TSTP Solution File: SEV034^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV034^5 : TPTP v8.2.0. 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 : n016.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 04:11:47 EDT 2024
% Result : Theorem 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 12
% Syntax : Number of formulae : 101 ( 87 unt; 11 typ; 0 def)
% Number of atoms : 956 ( 120 equ; 0 cnn)
% Maximal formula atoms : 2 ( 10 avg)
% Number of connectives : 3092 ( 6 ~; 0 |; 150 &;2245 @)
% ( 0 <=>; 295 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 137 ( 137 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 5 con; 0-3 aty)
% ( 396 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 530 ( 415 ^ 114 !; 0 ?; 530 :)
% ( 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_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a > b > b > $o ).
thf(func_def_22,type,
sK3: a > b ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a > b ).
thf(func_def_25,type,
sK6: a ).
thf(func_def_26,type,
sK7: a ).
thf(f364,plain,
$false,
inference(trivial_inequality_removal,[],[f363]) ).
thf(f363,plain,
$true = $false,
inference(forward_demodulation,[],[f358,f71]) ).
thf(f71,plain,
( $false
= ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK5 @ sK7 ) ) ),
inference(boolean_simplification,[],[f70]) ).
thf(f70,plain,
( $false
= ( $true
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK5 @ sK7 ) ) ) ),
inference(backward_demodulation,[],[f67,f69]) ).
thf(f69,plain,
( $true
= ( sK4 @ sK6 @ sK7 ) ),
inference(binary_proxy_clausification,[],[f67]) ).
thf(f67,plain,
( $false
= ( ( sK4 @ sK6 @ sK7 )
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK5 @ sK7 ) ) ) ),
inference(beta_eta_normalization,[],[f66]) ).
thf(f66,plain,
( ( ^ [Y0: a] :
( ( sK4 @ sK6 @ Y0 )
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK5 @ Y0 ) ) )
@ sK7 )
= $false ),
inference(sigma_clausification,[],[f65]) ).
thf(f65,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK6 @ Y0 )
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK5 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f64]) ).
thf(f64,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f63]) ).
thf(f63,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f62]) ).
thf(f62,plain,
( $false
= ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f35,f61]) ).
thf(f61,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y0 @ Y4 @ Y2 )
& ( sK2 @ Y0 @ Y2 @ Y3 ) )
=> ( sK2 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) )
& ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f35]) ).
thf(f35,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y0 @ Y4 @ Y2 )
& ( sK2 @ Y0 @ Y2 @ Y3 ) )
=> ( sK2 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) )
& ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f32]) ).
thf(f32,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y0 @ Y4 @ Y2 )
& ( sK2 @ Y0 @ Y2 @ Y3 ) )
=> ( sK2 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) )
& ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f31]) ).
thf(f31,plain,
( $false
= ( $true
=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y0 @ Y4 @ Y2 )
& ( sK2 @ Y0 @ Y2 @ Y3 ) )
=> ( sK2 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) )
& ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f20,f30]) ).
thf(f30,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( sK3 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f20,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( sK3 @ Y0 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y0 @ Y4 @ Y2 )
& ( sK2 @ Y0 @ Y2 @ Y3 ) )
=> ( sK2 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) )
& ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f19,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ Y0 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y0 ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( sK3 @ Y0 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y0 @ Y4 @ Y2 )
& ( sK2 @ Y0 @ Y2 @ Y3 ) )
=> ( sK2 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) )
& ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f18]) ).
thf(f18,plain,
( $false
= ( ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y1 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( Y0 @ Y1 ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( sK3 @ Y2 ) @ ( sK3 @ Y1 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( sK4 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( sK2 @ Y1 @ Y5 @ Y3 )
& ( sK2 @ Y1 @ Y3 @ Y4 ) )
=> ( sK2 @ Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( sK2 @ Y1 @ Y4 @ Y3 )
=> ( sK2 @ Y1 @ Y3 @ Y4 ) ) ) )
& ( ( sK2 @ Y1 )
= ( sK2 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[],[f17]) ).
