TSTP Solution File: SEV034^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV034^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.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 : Sun May 5 09:41:08 EDT 2024
% Result : Theorem 0.16s 0.38s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 12
% Syntax : Number of formulae : 108 ( 94 unt; 11 typ; 0 def)
% Number of atoms : 970 ( 130 equ; 0 cnn)
% Maximal formula atoms : 2 ( 10 avg)
% Number of connectives : 3140 ( 6 ~; 0 |; 156 &;2282 @)
% ( 0 <=>; 297 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 153 ( 153 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 5 con; 0-3 aty)
% ( 399 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 535 ( 418 ^ 116 !; 0 ?; 535 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a > a > $o ).
thf(func_def_21,type,
sK3: a > b ).
thf(func_def_22,type,
sK4: a > b ).
thf(func_def_23,type,
sK5: a > b > b > $o ).
thf(func_def_24,type,
sK6: a ).
thf(func_def_25,type,
sK7: a ).
thf(f338,plain,
$false,
inference(trivial_inequality_removal,[],[f337]) ).
thf(f337,plain,
$true = $false,
inference(forward_demodulation,[],[f333,f65]) ).
thf(f65,plain,
( $false
= ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK4 @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f64]) ).
thf(f64,plain,
( ( ( sK2 @ sK6 @ sK7 )
=> ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK4 @ sK7 ) ) )
= $false ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
( ( ^ [Y0: a] :
( ( sK2 @ sK6 @ Y0 )
=> ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK4 @ Y0 ) ) )
@ sK7 )
= $false ),
inference(sigma_clausification,[],[f62]) ).
thf(f62,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK6 @ Y0 )
=> ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f61]) ).
thf(f61,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y1 ) ) ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f60]) ).
thf(f60,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f59]) ).
thf(f59,plain,
( ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f40,f58]) ).
thf(f58,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( ( sK5 @ Y1 )
= ( sK5 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK5 @ Y1 @ Y2 @ Y3 )
=> ( sK5 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK5 @ Y1 @ Y4 @ Y3 )
& ( sK5 @ Y1 @ Y2 @ Y4 ) )
=> ( sK5 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f40]) ).
thf(f40,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( ( sK5 @ Y1 )
= ( sK5 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK5 @ Y1 @ Y2 @ Y3 )
=> ( sK5 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK5 @ Y1 @ Y4 @ Y3 )
& ( sK5 @ Y1 @ Y2 @ Y4 ) )
=> ( sK5 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f29,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( ( sK5 @ Y1 )
= ( sK5 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK5 @ Y1 @ Y2 @ Y3 )
=> ( sK5 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK5 @ Y1 @ Y4 @ Y3 )
& ( sK5 @ Y1 @ Y2 @ Y4 ) )
=> ( sK5 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f20,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK3 @ Y1 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( ( sK5 @ Y1 )
= ( sK5 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK5 @ Y1 @ Y2 @ Y3 )
=> ( sK5 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK5 @ Y1 @ Y4 @ Y3 )
& ( sK5 @ Y1 @ Y2 @ Y4 ) )
=> ( sK5 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f19,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y0 ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK3 @ Y1 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( ( sK5 @ Y1 )
= ( sK5 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK5 @ Y1 @ Y2 @ Y3 )
=> ( sK5 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK5 @ Y1 @ Y4 @ Y3 )
& ( sK5 @ Y1 @ Y2 @ Y4 ) )
=> ( sK5 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: a > b > b > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
=> ( Y0 @ Y1 @ ( sK3 @ Y1 ) @ ( sK4 @ Y1 ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ ( sK3 @ Y1 ) @ ( sK3 @ Y2 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK2 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( sK2 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( ( ( Y0 @ Y2 )
= ( Y0 @ Y1 ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y3 @ Y4 )
=> ( Y0 @ Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y5 @ Y4 )
& ( Y0 @ Y2 @ Y3 @ Y5 ) )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ ( sK3 @ Y1 ) @ ( sK4 @ Y2 ) ) ) ) ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f17]) ).
