TSTP Solution File: SEV214^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV214^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:02:18 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 418 ( 267 equ; 6 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 595 ( 60 ~; 117 |; 52 &; 312 @)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 17 con; 0-2 aty)
% ( 0 !!; 31 ??; 0 @@+; 0 @@-)
% Number of variables : 184 ( 95 ^ 75 !; 14 ?; 184 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
iS: $tType ).
thf(func_def_0,type,
iS: $tType ).
thf(func_def_1,type,
c0: iS ).
thf(func_def_2,type,
cP: iS > iS > iS ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK0: ( iS > $o ) > iS ).
thf(func_def_14,type,
sK1: ( iS > $o ) > iS ).
thf(func_def_16,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK4: iS ).
thf(func_def_18,type,
sK5: iS ).
thf(func_def_19,type,
sK6: iS ).
thf(func_def_20,type,
sK7: iS ).
thf(func_def_21,type,
sK8: iS ).
thf(func_def_22,type,
sK9: iS ).
thf(func_def_23,type,
sK10: iS > iS ).
thf(f163,plain,
$false,
inference(avatar_sat_refutation,[],[f27,f56,f57,f100,f101,f108,f162]) ).
thf(f162,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f161]) ).
thf(f161,plain,
( $false
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f160]) ).
thf(f160,plain,
( ( c0 != c0 )
| ~ spl2_4 ),
inference(superposition,[],[f11,f55]) ).
thf(f55,plain,
( ( c0
= ( cP @ sK5 @ sK4 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f53,plain,
( spl2_4
<=> ( c0
= ( cP @ sK5 @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f11,plain,
! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f10,plain,
( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
( ( ( cP @ X3 @ X2 )
!= ( cP @ X1 @ X0 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) ) )
& ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
!= $true )
| ! [X5: iS] :
( ( X4 @ X5 )
= $true )
| ( ( $true
= ( X4 @ ( sK0 @ X4 ) ) )
& ( ( X4 @ ( cP @ ( sK1 @ X4 ) @ ( sK0 @ X4 ) ) )
!= $true )
& ( ( X4 @ ( sK1 @ X4 ) )
= $true ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9]) ).
thf(f9,plain,
! [X4: iS > $o] :
( ? [X6: iS,X7: iS] :
( ( ( X4 @ X6 )
= $true )
& ( ( X4 @ ( cP @ X7 @ X6 ) )
!= $true )
& ( $true
= ( X4 @ X7 ) ) )
=> ( ( $true
= ( X4 @ ( sK0 @ X4 ) ) )
& ( ( X4 @ ( cP @ ( sK1 @ X4 ) @ ( sK0 @ X4 ) ) )
!= $true )
& ( ( X4 @ ( sK1 @ X4 ) )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f8,plain,
( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
( ( ( cP @ X3 @ X2 )
!= ( cP @ X1 @ X0 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) ) )
& ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
!= $true )
| ! [X5: iS] :
( ( X4 @ X5 )
= $true )
| ? [X6: iS,X7: iS] :
( ( ( X4 @ X6 )
= $true )
& ( ( X4 @ ( cP @ X7 @ X6 ) )
!= $true )
& ( $true
= ( X4 @ X7 ) ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,plain,
( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
( ( ( cP @ X3 @ X2 )
!= ( cP @ X1 @ X0 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) ) )
& ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
!= $true )
| ! [X7: iS] :
( $true
= ( X4 @ X7 ) )
| ? [X5: iS,X6: iS] :
( ( ( X4 @ X5 )
= $true )
& ( $true
!= ( X4 @ ( cP @ X6 @ X5 ) ) )
& ( ( X4 @ X6 )
= $true ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
( ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) )
& ! [X0: iS,X1: iS,X2: iS,X3: iS] :
( ( ( cP @ X3 @ X2 )
!= ( cP @ X1 @ X0 ) )
| ( ( X1 = X3 )
& ( X0 = X2 ) ) )
& ! [X4: iS > $o] :
( ! [X7: iS] :
( $true
= ( X4 @ X7 ) )
| ? [X5: iS,X6: iS] :
( ( $true
!= ( X4 @ ( cP @ X6 @ X5 ) ) )
& ( ( X4 @ X6 )