thf(f17,plain,
( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y1 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( Y0 @ Y1 ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( sK3 @ Y2 ) @ ( sK3 @ Y1 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( sK4 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( sK2 @ Y1 @ Y5 @ Y3 )
& ( sK2 @ Y1 @ Y3 @ Y4 ) )
=> ( sK2 @ Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( sK2 @ Y1 @ Y4 @ Y3 )
=> ( sK2 @ Y1 @ Y3 @ Y4 ) ) ) )
& ( ( sK2 @ Y1 )
= ( sK2 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
=> ( sK2 @ Y2 @ ( sK3 @ Y2 ) @ ( Y1 @ Y2 ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( sK3 @ Y3 ) @ ( sK3 @ Y2 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( ( sK2 @ Y2 @ Y6 @ Y4 )
& ( sK2 @ Y2 @ Y4 @ Y5 ) )
=> ( sK2 @ Y2 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( sK2 @ Y2 @ Y5 @ Y4 )
=> ( sK2 @ Y2 @ Y4 @ Y5 ) ) ) )
& ( ( sK2 @ Y2 )
= ( sK2 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK3 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
=> ( sK2 @ Y2 @ ( sK3 @ Y2 ) @ ( Y1 @ Y2 ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( sK3 @ Y3 ) @ ( sK3 @ Y2 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( ( sK2 @ Y2 @ Y6 @ Y4 )
& ( sK2 @ Y2 @ Y4 @ Y5 ) )
=> ( sK2 @ Y2 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( sK2 @ Y2 @ Y5 @ Y4 )
=> ( sK2 @ Y2 @ Y4 @ Y5 ) ) ) )
& ( ( sK2 @ Y2 )
= ( sK2 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK3 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y3 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( sK2 @ Y3 @ Y7 @ Y5 )
& ( sK2 @ Y3 @ Y5 @ Y6 ) )
=> ( sK2 @ Y3 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( sK2 @ Y3 @ Y6 @ Y5 )
=> ( sK2 @ Y3 @ Y5 @ Y6 ) ) ) )
& ( ( sK2 @ Y3 )
= ( sK2 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y3 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( sK2 @ Y3 @ Y7 @ Y5 )
& ( sK2 @ Y3 @ Y5 @ Y6 ) )
=> ( sK2 @ Y3 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( sK2 @ Y3 @ Y6 @ Y5 )
=> ( sK2 @ Y3 @ Y5 @ Y6 ) ) ) )
& ( ( sK2 @ Y3 )
= ( sK2 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > b > b > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y4 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y1 @ Y5 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y4 @ Y6 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y0 @ Y4 @ Y8 @ Y6 )
& ( Y0 @ Y4 @ Y6 @ Y7 ) )
=> ( Y0 @ Y4 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y0 @ Y4 @ Y7 @ Y6 )
=> ( Y0 @ Y4 @ Y6 @ Y7 ) ) ) )
& ( ( Y0 @ Y4 )
= ( Y0 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f9]) ).
thf(f9,plain,
( ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y4 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y1 @ Y5 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y4 @ Y6 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y0 @ Y4 @ Y8 @ Y6 )
& ( Y0 @ Y4 @ Y6 @ Y7 ) )
=> ( Y0 @ Y4 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y0 @ Y4 @ Y7 @ Y6 )
=> ( Y0 @ Y4 @ Y6 @ Y7 ) ) ) )
& ( ( Y0 @ Y4 )
= ( Y0 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y4 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y1 @ Y5 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y4 @ Y6 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y0 @ Y4 @ Y8 @ Y6 )
& ( Y0 @ Y4 @ Y6 @ Y7 ) )
=> ( Y0 @ Y4 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y0 @ Y4 @ Y7 @ Y6 )
=> ( Y0 @ Y4 @ Y6 @ Y7 ) ) ) )
& ( ( Y0 @ Y4 )
= ( Y0 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y4 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y1 @ Y5 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y4 @ Y6 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y2 @ Y4 @ Y5 ) ) ) )
& $true )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y0 @ Y4 @ Y8 @ Y6 )
& ( Y0 @ Y4 @ Y6 @ Y7 ) )