thf(f17,plain,
( ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
=> ( Y0 @ Y1 @ ( sK3 @ Y1 ) @ ( sK4 @ Y1 ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ ( sK3 @ Y1 ) @ ( sK3 @ Y2 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK2 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( sK2 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( ( ( Y0 @ Y2 )
= ( Y0 @ Y1 ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y3 @ Y4 )
=> ( Y0 @ Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y5 @ Y4 )
& ( Y0 @ Y2 @ Y3 @ Y5 ) )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ ( sK3 @ Y1 ) @ ( sK4 @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y2 )
=> ( Y1 @ Y2 @ ( sK3 @ Y2 ) @ ( Y0 @ Y2 ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ ( sK3 @ Y2 ) @ ( sK3 @ Y3 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK2 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( sK2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( ( ( Y1 @ Y3 )
= ( Y1 @ Y2 ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( Y1 @ Y3 @ Y4 @ Y5 )
=> ( Y1 @ Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( ( Y1 @ Y3 @ Y6 @ Y5 )
& ( Y1 @ Y3 @ Y4 @ Y6 ) )
=> ( Y1 @ Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ ( sK3 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y2 )
=> ( Y1 @ Y2 @ ( sK3 @ Y2 ) @ ( Y0 @ Y2 ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ ( sK3 @ Y2 ) @ ( sK3 @ Y3 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK2 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( sK2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( ( ( Y1 @ Y3 )
= ( Y1 @ Y2 ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( Y1 @ Y3 @ Y4 @ Y5 )
=> ( Y1 @ Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( ( Y1 @ Y3 @ Y6 @ Y5 )
& ( Y1 @ Y3 @ Y4 @ Y6 ) )
=> ( Y1 @ Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ ( sK3 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y2: a > b > b > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y3 )
=> ( Y2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y3 ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( sK2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( ( ( Y2 @ Y4 )
= ( Y2 @ Y3 ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( Y2 @ Y4 @ Y5 @ Y6 )
=> ( Y2 @ Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( Y2 @ Y4 @ Y7 @ Y6 )
& ( Y2 @ Y4 @ Y5 @ Y7 ) )
=> ( Y2 @ Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y2: a > b > b > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y3 )
=> ( Y2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y3 ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( sK2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( ( ( Y2 @ Y4 )
= ( Y2 @ Y3 ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( Y2 @ Y4 @ Y5 @ Y6 )
=> ( Y2 @ Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( Y2 @ Y4 @ Y7 @ Y6 )
& ( Y2 @ Y4 @ Y5 @ Y7 ) )
=> ( Y2 @ Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y3: a > b > b > $o] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y4 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y0 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y0 @ Y6 @ Y5 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( ( ( Y3 @ Y5 )
= ( Y3 @ Y4 ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y3 @ Y5 @ Y6 @ Y7 )
=> ( Y3 @ Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y3 @ Y5 @ Y8 @ Y7 )
& ( Y3 @ Y5 @ Y6 @ Y8 ) )
=> ( Y3 @ Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f9]) ).
thf(f9,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y3: a > b > b > $o] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y4 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y0 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y0 @ Y6 @ Y5 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( ( ( Y3 @ Y5 )
= ( Y3 @ Y4 ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y3 @ Y5 @ Y6 @ Y7 )
=> ( Y3 @ Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y3 @ Y5 @ Y8 @ Y7 )
& ( Y3 @ Y5 @ Y6 @ Y8 ) )
=> ( Y3 @ Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y3: a > b > b > $o] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y4 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y0 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y0 @ Y6 @ Y5 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( ( ( Y3 @ Y5 )
= ( Y3 @ Y4 ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y3 @ Y5 @ Y6 @ Y7 )