= $true )
& ( ( X4 @ X5 )
= $true ) )
| ( ( X4 @ c0 )
!= $true ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
( ( ( cP @ X3 @ X2 )
= ( cP @ X1 @ X0 ) )
=> ( ( X1 = X3 )
& ( X0 = X2 ) ) )
& ! [X4: iS > $o] :
( ( ! [X5: iS,X6: iS] :
( ( ( ( X4 @ X6 )
= $true )
& ( ( X4 @ X5 )
= $true ) )
=> ( $true
= ( X4 @ ( cP @ X6 @ X5 ) ) ) )
& ( ( X4 @ c0 )
= $true ) )
=> ! [X7: iS] :
( $true
= ( X4 @ X7 ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) )
=> ( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
& ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
( ( ( cP @ X3 @ X2 )
= ( cP @ X1 @ X0 ) )
=> ( ( X1 = X3 )
& ( X0 = X2 ) ) )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
& ! [X5: iS,X6: iS] :
( ( ( X4 @ X5 )
& ( X4 @ X6 ) )
=> ( X4 @ ( cP @ X6 @ X5 ) ) ) )
=> ! [X7: iS] : ( X4 @ X7 ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) )
=> ( ( ( ^ [X10: iS] :
( ? [X11: iS] :
( c0
= ( cP @ X11 @ X10 ) )
| ( c0 = X10 ) ) )
= ( ^ [X12: iS,X13: iS] : ( X12 = X13 )
@ c0 ) )
& ( ( ^ [X14: iS,X15: iS] : ( X14 = X15 )
@ c0 )
= ( ^ [X16: iS] :
( ? [X17: iS] :
( c0
= ( cP @ X16 @ X17 ) )
| ( c0 = X16 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: iS,X0: iS,X3: iS,X1: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X0 = X1 )
& ( X2 = X3 ) ) )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
& ! [X1: iS,X0: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ( ( ( ^ [X1: iS] :
( ? [X0: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X1 ) ) )
= ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 ) )
& ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 )
= ( ^ [X0: iS] :
( ? [X1: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X0 ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: iS,X0: iS,X3: iS,X1: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X0 = X1 )
& ( X2 = X3 ) ) )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
& ! [X1: iS,X0: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ( ( ( ^ [X1: iS] :
( ? [X0: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X1 ) ) )
= ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 ) )
& ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
@ c0 )
= ( ^ [X0: iS] :
( ? [X1: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ( c0 = X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_T_LR_LEM2_pme) ).
thf(f108,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f107]) ).
thf(f107,plain,
( $false
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f106,plain,
( ( c0 != c0 )
| ~ spl2_5 ),
inference(superposition,[],[f11,f95]) ).
thf(f95,plain,
( ( c0
= ( cP @ sK6 @ sK7 ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f93,plain,
( spl2_5
<=> ( c0
= ( cP @ sK6 @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
thf(f101,plain,
( ~ spl2_6
| spl2_2 ),
inference(avatar_split_clause,[],[f80,f24,f97]) ).
thf(f97,plain,
( spl2_6
<=> ( c0 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
thf(f24,plain,
( spl2_2
<=> ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
= ( (=) @ c0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f80,plain,
( ( c0 != sK6 )
| spl2_2 ),
inference(equality_proxy_clausification,[],[f79]) ).
thf(f79,plain,
( ( ( c0 = sK6 )
= $false )
| spl2_2 ),
inference(duplicate_literal_removal,[],[f78]) ).
thf(f78,plain,
( ( ( c0 = sK6 )
= $false )
| ( ( c0 = sK6 )
= $false )
| spl2_2 ),
inference(binary_proxy_clausification,[],[f76]) ).
thf(f76,plain,
( ( ( ( c0 = sK6 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( c0 = sK6 )
= $false )
| spl2_2 ),
inference(binary_proxy_clausification,[],[f74]) ).
