%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO246^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:07:55 AM UTC 2026
% Result : Theorem 0.67s 0.31s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 1
% Syntax : Number of formulae : 133 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 947 ( 313 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2099 ( 692 ~; 392 |; 18 &; 955 @)
% ( 0 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 956 ( 956 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 437 ( 22 ^; 381 !; 34 ?; 437 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_SY42,type,
sK10_SY42: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(tp_sK11_SY35,type,
sK11_SY35: ( ( a > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK12_SY35,type,
sK12_SY35: ( ( a > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK13_SY45,type,
sK13_SY45: ( a > $o ) > ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: ( ( a > $o ) > $o ) > $o ).
thf(tp_sK2_SY15,type,
sK2_SY15: ( ( ( a > $o ) > $o ) > $o ) > ( a > $o ) > $o ).
thf(tp_sK3_SV2,type,
sK3_SV2: a ).
thf(tp_sK4_SY17,type,
sK4_SY17: ( ( ( a > $o ) > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK5_SY19,type,
sK5_SY19: ( a > $o ) > $o ).
thf(tp_sK6_SY17,type,
sK6_SY17: ( a > $o ) > ( ( ( a > $o ) > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK7_SY33,type,
sK7_SY33: ( a > $o ) > $o ).
thf(tp_sK8_SY37,type,
sK8_SY37: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK9_SY39,type,
sK9_SY39: ( ( a > $o ) > $o ) > a > $o ).
thf(1,conjecture,
( ! [Xs: ( ( a > $o ) > $o ) > $o] :
( ! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ? [Xt: a > $o] : ( X @ Xt ) )
=> ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ( 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',cTHM535) ).
thf(2,negated_conjecture,
( ( ! [Xs: ( ( a > $o ) > $o ) > $o] :
( ! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ? [Xt: a > $o] : ( X @ Xt ) )
=> ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ( 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,
( ( ! [Xs: ( ( a > $o ) > $o ) > $o] :
( ! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ? [Xt: a > $o] : ( X @ Xt ) )
=> ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ( 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,
( ( ! [Xs: ( ( a > $o ) > $o ) > $o] :
( ! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ? [Xt: a > $o] : ( X @ Xt ) )
=> ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ( 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,
( ( ! [Xs: ( ( a > $o ) > $o ) > $o] :
( ! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ? [Xt: a > $o] : ( X @ Xt ) )
=> ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
! [X: ( a > $o ) > $o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,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(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: ( ( a > $o ) > $o ) > $o] :
( ~ ~ ( ~ ~ ! [SX1: ( a > $o ) > $o] :
~ ( SX0 @ SX1 )
| ~ ! [SX1: ( a > $o ) > $o] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: a > $o] :
~ ( SX1 @ SX2 ) ) )
| ( ( ^ [SX1: a] :
! [SX2: ( a > $o ) > $o] :
( ~ ( SX0 @ SX2 )
| ~ ! [SX3: a > $o] :
~ ~ ( ~ ( SX2 @ SX3 )
| ~ ( SX3 @ SX1 ) ) ) )
= ( ^ [SX1: a] :
~ ! [SX2: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX3: ( a > $o ) > $o] :
( ~ ( SX0 @ SX3 )
| ~ ( ~ ( SX3 @ ( SX2 @ SX3 ) )
| ~ ( SX2 @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: ( ( a > $o ) > $o ) > $o] :