=> ( Y3 @ Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y3 @ Y5 @ Y8 @ Y7 )
& ( Y3 @ Y5 @ Y6 @ Y8 ) )
=> ( Y3 @ Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y3: a > b > b > $o] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y4 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y0 @ Y4 @ Y5 ) ) ) )
& $true
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y0 @ Y6 @ Y5 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( ( ( Y3 @ Y5 )
= ( Y3 @ Y4 ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y3 @ Y5 @ Y6 @ Y7 )
=> ( Y3 @ Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y3 @ Y5 @ Y8 @ Y7 )
& ( Y3 @ Y5 @ Y6 @ Y8 ) )
=> ( Y3 @ Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y3: a > b > b > $o] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y4 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y0 @ Y4 @ Y5 ) ) ) )
& ( Y0 = Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y0 @ Y6 @ Y5 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( ( ( Y3 @ Y5 )
= ( Y3 @ Y4 ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y3 @ Y5 @ Y6 @ Y7 )
=> ( Y3 @ Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y3 @ Y5 @ Y8 @ Y7 )
& ( Y3 @ Y5 @ Y6 @ Y8 ) )
=> ( Y3 @ Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b > b > $o )
@ ^ [Y3: a > b > b > $o] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y4 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y0 @ Y4 @ Y5 ) ) ) )
& ( Y0 = Y0 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y0 @ Y6 @ Y5 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( ( ( Y3 @ Y5 )
= ( Y3 @ Y4 ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y3 @ Y5 @ Y6 @ Y7 )
=> ( Y3 @ Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y3 @ Y5 @ Y8 @ Y7 )
& ( Y3 @ Y5 @ Y6 @ Y8 ) )
=> ( Y3 @ Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > b > b > $o,X1: a > b,X2: a > b,X3: a > a > $o] :
( ! [X4: a] :
( ( X3 @ X4 @ X4 )
=> ( X0 @ X4 @ ( X2 @ X4 ) @ ( X1 @ X4 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X0 @ X6 @ ( X2 @ X6 ) @ ( X2 @ X5 ) ) )
=> ( ( ! [X7: a,X8: a,X9: a] :
( ( ( X3 @ X9 @ X8 )
& ( X3 @ X7 @ X9 ) )
=> ( X3 @ X7 @ X8 ) )
& ( X3 = X3 )
& ! [X10: a,X11: a] :
( ( X3 @ X10 @ X11 )
=> ( X3 @ X11 @ X10 ) ) )
=> ( ! [X12: a,X13: a] :
( ( X3 @ X12 @ X13 )
=> ( ! [X14: b,X15: b,X16: b] :
( ( ( X0 @ X12 @ X16 @ X14 )
& ( X0 @ X12 @ X14 @ X15 ) )
=> ( X0 @ X12 @ X16 @ X15 ) )
& ! [X17: b,X18: b] :
( ( X0 @ X12 @ X18 @ X17 )
=> ( X0 @ X12 @ X17 @ X18 ) )
& ( ( X0 @ X12 )
= ( X0 @ X13 ) ) ) )
=> ! [X19: a,X20: a] :
( ( X3 @ X20 @ X19 )
=> ( X0 @ X20 @ ( X2 @ X20 ) @ ( X1 @ X19 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > b > b > $o,X3: a > b,X2: a > b,X0: a > a > $o] :
( ! [X4: a] :
( ( X0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) )
=> ( ( ! [X4: a,X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X6 ) )
& ( X0 = X0 )
& ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X0 @ X5 @ X4 ) ) )
=> ( ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( ! [X8: b,X6: b,X7: b] :
( ( ( X1 @ X4 @ X7 @ X8 )
& ( X1 @ X4 @ X8 @ X6 ) )
=> ( X1 @ X4 @ X7 @ X6 ) )
& ! [X8: b,X7: b] :
( ( X1 @ X4 @ X7 @ X8 )
=> ( X1 @ X4 @ X8 @ X7 ) )
& ( ( X1 @ X4 )
= ( X1 @ X5 ) ) ) )
=> ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a > b > b > $o,X3: a > b,X2: a > b,X0: a > a > $o] :
( ! [X4: a] :
( ( X0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) )
=> ( ( ! [X4: a,X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X6 ) )
& ( X0 = X0 )
& ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X0 @ X5 @ X4 ) ) )
=> ( ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( ! [X8: b,X6: b,X7: b] :
( ( ( X1 @ X4 @ X7 @ X8 )
& ( X1 @ X4 @ X8 @ X6 ) )
=> ( X1 @ X4 @ X7 @ X6 ) )
& ! [X8: b,X7: b] :
( ( X1 @ X4 @ X7 @ X8 )
=> ( X1 @ X4 @ X8 @ X7 ) )
& ( ( X1 @ X4 )
= ( X1 @ X5 ) ) ) )
=> ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OdsQpGJndw/Vampire---4.8_13083',cTHM518_pme) ).
thf(f333,plain,
( $true
= ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK4 @ sK7 ) ) ),
inference(boolean_simplification,[],[f328]) ).
thf(f328,plain,
( ( $true
=> ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK4 @ sK7 ) ) )
= $true ),
inference(superposition,[],[f297,f238]) ).
thf(f238,plain,
( $true
= ( sK5 @ sK6 @ ( sK3 @ sK7 ) @ ( sK4 @ sK7 ) ) ),
inference(superposition,[],[f121,f230]) ).
thf(f230,plain,
! [X2: b,X1: b] :
( ( sK5 @ sK7 @ X1 @ X2 )
= ( sK5 @ sK6 @ X1 @ X2 ) ),
inference(argument_congruence,[],[f201]) ).
