% 1.54/1.28 % (30760)Instructions burned: 4 (million)
% 1.54/1.28 % (30760)------------------------------
% 1.54/1.28 % (30760)------------------------------
% 1.54/1.29 % (30767)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/37Mi)
% 1.54/1.30 % (30765)Instruction limit reached!
% 1.54/1.30 % (30765)------------------------------
% 1.54/1.30 % (30765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (30765)Termination reason: Unknown
% 1.54/1.30 % (30765)Termination phase: Saturation
% 1.54/1.30
% 1.54/1.30 % (30765)Memory used [KB]: 5628
% 1.54/1.30 % (30765)Time elapsed: 0.017 s
% 1.54/1.30 % (30765)Instructions burned: 18 (million)
% 1.54/1.30 % (30765)------------------------------
% 1.54/1.30 % (30765)------------------------------
% 1.54/1.30 % (30761)Instruction limit reached!
% 1.54/1.30 % (30761)------------------------------
% 1.54/1.30 % (30761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (30761)Termination reason: Unknown
% 1.54/1.30 % (30761)Termination phase: Saturation
% 1.54/1.30
% 1.54/1.30 % (30761)Memory used [KB]: 5628
% 1.54/1.30 % (30761)Time elapsed: 0.019 s
% 1.54/1.30 % (30761)Instructions burned: 27 (million)
% 1.54/1.30 % (30761)------------------------------
% 1.54/1.30 % (30761)------------------------------
% 1.62/1.30 % (30768)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/15Mi)
% 1.62/1.30 % (30769)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/3Mi)
% 1.62/1.30 % (30767)Instruction limit reached!
% 1.62/1.30 % (30767)------------------------------
% 1.62/1.30 % (30767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (30767)Termination reason: Unknown
% 1.62/1.30 % (30767)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (30767)Memory used [KB]: 5756
% 1.62/1.30 % (30767)Time elapsed: 0.014 s
% 1.62/1.30 % (30767)Instructions burned: 40 (million)
% 1.62/1.30 % (30767)------------------------------
% 1.62/1.30 % (30767)------------------------------
% 1.62/1.30 % (30769)Instruction limit reached!
% 1.62/1.30 % (30769)------------------------------
% 1.62/1.30 % (30769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (30769)Termination reason: Unknown
% 1.62/1.30 % (30769)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (30769)Memory used [KB]: 5500
% 1.62/1.30 % (30769)Time elapsed: 0.004 s
% 1.62/1.30 % (30769)Instructions burned: 3 (million)
% 1.62/1.30 % (30769)------------------------------
% 1.62/1.30 % (30769)------------------------------
% 1.62/1.30 % (30766)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/3Mi)
% 1.62/1.31 % (30766)Instruction limit reached!
% 1.62/1.31 % (30766)------------------------------
% 1.62/1.31 % (30766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (30766)Termination reason: Unknown
% 1.62/1.31 % (30766)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (30766)Memory used [KB]: 5500
% 1.62/1.31 % (30766)Time elapsed: 0.005 s
% 1.62/1.31 % (30766)Instructions burned: 3 (million)
% 1.62/1.31 % (30766)------------------------------
% 1.62/1.31 % (30766)------------------------------
% 1.62/1.31 % (30768)Instruction limit reached!
% 1.62/1.31 % (30768)------------------------------
% 1.62/1.31 % (30768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (30768)Termination reason: Unknown
% 1.62/1.31 % (30768)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (30768)Memory used [KB]: 5628
% 1.62/1.31 % (30768)Time elapsed: 0.012 s
% 1.62/1.31 % (30768)Instructions burned: 15 (million)
% 1.62/1.31 % (30768)------------------------------
% 1.62/1.31 % (30768)------------------------------
% 1.62/1.31 % (30772)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/16Mi)
% 1.62/1.31 % (30770)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/1041Mi)
% 1.62/1.31 % (30771)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/7Mi)
% 1.62/1.32 % (30772)Instruction limit reached!
% 1.62/1.32 % (30772)------------------------------
% 1.62/1.32 % (30772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (30772)Termination reason: Unknown
% 1.62/1.32 % (30772)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (30772)Memory used [KB]: 5628
% 1.62/1.32 % (30772)Time elapsed: 0.008 s
% 1.62/1.32 % (30772)Instructions burned: 16 (million)
% 1.62/1.32 % (30772)------------------------------
% 1.62/1.32 % (30772)------------------------------
% 1.62/1.32 % (30771)Instruction limit reached!
% 1.62/1.32 % (30771)------------------------------
% 1.62/1.32 % (30771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (30771)Termination reason: Unknown
% 1.62/1.32 % (30771)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (30771)Memory used [KB]: 1023
% 1.62/1.32 % (30771)Time elapsed: 0.007 s
% 1.62/1.32 % (30771)Instructions burned: 8 (million)
% 1.62/1.32 % (30771)------------------------------
% 1.62/1.32 % (30771)------------------------------
% 1.62/1.32 % (30773)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/3Mi)
% 1.62/1.32 % (30773)Instruction limit reached!
% 1.62/1.32 % (30773)------------------------------
% 1.62/1.32 % (30773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (30773)Termination reason: Unknown
% 1.62/1.32 % (30773)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (30773)Memory used [KB]: 5500
% 1.62/1.32 % (30773)Time elapsed: 0.004 s
% 1.62/1.32 % (30773)Instructions burned: 3 (million)
% 1.62/1.32 % (30773)------------------------------
% 1.62/1.32 % (30773)------------------------------
% 1.62/1.32 % (30774)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/3Mi)
% 1.62/1.32 % (30774)Instruction limit reached!
