TSTP Solution File: SYO040^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO040^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Tue May 21 09:10:03 EDT 2024
% Result : Unsatisfiable 0.21s 0.37s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 131 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 1114 ( 161 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 418 ( 192 ~; 222 |; 0 &; 0 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 19 >; 1 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-6 aty)
% Number of variables : 10 ( 0 ^ 4 !; 0 ?; 10 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: $o > $o ).
thf(func_def_1,type,
h: $o > $i ).
thf(func_def_2,type,
x: $o ).
thf(func_def_7,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_8,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
vOR: $o > $o > $o ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f233,plain,
$false,
inference(avatar_sat_refutation,[],[f48,f74,f100,f116,f121,f147,f154,f161,f170,f227,f232]) ).
thf(f232,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f231]) ).
thf(f231,plain,
( $false
| spl0_2
| spl0_3 ),
inference(subsumption_resolution,[],[f230,f202]) ).
thf(f202,plain,
( ( $false = vAPP($o,$o,f,$false) )
| spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f201,f173]) ).
thf(f173,plain,
( ( vAPP($o,$o,f,x) = $false )
| spl0_2 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f172,plain,
( ( $true != $true )
| ( vAPP($o,$o,f,x) = $false )
| spl0_2 ),
inference(superposition,[],[f46,f3]) ).
thf(f3,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f46,plain,
( ( vAPP($o,$o,f,x) != $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f45,plain,
( spl0_2
<=> ( vAPP($o,$o,f,x) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f201,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| spl0_2
| spl0_3 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f200,plain,
( ( vAPP($o,$i,h,$false) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f199,f173]) ).
thf(f199,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| spl0_2
| spl0_3 ),
inference(subsumption_resolution,[],[f189,f68]) ).
thf(f68,plain,
( ( x != $false )
| spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f67,plain,
( spl0_3
<=> ( x = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f189,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$false) )
| ( x = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| spl0_2 ),
inference(binary_proxy_clausification,[],[f186]) ).
thf(f186,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$false) )
| ( x != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| spl0_2 ),
inference(constrained_superposition,[],[f4,f173]) ).
thf(f4,plain,
vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x)))) != vAPP($o,$i,h,vAPP($o,$o,f,x)),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x)))) != vAPP($o,$i,h,vAPP($o,$o,f,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',2) ).
thf(f230,plain,
( ( $false != vAPP($o,$o,f,$false) )
| spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f229,f173]) ).
thf(f229,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| spl0_2
| spl0_3 ),
inference(trivial_inequality_removal,[],[f228]) ).
thf(f228,plain,
( ( vAPP($o,$i,h,$false) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f219,f173]) ).
thf(f219,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| spl0_2
| spl0_3 ),
inference(constrained_superposition,[],[f4,f202]) ).
thf(f227,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f226]) ).
thf(f226,plain,
( $false
| spl0_2
| spl0_3 ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f225,plain,
( ( vAPP($o,$i,h,$false) != vAPP($o,$i,h,$false) )
| spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f224,f173]) ).
thf(f224,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$false) )
| spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f223,f202]) ).
thf(f223,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$false)) )
| spl0_2
| spl0_3 ),
inference(subsumption_resolution,[],[f218,f173]) ).
thf(f218,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$false)) )
| ( vAPP($o,$o,f,x) != $false )
| spl0_2
| spl0_3 ),
inference(constrained_superposition,[],[f4,f202]) ).
thf(f170,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f169]) ).
thf(f169,plain,
( $false
| spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f168,f68]) ).
thf(f168,plain,
( ( x = $false )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f167,plain,
( ( $true != $true )
| ( x = $false )
| ~ spl0_4 ),
inference(superposition,[],[f110,f3]) ).
thf(f110,plain,
( ( x != $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( vAPP($o,$i,h,$true) != vAPP($o,$i,h,$true) )
| ( x != $true )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f108,f73]) ).
thf(f73,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f71,plain,
( spl0_4
<=> ( $true = vAPP($o,$o,f,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f108,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,$true)) != vAPP($o,$i,h,$true) )
| ( x != $true )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f102,f73]) ).
thf(f102,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,$true))) != vAPP($o,$i,h,$true) )
| ( x != $true )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f4,f73]) ).
thf(f161,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f160]) ).