=> ( Y0 @ Y4 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y0 @ Y4 @ Y7 @ Y6 )
=> ( Y0 @ Y4 @ Y6 @ Y7 ) ) ) )
& ( ( Y0 @ Y4 )
= ( Y0 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y4 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y1 @ Y5 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y4 @ Y6 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y2 @ Y4 @ Y5 ) ) ) )
& ( Y2 = Y2 ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y0 @ Y4 @ Y8 @ Y6 )
& ( Y0 @ Y4 @ Y6 @ Y7 ) )
=> ( Y0 @ Y4 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y0 @ Y4 @ Y7 @ Y6 )
=> ( Y0 @ Y4 @ Y6 @ Y7 ) ) ) )
& ( ( Y0 @ Y4 )
= ( Y0 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y4 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y4 ) ) ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y1 @ Y5 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y4 @ Y6 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y2 @ Y4 @ Y5 ) ) ) )
& ( Y2 = Y2 ) )
=> ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( !! @ b
@ ^ [Y8: b] :
( ( ( Y0 @ Y4 @ Y8 @ Y6 )
& ( Y0 @ Y4 @ Y6 @ Y7 ) )
=> ( Y0 @ Y4 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( Y0 @ Y4 @ Y7 @ Y6 )
=> ( Y0 @ Y4 @ Y6 @ Y7 ) ) ) )
& ( ( Y0 @ Y4 )
= ( Y0 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > b,X1: a > a > $o,X2: a > b,X3: a > b > b > $o] :
( ! [X4: a] :
( ( X1 @ X4 @ X4 )
=> ( X3 @ X4 @ ( X2 @ X4 ) @ ( X0 @ X4 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X3 @ X5 @ ( X2 @ X5 ) @ ( X2 @ X6 ) ) )
=> ( ( ( X1 = X1 )
& ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X1 @ X8 @ X7 ) )
& ! [X9: a,X10: a,X11: a] :
( ( ( X1 @ X10 @ X11 )
& ( X1 @ X11 @ X9 ) )
=> ( X1 @ X10 @ X9 ) ) )
=> ( ! [X12: a,X13: a] :
( ( X1 @ X13 @ X12 )
=> ( ( ( X3 @ X13 )
= ( X3 @ X12 ) )
& ! [X14: b,X15: b] :
( ( X3 @ X13 @ X14 @ X15 )
=> ( X3 @ X13 @ X15 @ X14 ) )
& ! [X16: b,X17: b,X18: b] :
( ( ( X3 @ X13 @ X18 @ X17 )
& ( X3 @ X13 @ X16 @ X18 ) )
=> ( X3 @ X13 @ X16 @ X17 ) ) ) )
=> ! [X19: a,X20: a] :
( ( X1 @ X20 @ X19 )
=> ( X3 @ X20 @ ( X2 @ X20 ) @ ( X0 @ X19 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a > b,X0: a > a > $o,X2: a > b,X1: a > b > b > $o] :
( ! [X4: a] :
( ( X0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ( ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) )
=> ( ( ( X0 = X0 )
& ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X0 @ X5 @ X4 ) )
& ! [X6: a,X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X6 ) )
=> ( X0 @ X4 @ X6 ) ) )
=> ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( ( ( X1 @ X4 )
= ( X1 @ X5 ) )
& ! [X7: b,X8: b] :
( ( X1 @ X4 @ X7 @ X8 )
=> ( X1 @ X4 @ X8 @ X7 ) )
& ! [X7: b,X6: b,X8: b] :
( ( ( X1 @ X4 @ X8 @ X6 )
& ( X1 @ X4 @ X7 @ X8 ) )
=> ( X1 @ X4 @ X7 @ X6 ) ) ) )
=> ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X3: a > b,X0: a > a > $o,X2: a > b,X1: a > b > b > $o] :
( ! [X4: a] :
( ( X0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ( ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) )
=> ( ( ( X0 = X0 )
& ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X0 @ X5 @ X4 ) )
& ! [X6: a,X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X6 ) )
=> ( X0 @ X4 @ X6 ) ) )
=> ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( ( ( X1 @ X4 )
= ( X1 @ X5 ) )
& ! [X7: b,X8: b] :
( ( X1 @ X4 @ X7 @ X8 )
=> ( X1 @ X4 @ X8 @ X7 ) )
& ! [X7: b,X6: b,X8: b] :
( ( ( X1 @ X4 @ X8 @ X6 )
& ( X1 @ X4 @ X7 @ X8 ) )
=> ( X1 @ X4 @ X7 @ X6 ) ) ) )
=> ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM518_pme) ).
thf(f358,plain,
( $true
= ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK5 @ sK7 ) ) ),
inference(boolean_simplification,[],[f354]) ).
thf(f354,plain,
( $true
= ( $true
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK5 @ sK7 ) ) ) ),
inference(superposition,[],[f297,f240]) ).
