TSTP Solution File: SYO244^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO244^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 : 600s
% DateTime : Thu Jul 21 17:32:56 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 13
% Syntax : Number of formulae : 123 ( 35 unt; 12 typ; 0 def)
% Number of atoms : 858 ( 268 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1848 ( 602 ~; 347 |; 23 &; 845 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 771 ( 771 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 341 ( 26 ^ 283 !; 32 ?; 341 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_SY31,type,
sK10_SY31: ( ( a > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK11_SY38,type,
sK11_SY38: ( a > $o ) > ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(tp_sK1_A,type,
sK1_A: ( ( a > $o ) > $o ) > $o ).
thf(tp_sK2_SY15,type,
sK2_SY15: ( a > $o ) > $o ).
thf(tp_sK3_Xu,type,
sK3_Xu: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK4_Xf,type,
sK4_Xf: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK5_SV3,type,
sK5_SV3: a ).
thf(tp_sK6_SY29,type,
sK6_SY29: ( a > $o ) > $o ).
thf(tp_sK7_SY33,type,
sK7_SY33: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK8_SY35,type,
sK8_SY35: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(tp_sK9_SY31,type,
sK9_SY31: ( ( a > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(1,conjecture,
( ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ? [Xt: a > $o] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
=> ! [A: ( ( a > $o ) > $o ) > $o] :
( ( ? [X: ( a > $o ) > $o] : ( A @ X )
& ! [X: ( a > $o ) > $o] :
( ( A @ X )
=> ? [Xu: a > $o] : ( X @ Xu ) ) )
=> ( ( ^ [Xx: a] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ? [Xb: a > $o] :
( ( Xa @ Xb )
& ( Xb @ Xx ) ) ) )
= ( ^ [Xx: a] :
? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ( ( Xa @ ( Xf @ Xa ) )
& ( Xf @ Xa @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM535B) ).
thf(2,negated_conjecture,
( ( ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ? [Xt: a > $o] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
=> ! [A: ( ( a > $o ) > $o ) > $o] :
( ( ? [X: ( a > $o ) > $o] : ( A @ X )
& ! [X: ( a > $o ) > $o] :
( ( A @ X )
=> ? [Xu: a > $o] : ( X @ Xu ) ) )
=> ( ( ^ [Xx: a] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ? [Xb: a > $o] :
( ( Xa @ Xb )
& ( Xb @ Xx ) ) ) )
= ( ^ [Xx: a] :
? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ( ( Xa @ ( Xf @ Xa ) )
& ( Xf @ Xa @ Xx ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ? [Xt: a > $o] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
=> ! [A: ( ( a > $o ) > $o ) > $o] :
( ( ? [X: ( a > $o ) > $o] : ( A @ X )
& ! [X: ( a > $o ) > $o] :
( ( A @ X )
=> ? [Xu: a > $o] : ( X @ Xu ) ) )
=> ( ( ^ [Xx: a] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ? [Xb: a > $o] :
( ( Xa @ Xb )
& ( Xb @ Xx ) ) ) )
= ( ^ [Xx: a] :
? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ( ( Xa @ ( Xf @ Xa ) )
& ( Xf @ Xa @ Xx ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ? [Xt: a > $o] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: ( ( a > $o ) > $o ) > $o] :
( ( ? [X: ( a > $o ) > $o] : ( A @ X )
& ! [X: ( a > $o ) > $o] :
( ( A @ X )
=> ? [Xu: a > $o] : ( X @ Xu ) ) )
=> ( ( ^ [Xx: a] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ? [Xb: a > $o] :
( ( Xa @ Xb )
& ( Xb @ Xx ) ) ) )
= ( ^ [Xx: a] :
? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ( ( Xa @ ( Xf @ Xa ) )
& ( Xf @ Xa @ Xx ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [A: ( ( a > $o ) > $o ) > $o] :
( ( ? [X: ( a > $o ) > $o] : ( A @ X )
& ! [X: ( a > $o ) > $o] :
( ( A @ X )
=> ? [Xu: a > $o] : ( X @ Xu ) ) )
=> ( ( ^ [Xx: a] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ? [Xb: a > $o] :
( ( Xa @ Xb )
& ( Xb @ Xx ) ) ) )
= ( ^ [Xx: a] :
? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [Xa: ( a > $o ) > $o] :
( ( A @ Xa )
=> ( ( Xa @ ( Xf @ Xa ) )