thf(f74,plain,
( ( ( c0 = sK6 )
!= ( ( c0 = sK6 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK6 @ Y0 ) ) ) ) )
| spl2_2 ),
inference(beta_eta_normalization,[],[f73]) ).
thf(f73,plain,
( ( ( c0 = sK6 )
!= ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) )
@ sK6 ) )
| spl2_2 ),
inference(negative_extensionality,[],[f26]) ).
thf(f26,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( (=) @ c0 ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f100,plain,
( spl2_5
| spl2_6
| spl2_2 ),
inference(avatar_split_clause,[],[f91,f24,f97,f93]) ).
thf(f91,plain,
( ( c0
= ( cP @ sK6 @ sK7 ) )
| ( c0 = sK6 )
| spl2_2 ),
inference(equality_proxy_clausification,[],[f90]) ).
thf(f90,plain,
( ( $true
= ( c0
= ( cP @ sK6 @ sK7 ) ) )
| ( c0 = sK6 )
| spl2_2 ),
inference(duplicate_literal_removal,[],[f89]) ).
thf(f89,plain,
( ( c0 = sK6 )
| ( c0 = sK6 )
| ( $true
= ( c0
= ( cP @ sK6 @ sK7 ) ) )
| spl2_2 ),
inference(equality_proxy_clausification,[],[f88]) ).
thf(f88,plain,
( ( c0 = sK6 )
| ( ( c0 = sK6 )
= $true )
| ( $true
= ( c0
= ( cP @ sK6 @ sK7 ) ) )
| spl2_2 ),
inference(beta_eta_normalization,[],[f87]) ).
thf(f87,plain,
( ( ( c0 = sK6 )
= $true )
| ( c0 = sK6 )
| ( ( ^ [Y0: iS] :
( c0
= ( cP @ sK6 @ Y0 ) )
@ sK7 )
= $true )
| spl2_2 ),
inference(sigma_clausification,[],[f86]) ).
thf(f86,plain,
( ( ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK6 @ Y0 ) ) )
= $true )
| ( ( c0 = sK6 )
= $true )
| ( c0 = sK6 )
| spl2_2 ),
inference(binary_proxy_clausification,[],[f85]) ).
thf(f85,plain,
( ( ( ( c0 = sK6 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK6 @ Y0 ) ) ) )
= $true )
| ( c0 = sK6 )
| spl2_2 ),
inference(equality_proxy_clausification,[],[f75]) ).
thf(f75,plain,
( ( ( c0 = sK6 )
= $true )
| ( ( ( c0 = sK6 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ sK6 @ Y0 ) ) ) )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[],[f74]) ).
thf(f57,plain,
( ~ spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f37,f20,f49]) ).
thf(f49,plain,
( spl2_3
<=> ( c0 = sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f20,plain,
( spl2_1
<=> ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
= ( (=) @ c0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f37,plain,
( ( c0 != sK4 )
| spl2_1 ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f36,plain,
( ( ( c0 = sK4 )
= $false )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f35]) ).
thf(f35,plain,
( ( ( c0 = sK4 )
= $false )
| ( ( c0 = sK4 )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
( ( ( ( c0 = sK4 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) )
= $false )
| ( ( c0 = sK4 )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f31,plain,
( ( ( ( c0 = sK4 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) )
!= ( c0 = sK4 ) )
| spl2_1 ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) )
@ sK4 )
!= ( c0 = sK4 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f22]) ).
thf(f22,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( (=) @ c0 ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f56,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[],[f47,f20,f53,f49]) ).
thf(f47,plain,
( ( c0
= ( cP @ sK5 @ sK4 ) )
| ( c0 = sK4 )
| spl2_1 ),
inference(equality_proxy_clausification,[],[f46]) ).
thf(f46,plain,
( ( c0 = sK4 )
| ( ( c0
= ( cP @ sK5 @ sK4 ) )
= $true )
| spl2_1 ),
inference(beta_eta_normalization,[],[f45]) ).
thf(f45,plain,
( ( $true
= ( ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) )
@ sK5 ) )
| ( c0 = sK4 )
| spl2_1 ),
inference(sigma_clausification,[],[f44]) ).