% 1.62/1.32 % (30774)------------------------------
% 1.62/1.32 % (30774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (30774)Termination reason: Unknown
% 1.62/1.32 % (30774)Termination phase: Property scanning
% 1.62/1.32
% 1.62/1.32 % (30774)Memory used [KB]: 1023
% 1.62/1.32 % (30774)Time elapsed: 0.003 s
% 1.62/1.32 % (30774)Instructions burned: 3 (million)
% 1.62/1.32 % (30774)------------------------------
% 1.62/1.32 % (30774)------------------------------
% 1.62/1.32 % (30759)Instruction limit reached!
% 1.62/1.32 % (30759)------------------------------
% 1.62/1.32 % (30759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (30759)Termination reason: Unknown
% 1.62/1.32 % (30759)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (30759)Memory used [KB]: 6908
% 1.62/1.32 % (30759)Time elapsed: 0.055 s
% 1.62/1.32 % (30759)Instructions burned: 185 (million)
% 1.62/1.32 % (30759)------------------------------
% 1.62/1.32 % (30759)------------------------------
% 1.62/1.33 % (30775)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/7Mi)
% 1.62/1.33 % (30775)Instruction limit reached!
% 1.62/1.33 % (30775)------------------------------
% 1.62/1.33 % (30775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (30775)Termination reason: Unknown
% 1.62/1.33 % (30775)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (30775)Memory used [KB]: 5500
% 1.62/1.33 % (30775)Time elapsed: 0.007 s
% 1.62/1.33 % (30775)Instructions burned: 8 (million)
% 1.62/1.33 % (30775)------------------------------
% 1.62/1.33 % (30775)------------------------------
% 1.62/1.33 % (30780)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/6Mi)
% 1.62/1.34 % (30780)Instruction limit reached!
% 1.62/1.34 % (30780)------------------------------
% 1.62/1.34 % (30780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (30780)Termination reason: Unknown
% 1.62/1.34 % (30780)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (30780)Memory used [KB]: 5500
% 1.62/1.34 % (30780)Time elapsed: 0.004 s
% 1.62/1.34 % (30780)Instructions burned: 8 (million)
% 1.62/1.34 % (30780)------------------------------
% 1.62/1.34 % (30780)------------------------------
% 1.62/1.34 % (30777)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/4Mi)
% 1.62/1.34 % (30778)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/18Mi)
% 1.62/1.34 % (30777)Instruction limit reached!
% 1.62/1.34 % (30777)------------------------------
% 1.62/1.34 % (30777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (30777)Termination reason: Unknown
% 1.62/1.34 % (30777)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (30777)Memory used [KB]: 5500
% 1.62/1.34 % (30777)Time elapsed: 0.029 s
% 1.62/1.34 % (30777)Instructions burned: 5 (million)
% 1.62/1.34 % (30777)------------------------------
% 1.62/1.34 % (30777)------------------------------
% 1.62/1.34 % (30779)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/710Mi)
% 1.62/1.34 % (30776)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/3Mi)
% 1.62/1.34 % (30776)Instruction limit reached!
% 1.62/1.34 % (30776)------------------------------
% 1.62/1.34 % (30776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (30776)Termination reason: Unknown
% 1.62/1.34 % (30776)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (30776)Memory used [KB]: 5500
% 1.62/1.34 % (30776)Time elapsed: 0.003 s
% 1.62/1.34 % (30776)Instructions burned: 3 (million)
% 1.62/1.34 % (30776)------------------------------
% 1.62/1.34 % (30776)------------------------------
% 1.62/1.35 % (30778)Refutation not found, incomplete strategy
% 1.62/1.35 % (30778)------------------------------
% 1.62/1.35 % (30778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (30778)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.35
% 1.62/1.35
% 1.62/1.35 % (30778)Memory used [KB]: 5500
% 1.62/1.35 % (30778)Time elapsed: 0.010 s
% 1.62/1.35 % (30778)Instructions burned: 10 (million)
% 1.62/1.35 % (30778)------------------------------
% 1.62/1.35 % (30778)------------------------------
% 1.62/1.35 % (30782)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/21Mi)
% 1.62/1.35 % (30781)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/902Mi)
% 1.62/1.35 % (30783)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/5Mi)
% 1.62/1.35 % (30783)Instruction limit reached!
% 1.62/1.35 % (30783)------------------------------
% 1.62/1.35 % (30783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (30783)Termination reason: Unknown
% 1.62/1.35 % (30783)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (30783)Memory used [KB]: 5500
% 1.62/1.35 % (30783)Time elapsed: 0.003 s
% 1.62/1.35 % (30783)Instructions burned: 5 (million)
% 1.62/1.35 % (30783)------------------------------
% 1.62/1.35 % (30783)------------------------------
% 1.62/1.35 % (30782)Instruction limit reached!
% 1.62/1.35 % (30782)------------------------------
% 1.62/1.35 % (30782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (30782)Termination reason: Unknown
% 1.62/1.35 % (30782)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (30782)Memory used [KB]: 5628
% 1.62/1.35 % (30782)Time elapsed: 0.008 s
% 1.62/1.35 % (30782)Instructions burned: 21 (million)
% 1.62/1.35 % (30782)------------------------------
% 1.62/1.35 % (30782)------------------------------
% 1.62/1.36 % (30784)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/6Mi)
% 1.62/1.36 % (30786)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/779Mi)
% 1.62/1.36 % (30784)Instruction limit reached!