( ~ ! [SX1: ( a > $o ) > $o] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: a > $o] :
~ ( SX1 @ SX2 ) )
| ~ ! [SX1: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX2: ( a > $o ) > $o] :
( ~ ( SX0 @ SX2 )
| ( SX2 @ ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: ( ( a > $o ) > $o ) > $o] :
( ~ ~ ( ~ ~ ! [SX1: ( a > $o ) > $o] :
~ ( SX0 @ SX1 )
| ~ ! [SX1: ( a > $o ) > $o] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: a > $o] :
~ ( SX1 @ SX2 ) ) )
| ( ( ^ [SX1: a] :
! [SX2: ( a > $o ) > $o] :
( ~ ( SX0 @ SX2 )
| ~ ! [SX3: a > $o] :
~ ~ ( ~ ( SX2 @ SX3 )
| ~ ( SX3 @ SX1 ) ) ) )
= ( ^ [SX1: a] :
~ ! [SX2: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SX3: ( a > $o ) > $o] :
( ~ ( SX0 @ SX3 )
| ~ ( ~ ( SX3 @ ( SX2 @ SX3 ) )
| ~ ( SX2 @ SX3 @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ~ ! [SY15: ( a > $o ) > $o] :
( ~ ( SV1 @ SY15 )
| ~ ! [SX2: a > $o] :
~ ( SY15 @ SX2 ) )
| ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ~ ( ~ ~ ! [SY19: ( a > $o ) > $o] :
~ ( sK1_SX0 @ SY19 )
| ~ ! [SY20: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY20 )
| ~ ! [SX2: a > $o] :
~ ( SY20 @ SX2 ) ) )
| ( ( ^ [SY22: a] :
! [SY23: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY23 )
| ~ ! [SX3: a > $o] :
~ ~ ( ~ ( SY23 @ SX3 )
| ~ ( SX3 @ SY22 ) ) ) )
= ( ^ [SY25: a] :
~ ! [SY26: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY27: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY27 )
| ~ ( ~ ( SY27 @ ( SY26 @ SY27 ) )
| ~ ( SY26 @ SY27 @ SY25 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ! [SY15: ( a > $o ) > $o] :
( ~ ( SV1 @ SY15 )
| ~ ! [SX2: a > $o] :
~ ( SY15 @ SX2 ) ) )
= $true )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( ~ ~ ! [SY19: ( a > $o ) > $o] :
~ ( sK1_SX0 @ SY19 )
| ~ ! [SY20: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY20 )
| ~ ! [SX2: a > $o] :
~ ( SY20 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ( ^ [SY22: a] :
! [SY23: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY23 )
| ~ ! [SX3: a > $o] :
~ ~ ( ~ ( SY23 @ SX3 )
| ~ ( SX3 @ SY22 ) ) ) )
= ( ^ [SY25: a] :
~ ! [SY26: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY27: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY27 )
| ~ ( ~ ( SY27 @ ( SY26 @ SY27 ) )
| ~ ( SY26 @ SY27 @ SY25 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ! [SY15: ( a > $o ) > $o] :
( ~ ( SV1 @ SY15 )
| ~ ! [SX2: a > $o] :
~ ( SY15 @ SX2 ) ) )
= $false )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ~ ~ ! [SY19: ( a > $o ) > $o] :
~ ( sK1_SX0 @ SY19 )
| ~ ! [SY20: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY20 )
| ~ ! [SX2: a > $o] :
~ ( SY20 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SV2: a] :
( ( ! [SY28: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY28 )
| ~ ! [SY29: a > $o] :
~ ~ ( ~ ( SY28 @ SY29 )
| ~ ( SY29 @ SV2 ) ) ) )
= ( ~ ! [SY30: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY31: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY31 )
| ~ ( ~ ( SY31 @ ( SY30 @ SY31 ) )
| ~ ( SY30 @ SY31 @ SV2 ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ( ^ [SY22: a] :
! [SY23: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY23 )
| ~ ! [SX3: a > $o] :
~ ~ ( ~ ( SY23 @ SX3 )
| ~ ( SX3 @ SY22 ) ) ) )
= ( ^ [SY25: a] :
~ ! [SY26: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY27: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY27 )
| ~ ( ~ ( SY27 @ ( SY26 @ SY27 ) )
| ~ ( SY26 @ SY27 @ SY25 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[16]) ).