thf(f240,plain,
( $true
= ( sK2 @ sK6 @ ( sK3 @ sK7 ) @ ( sK5 @ sK7 ) ) ),
inference(superposition,[],[f130,f211]) ).
thf(f211,plain,
! [X2: b,X1: b] :
( ( sK2 @ sK6 @ X1 @ X2 )
= ( sK2 @ sK7 @ X1 @ X2 ) ),
inference(argument_congruence,[],[f184]) ).
thf(f184,plain,
! [X1: b] :
( ( sK2 @ sK7 @ X1 )
= ( sK2 @ sK6 @ X1 ) ),
inference(argument_congruence,[],[f175]) ).
thf(f175,plain,
( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ),
inference(equality_proxy_clausification,[],[f150]) ).
thf(f150,plain,
( $true
= ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ) ),
inference(boolean_simplification,[],[f149]) ).
thf(f149,plain,
( $true
= ( $true
& ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ) ) ),
inference(backward_demodulation,[],[f107,f146]) ).
thf(f146,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK6 @ Y2 @ Y0 )
& ( sK2 @ sK6 @ Y0 @ Y1 ) )
=> ( sK2 @ sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK6 @ Y1 @ Y0 )
=> ( sK2 @ sK6 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f107]) ).
thf(f107,plain,
( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK6 @ Y2 @ Y0 )
& ( sK2 @ sK6 @ Y0 @ Y1 ) )
=> ( sK2 @ sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK6 @ Y1 @ Y0 )
=> ( sK2 @ sK6 @ Y0 @ Y1 ) ) ) )
& ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ) ) ),
inference(boolean_simplification,[],[f106]) ).
thf(f106,plain,
( $true
= ( $true
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK6 @ Y2 @ Y0 )
& ( sK2 @ sK6 @ Y0 @ Y1 ) )
=> ( sK2 @ sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK6 @ Y1 @ Y0 )
=> ( sK2 @ sK6 @ Y0 @ Y1 ) ) ) )
& ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ) ) ) ),
inference(superposition,[],[f101,f69]) ).
thf(f101,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK4 @ X1 @ X2 )
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ X1 @ Y2 @ Y0 )
& ( sK2 @ X1 @ Y0 @ Y1 ) )
=> ( sK2 @ X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ X1 @ Y1 @ Y0 )
=> ( sK2 @ X1 @ Y0 @ Y1 ) ) ) )
& ( ( sK2 @ X1 )
= ( sK2 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[],[f100]) ).
thf(f100,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ X1 @ Y3 @ Y1 )
& ( sK2 @ X1 @ Y1 @ Y2 ) )
=> ( sK2 @ X1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ X1 @ Y2 @ Y1 )
=> ( sK2 @ X1 @ Y1 @ Y2 ) ) ) )
& ( ( sK2 @ X1 )
= ( sK2 @ Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f97]) ).
thf(f97,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ X1 @ Y3 @ Y1 )
& ( sK2 @ X1 @ Y1 @ Y2 ) )
=> ( sK2 @ X1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ X1 @ Y2 @ Y1 )
=> ( sK2 @ X1 @ Y1 @ Y2 ) ) ) )
& ( ( sK2 @ X1 )
= ( sK2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f96]) ).
thf(f96,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y0 @ Y4 @ Y2 )
& ( sK2 @ Y0 @ Y2 @ Y3 ) )
=> ( sK2 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y0 @ Y3 @ Y2 )
=> ( sK2 @ Y0 @ Y2 @ Y3 ) ) ) )
& ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f61]) ).
thf(f130,plain,
( $true
= ( sK2 @ sK7 @ ( sK3 @ sK7 ) @ ( sK5 @ sK7 ) ) ),
inference(boolean_simplification,[],[f121]) ).
thf(f121,plain,
( ( $true
=> ( sK2 @ sK7 @ ( sK3 @ sK7 ) @ ( sK5 @ sK7 ) ) )
= $true ),
inference(superposition,[],[f27,f113]) ).
thf(f113,plain,
( $true
= ( sK4 @ sK7 @ sK7 ) ),
inference(boolean_simplification,[],[f111]) ).
thf(f111,plain,
( ( $true
=> ( sK4 @ sK7 @ sK7 ) )
= $true ),
inference(superposition,[],[f82,f78]) ).