% 1.62/1.36 % (30784)------------------------------
% 1.62/1.36 % (30784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (30784)Termination reason: Unknown
% 1.62/1.36 % (30784)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (30784)Memory used [KB]: 5500
% 1.62/1.36 % (30784)Time elapsed: 0.004 s
% 1.62/1.36 % (30784)Instructions burned: 7 (million)
% 1.62/1.36 % (30784)------------------------------
% 1.62/1.36 % (30784)------------------------------
% 1.62/1.36 % (30785)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/377Mi)
% 1.62/1.37 % (30787)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/19Mi)
% 1.62/1.37 % (30787)Instruction limit reached!
% 1.62/1.37 % (30787)------------------------------
% 1.62/1.37 % (30787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (30787)Termination reason: Unknown
% 1.62/1.37 % (30787)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (30787)Memory used [KB]: 5500
% 1.62/1.37 % (30787)Time elapsed: 0.007 s
% 1.62/1.37 % (30787)Instructions burned: 20 (million)
% 1.62/1.37 % (30787)------------------------------
% 1.62/1.37 % (30787)------------------------------
% 1.62/1.37 % (30788)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30570 for (2998ds/879Mi)
% 1.62/1.38 % (30794)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30570 for (2998ds/17Mi)
% 1.62/1.39 % (30794)Instruction limit reached!
% 1.62/1.39 % (30794)------------------------------
% 1.62/1.39 % (30794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (30794)Termination reason: Unknown
% 1.62/1.39 % (30794)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (30794)Memory used [KB]: 5628
% 1.62/1.39 % (30794)Time elapsed: 0.010 s
% 1.62/1.39 % (30794)Instructions burned: 19 (million)
% 1.62/1.39 % (30794)------------------------------
% 1.62/1.39 % (30794)------------------------------
% 1.62/1.40 % (30805)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2998ds/3Mi)
% 1.62/1.40 % (30805)Instruction limit reached!
% 1.62/1.40 % (30805)------------------------------
% 1.62/1.40 % (30805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (30805)Termination reason: Unknown
% 1.62/1.40 % (30805)Termination phase: Property scanning
% 1.62/1.40
% 1.62/1.40 % (30805)Memory used [KB]: 1023
% 1.62/1.40 % (30805)Time elapsed: 0.002 s
% 1.62/1.40 % (30805)Instructions burned: 3 (million)
% 1.62/1.40 % (30805)------------------------------
% 1.62/1.40 % (30805)------------------------------
% 1.62/1.41 % (30806)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30570 for (2998ds/30Mi)
% 1.62/1.42 % (30806)Instruction limit reached!
% 1.62/1.42 % (30806)------------------------------
% 1.62/1.42 % (30806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.42 % (30806)Termination reason: Unknown
% 1.62/1.42 % (30806)Termination phase: Saturation
% 1.62/1.42
% 1.62/1.42 % (30806)Memory used [KB]: 5628
% 1.62/1.42 % (30806)Time elapsed: 0.011 s
% 1.62/1.42 % (30806)Instructions burned: 33 (million)
% 1.62/1.42 % (30806)------------------------------
% 1.62/1.42 % (30806)------------------------------
% 1.62/1.43 % (30807)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30570 for (2998ds/127Mi)
% 1.62/1.47 % (30807)Instruction limit reached!
% 1.62/1.47 % (30807)------------------------------
% 1.62/1.47 % (30807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.47 % (30807)Termination reason: Unknown
% 1.62/1.47 % (30807)Termination phase: Saturation
% 1.62/1.47
% 1.62/1.47 % (30807)Memory used [KB]: 6012
% 1.62/1.47 % (30807)Time elapsed: 0.041 s
% 1.62/1.47 % (30807)Instructions burned: 128 (million)
% 1.62/1.47 % (30807)------------------------------
% 1.62/1.47 % (30807)------------------------------
% 1.62/1.48 % (30808)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/100Mi)
% 1.62/1.48 % (30808)Refutation not found, incomplete strategy
% 1.62/1.48 % (30808)------------------------------
% 1.62/1.48 % (30808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (30808)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.48
% 1.62/1.48
% 1.62/1.48 % (30808)Memory used [KB]: 5500
% 1.62/1.48 % (30808)Time elapsed: 0.005 s
% 1.62/1.48 % (30808)Instructions burned: 11 (million)
% 1.62/1.48 % (30808)------------------------------
% 1.62/1.48 % (30808)------------------------------
% 1.62/1.49 % (30809)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/3Mi)
% 1.62/1.49 % (30785)Instruction limit reached!
% 1.62/1.49 % (30785)------------------------------
% 1.62/1.49 % (30785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.49 % (30785)Termination reason: Unknown
% 1.62/1.49 % (30785)Termination phase: Saturation
% 1.62/1.49
% 1.62/1.49 % (30785)Memory used [KB]: 6012
% 1.62/1.49 % (30785)Time elapsed: 0.132 s
% 1.62/1.49 % (30785)Instructions burned: 377 (million)
% 1.62/1.49 % (30785)------------------------------
% 1.62/1.49 % (30785)------------------------------
% 1.62/1.50 % (30809)Instruction limit reached!
% 1.62/1.50 % (30809)------------------------------
% 1.62/1.50 % (30809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.50 % (30809)Termination reason: Unknown
% 1.62/1.50 % (30809)Termination phase: Saturation
% 1.62/1.50
% 1.62/1.50 % (30809)Memory used [KB]: 5500
% 1.62/1.50 % (30809)Time elapsed: 0.002 s
% 1.62/1.50 % (30809)Instructions burned: 3 (million)
% 1.62/1.50 % (30809)------------------------------
% 1.62/1.50 % (30809)------------------------------
% 1.62/1.50 % (30810)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/20Mi)
% 1.62/1.50 % (30811)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/86Mi)
% 1.62/1.51 % (30810)Instruction limit reached!