thf(21,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK2_SY15 @ SV1 ) )
| ~ ! [SY32: a > $o] :
~ ( sK2_SY15 @ SV1 @ SY32 ) )
= $false )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(22,plain,
( ( ~ ~ ! [SY19: ( a > $o ) > $o] :
~ ( sK1_SX0 @ SY19 )
| ~ ! [SY20: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY20 )
| ~ ! [SX2: a > $o] :
~ ( SY20 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ( ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) ) )
= ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(24,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK2_SY15 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ! [SY32: a > $o] :
~ ( sK2_SY15 @ SV1 @ SY32 ) )
= $false )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ~ ! [SY19: ( a > $o ) > $o] :
~ ( sK1_SX0 @ SY19 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ! [SY20: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY20 )
| ~ ! [SX2: a > $o] :
~ ( SY20 @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
( ( ~ ( ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) )
| ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
| ~ ( ~ ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) )
| ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(29,plain,
( ( ( ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) ) )
= ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[23]) ).
thf(30,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( SV1 @ ( sK2_SY15 @ SV1 ) )
= $true )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(31,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ! [SY32: a > $o] :
~ ( sK2_SY15 @ SV1 @ SY32 ) )
= $true )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(32,plain,
( ( ~ ! [SY19: ( a > $o ) > $o] :
~ ( sK1_SX0 @ SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(33,plain,
( ( ! [SY20: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY20 )
| ~ ! [SX2: a > $o] :
~ ( SY20 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ( ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) )
| ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(35,plain,
( ( ~ ( ~ ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) )
| ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(36,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY15 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV3: a > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ( sK2_SY15 @ SV1 @ SV3 ) )
= $true )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [SY19: ( a > $o ) > $o] :
~ ( sK1_SX0 @ SY19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV4: ( a > $o ) > $o] :
( ( ~ ( sK1_SX0 @ SV4 )
| ~ ! [SY37: a > $o] :
~ ( SV4 @ SY37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) )
| ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) )
| ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(42,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ! [SY38: ( a > $o ) > $o] :
( ~ ( SV1 @ SY38 )
| ( SY38 @ ( sK4_SY17 @ SV1 @ SY38 ) ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY15 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(43,plain,
! [SV3: a > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( sK2_SY15 @ SV1 @ SV3 )
= $false )
| ( ( ~ ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(44,plain,
( ( ~ ( sK1_SX0 @ sK5_SY19 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(45,plain,
! [SV4: ( a > $o ) > $o] :
( ( ( ~ ( sK1_SX0 @ SV4 ) )
= $true )
| ( ( ~ ! [SY37: a > $o] :
~ ( SV4 @ SY37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ( ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) ) )
= $true )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(47,plain,