thf(f201,plain,
! [X1: b] :
( ( sK5 @ sK6 @ X1 )
= ( sK5 @ sK7 @ X1 ) ),
inference(argument_congruence,[],[f187]) ).
thf(f187,plain,
( ( sK5 @ sK6 )
= ( sK5 @ sK7 ) ),
inference(equality_proxy_clausification,[],[f182]) ).
thf(f182,plain,
( ( ( sK5 @ sK6 )
= ( sK5 @ sK7 ) )
= $true ),
inference(boolean_simplification,[],[f181]) ).
thf(f181,plain,
( $true
= ( ( ( sK5 @ sK6 )
= ( sK5 @ sK7 ) )
& $true ) ),
inference(forward_demodulation,[],[f179,f180]) ).
thf(f180,plain,
( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f177]) ).
thf(f177,plain,
( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& $true ) ),
inference(backward_demodulation,[],[f170,f173]) ).
thf(f173,plain,
( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f139]) ).
thf(f139,plain,
( ( ( ( sK5 @ sK6 )
= ( sK5 @ sK7 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f133]) ).
thf(f133,plain,
( $true
= ( $true
=> ( ( ( sK5 @ sK6 )
= ( sK5 @ sK7 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(superposition,[],[f112,f66]) ).
thf(f66,plain,
( $true
= ( sK2 @ sK6 @ sK7 ) ),
inference(binary_proxy_clausification,[],[f64]) ).
thf(f112,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( ( ( sK5 @ X2 )
= ( sK5 @ X1 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ X2 @ Y0 @ Y1 )
=> ( sK5 @ X2 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ X2 @ Y2 @ Y1 )
& ( sK5 @ X2 @ Y0 @ Y2 ) )
=> ( sK5 @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f111]) ).
thf(f111,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( ( ( sK5 @ Y0 )
= ( sK5 @ X1 ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK5 @ Y0 @ Y1 @ Y2 )
=> ( sK5 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK5 @ Y0 @ Y3 @ Y2 )
& ( sK5 @ Y0 @ Y1 @ Y3 ) )
=> ( sK5 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f105]) ).
thf(f105,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( ( ( sK5 @ Y0 )
= ( sK5 @ X1 ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK5 @ Y0 @ Y1 @ Y2 )
=> ( sK5 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK5 @ Y0 @ Y3 @ Y2 )
& ( sK5 @ Y0 @ Y1 @ Y3 ) )
=> ( sK5 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f104]) ).
thf(f104,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( ( sK5 @ Y1 )
= ( sK5 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK5 @ Y1 @ Y2 @ Y3 )
=> ( sK5 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK5 @ Y1 @ Y4 @ Y3 )
& ( sK5 @ Y1 @ Y2 @ Y4 ) )
=> ( sK5 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f58]) ).
thf(f170,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f169]) ).
thf(f169,plain,
( ( $true
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f168]) ).
thf(f168,plain,
( $true
= ( ( ( sK5 @ sK6 )
= ( sK5 @ sK6 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f158]) ).
thf(f158,plain,
( $true
= ( $true
=> ( ( ( sK5 @ sK6 )
= ( sK5 @ sK6 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(superposition,[],[f112,f148]) ).
thf(f148,plain,
( ( sK2 @ sK6 @ sK6 )
= $true ),
inference(boolean_simplification,[],[f144]) ).
thf(f144,plain,
( $true
= ( $true
=> ( sK2 @ sK6 @ sK6 ) ) ),
inference(superposition,[],[f103,f76]) ).
thf(f76,plain,
( $true
= ( sK2 @ sK7 @ sK6 ) ),
inference(boolean_simplification,[],[f71]) ).
thf(f71,plain,
( $true
= ( $true
=> ( sK2 @ sK7 @ sK6 ) ) ),
inference(superposition,[],[f53,f66]) ).
thf(f53,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( sK2 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f52]) ).
thf(f52,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f51]) ).
thf(f51,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f49]) ).
thf(f49,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f48]) ).
thf(f48,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f41,f46]) ).
thf(f46,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f103,plain,
! [X0: a] :
( ( ( sK2 @ sK7 @ X0 )
=> ( sK2 @ sK6 @ X0 ) )
= $true ),
inference(boolean_simplification,[],[f97]) ).