% 1.62/1.51 % (30810)------------------------------
% 1.62/1.51 % (30810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.51 % (30810)Termination reason: Unknown
% 1.62/1.51 % (30810)Termination phase: Saturation
% 1.62/1.51
% 1.62/1.51 % (30810)Memory used [KB]: 5628
% 1.62/1.51 % (30810)Time elapsed: 0.009 s
% 1.62/1.51 % (30810)Instructions burned: 21 (million)
% 1.62/1.51 % (30810)------------------------------
% 1.62/1.51 % (30810)------------------------------
% 1.62/1.52 % (30812)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/107Mi)
% 1.62/1.53 % (30812)Refutation not found, incomplete strategy
% 1.62/1.53 % (30812)------------------------------
% 1.62/1.53 % (30812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.53 % (30812)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.53
% 1.62/1.53
% 1.62/1.53 % (30812)Memory used [KB]: 5628
% 1.62/1.53 % (30812)Time elapsed: 0.009 s
% 1.62/1.53 % (30812)Instructions burned: 20 (million)
% 1.62/1.53 % (30812)------------------------------
% 1.62/1.53 % (30812)------------------------------
% 1.62/1.53 % (30811)Instruction limit reached!
% 1.62/1.53 % (30811)------------------------------
% 1.62/1.53 % (30811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.53 % (30811)Termination reason: Unknown
% 1.62/1.53 % (30811)Termination phase: Saturation
% 1.62/1.53
% 1.62/1.53 % (30811)Memory used [KB]: 6012
% 1.62/1.53 % (30811)Time elapsed: 0.028 s
% 1.62/1.53 % (30811)Instructions burned: 88 (million)
% 1.62/1.53 % (30811)------------------------------
% 1.62/1.53 % (30811)------------------------------
% 1.62/1.54 % (30814)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/448Mi)
% 1.62/1.54 % (30813)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/39Mi)
% 1.62/1.55 % (30813)Instruction limit reached!
% 1.62/1.55 % (30813)------------------------------
% 1.62/1.55 % (30813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.55 % (30813)Termination reason: Unknown
% 1.62/1.55 % (30813)Termination phase: Saturation
% 1.62/1.55
% 1.62/1.55 % (30813)Memory used [KB]: 5756
% 1.62/1.55 % (30813)Time elapsed: 0.015 s
% 1.62/1.55 % (30813)Instructions burned: 41 (million)
% 1.62/1.55 % (30813)------------------------------
% 1.62/1.55 % (30813)------------------------------
% 1.62/1.56 % (30815)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_30570 for (2997ds/46Mi)
% 1.62/1.58 % (30779)Instruction limit reached!
% 1.62/1.58 % (30779)------------------------------
% 1.62/1.58 % (30779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.58 % (30779)Termination reason: Unknown
% 1.62/1.58 % (30779)Termination phase: Saturation
% 1.62/1.58
% 1.62/1.58 % (30779)Memory used [KB]: 7036
% 1.62/1.58 % (30779)Time elapsed: 0.241 s
% 1.62/1.58 % (30779)Instructions burned: 711 (million)
% 1.62/1.58 % (30779)------------------------------
% 1.62/1.58 % (30779)------------------------------
% 1.62/1.58 % (30815)Instruction limit reached!
% 1.62/1.58 % (30815)------------------------------
% 1.62/1.58 % (30815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.58 % (30815)Termination reason: Unknown
% 1.62/1.58 % (30815)Termination phase: Saturation
% 1.62/1.58
% 1.62/1.58 % (30815)Memory used [KB]: 5756
% 1.62/1.58 % (30815)Time elapsed: 0.019 s
% 1.62/1.58 % (30815)Instructions burned: 47 (million)
% 1.62/1.58 % (30815)------------------------------
% 1.62/1.58 % (30815)------------------------------
% 1.62/1.59 % (30826)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_30570 for (2996ds/98Mi)
% 1.62/1.59 % (30828)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_30570 for (2996ds/507Mi)
% 1.62/1.61 % (30786)Instruction limit reached!
% 1.62/1.61 % (30786)------------------------------
% 1.62/1.61 % (30786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.61 % (30786)Termination reason: Unknown
% 1.62/1.61 % (30786)Termination phase: Saturation
% 1.62/1.61
% 1.62/1.61 % (30786)Memory used [KB]: 6396
% 1.62/1.61 % (30786)Time elapsed: 0.248 s
% 1.62/1.61 % (30786)Instructions burned: 780 (million)
% 1.62/1.61 % (30786)------------------------------
% 1.62/1.61 % (30786)------------------------------
% 1.62/1.62 % (30840)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_30570 for (2996ds/149Mi)
% 1.62/1.62 % (30826)Instruction limit reached!
% 1.62/1.62 % (30826)------------------------------
% 1.62/1.62 % (30826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.62 % (30826)Termination reason: Unknown
% 1.62/1.62 % (30826)Termination phase: Saturation
% 1.62/1.62
% 1.62/1.62 % (30826)Memory used [KB]: 1151
% 1.62/1.62 % (30826)Time elapsed: 0.034 s
% 1.62/1.62 % (30826)Instructions burned: 100 (million)
% 1.62/1.62 % (30826)------------------------------
% 1.62/1.62 % (30826)------------------------------
% 1.62/1.63 % (30846)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30570 for (2996ds/39Mi)
% 1.62/1.63 % (30781)Instruction limit reached!