& ( Xf @ Xa @ Xx ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY13: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY13 )
| ( SY13 @ ( sK3_Xu @ SY13 ) ) )
& ( sK1_A @ sK2_SY15 )
& ( ( ^ [SY16: a] :
! [SY17: ( a > $o ) > $o] :
( ( sK1_A @ SY17 )
=> ? [Xb: a > $o] :
( ( SY17 @ Xb )
& ( Xb @ SY16 ) ) ) )
!= ( ^ [SY19: a] :
? [SY20: ( ( a > $o ) > $o ) > a > $o] :
! [SY21: ( a > $o ) > $o] :
( ( sK1_A @ SY21 )
=> ( ( SY21 @ ( SY20 @ SY21 ) )
& ( SY20 @ SY21 @ SY19 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY22: ( a > $o ) > $o] :
( ! [Xt: a > $o] :
~ ( SY22 @ Xt )
| ( SY22 @ ( sK4_Xf @ SY22 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [SY22: ( a > $o ) > $o] :
( ! [Xt: a > $o] :
~ ( SY22 @ Xt )
| ( SY22 @ ( sK4_Xf @ SY22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY13: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY13 )
| ( SY13 @ ( sK3_Xu @ SY13 ) ) )
& ( sK1_A @ sK2_SY15 )
& ( ( ^ [SY16: a] :
! [SY17: ( a > $o ) > $o] :
( ( sK1_A @ SY17 )
=> ? [Xb: a > $o] :
( ( SY17 @ Xb )
& ( Xb @ SY16 ) ) ) )
!= ( ^ [SY19: a] :
? [SY20: ( ( a > $o ) > $o ) > a > $o] :
! [SY21: ( a > $o ) > $o] :
( ( sK1_A @ SY21 )
=> ( ( SY21 @ ( SY20 @ SY21 ) )
& ( SY20 @ SY21 @ SY19 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX0 )
| ( SX0 @ ( sK3_Xu @ SX0 ) ) )
| ~ ( sK1_A @ sK2_SY15 ) )
| ~ ( ( ( ^ [SX0: a] :
! [SX1: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX1 )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ( SX2 @ SX0 ) ) ) )
!= ( ^ [SX0: a] :
~ ! [SX1: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX2: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX2 )
| ~ ( ~ ( SX2 @ ( SX1 @ SX2 ) )
| ~ ( SX1 @ SX2 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: ( a > $o ) > $o] :
( ( ! [SY24: a > $o] :
~ ( SV1 @ SY24 )
| ( SV1 @ ( sK4_Xf @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SX0: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX0 )
| ( SX0 @ ( sK3_Xu @ SX0 ) ) )
| ~ ( sK1_A @ sK2_SY15 ) )
| ~ ( ( ( ^ [SX0: a] :
! [SX1: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX1 )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ( SX2 @ SX0 ) ) ) )
!= ( ^ [SX0: a] :
~ ! [SX1: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX2: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX2 )
| ~ ( ~ ( SX2 @ ( SX1 @ SX2 ) )
| ~ ( SX1 @ SX2 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ! [SY24: a > $o] :
~ ( SV1 @ SY24 ) )
= $true )
| ( ( SV1 @ ( sK4_Xf @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( ~ ! [SX0: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX0 )
| ( SX0 @ ( sK3_Xu @ SX0 ) ) )
| ~ ( sK1_A @ sK2_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ( ( ^ [SX0: a] :
! [SX1: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX1 )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ( SX2 @ SX0 ) ) ) )
!= ( ^ [SX0: a] :
~ ! [SX1: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX2: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX2 )
| ~ ( ~ ( SX2 @ ( SX1 @ SX2 ) )
| ~ ( SX1 @ SX2 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: a > $o,SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ SV2 ) )
= $true )
| ( ( SV1 @ ( sK4_Xf @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX0 )
| ( SX0 @ ( sK3_Xu @ SX0 ) ) )
| ~ ( sK1_A @ sK2_SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ( ( ^ [SX0: a] :
! [SX1: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX1 )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ( SX2 @ SX0 ) ) ) )
!= ( ^ [SX0: a] :
~ ! [SX1: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX2: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX2 )
| ~ ( ~ ( SX2 @ ( SX1 @ SX2 ) )
| ~ ( SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: a > $o,SV1: ( a > $o ) > $o] :
( ( ( SV1 @ SV2 )
= $false )
| ( ( SV1 @ ( sK4_Xf @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX0 )
| ( SX0 @ ( sK3_Xu @ SX0 ) ) )
| ~ ( sK1_A @ sK2_SY15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ( ^ [SX0: a] :