thf(f97,plain,
! [X0: a] :
( ( ( $true
& ( sK2 @ sK7 @ X0 ) )
=> ( sK2 @ sK6 @ X0 ) )
= $true ),
inference(superposition,[],[f90,f66]) ).
thf(f90,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X3 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK2 @ X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[],[f89]) ).
thf(f89,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK2 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[],[f86]) ).
thf(f86,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK2 @ Y0 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f85]) ).
thf(f85,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f56]) ).
thf(f56,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f55]) ).
thf(f55,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f46]) ).
thf(f179,plain,
( ( ( ( sK5 @ sK6 )
= ( sK5 @ sK7 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f178]) ).
thf(f178,plain,
( ( ( ( sK5 @ sK6 )
= ( sK5 @ sK7 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK5 @ sK6 @ Y0 @ Y1 )
=> ( sK5 @ sK6 @ Y1 @ Y0 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f139,f173]) ).
thf(f121,plain,
( ( sK5 @ sK7 @ ( sK3 @ sK7 ) @ ( sK4 @ sK7 ) )
= $true ),
inference(boolean_simplification,[],[f114]) ).
thf(f114,plain,
( $true
= ( $true
=> ( sK5 @ sK7 @ ( sK3 @ sK7 ) @ ( sK4 @ sK7 ) ) ) ),
inference(superposition,[],[f27,f110]) ).
thf(f110,plain,
( ( sK2 @ sK7 @ sK7 )
= $true ),
inference(boolean_simplification,[],[f108]) ).
thf(f108,plain,
( $true
= ( $true
=> ( sK2 @ sK7 @ sK7 ) ) ),
inference(superposition,[],[f98,f76]) ).
thf(f98,plain,
! [X0: a] :
( $true
= ( ( sK2 @ X0 @ sK6 )
=> ( sK2 @ X0 @ sK7 ) ) ),
inference(boolean_simplification,[],[f95]) ).
thf(f95,plain,
! [X0: a] :
( $true
= ( ( ( sK2 @ X0 @ sK6 )
& $true )
=> ( sK2 @ X0 @ sK7 ) ) ),
inference(superposition,[],[f90,f66]) ).
thf(f27,plain,
! [X1: a] :
( $true
= ( ( sK2 @ X1 @ X1 )
=> ( sK5 @ X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f21]) ).
thf(f21,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f297,plain,
! [X0: b] :
( ( ( sK5 @ sK6 @ ( sK3 @ sK7 ) @ X0 )
=> ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ X0 ) )
= $true ),
inference(boolean_simplification,[],[f282]) ).
thf(f282,plain,
! [X0: b] :
( $true
= ( ( ( sK5 @ sK6 @ ( sK3 @ sK7 ) @ X0 )
& $true )
=> ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ X0 ) ) ),
inference(superposition,[],[f263,f75]) ).
thf(f75,plain,
( $true
= ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK3 @ sK7 ) ) ),
inference(boolean_simplification,[],[f73]) ).
thf(f73,plain,
( $true
= ( $true
=> ( sK5 @ sK6 @ ( sK3 @ sK6 ) @ ( sK3 @ sK7 ) ) ) ),
inference(superposition,[],[f38,f66]) ).
thf(f38,plain,
! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK5 @ X1 @ ( sK3 @ X1 ) @ ( sK3 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f37]) ).
thf(f37,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK5 @ X1 @ ( sK3 @ X1 ) @ ( sK3 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f36]) ).
thf(f36,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK5 @ X1 @ ( sK3 @ X1 ) @ ( sK3 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f35]) ).
thf(f35,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK3 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f30]) ).
thf(f30,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ ( sK3 @ Y0 ) @ ( sK3 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f263,plain,
! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK5 @ sK6 @ X3 @ X2 )
& ( sK5 @ sK6 @ X1 @ X3 ) )
=> ( sK5 @ sK6 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f262]) ).
thf(f262,plain,
! [X2: b,X3: b,X1: b] :
( ( ^ [Y0: b] :
( ( ( sK5 @ sK6 @ Y0 @ X2 )
& ( sK5 @ sK6 @ X1 @ Y0 ) )
=> ( sK5 @ sK6 @ X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f261]) ).
thf(f261,plain,
! [X2: b,X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( ( ( sK5 @ sK6 @ Y0 @ X2 )
& ( sK5 @ sK6 @ X1 @ Y0 ) )
=> ( sK5 @ sK6 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f260]) ).