% 1.62/1.63 % (30781)------------------------------
% 1.62/1.63 % (30781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.63 % (30781)Termination reason: Unknown
% 1.62/1.63 % (30781)Termination phase: Saturation
% 1.62/1.63
% 1.62/1.63 % (30781)Memory used [KB]: 6012
% 1.62/1.63 % (30781)Time elapsed: 0.289 s
% 1.62/1.63 % (30781)Instructions burned: 902 (million)
% 1.62/1.63 % (30781)------------------------------
% 1.62/1.63 % (30781)------------------------------
% 1.62/1.64 % (30846)First to succeed.
% 1.62/1.64 % (30854)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30570 for (2996ds/6Mi)
% 1.62/1.65 % (30846)Refutation found. Thanks to Tanya!
% 1.62/1.65 % SZS status Theorem for DTF2THF_30570
% 1.62/1.65 % SZS output start Proof for DTF2THF_30570
% 1.62/1.65 thf(func_def_0, type, cQ: $i > $o).
% 1.62/1.65 thf(func_def_1, type, cP: $i > $o).
% 1.62/1.65 thf(func_def_5, type, sP0: ($i > $o) > $o).
% 1.62/1.65 thf(func_def_6, type, sK1: ($i > $o) > $i > $o).
% 1.62/1.65 thf(func_def_7, type, sK2: ($i > $o) > $i).
% 1.62/1.65 thf(func_def_8, type, sK3: ($i > $o) > $i).
% 1.62/1.65 thf(func_def_9, type, sK4: ($i > $o) > $i).
% 1.62/1.65 thf(func_def_12, type, ph6: !>[X0: $tType]:(X0)).
% 1.62/1.65 thf(f205,plain,(
% 1.62/1.65 $false),
% 1.62/1.65 inference(avatar_sat_refutation,[status(thm)],[f176,f187,f195,f204])).
% 1.62/1.65 thf(f204,plain,(
% 1.62/1.65 ~spl5_1 | ~spl5_4),
% 1.62/1.65 inference(avatar_contradiction_clause,[status(thm)],[f203])).
% 1.62/1.65 thf(f203,plain,(
% 1.62/1.65 $false | (~spl5_1 | ~spl5_4)),
% 1.62/1.65 inference(subsumption_resolution,[status(thm)],[f199,f169])).
% 1.62/1.65 thf(f169,plain,(
% 1.62/1.65 ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) = $true) | ~spl5_1),
% 1.62/1.65 inference(avatar_component_clause,[status(thm)],[f167])).
% 1.62/1.65 thf(f167,definition,(
% 1.62/1.65 spl5_1 <=> ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) = $true)),
% 1.62/1.65 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.62/1.65 thf(f199,plain,(
% 1.62/1.65 ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) != $true) | ~spl5_4),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f197])).
% 1.62/1.65 thf(f197,plain,(
% 1.62/1.65 ($false = $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) != $true) | ~spl5_4),
% 1.62/1.65 inference(superposition,[status(thm)],[f186,f43])).
% 1.62/1.65 thf(f43,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((cQ @ (sK2 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.62/1.65 thf(f42,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((cQ @ (sK2 @ X0)) = $true) | ($true != $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(duplicate_literal_removal,[status(thm)],[f41])).
% 1.62/1.65 thf(f41,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (($true != $true) | ((cQ @ (sK2 @ X0)) = $true) | ((sP0 @ X0) != $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(superposition,[status(thm)],[f22,f19])).
% 1.62/1.65 thf(f19,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((sK1 @ X0 @ (sK2 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.65 thf(f14,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : ((! [X2 : $i] : (((cQ @ X2) = $true) | ((sK1 @ X0 @ X2) != $true)) & ! [X3 : $i] : (((cP @ X3) = $true) | ((sK1 @ X0 @ X3) != $true)) & (((X0 @ (sK2 @ X0)) != $true) & ((sK1 @ X0 @ (sK2 @ X0)) = $true))) | ((sP0 @ X0) != $true))),
% 1.62/1.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f11,f13,f12])).
% 1.62/1.65 thf(f12,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X1 : $i > $o] : (! [X2 : $i] : (((cQ @ X2) = $true) | ((X1 @ X2) != $true)) & ! [X3 : $i] : (((cP @ X3) = $true) | ((X1 @ X3) != $true)) & ? [X4 : $i] : (((X0 @ X4) != $true) & ((X1 @ X4) = $true))) => (! [X2 : $i] : (((cQ @ X2) = $true) | ((sK1 @ X0 @ X2) != $true)) & ! [X3 : $i] : (((cP @ X3) = $true) | ((sK1 @ X0 @ X3) != $true)) & ? [X4 : $i] : (((X0 @ X4) != $true) & ((sK1 @ X0 @ X4) = $true))))),
% 1.62/1.65 introduced(definition,[],[choice_axiom])).
% 1.62/1.65 thf(f13,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X4 : $i] : (((X0 @ X4) != $true) & ((sK1 @ X0 @ X4) = $true)) => (((X0 @ (sK2 @ X0)) != $true) & ((sK1 @ X0 @ (sK2 @ X0)) = $true)))),
% 1.62/1.65 introduced(definition,[],[choice_axiom])).
% 1.62/1.65 thf(f11,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X1 : $i > $o] : (! [X2 : $i] : (((cQ @ X2) = $true) | ((X1 @ X2) != $true)) & ! [X3 : $i] : (((cP @ X3) = $true) | ((X1 @ X3) != $true)) & ? [X4 : $i] : (((X0 @ X4) != $true) & ((X1 @ X4) = $true))) | ((sP0 @ X0) != $true))),
% 1.62/1.65 inference(rectify,[status(thm)],[f10])).