! [SX1: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX1 )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ( SX2 @ SX0 ) ) ) )
= ( ^ [SX0: a] :
~ ! [SX1: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX2: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX2 )
| ~ ( ~ ( SX2 @ ( SX1 @ SX2 ) )
| ~ ( SX1 @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX0 )
| ( SX0 @ ( sK3_Xu @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( sK1_A @ sK2_SY15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SV3: a] :
( ( ! [SY25: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY25 )
| ~ ! [SY26: a > $o] :
~ ~ ( ~ ( SY25 @ SY26 )
| ~ ( SY26 @ SV3 ) ) ) )
= ( ~ ! [SY27: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY28: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY28 )
| ~ ( ~ ( SY28 @ ( SY27 @ SY28 ) )
| ~ ( SY27 @ SY28 @ SV3 ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ( ^ [SX0: a] :
! [SX1: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX1 )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ( SX2 @ SX0 ) ) ) )
= ( ^ [SX0: a] :
~ ! [SX1: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX2: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX2 )
| ~ ( ~ ( SX2 @ ( SX1 @ SX2 ) )
| ~ ( SX1 @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [SX0: ( a > $o ) > $o] :
( ~ ( sK1_A @ SX0 )
| ( SX0 @ ( sK3_Xu @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( sK1_A @ sK2_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ( ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) ) )
= ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(30,plain,
! [SV4: ( a > $o ) > $o] :
( ( ~ ( sK1_A @ SV4 )
| ( SV4 @ ( sK3_Xu @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) )
| ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
| ~ ( ~ ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) )
| ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ( ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) ) )
= ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: ( a > $o ) > $o] :
( ( ( ~ ( sK1_A @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK3_Xu @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) )
| ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ( ~ ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) )
| ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV4: ( a > $o ) > $o] :
( ( ( sK1_A @ SV4 )
= $false )
| ( ( SV4 @ ( sK3_Xu @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) )
| ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) )
| ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ( ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) ) )
= $true )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ( ~ ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK1_A @ SV5 )
| ~ ! [SY33: a > $o] :
~ ~ ( ~ ( SV5 @ SY33 )
| ~ ( SY33 @ sK5_SV3 ) ) )
= $true )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
( ( ( ! [SY29: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY29 )
| ~ ! [SY30: a > $o] :
~ ~ ( ~ ( SY29 @ SY30 )
| ~ ( SY30 @ sK5_SV3 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK1_A @ SV5 ) )
= $true )
| ( ( ~ ! [SY33: a > $o] :
~ ~ ( ~ ( SV5 @ SY33 )
| ~ ( SY33 @ sK5_SV3 ) ) )
= $true )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
( ( ( ~ ( sK1_A @ sK6_SY29 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( sK6_SY29 @ SY34 )
| ~ ( SY34 @ sK5_SV3 ) ) )
= $false )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(45,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY33: a > $o] :
~ ~ ( ~ ( SV5 @ SY33 )
| ~ ( SY33 @ sK5_SV3 ) ) )
= $true )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
( ( ( ~ ( sK1_A @ sK6_SY29 ) )
= $false )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( ( ~ ! [SY34: a > $o] :
~ ~ ( ~ ( sK6_SY29 @ SY34 )
| ~ ( SY34 @ sK5_SV3 ) ) )
= $false )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY33: a > $o] :