( ( ( ~ ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ! [SY38: ( a > $o ) > $o] :
( ~ ( SV1 @ SY38 )
| ( SY38 @ ( sK4_SY17 @ SV1 @ SY38 ) ) ) )
= $true )
| ( ( SV1 @ ( sK2_SY15 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(49,plain,
! [SV3: a > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ! [SY17: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY18: ( a > $o ) > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( SY17 @ SY18 ) ) ) )
= $false )
| ( ( sK2_SY15 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( sK1_SX0 @ sK5_SY19 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(51,plain,
! [SV4: ( a > $o ) > $o] :
( ( ( sK1_SX0 @ SV4 )
= $false )
| ( ( ~ ! [SY37: a > $o] :
~ ( SV4 @ SY37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK1_SX0 @ SV5 )
| ~ ! [SY39: a > $o] :
~ ~ ( ~ ( SV5 @ SY39 )
| ~ ( SY39 @ sK3_SV2 ) ) )
= $true )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
( ( ( ! [SY33: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY33 )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY33 @ SY34 )
| ~ ( SY34 @ sK3_SV2 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV6: ( a > $o ) > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ( SV1 @ SV6 )
| ( SV6 @ ( sK4_SY17 @ SV1 @ SV6 ) ) )
= $true )
| ( ( SV1 @ ( sK2_SY15 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV3: a > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ! [SY40: ( a > $o ) > $o] :
( ~ ( SV1 @ SY40 )
| ( SY40 @ ( sK6_SY17 @ SV3 @ SV1 @ SY40 ) ) ) )
= $false )
| ( ( sK2_SY15 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(56,plain,
! [SV4: ( a > $o ) > $o] :
( ( ( ! [SY37: a > $o] :
~ ( SV4 @ SY37 ) )
= $false )
| ( ( sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK1_SX0 @ SV5 ) )
= $true )
| ( ( ~ ! [SY39: a > $o] :
~ ~ ( ~ ( SV5 @ SY39 )
| ~ ( SY39 @ sK3_SV2 ) ) )
= $true )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
( ( ( ~ ( sK1_SX0 @ sK7_SY33 )
| ~ ! [SY41: a > $o] :
~ ~ ( ~ ( sK7_SY33 @ SY41 )
| ~ ( SY41 @ sK3_SV2 ) ) )
= $false )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(59,plain,
! [SV6: ( a > $o ) > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ( SV1 @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK4_SY17 @ SV1 @ SV6 ) )
= $true )
| ( ( SV1 @ ( sK2_SY15 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV3: a > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ! [SY40: ( a > $o ) > $o] :
( ~ ( SV1 @ SY40 )
| ( SY40 @ ( sK6_SY17 @ SV3 @ SV1 @ SY40 ) ) ) )
= $true )
| ( ( sK2_SY15 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(61,plain,
! [SV4: ( a > $o ) > $o] :
( ( ( ~ ( SV4 @ ( sK8_SY37 @ SV4 ) ) )
= $false )
| ( ( sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(62,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY39: a > $o] :
~ ~ ( ~ ( SV5 @ SY39 )
| ~ ( SY39 @ sK3_SV2 ) ) )
= $true )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
( ( ( ~ ( sK1_SX0 @ sK7_SY33 ) )
= $false )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
( ( ( ~ ! [SY41: a > $o] :
~ ~ ( ~ ( sK7_SY33 @ SY41 )
| ~ ( SY41 @ sK3_SV2 ) ) )
= $false )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
! [SV6: ( a > $o ) > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( SV1 @ SV6 )
= $false )
| ( ( SV6 @ ( sK4_SY17 @ SV1 @ SV6 ) )
= $true )
| ( ( SV1 @ ( sK2_SY15 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV3: a > $o,SV7: ( a > $o ) > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ( SV1 @ SV7 )
| ( SV7 @ ( sK6_SY17 @ SV3 @ SV1 @ SV7 ) ) )
= $true )
| ( ( sK2_SY15 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV4: ( a > $o ) > $o] :
( ( ( SV4 @ ( sK8_SY37 @ SV4 ) )
= $true )
| ( ( sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY39: a > $o] :