% 1.62/1.65 thf(f10,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X2 : $i > $o] : (! [X3 : $i] : (((cQ @ X3) = $true) | ((X2 @ X3) != $true)) & ! [X4 : $i] : (((cP @ X4) = $true) | ((X2 @ X4) != $true)) & ? [X5 : $i] : (((X0 @ X5) != $true) & ((X2 @ X5) = $true))) | ((sP0 @ X0) != $true))),
% 1.62/1.65 inference(nnf_transformation,[status(thm)],[f8])).
% 1.62/1.65 thf(f8,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X2 : $i > $o] : (! [X3 : $i] : (((cQ @ X3) = $true) | ((X2 @ X3) != $true)) & ! [X4 : $i] : (((cP @ X4) = $true) | ((X2 @ X4) != $true)) & ? [X5 : $i] : (((X0 @ X5) != $true) & ((X2 @ X5) = $true))) | ~((sP0 @ X0) = $true))),
% 1.62/1.65 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.62/1.65 thf(f22,plain,(
% 1.62/1.65 ( ! [X2 : $i,X0 : $i > $o] : (((sK1 @ X0 @ X2) != $true) | ((sP0 @ X0) != $true) | ((cQ @ X2) = $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.65 thf(f186,plain,(
% 1.62/1.65 ($false = (cQ @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))))) | ~spl5_4),
% 1.62/1.65 inference(avatar_component_clause,[status(thm)],[f184])).
% 1.62/1.65 thf(f184,definition,(
% 1.62/1.65 spl5_4 <=> ($false = (cQ @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0))))))),
% 1.62/1.65 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.62/1.65 thf(f195,plain,(
% 1.62/1.65 ~spl5_1 | ~spl5_3),
% 1.62/1.65 inference(avatar_contradiction_clause,[status(thm)],[f194])).
% 1.62/1.65 thf(f194,plain,(
% 1.62/1.65 $false | (~spl5_1 | ~spl5_3)),
% 1.62/1.65 inference(subsumption_resolution,[status(thm)],[f190,f169])).
% 1.62/1.65 thf(f190,plain,(
% 1.62/1.65 ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) != $true) | ~spl5_3),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f188])).
% 1.62/1.65 thf(f188,plain,(
% 1.62/1.65 ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) != $true) | ($false = $true) | ~spl5_3),
% 1.62/1.65 inference(superposition,[status(thm)],[f182,f37])).
% 1.62/1.65 thf(f37,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((cP @ (sK2 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.62/1.65 thf(f36,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((cP @ (sK2 @ X0)) = $true) | ((sP0 @ X0) != $true) | ($true != $true)) )),
% 1.62/1.65 inference(duplicate_literal_removal,[status(thm)],[f35])).
% 1.62/1.65 thf(f35,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (($true != $true) | ((sP0 @ X0) != $true) | ((cP @ (sK2 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(superposition,[status(thm)],[f21,f19])).
% 1.62/1.65 thf(f21,plain,(
% 1.62/1.65 ( ! [X3 : $i,X0 : $i > $o] : (((sK1 @ X0 @ X3) != $true) | ((cP @ X3) = $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.65 thf(f182,plain,(
% 1.62/1.65 ($false = (cP @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))))) | ~spl5_3),
% 1.62/1.65 inference(avatar_component_clause,[status(thm)],[f180])).
% 1.62/1.65 thf(f180,definition,(
% 1.62/1.65 spl5_3 <=> ($false = (cP @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0))))))),
% 1.62/1.65 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.62/1.65 thf(f187,plain,(
% 1.62/1.65 spl5_3 | spl5_4 | ~spl5_1),
% 1.62/1.65 inference(avatar_split_clause,[status(thm)],[f178,f167,f184,f180])).
% 1.62/1.65 thf(f178,plain,(
% 1.62/1.65 ($false = (cP @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))))) | ($false = (cQ @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))))) | ~spl5_1),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.62/1.65 thf(f177,plain,(
% 1.62/1.65 ($false = (cP @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))))) | ($false = (cQ @ (sK2 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))))) | ($true != $true) | ~spl5_1),
% 1.62/1.65 inference(superposition,[status(thm)],[f31,f169])).
% 1.62/1.65 thf(f31,plain,(
% 1.62/1.65 ( ! [X3 : $i > $o,X4 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))) != $true) | ($false = (X4 @ (sK2 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))))) | ((X3 @ (sK2 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) = $false)) )),
% 1.62/1.65 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.62/1.65 thf(f30,plain,(
% 1.62/1.65 ( ! [X3 : $i > $o,X4 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))) != $true) | (((X4 @ (sK2 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) & (X3 @ (sK2 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))))) != $true)) )),
% 1.62/1.65 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.62/1.65 thf(f29,plain,(
% 1.62/1.65 ( ! [X3 : $i > $o,X4 : $i > $o] : ((((^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))) @ (sK2 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) != $true) | ((sP0 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))) != $true)) )),
% 1.62/1.65 inference(primitive_instantiation,[status(thm)],[f20])).
% 1.62/1.65 thf(f20,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((X0 @ (sK2 @ X0)) != $true) | ((sP0 @ X0) != $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.65 thf(f176,plain,(
% 1.62/1.65 spl5_1),
% 1.62/1.65 inference(avatar_split_clause,[status(thm)],[f175,f167])).
% 1.62/1.65 thf(f175,plain,(
% 1.62/1.65 ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) = $true)),
% 1.62/1.65 inference(subsumption_resolution,[status(thm)],[f158,f138])).
% 1.62/1.65 thf(f138,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))) = $true)) )),
% 1.62/1.65 inference(duplicate_literal_removal,[status(thm)],[f137])).