~ ~ ( ~ ( SV5 @ SY33 )
| ~ ( SY33 @ sK5_SV3 ) ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
( ( ( sK1_A @ sK6_SY29 )
= $true )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
( ( ( ! [SY34: a > $o] :
~ ~ ( ~ ( sK6_SY29 @ SY34 )
| ~ ( SY34 @ sK5_SV3 ) ) )
= $true )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV5 @ ( sK7_SY33 @ SV5 ) )
| ~ ( sK7_SY33 @ SV5 @ sK5_SV3 ) ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(52,plain,
( ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV6: a > $o] :
( ( ( ~ ~ ( ~ ( sK6_SY29 @ SV6 )
| ~ ( SV6 @ sK5_SV3 ) ) )
= $true )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK7_SY33 @ SV5 ) )
| ~ ( sK7_SY33 @ SV5 @ sK5_SV3 ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
( ( ( ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV6: a > $o] :
( ( ( ~ ( ~ ( sK6_SY29 @ SV6 )
| ~ ( SV6 @ sK5_SV3 ) ) )
= $false )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK7_SY33 @ SV5 ) )
| ~ ( sK7_SY33 @ SV5 @ sK5_SV3 ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ! [SY35: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY35 )
| ~ ( ~ ( SY35 @ ( SV7 @ SY35 ) )
| ~ ( SV7 @ SY35 @ sK5_SV3 ) ) ) )
= $true )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV6: a > $o] :
( ( ( ~ ( sK6_SY29 @ SV6 )
| ~ ( SV6 @ sK5_SV3 ) )
= $true )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK7_SY33 @ SV5 ) ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK7_SY33 @ SV5 @ sK5_SV3 ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ! [SY35: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY35 )
| ~ ( ~ ( SY35 @ ( SV7 @ SY35 ) )
| ~ ( SV7 @ SY35 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV6: a > $o] :
( ( ( ~ ( sK6_SY29 @ SV6 ) )
= $true )
| ( ( ~ ( SV6 @ sK5_SV3 ) )
= $true )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK1_A @ ( sK8_SY35 @ SV7 ) )
| ~ ( ~ ( sK8_SY35 @ SV7 @ ( SV7 @ ( sK8_SY35 @ SV7 ) ) )
| ~ ( SV7 @ ( sK8_SY35 @ SV7 ) @ sK5_SV3 ) ) )
= $false )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(67,plain,
! [SV6: a > $o] :
( ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( ~ ( SV6 @ sK5_SV3 ) )
= $true )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK1_A @ ( sK8_SY35 @ SV7 ) ) )
= $false )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( ~ ( sK8_SY35 @ SV7 @ ( SV7 @ ( sK8_SY35 @ SV7 ) ) )
| ~ ( SV7 @ ( sK8_SY35 @ SV7 ) @ sK5_SV3 ) ) )
= $false )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV6: a > $o] :
( ( ( SV6 @ sK5_SV3 )
= $false )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( ~ ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY36 )
| ~ ( ~ ( SY36 @ ( sK9_SY31 @ SV5 @ SY36 ) )
| ~ ( sK9_SY31 @ SV5 @ SY36 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(74,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY37: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY37 )
| ~ ( ~ ( SY37 @ ( sK10_SY31 @ SV5 @ SY37 ) )
| ~ ( sK10_SY31 @ SV5 @ SY37 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(75,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK1_A @ ( sK8_SY35 @ SV7 ) )
= $true )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(76,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK8_SY35 @ SV7 @ ( SV7 @ ( sK8_SY35 @ SV7 ) ) )
| ~ ( SV7 @ ( sK8_SY35 @ SV7 ) @ sK5_SV3 ) )
= $true )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(77,plain,
! [SV6: a > $o] :
( ( ( ~ ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY36 )
| ~ ( ~ ( SY36 @ ( sK9_SY31 @ SV5 @ SY36 ) )
| ~ ( sK9_SY31 @ SV5 @ SY36 @ sK5_SV3 ) ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(79,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY37: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY37 )
| ~ ( ~ ( SY37 @ ( sK10_SY31 @ SV5 @ SY37 ) )
| ~ ( sK10_SY31 @ SV5 @ SY37 @ sK5_SV3 ) ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK8_SY35 @ SV7 @ ( SV7 @ ( sK8_SY35 @ SV7 ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( sK8_SY35 @ SV7 ) @ sK5_SV3 ) )