thf(f78,plain,
( $true
= ( sK4 @ sK7 @ sK6 ) ),
inference(boolean_simplification,[],[f75]) ).
thf(f75,plain,
( $true
= ( $true
=> ( sK4 @ sK7 @ sK6 ) ) ),
inference(superposition,[],[f55,f69]) ).
thf(f55,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK4 @ X2 @ X1 )
=> ( sK4 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f54]) ).
thf(f54,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( sK4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f51]) ).
thf(f51,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( sK4 @ X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f44]) ).
thf(f44,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f36]) ).
thf(f36,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f32]) ).
thf(f82,plain,
! [X0: a] :
( $true
= ( ( sK4 @ X0 @ sK6 )
=> ( sK4 @ X0 @ sK7 ) ) ),
inference(boolean_simplification,[],[f72]) ).
thf(f72,plain,
! [X0: a] :
( $true
= ( ( $true
& ( sK4 @ X0 @ sK6 ) )
=> ( sK4 @ X0 @ sK7 ) ) ),
inference(superposition,[],[f57,f69]) ).
thf(f57,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK4 @ X1 @ X3 )
& ( sK4 @ X2 @ X1 ) )
=> ( sK4 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[],[f56]) ).
thf(f56,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
& ( sK4 @ X2 @ X1 ) )
=> ( sK4 @ X2 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[],[f53]) ).
thf(f53,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
& ( sK4 @ X2 @ X1 ) )
=> ( sK4 @ X2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f52]) ).
thf(f52,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ X1 @ Y1 )
& ( sK4 @ Y0 @ X1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f49]) ).
thf(f49,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ X1 @ Y1 )
& ( sK4 @ Y0 @ X1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f48]) ).
thf(f48,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f47]) ).
thf(f47,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) ) ),
inference(boolean_simplification,[],[f46]) ).
thf(f46,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f36,f44]) ).
thf(f27,plain,
! [X1: a] :
( $true
= ( ( sK4 @ X1 @ X1 )
=> ( sK2 @ X1 @ ( sK3 @ X1 ) @ ( sK5 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK4 @ Y0 @ Y0 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f21]) ).
thf(f21,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ Y0 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK5 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f297,plain,
! [X0: b] :
( $true
= ( ( sK2 @ sK6 @ ( sK3 @ sK7 ) @ X0 )
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ X0 ) ) ),
inference(boolean_simplification,[],[f271]) ).
thf(f271,plain,
! [X0: b] :
( $true
= ( ( $true
& ( sK2 @ sK6 @ ( sK3 @ sK7 ) @ X0 ) )
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ X0 ) ) ),
inference(superposition,[],[f254,f81]) ).
thf(f81,plain,
( $true
= ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK3 @ sK7 ) ) ),
inference(boolean_simplification,[],[f77]) ).
thf(f77,plain,
( $true
= ( $true
=> ( sK2 @ sK6 @ ( sK3 @ sK6 ) @ ( sK3 @ sK7 ) ) ) ),
inference(superposition,[],[f42,f69]) ).
thf(f42,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK4 @ X2 @ X1 )
=> ( sK2 @ X2 @ ( sK3 @ X2 ) @ ( sK3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK3 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f34]) ).
thf(f34,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( sK2 @ Y0 @ ( sK3 @ Y0 ) @ ( sK3 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f33]) ).
thf(f33,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK3 @ Y1 ) @ ( sK3 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f30]) ).
thf(f254,plain,
! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK2 @ sK6 @ X3 @ X1 )
& ( sK2 @ sK6 @ X1 @ X2 ) )
=> ( sK2 @ sK6 @ X3 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f253]) ).
thf(f253,plain,
! [X2: b,X3: b,X1: b] :
( ( ^ [Y0: b] :
( ( ( sK2 @ sK6 @ Y0 @ X1 )
& ( sK2 @ sK6 @ X1 @ X2 ) )
=> ( sK2 @ sK6 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f252]) ).
thf(f252,plain,
! [X2: b,X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( ( ( sK2 @ sK6 @ Y0 @ X1 )
& ( sK2 @ sK6 @ X1 @ X2 ) )
=> ( sK2 @ sK6 @ Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f251]) ).
thf(f251,plain,
! [X2: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK2 @ sK6 @ Y1 @ X1 )
& ( sK2 @ sK6 @ X1 @ Y0 ) )
=> ( sK2 @ sK6 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f247]) ).