% 1.62/1.65 thf(f137,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true) | ((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))) = $true)) )),
% 1.62/1.65 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.62/1.65 thf(f135,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))) = $true) | ((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true) | (((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) & (cP @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))))) = $true)) )),
% 1.62/1.65 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.62/1.65 thf(f134,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : ((((^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))) @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))) = $true) | ((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true)) )),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.62/1.65 thf(f133,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))) = $true) | ($true != $true) | (((^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))) @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true) | ((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true)) )),
% 1.62/1.65 inference(duplicate_literal_removal,[status(thm)],[f105])).
% 1.62/1.65 thf(f105,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))) = $true) | (((^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))) @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0)))) = $true) | ($true != $true) | ((X0 @ (sK4 @ (^[Y0 : $i]: ((X0 @ Y0) & (cP @ Y0))))) = $true)) )),
% 1.62/1.65 inference(superposition,[status(thm)],[f25,f55])).
% 1.62/1.65 thf(f55,plain,(
% 1.62/1.65 ( ! [X3 : $i > $o,X4 : $i > $o] : (((X3 @ (sK3 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) = $true) | ((X4 @ (sK4 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))) = $true)) )),
% 1.62/1.65 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.62/1.65 thf(f54,plain,(
% 1.62/1.65 ( ! [X3 : $i > $o,X4 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))) = $true) | (((X4 @ (sK3 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) & (X3 @ (sK3 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))))) = $true) | ((X4 @ (sK4 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) = $true)) )),
% 1.62/1.65 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.62/1.65 thf(f52,plain,(
% 1.62/1.65 ( ! [X3 : $i > $o,X4 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))) = $true) | (((X4 @ (sK4 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) & (X3 @ (sK4 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))))) = $true) | (((X4 @ (sK3 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) & (X3 @ (sK3 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))))) = $true)) )),
% 1.62/1.65 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.62/1.65 thf(f49,plain,(
% 1.62/1.65 ( ! [X3 : $i > $o,X4 : $i > $o] : ((((^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))) @ (sK4 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) = $true) | (((^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))) @ (sK3 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((X4 @ Y0) & (X3 @ Y0)))) = $true)) )),
% 1.62/1.65 inference(primitive_instantiation,[status(thm)],[f23])).
% 1.62/1.65 thf(f23,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((X0 @ (sK4 @ X0)) = $true) | ((X0 @ (sK3 @ X0)) = $true) | ((sP0 @ X0) = $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f18])).
% 1.62/1.65 thf(f18,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (((sP0 @ X0) = $true) | (((cP @ (sK3 @ X0)) != $true) & ((X0 @ (sK3 @ X0)) = $true)) | (((cQ @ (sK4 @ X0)) != $true) & ((X0 @ (sK4 @ X0)) = $true)))),
% 1.62/1.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f15,f17,f16])).
% 1.62/1.65 thf(f16,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X1 : $i] : (((cP @ X1) != $true) & ((X0 @ X1) = $true)) => (((cP @ (sK3 @ X0)) != $true) & ((X0 @ (sK3 @ X0)) = $true)))),
% 1.62/1.65 introduced(definition,[],[choice_axiom])).
% 1.62/1.65 thf(f17,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X2 : $i] : (((cQ @ X2) != $true) & ((X0 @ X2) = $true)) => (((cQ @ (sK4 @ X0)) != $true) & ((X0 @ (sK4 @ X0)) = $true)))),
% 1.62/1.65 introduced(definition,[],[choice_axiom])).
% 1.62/1.65 thf(f15,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (((sP0 @ X0) = $true) | ? [X1 : $i] : (((cP @ X1) != $true) & ((X0 @ X1) = $true)) | ? [X2 : $i] : (((cQ @ X2) != $true) & ((X0 @ X2) = $true)))),
% 1.62/1.65 inference(rectify,[status(thm)],[f9])).
% 1.62/1.65 thf(f9,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (((sP0 @ X0) = $true) | ? [X1 : $i] : (((cP @ X1) != $true) & ((X0 @ X1) = $true)) | ? [X6 : $i] : (((cQ @ X6) != $true) & ((X0 @ X6) = $true)))),
% 1.62/1.65 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.62/1.65 thf(f7,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X2 : $i > $o] : (! [X3 : $i] : (((cQ @ X3) = $true) | ((X2 @ X3) != $true)) & ! [X4 : $i] : (((cP @ X4) = $true) | ((X2 @ X4) != $true)) & ? [X5 : $i] : (((X0 @ X5) != $true) & ((X2 @ X5) = $true))) | ? [X1 : $i] : (((cP @ X1) != $true) & ((X0 @ X1) = $true)) | ? [X6 : $i] : (((cQ @ X6) != $true) & ((X0 @ X6) = $true)))),
% 1.62/1.65 inference(flattening,[status(thm)],[f6])).