= $true )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV6: a > $o] :
( ( ( ! [SY31: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY32: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY32 )
| ~ ( ~ ( SY32 @ ( SY31 @ SY32 ) )
| ~ ( SY31 @ SY32 @ sK5_SV3 ) ) ) )
= $true )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV5: ( a > $o ) > $o,SV8: ( a > $o ) > $o] :
( ( ( ~ ( sK1_A @ SV8 )
| ~ ( ~ ( SV8 @ ( sK9_SY31 @ SV5 @ SV8 ) )
| ~ ( sK9_SY31 @ SV5 @ SV8 @ sK5_SV3 ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV5: ( a > $o ) > $o,SV9: ( a > $o ) > $o] :
( ( ( ~ ( sK1_A @ SV9 )
| ~ ( ~ ( SV9 @ ( sK10_SY31 @ SV5 @ SV9 ) )
| ~ ( sK10_SY31 @ SV5 @ SV9 @ sK5_SV3 ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK8_SY35 @ SV7 @ ( SV7 @ ( sK8_SY35 @ SV7 ) ) )
= $false )
| ( ( ~ ( SV7 @ ( sK8_SY35 @ SV7 ) @ sK5_SV3 ) )
= $true )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV6: a > $o,SV10: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ! [SY38: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY38 )
| ~ ( ~ ( SY38 @ ( SV10 @ SY38 ) )
| ~ ( SV10 @ SY38 @ sK5_SV3 ) ) ) )
= $true )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV5: ( a > $o ) > $o,SV8: ( a > $o ) > $o] :
( ( ( ~ ( sK1_A @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( SV8 @ ( sK9_SY31 @ SV5 @ SV8 ) )
| ~ ( sK9_SY31 @ SV5 @ SV8 @ sK5_SV3 ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV5: ( a > $o ) > $o,SV9: ( a > $o ) > $o] :
( ( ( ~ ( sK1_A @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( SV9 @ ( sK10_SY31 @ SV5 @ SV9 ) )
| ~ ( sK10_SY31 @ SV5 @ SV9 @ sK5_SV3 ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV7: ( ( a > $o ) > $o ) > a > $o] :
( ( ( SV7 @ ( sK8_SY35 @ SV7 ) @ sK5_SV3 )
= $false )
| ( ( sK8_SY35 @ SV7 @ ( SV7 @ ( sK8_SY35 @ SV7 ) ) )
= $false )
| ( ( sK1_A @ sK6_SY29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV6: a > $o,SV10: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ! [SY38: ( a > $o ) > $o] :
( ~ ( sK1_A @ SY38 )
| ~ ( ~ ( SY38 @ ( SV10 @ SY38 ) )
| ~ ( SV10 @ SY38 @ sK5_SV3 ) ) ) )
= $false )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV5: ( a > $o ) > $o,SV8: ( a > $o ) > $o] :
( ( ( sK1_A @ SV8 )
= $false )
| ( ( ~ ( ~ ( SV8 @ ( sK9_SY31 @ SV5 @ SV8 ) )
| ~ ( sK9_SY31 @ SV5 @ SV8 @ sK5_SV3 ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV5: ( a > $o ) > $o,SV9: ( a > $o ) > $o] :
( ( ( sK1_A @ SV9 )
= $false )
| ( ( ~ ( ~ ( SV9 @ ( sK10_SY31 @ SV5 @ SV9 ) )
| ~ ( sK10_SY31 @ SV5 @ SV9 @ sK5_SV3 ) ) )
= $true )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV10: ( ( a > $o ) > $o ) > a > $o,SV6: a > $o] :
( ( ( ~ ( sK1_A @ ( sK11_SY38 @ SV6 @ SV10 ) )
| ~ ( ~ ( sK11_SY38 @ SV6 @ SV10 @ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) ) )
| ~ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) @ sK5_SV3 ) ) )
= $false )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(93,plain,
! [SV5: ( a > $o ) > $o,SV8: ( a > $o ) > $o] :
( ( ( ~ ( SV8 @ ( sK9_SY31 @ SV5 @ SV8 ) )
| ~ ( sK9_SY31 @ SV5 @ SV8 @ sK5_SV3 ) )
= $false )
| ( ( sK1_A @ SV8 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV5: ( a > $o ) > $o,SV9: ( a > $o ) > $o] :
( ( ( ~ ( SV9 @ ( sK10_SY31 @ SV5 @ SV9 ) )
| ~ ( sK10_SY31 @ SV5 @ SV9 @ sK5_SV3 ) )
= $false )
| ( ( sK1_A @ SV9 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV10: ( ( a > $o ) > $o ) > a > $o,SV6: a > $o] :
( ( ( ~ ( sK1_A @ ( sK11_SY38 @ SV6 @ SV10 ) ) )
= $false )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(96,plain,
! [SV10: ( ( a > $o ) > $o ) > a > $o,SV6: a > $o] :
( ( ( ~ ( ~ ( sK11_SY38 @ SV6 @ SV10 @ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) ) )
| ~ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) @ sK5_SV3 ) ) )
= $false )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV5: ( a > $o ) > $o,SV8: ( a > $o ) > $o] :
( ( ( ~ ( SV8 @ ( sK9_SY31 @ SV5 @ SV8 ) ) )