thf(f247,plain,
! [X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK2 @ sK6 @ Y1 @ X1 )
& ( sK2 @ sK6 @ X1 @ Y0 ) )
=> ( sK2 @ sK6 @ Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f245]) ).
thf(f245,plain,
! [X1: b] :
( ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK6 @ Y2 @ Y0 )
& ( sK2 @ sK6 @ Y0 @ Y1 ) )
=> ( sK2 @ sK6 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f232]) ).
thf(f232,plain,
( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK6 @ Y2 @ Y0 )
& ( sK2 @ sK6 @ Y0 @ Y1 ) )
=> ( sK2 @ sK6 @ Y2 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f231]) ).
thf(f231,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK6 @ Y2 @ Y0 )
& ( sK2 @ sK6 @ Y0 @ Y1 ) )
=> ( sK2 @ sK6 @ Y2 @ Y1 ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f146,f227]) ).
thf(f227,plain,
( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK6 @ Y1 @ Y0 )
=> ( sK2 @ sK6 @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEV034^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.12 % 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
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun May 19 18:37:37 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 This is a TH0_THM_EQU_NAR problem
% 0.11/0.33 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/benchmark/theBenchmark.p
% 0.11/0.35 % (28525)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)
% 0.11/0.35 % (28527)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.35 % (28523)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)
% 0.11/0.35 % (28526)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)
% 0.11/0.35 % (28524)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.35 % (28528)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.11/0.35 % (28522)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)
% 0.11/0.35 % (28524)Instruction limit reached!
% 0.11/0.35 % (28524)------------------------------
% 0.11/0.35 % (28524)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28524)Termination reason: Unknown
% 0.11/0.35 % (28524)Termination phase: Preprocessing 3
% 0.11/0.35 % (28525)Instruction limit reached!
% 0.11/0.35 % (28525)------------------------------
% 0.11/0.35 % (28525)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28525)Termination reason: Unknown
% 0.11/0.35 % (28525)Termination phase: Property scanning
% 0.11/0.35
% 0.11/0.35 % (28525)Memory used [KB]: 1023
% 0.11/0.35 % (28525)Time elapsed: 0.003 s
% 0.11/0.35 % (28525)Instructions burned: 3 (million)
% 0.11/0.35 % (28525)------------------------------
% 0.11/0.35 % (28525)------------------------------
% 0.11/0.35
% 0.11/0.35 % (28524)Memory used [KB]: 1023
% 0.11/0.35 % (28524)Time elapsed: 0.003 s
% 0.11/0.35 % (28524)Instructions burned: 2 (million)
% 0.11/0.35 % (28524)------------------------------
% 0.11/0.35 % (28524)------------------------------
% 0.11/0.35 % (28528)Instruction limit reached!
% 0.11/0.35 % (28528)------------------------------
% 0.11/0.35 % (28528)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28528)Termination reason: Unknown
% 0.11/0.35 % (28528)Termination phase: Clausification
% 0.11/0.35
% 0.11/0.35 % (28528)Memory used [KB]: 1023
% 0.11/0.35 % (28528)Time elapsed: 0.003 s
% 0.11/0.35 % (28528)Instructions burned: 3 (million)
% 0.11/0.35 % (28528)------------------------------
% 0.11/0.35 % (28528)------------------------------
% 0.11/0.35 % (28521)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.35 % (28522)Instruction limit reached!
% 0.11/0.35 % (28522)------------------------------
% 0.11/0.35 % (28522)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (28522)Termination reason: Unknown
% 0.11/0.35 % (28522)Termination phase: Saturation
% 0.11/0.35
% 0.11/0.35 % (28522)Memory used [KB]: 5500
% 0.11/0.35 % (28522)Time elapsed: 0.004 s
% 0.11/0.35 % (28522)Instructions burned: 5 (million)
% 0.11/0.35 % (28522)------------------------------
% 0.11/0.35 % (28522)------------------------------
% 0.11/0.36 % (28527)Instruction limit reached!