% 1.62/1.65 thf(f6,plain,(
% 1.62/1.65 ! [X0 : $i > $o] : (? [X1 : $i] : (((cP @ X1) != $true) & ((X0 @ X1) = $true)) | ? [X6 : $i] : (((cQ @ X6) != $true) & ((X0 @ X6) = $true)) | ? [X2 : $i > $o] : (? [X5 : $i] : (((X0 @ X5) != $true) & ((X2 @ X5) = $true)) & (! [X4 : $i] : (((cP @ X4) = $true) | ((X2 @ X4) != $true)) & ! [X3 : $i] : (((cQ @ X3) = $true) | ((X2 @ X3) != $true)))))),
% 1.62/1.65 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.65 thf(f5,plain,(
% 1.62/1.65 ~? [X0 : $i > $o] : (! [X1 : $i] : (((X0 @ X1) = $true) => ((cP @ X1) = $true)) & ! [X6 : $i] : (((X0 @ X6) = $true) => ((cQ @ X6) = $true)) & ! [X2 : $i > $o] : ((! [X4 : $i] : (((X2 @ X4) = $true) => ((cP @ X4) = $true)) & ! [X3 : $i] : (((X2 @ X3) = $true) => ((cQ @ X3) = $true))) => ! [X5 : $i] : (((X2 @ X5) = $true) => ((X0 @ X5) = $true))))),
% 1.62/1.65 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.65 thf(f4,plain,(
% 1.62/1.65 ~? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ! [X2 : $i > $o] : ((! [X3 : $i] : ((X2 @ X3) => (cQ @ X3)) & ! [X4 : $i] : ((X2 @ X4) => (cP @ X4))) => ! [X5 : $i] : ((X2 @ X5) => (X0 @ X5))) & ! [X6 : $i] : ((X0 @ X6) => (cQ @ X6)))),
% 1.62/1.65 inference(rectify,[status(thm)],[f2])).
% 1.62/1.65 thf(f2,negated_conjecture,(
% 1.62/1.65 ~? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ! [X2 : $i > $o] : ((! [X1 : $i] : ((X2 @ X1) => (cQ @ X1)) & ! [X1 : $i] : ((X2 @ X1) => (cP @ X1))) => ! [X1 : $i] : ((X2 @ X1) => (X0 @ X1))) & ! [X1 : $i] : ((X0 @ X1) => (cQ @ X1)))),
% 1.62/1.65 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.65 thf(f1,conjecture,(
% 1.62/1.65 ? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ! [X2 : $i > $o] : ((! [X1 : $i] : ((X2 @ X1) => (cQ @ X1)) & ! [X1 : $i] : ((X2 @ X1) => (cP @ X1))) => ! [X1 : $i] : ((X2 @ X1) => (X0 @ X1))) & ! [X1 : $i] : ((X0 @ X1) => (cQ @ X1)))),
% 1.62/1.65 file('/export/starexec/sandbox/tmp/tmp.Z7iZWmoUqd/DTF2THF_30570.p',cTHM590_pme)).
% 1.62/1.65 thf(f25,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((cP @ (sK3 @ X0)) != $true) | ((X0 @ (sK4 @ X0)) = $true) | ((sP0 @ X0) = $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f18])).
% 1.62/1.65 thf(f158,plain,(
% 1.62/1.65 ((cQ @ (sK4 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0))))) != $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) = $true)),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.62/1.65 thf(f157,plain,(
% 1.62/1.65 ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) = $true) | ($true != $true) | ((cQ @ (sK4 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0))))) != $true)),
% 1.62/1.65 inference(duplicate_literal_removal,[status(thm)],[f148])).
% 1.62/1.65 thf(f148,plain,(
% 1.62/1.65 ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) = $true) | ($true != $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0)))) = $true) | ((cQ @ (sK4 @ (^[Y0 : $i]: ((cQ @ Y0) & (cP @ Y0))))) != $true)),
% 1.62/1.65 inference(superposition,[status(thm)],[f26,f116])).
% 1.62/1.65 thf(f116,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))) = $true)) )),
% 1.62/1.65 inference(duplicate_literal_removal,[status(thm)],[f114])).
% 1.62/1.65 thf(f114,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))) = $true) | ((X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true)) )),
% 1.62/1.65 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.62/1.65 thf(f113,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | (((cQ @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) & (X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))) = $true)) )),
% 1.62/1.65 inference(beta_eta_normalization,[status(thm)],[f112])).
% 1.62/1.65 thf(f112,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : ((((^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))) @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))) = $true)) )),
% 1.62/1.65 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.62/1.65 thf(f111,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (($true != $true) | (((^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))) @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))) = $true)) )),
% 1.62/1.65 inference(duplicate_literal_removal,[status(thm)],[f108])).
% 1.62/1.65 thf(f108,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (($true != $true) | (((^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))) @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))) = $true) | ((X0 @ (sK3 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0))))) = $true) | ((sP0 @ (^[Y0 : $i]: ((cQ @ Y0) & (X0 @ Y0)))) = $true)) )),
% 1.62/1.65 inference(superposition,[status(thm)],[f24,f55])).
% 1.62/1.65 thf(f24,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((cQ @ (sK4 @ X0)) != $true) | ((sP0 @ X0) = $true) | ((X0 @ (sK3 @ X0)) = $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f18])).
% 1.62/1.65 thf(f26,plain,(
% 1.62/1.65 ( ! [X0 : $i > $o] : (((cP @ (sK3 @ X0)) != $true) | ((cQ @ (sK4 @ X0)) != $true) | ((sP0 @ X0) = $true)) )),
% 1.62/1.65 inference(cnf_transformation,[status(thm)],[f18])).
% 1.62/1.65 % SZS output end Proof for DTF2THF_30570
% 1.62/1.65 % (30846)------------------------------
% 1.62/1.65 % (30846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.65 % (30846)Termination reason: Refutation
% 1.62/1.65
% 1.62/1.65 % (30846)Memory used [KB]: 5628
% 1.62/1.65 % (30846)Time elapsed: 0.015 s
% 1.62/1.65 % (30846)Instructions burned: 30 (million)
% 1.62/1.65 % (30846)------------------------------
% 1.62/1.65 % (30846)------------------------------
% 1.62/1.65 % (30758)Success in time 0.379 s
%------------------------------------------------------------------------------