thf(f160,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f159,f133]) ).
thf(f133,plain,
( ( $false = vAPP($o,$o,f,$false) )
| spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f132,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,$false) )
| spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f129,f3]) ).
thf(f129,plain,
( ( $true != vAPP($o,$o,f,$false) )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f46,f69]) ).
thf(f69,plain,
( ( x = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f159,plain,
( ( $false != vAPP($o,$o,f,$false) )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f158,f133]) ).
thf(f158,plain,
( ( $false != vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f157,f69]) ).
thf(f157,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f156,plain,
( ( vAPP($o,$i,h,$false) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f155,f133]) ).
thf(f155,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,$false)) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f139,f69]) ).
thf(f139,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f4,f133]) ).
thf(f154,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f153]) ).
thf(f153,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f152,f133]) ).
thf(f152,plain,
( ( $false != vAPP($o,$o,f,$false) )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f151,f69]) ).
thf(f151,plain,
( ( vAPP($o,$o,f,x) != $false )
| spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f150,plain,
( ( vAPP($o,$i,h,$false) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,x) != $false )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f149,f133]) ).
thf(f149,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,$false)) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,x) != $false )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f148,f69]) ).
thf(f148,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$false) )
| ( vAPP($o,$o,f,x) != $false )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f138,f133]) ).
thf(f138,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$false)) )
| ( vAPP($o,$o,f,x) != $false )
| spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f4,f133]) ).
thf(f147,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f146]) ).
thf(f146,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f145,plain,
( ( vAPP($o,$i,h,$false) != vAPP($o,$i,h,$false) )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f144,f133]) ).
thf(f144,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,$false)) != vAPP($o,$i,h,$false) )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f143,f133]) ).
thf(f143,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,$false))) != vAPP($o,$i,h,$false) )
| spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f137,f69]) ).
thf(f137,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,$false))) != vAPP($o,$i,h,$false) )
| ( x != $false )
| spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f4,f133]) ).
thf(f121,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f120]) ).
thf(f120,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f119,f73]) ).
thf(f119,plain,
( ( $true != vAPP($o,$o,f,$true) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f118,f47]) ).
thf(f47,plain,
( ( vAPP($o,$o,f,x) = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f118,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f117,plain,
( ( vAPP($o,$i,h,$true) != vAPP($o,$i,h,$true) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f104,f47]) ).
thf(f104,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$true) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $true )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f4,f73]) ).
thf(f116,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f115]) ).
thf(f115,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f114,plain,
( ( vAPP($o,$i,h,$true) != vAPP($o,$i,h,$true) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f113,f47]) ).
thf(f113,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$true) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f112,f73]) ).
thf(f112,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$true)) )
| ~ spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f103,f47]) ).
thf(f103,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$true)) )
| ( vAPP($o,$o,f,x) != $true )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f4,f73]) ).
thf(f100,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f99]) ).
thf(f99,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(global_subsumption,[],[f2,f3,f4,f33,f34,f35,f36,f39,f38,f47,f50,f59,f62,f65,f49,f69,f77,f72,f86,f82,f76,f93,f98]) ).
thf(f98,plain,
( ( $false != vAPP($o,$o,f,$true) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f97,f47]) ).
thf(f97,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f96,plain,
( ( vAPP($o,$i,h,$true) != vAPP($o,$i,h,$true) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f90,f47]) ).
thf(f90,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$true) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f4,f76]) ).
thf(f93,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,$true))) != vAPP($o,$i,h,$true) )
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f88,f69]) ).
thf(f88,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,$true))) != vAPP($o,$i,h,$true) )
| ( x != $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f4,f76]) ).
thf(f76,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f47,f69]) ).
thf(f82,plain,
( ( $false = vAPP($o,$o,f,$true) )
| spl0_4 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,$true) )
| spl0_4 ),
inference(superposition,[],[f72,f3]) ).
thf(f86,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f,X0) )
| ( $false = X0 ) )
| spl0_4 ),
inference(duplicate_literal_removal,[],[f85]) ).
thf(f85,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| spl0_4 ),
inference(binary_proxy_clausification,[],[f79]) ).
thf(f79,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f,X0) != X0 )
| ( $false = X0 ) )
| spl0_4 ),
inference(superposition,[],[f72,f3]) ).