% 0.11/0.36 % (28527)------------------------------
% 0.11/0.36 % (28527)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (28527)Termination reason: Unknown
% 0.11/0.36 % (28527)Termination phase: Saturation
% 0.11/0.36
% 0.11/0.36 % (28527)Memory used [KB]: 5628
% 0.11/0.36 % (28527)Time elapsed: 0.012 s
% 0.11/0.36 % (28527)Instructions burned: 18 (million)
% 0.11/0.36 % (28527)------------------------------
% 0.11/0.36 % (28527)------------------------------
% 0.11/0.36 % (28531)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.11/0.36 % (28530)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 theBenchmark for (2999ds/15Mi)
% 0.11/0.37 % (28531)Instruction limit reached!
% 0.11/0.37 % (28531)------------------------------
% 0.11/0.37 % (28531)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (28531)Termination reason: Unknown
% 0.11/0.37 % (28531)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (28531)Memory used [KB]: 5500
% 0.11/0.37 % (28531)Time elapsed: 0.003 s
% 0.11/0.37 % (28531)Instructions burned: 3 (million)
% 0.11/0.37 % (28523)Instruction limit reached!
% 0.11/0.37 % (28523)------------------------------
% 0.11/0.37 % (28523)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (28531)------------------------------
% 0.11/0.37 % (28531)------------------------------
% 0.11/0.37 % (28523)Termination reason: Unknown
% 0.11/0.37 % (28523)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (28523)Memory used [KB]: 5628
% 0.11/0.37 % (28523)Time elapsed: 0.018 s
% 0.11/0.37 % (28523)Instructions burned: 28 (million)
% 0.11/0.37 % (28523)------------------------------
% 0.11/0.37 % (28523)------------------------------
% 0.11/0.37 % (28532)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 theBenchmark for (2999ds/1041Mi)
% 0.11/0.37 % (28529)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 theBenchmark for (2999ds/37Mi)
% 0.11/0.37 % (28530)Instruction limit reached!
% 0.11/0.37 % (28530)------------------------------
% 0.11/0.37 % (28530)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (28530)Termination reason: Unknown
% 0.11/0.37 % (28530)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (28530)Memory used [KB]: 5628
% 0.11/0.37 % (28530)Time elapsed: 0.010 s
% 0.11/0.37 % (28530)Instructions burned: 16 (million)
% 0.11/0.37 % (28530)------------------------------
% 0.11/0.37 % (28530)------------------------------
% 0.19/0.38 % (28533)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.38 % (28535)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 theBenchmark for (2999ds/3Mi)
% 0.19/0.38 % (28533)Instruction limit reached!
% 0.19/0.38 % (28533)------------------------------
% 0.19/0.38 % (28533)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (28533)Termination reason: Unknown
% 0.19/0.38 % (28533)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (28533)Memory used [KB]: 1023
% 0.19/0.38 % (28533)Time elapsed: 0.028 s
% 0.19/0.38 % (28533)Instructions burned: 8 (million)
% 0.19/0.38 % (28533)------------------------------
% 0.19/0.38 % (28533)------------------------------
% 0.19/0.38 % (28535)Instruction limit reached!
% 0.19/0.38 % (28535)------------------------------
% 0.19/0.38 % (28535)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (28535)Termination reason: Unknown
% 0.19/0.38 % (28535)Termination phase: Property scanning
% 0.19/0.38
% 0.19/0.38 % (28535)Memory used [KB]: 1023
% 0.19/0.38 % (28535)Time elapsed: 0.003 s
% 0.19/0.38 % (28535)Instructions burned: 3 (million)
% 0.19/0.38 % (28535)------------------------------
% 0.19/0.38 % (28535)------------------------------
% 0.19/0.39 % (28529)Instruction limit reached!
% 0.19/0.39 % (28529)------------------------------
% 0.19/0.39 % (28529)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (28529)Termination reason: Unknown
% 0.19/0.39 % (28529)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (28529)Memory used [KB]: 5756
% 0.19/0.39 % (28529)Time elapsed: 0.041 s
% 0.19/0.39 % (28529)Instructions burned: 38 (million)
% 0.19/0.39 % (28529)------------------------------
% 0.19/0.39 % (28529)------------------------------
% 0.19/0.39 % (28536)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 theBenchmark for (2999ds/3Mi)
% 0.19/0.39 % (28536)Instruction limit reached!