thf(f260,plain,
! [X2: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK5 @ sK6 @ Y1 @ Y0 )
& ( sK5 @ sK6 @ X1 @ Y1 ) )
=> ( sK5 @ sK6 @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f257]) ).
thf(f257,plain,
! [X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK5 @ sK6 @ Y1 @ Y0 )
& ( sK5 @ sK6 @ X1 @ Y1 ) )
=> ( sK5 @ sK6 @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f254]) ).
thf(f254,plain,
! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK5 @ sK6 @ Y2 @ Y1 )
& ( sK5 @ sK6 @ Y0 @ Y2 ) )
=> ( sK5 @ sK6 @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV034^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.30 % Computer : n006.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 11:49:19 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 This is a TH0_THM_EQU_NAR problem
% 0.10/0.31 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.OdsQpGJndw/Vampire---4.8_13083
% 0.16/0.32 % (13195)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.16/0.32 % (13194)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.16/0.32 % (13194)Instruction limit reached!
% 0.16/0.32 % (13194)------------------------------
% 0.16/0.32 % (13194)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (13194)Termination reason: Unknown
% 0.16/0.32 % (13191)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.16/0.32 % (13194)Termination phase: Property scanning
% 0.16/0.32 % (13195)Instruction limit reached!
% 0.16/0.32 % (13195)------------------------------
% 0.16/0.32 % (13195)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32
% 0.16/0.32 % (13195)Termination reason: Unknown
% 0.16/0.32 % (13195)Termination phase: shuffling
% 0.16/0.32 % (13194)Memory used [KB]: 895
% 0.16/0.32
% 0.16/0.32 % (13194)Time elapsed: 0.002 s
% 0.16/0.32 % (13195)Memory used [KB]: 895
% 0.16/0.32 % (13194)Instructions burned: 2 (million)
% 0.16/0.32 % (13195)Time elapsed: 0.002 s
% 0.16/0.32 % (13194)------------------------------
% 0.16/0.32 % (13194)------------------------------
% 0.16/0.32 % (13195)Instructions burned: 2 (million)
% 0.16/0.32 % (13195)------------------------------
% 0.16/0.32 % (13195)------------------------------
% 0.16/0.32 % (13192)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 Vampire---4 for (3000ds/4Mi)
% 0.16/0.32 % (13193)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 Vampire---4 for (3000ds/27Mi)
% 0.16/0.32 % (13198)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (3000ds/3Mi)
% 0.16/0.32 % (13197)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (3000ds/18Mi)
% 0.16/0.32 % (13196)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (3000ds/275Mi)
% 0.16/0.32 % (13198)Instruction limit reached!
% 0.16/0.32 % (13198)------------------------------
% 0.16/0.32 % (13198)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (13198)Termination reason: Unknown
% 0.16/0.32 % (13198)Termination phase: Saturation
% 0.16/0.32
% 0.16/0.32 % (13198)Memory used [KB]: 5500
% 0.16/0.32 % (13198)Time elapsed: 0.003 s
% 0.16/0.32 % (13198)Instructions burned: 3 (million)
% 0.16/0.32 % (13198)------------------------------
% 0.16/0.32 % (13198)------------------------------
% 0.16/0.32 % (13192)Instruction limit reached!
% 0.16/0.32 % (13192)------------------------------
% 0.16/0.32 % (13192)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (13192)Termination reason: Unknown
% 0.16/0.32 % (13192)Termination phase: Saturation
% 0.16/0.32
% 0.16/0.32 % (13192)Memory used [KB]: 5500
% 0.16/0.32 % (13192)Time elapsed: 0.004 s
% 0.16/0.32 % (13192)Instructions burned: 5 (million)
% 0.16/0.32 % (13192)------------------------------
% 0.16/0.32 % (13192)------------------------------
% 0.16/0.33 % (13197)Instruction limit reached!
% 0.16/0.33 % (13197)------------------------------
% 0.16/0.33 % (13197)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (13197)Termination reason: Unknown
% 0.16/0.33 % (13197)Termination phase: Saturation
% 0.16/0.33
% 0.16/0.33 % (13197)Memory used [KB]: 5628
% 0.16/0.33 % (13197)Time elapsed: 0.012 s
% 0.16/0.33 % (13197)Instructions burned: 19 (million)
% 0.16/0.33 % (13197)------------------------------
% 0.16/0.33 % (13197)------------------------------
% 0.16/0.33 % (13199)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 Vampire---4 for (2999ds/37Mi)
% 0.16/0.33 % (13200)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 Vampire---4 for (2999ds/15Mi)
% 0.16/0.34 % (13201)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.34 % (13202)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 Vampire---4 for (2999ds/1041Mi)
% 0.16/0.34 % (13193)Instruction limit reached!