~ ~ ( ~ ( SV5 @ SY39 )
| ~ ( SY39 @ sK3_SV2 ) ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
( ( ( sK1_SX0 @ sK7_SY33 )
= $true )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
( ( ( ! [SY41: a > $o] :
~ ~ ( ~ ( sK7_SY33 @ SY41 )
| ~ ( SY41 @ sK3_SV2 ) ) )
= $true )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV3: a > $o,SV7: ( a > $o ) > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( ~ ( SV1 @ SV7 ) )
= $true )
| ( ( SV7 @ ( sK6_SY17 @ SV3 @ SV1 @ SV7 ) )
= $true )
| ( ( sK2_SY15 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV5 @ ( sK9_SY39 @ SV5 ) )
| ~ ( sK9_SY39 @ SV5 @ sK3_SV2 ) ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(73,plain,
( ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV8: a > $o] :
( ( ( ~ ~ ( ~ ( sK7_SY33 @ SV8 )
| ~ ( SV8 @ sK3_SV2 ) ) )
= $true )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV3: a > $o,SV7: ( a > $o ) > $o,SV1: ( ( a > $o ) > $o ) > $o] :
( ( ( SV1 @ SV7 )
= $false )
| ( ( SV7 @ ( sK6_SY17 @ SV3 @ SV1 @ SV7 ) )
= $true )
| ( ( sK2_SY15 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK9_SY39 @ SV5 ) )
| ~ ( sK9_SY39 @ SV5 @ sK3_SV2 ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(77,plain,
( ( ( ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV8: a > $o] :
( ( ( ~ ( ~ ( sK7_SY33 @ SV8 )
| ~ ( SV8 @ sK3_SV2 ) ) )
= $false )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK9_SY39 @ SV5 ) )
| ~ ( sK9_SY39 @ SV5 @ sK3_SV2 ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ! [SY42: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY42 )
| ~ ( ~ ( SY42 @ ( SV9 @ SY42 ) )
| ~ ( SV9 @ SY42 @ sK3_SV2 ) ) ) )
= $true )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV8: a > $o] :
( ( ( ~ ( sK7_SY33 @ SV8 )
| ~ ( SV8 @ sK3_SV2 ) )
= $true )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(82,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK9_SY39 @ SV5 ) ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(83,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK9_SY39 @ SV5 @ sK3_SV2 ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(84,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ! [SY42: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY42 )
| ~ ( ~ ( SY42 @ ( SV9 @ SY42 ) )
| ~ ( SV9 @ SY42 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV8: a > $o] :
( ( ( ~ ( sK7_SY33 @ SV8 ) )
= $true )
| ( ( ~ ( SV8 @ sK3_SV2 ) )
= $true )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK10_SY42 @ SV9 ) )
| ~ ( ~ ( sK10_SY42 @ SV9 @ ( SV9 @ ( sK10_SY42 @ SV9 ) ) )
| ~ ( SV9 @ ( sK10_SY42 @ SV9 ) @ sK3_SV2 ) ) )
= $false )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(89,plain,
! [SV8: a > $o] :
( ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( ~ ( SV8 @ sK3_SV2 ) )
= $true )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK10_SY42 @ SV9 ) ) )
= $false )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(93,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( ~ ( sK10_SY42 @ SV9 @ ( SV9 @ ( sK10_SY42 @ SV9 ) ) )
| ~ ( SV9 @ ( sK10_SY42 @ SV9 ) @ sK3_SV2 ) ) )
= $false )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV8: a > $o] :
( ( ( SV8 @ sK3_SV2 )
= $false )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( ~ ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY43: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY43 )
| ~ ( ~ ( SY43 @ ( sK11_SY35 @ SV5 @ SY43 ) )
| ~ ( sK11_SY35 @ SV5 @ SY43 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(96,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY44: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY44 )
| ~ ( ~ ( SY44 @ ( sK12_SY35 @ SV5 @ SY44 ) )