% 0.19/0.39 % (28536)------------------------------
% 0.19/0.39 % (28536)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (28536)Termination reason: Unknown
% 0.19/0.39 % (28536)Termination phase: Equality resolution with deletion
% 0.19/0.39
% 0.19/0.39 % (28536)Memory used [KB]: 1023
% 0.19/0.39 % (28536)Time elapsed: 0.003 s
% 0.19/0.39 % (28536)Instructions burned: 4 (million)
% 0.19/0.39 % (28536)------------------------------
% 0.19/0.39 % (28536)------------------------------
% 0.19/0.39 % (28534)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.39 % (28538)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.40 % (28538)Instruction limit reached!
% 0.19/0.40 % (28538)------------------------------
% 0.19/0.40 % (28538)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (28538)Termination reason: Unknown
% 0.19/0.40 % (28538)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (28538)Memory used [KB]: 5500
% 0.19/0.40 % (28538)Time elapsed: 0.003 s
% 0.19/0.40 % (28538)Instructions burned: 4 (million)
% 0.19/0.40 % (28538)------------------------------
% 0.19/0.40 % (28538)------------------------------
% 0.19/0.40 % (28534)Instruction limit reached!
% 0.19/0.40 % (28534)------------------------------
% 0.19/0.40 % (28534)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (28534)Termination reason: Unknown
% 0.19/0.40 % (28534)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (28534)Memory used [KB]: 5756
% 0.19/0.40 % (28534)Time elapsed: 0.035 s
% 0.19/0.40 % (28534)Instructions burned: 17 (million)
% 0.19/0.40 % (28534)------------------------------
% 0.19/0.40 % (28534)------------------------------
% 0.19/0.40 % (28537)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.40 % (28539)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.40 % (28537)Refutation not found, incomplete strategy
% 0.19/0.40 % (28537)------------------------------
% 0.19/0.40 % (28537)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (28537)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 % (28537)Memory used [KB]: 5500
% 0.19/0.40 % (28537)Time elapsed: 0.029 s
% 0.19/0.40 % (28537)Instructions burned: 5 (million)
% 0.19/0.40 % (28537)------------------------------
% 0.19/0.40 % (28537)------------------------------
% 0.19/0.40 % (28539)Instruction limit reached!
% 0.19/0.40 % (28539)------------------------------
% 0.19/0.40 % (28539)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (28539)Termination reason: Unknown
% 0.19/0.40 % (28539)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (28539)Memory used [KB]: 5500
% 0.19/0.40 % (28539)Time elapsed: 0.025 s
% 0.19/0.40 % (28539)Instructions burned: 5 (million)
% 0.19/0.40 % (28539)------------------------------
% 0.19/0.40 % (28539)------------------------------
% 0.19/0.40 % (28540)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.41 % (28532)First to succeed.
% 0.19/0.41 % (28542)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.41 % (28541)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.19/0.41 % (28540)Instruction limit reached!
% 0.19/0.41 % (28540)------------------------------
% 0.19/0.41 % (28540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (28540)Termination reason: Unknown
% 0.19/0.41 % (28540)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (28540)Memory used [KB]: 5628
% 0.19/0.41 % (28540)Time elapsed: 0.036 s
% 0.19/0.41 % (28540)Instructions burned: 18 (million)
% 0.19/0.41 % (28540)------------------------------
% 0.19/0.41 % (28540)------------------------------
% 0.19/0.41 % (28542)Instruction limit reached!
% 0.19/0.41 % (28542)------------------------------
% 0.19/0.41 % (28542)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (28542)Termination reason: Unknown
% 0.19/0.41 % (28542)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (28542)Memory used [KB]: 5500
% 0.19/0.41 % (28542)Time elapsed: 0.005 s
% 0.19/0.41 % (28542)Instructions burned: 6 (million)
% 0.19/0.41 % (28542)------------------------------
% 0.19/0.41 % (28542)------------------------------
% 0.19/0.42 % (28532)Refutation found. Thanks to Tanya!
% 0.19/0.42 % SZS status Theorem for theBenchmark
% 0.19/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.42 % (28532)------------------------------
% 0.19/0.42 % (28532)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (28532)Termination reason: Refutation
% 0.19/0.42
% 0.19/0.42 % (28532)Memory used [KB]: 6140
% 0.19/0.42 % (28532)Time elapsed: 0.049 s
% 0.19/0.42 % (28532)Instructions burned: 83 (million)
% 0.19/0.42 % (28532)------------------------------
% 0.19/0.42 % (28532)------------------------------
% 0.19/0.42 % (28520)Success in time 0.081 s
% 0.19/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------