thf(f44,plain,
( ( c0 = sK4 )
| ( ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) )
= $true )
| spl2_1 ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f43,plain,
( ( $true
= ( c0 = sK4 ) )
| ( ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) )
= $true )
| spl2_1 ),
inference(duplicate_literal_removal,[],[f42]) ).
thf(f42,plain,
( ( ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) )
= $true )
| ( $true
= ( c0 = sK4 ) )
| ( $true
= ( c0 = sK4 ) )
| spl2_1 ),
inference(binary_proxy_clausification,[],[f32]) ).
thf(f32,plain,
( ( $true
= ( ( c0 = sK4 )
| ( ?? @ iS
@ ^ [Y0: iS] :
( c0
= ( cP @ Y0 @ sK4 ) ) ) ) )
| ( $true
= ( c0 = sK4 ) )
| spl2_1 ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f27,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f18,f24,f20]) ).
thf(f18,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( (=) @ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( (=) @ c0 ) ) ),
inference(beta_eta_normalization,[],[f15]) ).
thf(f15,plain,
( ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) )
| ( ( ^ [Y0: iS] :
( ( c0 = Y0 )
| ( ?? @ iS
@ ^ [Y1: iS] :
( c0
= ( cP @ Y1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
@ c0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV214^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 19:39:09 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 This is a TH0_THM_EQU_NAR problem
% 0.13/0.37 Running higher-order theorem proving
% 0.13/0.37 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
% 0.22/0.39 % (21413)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.39 % (21416)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (21414)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)
% 0.22/0.39 % (21415)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)
% 0.22/0.39 % (21418)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.22/0.39 % (21419)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39 % (21417)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)
% 0.22/0.39 % (21416)Instruction limit reached!
% 0.22/0.39 % (21416)------------------------------
% 0.22/0.39 % (21416)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (21416)Termination reason: Unknown
% 0.22/0.39 % (21416)Termination phase: Preprocessing 3
% 0.22/0.39
% 0.22/0.39 % (21416)Memory used [KB]: 895
% 0.22/0.39 % (21416)Time elapsed: 0.003 s
% 0.22/0.39 % (21416)Instructions burned: 2 (million)
% 0.22/0.39 % (21416)------------------------------
% 0.22/0.39 % (21416)------------------------------
% 0.22/0.39 % (21417)Instruction limit reached!
% 0.22/0.39 % (21417)------------------------------
% 0.22/0.39 % (21417)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (21417)Termination reason: Unknown
% 0.22/0.39 % (21417)Termination phase: Property scanning
% 0.22/0.39
% 0.22/0.39 % (21417)Memory used [KB]: 1023
% 0.22/0.39 % (21417)Time elapsed: 0.004 s
% 0.22/0.39 % (21417)Instructions burned: 2 (million)
% 0.22/0.39 % (21417)------------------------------
% 0.22/0.39 % (21417)------------------------------
% 0.22/0.39 % (21414)Instruction limit reached!
% 0.22/0.39 % (21414)------------------------------
% 0.22/0.39 % (21414)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (21414)Termination reason: Unknown
% 0.22/0.39 % (21414)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (21414)Memory used [KB]: 5500
% 0.22/0.39 % (21414)Time elapsed: 0.006 s
% 0.22/0.39 % (21414)Instructions burned: 5 (million)
% 0.22/0.39 % (21414)------------------------------
% 0.22/0.39 % (21414)------------------------------
% 0.22/0.39 % (21415)First to succeed.
% 0.22/0.40 % (21418)Also succeeded, but the first one will report.
% 0.22/0.40 % (21415)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (21415)------------------------------
% 0.22/0.40 % (21415)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (21415)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (21415)Memory used [KB]: 5628
% 0.22/0.40 % (21415)Time elapsed: 0.011 s
% 0.22/0.40 % (21415)Instructions burned: 7 (million)
% 0.22/0.40 % (21415)------------------------------
% 0.22/0.40 % (21415)------------------------------
% 0.22/0.40 % (21412)Success in time 0.025 s
%------------------------------------------------------------------------------