= $false )
| ( ( sK1_A @ SV8 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(98,plain,
! [SV8: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK9_SY31 @ SV5 @ SV8 @ sK5_SV3 ) )
= $false )
| ( ( sK1_A @ SV8 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(99,plain,
! [SV5: ( a > $o ) > $o,SV9: ( a > $o ) > $o] :
( ( ( ~ ( SV9 @ ( sK10_SY31 @ SV5 @ SV9 ) ) )
= $false )
| ( ( sK1_A @ SV9 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV9: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK10_SY31 @ SV5 @ SV9 @ sK5_SV3 ) )
= $false )
| ( ( sK1_A @ SV9 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV10: ( ( a > $o ) > $o ) > a > $o,SV6: a > $o] :
( ( ( sK1_A @ ( sK11_SY38 @ SV6 @ SV10 ) )
= $true )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV10: ( ( a > $o ) > $o ) > a > $o,SV6: a > $o] :
( ( ( ~ ( sK11_SY38 @ SV6 @ SV10 @ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) ) )
| ~ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) @ sK5_SV3 ) )
= $true )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
! [SV5: ( a > $o ) > $o,SV8: ( a > $o ) > $o] :
( ( ( SV8 @ ( sK9_SY31 @ SV5 @ SV8 ) )
= $true )
| ( ( sK1_A @ SV8 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV8: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( sK9_SY31 @ SV5 @ SV8 @ sK5_SV3 )
= $true )
| ( ( sK1_A @ SV8 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( SV5 @ ( sK7_SY33 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(105,plain,
! [SV5: ( a > $o ) > $o,SV9: ( a > $o ) > $o] :
( ( ( SV9 @ ( sK10_SY31 @ SV5 @ SV9 ) )
= $true )
| ( ( sK1_A @ SV9 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV9: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( sK10_SY31 @ SV5 @ SV9 @ sK5_SV3 )
= $true )
| ( ( sK1_A @ SV9 )
= $false )
| ( ( sK1_A @ SV5 )
= $false )
| ( ( sK7_SY33 @ SV5 @ sK5_SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(107,plain,
! [SV10: ( ( a > $o ) > $o ) > a > $o,SV6: a > $o] :
( ( ( ~ ( sK11_SY38 @ SV6 @ SV10 @ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) @ sK5_SV3 ) )
= $true )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV10: ( ( a > $o ) > $o ) > a > $o,SV6: a > $o] :
( ( ( sK11_SY38 @ SV6 @ SV10 @ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) ) )
= $false )
| ( ( ~ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) @ sK5_SV3 ) )
= $true )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(109,plain,
! [SV6: a > $o,SV10: ( ( a > $o ) > $o ) > a > $o] :
( ( ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) @ sK5_SV3 )
= $false )
| ( ( sK11_SY38 @ SV6 @ SV10 @ ( SV10 @ ( sK11_SY38 @ SV6 @ SV10 ) ) )
= $false )
| ( ( sK6_SY29 @ SV6 )
= $false )
| ( ( SV6 @ sK5_SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(110,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,109,106,105,104,103,101,88,75,36,32,28,26]) ).
thf(111,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO244^5 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 05:26:11 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.35
% 0.20/0.35 No.of.Axioms: 0
% 0.20/0.35
% 0.20/0.35 Length.of.Defs: 0
% 0.20/0.35
% 0.20/0.35 Contains.Choice.Funs: false
% 0.20/0.36 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)........
% 0.20/0.53
% 0.20/0.53 ********************************
% 0.20/0.53 * All subproblems solved! *
% 0.20/0.53 ********************************
% 0.20/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:110,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.54
% 0.20/0.54 %**** Beginning of derivation protocol ****
% 0.20/0.54 % SZS output start CNFRefutation
% See solution above
% 0.20/0.54
% 0.20/0.54 %**** End of derivation protocol ****
% 0.20/0.54 %**** no. of clauses in derivation: 111 ****
% 0.20/0.54 %**** clause counter: 110 ****
% 0.20/0.54
% 0.20/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:110,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------