% 0.16/0.34 % (13193)------------------------------
% 0.16/0.34 % (13193)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (13193)Termination reason: Unknown
% 0.16/0.34 % (13193)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (13193)Memory used [KB]: 5628
% 0.16/0.34 % (13193)Time elapsed: 0.017 s
% 0.16/0.34 % (13193)Instructions burned: 28 (million)
% 0.16/0.34 % (13193)------------------------------
% 0.16/0.34 % (13193)------------------------------
% 0.16/0.34 % (13201)Instruction limit reached!
% 0.16/0.34 % (13201)------------------------------
% 0.16/0.34 % (13201)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (13201)Termination reason: Unknown
% 0.16/0.34 % (13201)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (13201)Memory used [KB]: 5500
% 0.16/0.34 % (13201)Time elapsed: 0.003 s
% 0.16/0.34 % (13201)Instructions burned: 4 (million)
% 0.16/0.34 % (13201)------------------------------
% 0.16/0.34 % (13201)------------------------------
% 0.16/0.34 % (13200)Instruction limit reached!
% 0.16/0.34 % (13200)------------------------------
% 0.16/0.34 % (13200)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (13200)Termination reason: Unknown
% 0.16/0.34 % (13200)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (13200)Memory used [KB]: 5628
% 0.16/0.34 % (13200)Time elapsed: 0.009 s
% 0.16/0.34 % (13200)Instructions burned: 16 (million)
% 0.16/0.34 % (13200)------------------------------
% 0.16/0.34 % (13200)------------------------------
% 0.16/0.35 % (13203)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.16/0.35 % (13199)Instruction limit reached!
% 0.16/0.35 % (13199)------------------------------
% 0.16/0.35 % (13199)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (13199)Termination reason: Unknown
% 0.16/0.35 % (13199)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (13199)Memory used [KB]: 5756
% 0.16/0.35 % (13199)Time elapsed: 0.018 s
% 0.16/0.35 % (13199)Instructions burned: 38 (million)
% 0.16/0.35 % (13199)------------------------------
% 0.16/0.35 % (13199)------------------------------
% 0.16/0.35 % (13204)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.16/0.35 % (13203)Instruction limit reached!
% 0.16/0.35 % (13203)------------------------------
% 0.16/0.35 % (13203)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (13203)Termination reason: Unknown
% 0.16/0.35 % (13203)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (13203)Memory used [KB]: 1023
% 0.16/0.35 % (13203)Time elapsed: 0.006 s
% 0.16/0.35 % (13203)Instructions burned: 8 (million)
% 0.16/0.35 % (13203)------------------------------
% 0.16/0.35 % (13203)------------------------------
% 0.16/0.35 % (13205)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 Vampire---4 for (2999ds/3Mi)
% 0.16/0.35 % (13205)Instruction limit reached!
% 0.16/0.35 % (13205)------------------------------
% 0.16/0.35 % (13205)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (13205)Termination reason: Unknown
% 0.16/0.35 % (13205)Termination phase: Twee Goal Transformation
% 0.16/0.35
% 0.16/0.35 % (13205)Memory used [KB]: 1023
% 0.16/0.35 % (13205)Time elapsed: 0.004 s
% 0.16/0.35 % (13205)Instructions burned: 5 (million)
% 0.16/0.35 % (13205)------------------------------
% 0.16/0.35 % (13205)------------------------------
% 0.16/0.35 % (13206)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 Vampire---4 for (2999ds/3Mi)
% 0.16/0.35 % (13206)Instruction limit reached!
% 0.16/0.35 % (13206)------------------------------
% 0.16/0.35 % (13206)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (13206)Termination reason: Unknown
% 0.16/0.35 % (13206)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (13206)Memory used [KB]: 1023
% 0.16/0.35 % (13206)Time elapsed: 0.003 s
% 0.16/0.35 % (13206)Instructions burned: 4 (million)
% 0.16/0.35 % (13206)------------------------------
% 0.16/0.35 % (13206)------------------------------
% 0.16/0.36 % (13204)Instruction limit reached!