thf(f72,plain,
( ( $true != vAPP($o,$o,f,$true) )
| spl0_4 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f77,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false)))) != vAPP($o,$i,h,vAPP($o,$o,f,$false)) )
| ~ spl0_3 ),
inference(superposition,[],[f4,f69]) ).
thf(f49,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( x = $false )
| ~ spl0_2 ),
inference(superposition,[],[f47,f3]) ).
thf(f65,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ( x = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f64,f47]) ).
thf(f64,plain,
( ( x = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f63,plain,
( ( vAPP($o,$i,h,$true) != vAPP($o,$i,h,$true) )
| ( x = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f54,f47]) ).
thf(f54,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$true) )
| ( x = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f52]) ).
thf(f52,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$true) )
| ( x != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f4,f47]) ).
thf(f62,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( x = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f61,f47]) ).
thf(f61,plain,
( ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f60,plain,
( ( vAPP($o,$i,h,$true) != vAPP($o,$i,h,$true) )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f53,f47]) ).
thf(f53,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$true) )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f52]) ).
thf(f59,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,$true)) != vAPP($o,$i,h,$true) )
| ( x = $false )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f58,plain,
( ( $true = $false )
| ( vAPP($o,$i,h,vAPP($o,$o,f,$true)) != vAPP($o,$i,h,$true) )
| ( x = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f57,f47]) ).
thf(f57,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,$true)) != vAPP($o,$i,h,$true) )
| ( x = $false )
| ( vAPP($o,$o,f,x) = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f56,f47]) ).
thf(f56,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$true)) )
| ( x = $false )
| ( vAPP($o,$o,f,x) = $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f51,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$true)) )
| ( x != vAPP($o,$o,f,x) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f4,f47]) ).
thf(f50,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,$true))) != vAPP($o,$i,h,$true) )
| ~ spl0_2 ),
inference(superposition,[],[f4,f47]) ).
thf(f38,plain,
( ( vAPP($o,$o,f,x) = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $true ) ),
inference(binary_proxy_clausification,[],[f37]) ).
thf(f37,plain,
vAPP($o,$o,f,x) != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))),
inference(equality_resolution,[],[f4]) ).
thf(f39,plain,
( ( vAPP($o,$o,f,x) = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false ) ),
inference(binary_proxy_clausification,[],[f37]) ).
thf(f36,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,$true) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false ) ),
inference(superposition,[],[f4,f3]) ).
thf(f35,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,x)) != vAPP($o,$i,h,vAPP($o,$o,f,$true)) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false ) ),
inference(superposition,[],[f4,f3]) ).
thf(f34,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,$true))) != vAPP($o,$i,h,$true) )
| ( vAPP($o,$o,f,x) = $false ) ),
inference(superposition,[],[f4,f3]) ).
thf(f33,plain,
( ( vAPP($o,$i,h,vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true)))) != vAPP($o,$i,h,vAPP($o,$o,f,$true)) )
| ( x = $false ) ),
inference(superposition,[],[f4,f3]) ).
thf(f2,plain,
$true != $false,
introduced(fool_axiom,[]) ).
thf(f74,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f49,f45,f71,f67]) ).
thf(f48,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f38,f45,f41]) ).
thf(f41,plain,
( spl0_1
<=> ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO040^1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 10:57:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (9454)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (9457)WARNING: value z3 for option sas not known
% 0.14/0.36 % (9458)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 % (9457)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.36 % (9455)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % Exception at run slice level
% 0.14/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.36 % Exception at run slice level
% 0.14/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.36 % (9460)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37 % (9456)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % (9457)First to succeed.
% 0.21/0.37 % (9461)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.37 % (9457)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9454"
% 0.21/0.37 % (9461)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37 % (9457)Refutation found. Thanks to Tanya!
% 0.21/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.37 % (9457)------------------------------
% 0.21/0.37 % (9457)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.37 % (9457)Termination reason: Refutation
% 0.21/0.37
% 0.21/0.37 % (9457)Memory used [KB]: 806
% 0.21/0.37 % (9457)Time elapsed: 0.010 s
% 0.21/0.37 % (9457)Instructions burned: 13 (million)
% 0.21/0.37 % (9454)Success in time 0.014 s
%------------------------------------------------------------------------------