% 0.16/0.36 % (13204)------------------------------
% 0.16/0.36 % (13204)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (13204)Termination reason: Unknown
% 0.16/0.36 % (13204)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (13204)Memory used [KB]: 5756
% 0.16/0.36 % (13204)Time elapsed: 0.010 s
% 0.16/0.36 % (13204)Instructions burned: 16 (million)
% 0.16/0.36 % (13204)------------------------------
% 0.16/0.36 % (13204)------------------------------
% 0.16/0.36 % (13208)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.36 % (13207)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.16/0.36 % (13208)Instruction limit reached!
% 0.16/0.36 % (13208)------------------------------
% 0.16/0.36 % (13208)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (13208)Termination reason: Unknown
% 0.16/0.36 % (13208)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (13208)Memory used [KB]: 5500
% 0.16/0.36 % (13208)Time elapsed: 0.003 s
% 0.16/0.36 % (13208)Instructions burned: 4 (million)
% 0.16/0.36 % (13208)------------------------------
% 0.16/0.36 % (13208)------------------------------
% 0.16/0.36 % (13209)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.16/0.36 % (13207)Refutation not found, incomplete strategy
% 0.16/0.36 % (13207)------------------------------
% 0.16/0.36 % (13207)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (13207)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.36
% 0.16/0.36
% 0.16/0.36 % (13207)Memory used [KB]: 5500
% 0.16/0.36 % (13207)Time elapsed: 0.004 s
% 0.16/0.36 % (13207)Instructions burned: 3 (million)
% 0.16/0.36 % (13207)------------------------------
% 0.16/0.36 % (13207)------------------------------
% 0.16/0.37 % (13210)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.16/0.37 % (13209)Instruction limit reached!
% 0.16/0.37 % (13209)------------------------------
% 0.16/0.37 % (13209)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (13209)Termination reason: Unknown
% 0.16/0.37 % (13209)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (13209)Memory used [KB]: 5500
% 0.16/0.37 % (13209)Time elapsed: 0.003 s
% 0.16/0.37 % (13209)Instructions burned: 4 (million)
% 0.16/0.37 % (13209)------------------------------
% 0.16/0.37 % (13209)------------------------------
% 0.16/0.37 % (13211)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.16/0.37 % (13202)First to succeed.
% 0.16/0.37 % (13210)Instruction limit reached!
% 0.16/0.37 % (13210)------------------------------
% 0.16/0.37 % (13210)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (13210)Termination reason: Unknown
% 0.16/0.37 % (13210)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (13210)Memory used [KB]: 5628
% 0.16/0.37 % (13210)Time elapsed: 0.010 s
% 0.16/0.37 % (13210)Instructions burned: 18 (million)
% 0.16/0.37 % (13210)------------------------------
% 0.16/0.37 % (13210)------------------------------
% 0.16/0.37 % (13212)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.16/0.38 % (13212)Instruction limit reached!
% 0.16/0.38 % (13212)------------------------------
% 0.16/0.38 % (13212)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (13212)Termination reason: Unknown
% 0.16/0.38 % (13212)Termination phase: Saturation
% 0.16/0.38
% 0.16/0.38 % (13212)Memory used [KB]: 5500
% 0.16/0.38 % (13212)Time elapsed: 0.004 s
% 0.16/0.38 % (13212)Instructions burned: 6 (million)
% 0.16/0.38 % (13212)------------------------------
% 0.16/0.38 % (13212)------------------------------
% 0.16/0.38 % (13213)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 Vampire---4 for (2999ds/902Mi)
% 0.16/0.38 % (13214)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 Vampire---4 for (2999ds/21Mi)
% 0.16/0.38 % (13202)Refutation found. Thanks to Tanya!
% 0.16/0.38 % SZS status Theorem for Vampire---4
% 0.16/0.38 % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.38 % (13202)------------------------------
% 0.16/0.38 % (13202)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (13202)Termination reason: Refutation
% 0.16/0.38
% 0.16/0.38 % (13202)Memory used [KB]: 6268
% 0.16/0.38 % (13202)Time elapsed: 0.067 s
% 0.16/0.38 % (13202)Instructions burned: 78 (million)
% 0.16/0.38 % (13202)------------------------------
% 0.16/0.38 % (13202)------------------------------
% 0.16/0.38 % (13190)Success in time 0.076 s
% 0.16/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------