| ~ ( sK12_SY35 @ SV5 @ SY44 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(97,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK1_SX0 @ ( sK10_SY42 @ SV9 ) )
= $true )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK10_SY42 @ SV9 @ ( SV9 @ ( sK10_SY42 @ SV9 ) ) )
| ~ ( SV9 @ ( sK10_SY42 @ SV9 ) @ sK3_SV2 ) )
= $true )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(99,plain,
! [SV8: a > $o] :
( ( ( ~ ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY43: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY43 )
| ~ ( ~ ( SY43 @ ( sK11_SY35 @ SV5 @ SY43 ) )
| ~ ( sK11_SY35 @ SV5 @ SY43 @ sK3_SV2 ) ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY44: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY44 )
| ~ ( ~ ( SY44 @ ( sK12_SY35 @ SV5 @ SY44 ) )
| ~ ( sK12_SY35 @ SV5 @ SY44 @ sK3_SV2 ) ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(102,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ( sK10_SY42 @ SV9 @ ( SV9 @ ( sK10_SY42 @ SV9 ) ) ) )
= $true )
| ( ( ~ ( SV9 @ ( sK10_SY42 @ SV9 ) @ sK3_SV2 ) )
= $true )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV8: a > $o] :
( ( ( ! [SY35: ( ( a > $o ) > $o ) > a > $o] :
~ ! [SY36: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY36 )
| ~ ( ~ ( SY36 @ ( SY35 @ SY36 ) )
| ~ ( SY35 @ SY36 @ sK3_SV2 ) ) ) )
= $true )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(104,plain,
! [SV5: ( a > $o ) > $o,SV10: ( a > $o ) > $o] :
( ( ( ~ ( sK1_SX0 @ SV10 )
| ~ ( ~ ( SV10 @ ( sK11_SY35 @ SV5 @ SV10 ) )
| ~ ( sK11_SY35 @ SV5 @ SV10 @ sK3_SV2 ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV5: ( a > $o ) > $o,SV11: ( a > $o ) > $o] :
( ( ( ~ ( sK1_SX0 @ SV11 )
| ~ ( ~ ( SV11 @ ( sK12_SY35 @ SV5 @ SV11 ) )
| ~ ( sK12_SY35 @ SV5 @ SV11 @ sK3_SV2 ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK10_SY42 @ SV9 @ ( SV9 @ ( sK10_SY42 @ SV9 ) ) )
= $false )
| ( ( ~ ( SV9 @ ( sK10_SY42 @ SV9 ) @ sK3_SV2 ) )
= $true )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV8: a > $o,SV12: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ~ ! [SY45: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY45 )
| ~ ( ~ ( SY45 @ ( SV12 @ SY45 ) )
| ~ ( SV12 @ SY45 @ sK3_SV2 ) ) ) )
= $true )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV5: ( a > $o ) > $o,SV10: ( a > $o ) > $o] :
( ( ( ~ ( sK1_SX0 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( SV10 @ ( sK11_SY35 @ SV5 @ SV10 ) )
| ~ ( sK11_SY35 @ SV5 @ SV10 @ sK3_SV2 ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV5: ( a > $o ) > $o,SV11: ( a > $o ) > $o] :
( ( ( ~ ( sK1_SX0 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( SV11 @ ( sK12_SY35 @ SV5 @ SV11 ) )
| ~ ( sK12_SY35 @ SV5 @ SV11 @ sK3_SV2 ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV9: ( ( a > $o ) > $o ) > a > $o] :
( ( ( SV9 @ ( sK10_SY42 @ SV9 ) @ sK3_SV2 )
= $false )
| ( ( sK10_SY42 @ SV9 @ ( SV9 @ ( sK10_SY42 @ SV9 ) ) )
= $false )
| ( ( sK1_SX0 @ sK7_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV8: a > $o,SV12: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ! [SY45: ( a > $o ) > $o] :
( ~ ( sK1_SX0 @ SY45 )
| ~ ( ~ ( SY45 @ ( SV12 @ SY45 ) )
| ~ ( SV12 @ SY45 @ sK3_SV2 ) ) ) )
= $false )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV5: ( a > $o ) > $o,SV10: ( a > $o ) > $o] :
( ( ( sK1_SX0 @ SV10 )
= $false )
| ( ( ~ ( ~ ( SV10 @ ( sK11_SY35 @ SV5 @ SV10 ) )
| ~ ( sK11_SY35 @ SV5 @ SV10 @ sK3_SV2 ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV5: ( a > $o ) > $o,SV11: ( a > $o ) > $o] :
( ( ( sK1_SX0 @ SV11 )
= $false )
| ( ( ~ ( ~ ( SV11 @ ( sK12_SY35 @ SV5 @ SV11 ) )
| ~ ( sK12_SY35 @ SV5 @ SV11 @ sK3_SV2 ) ) )
= $true )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV12: ( ( a > $o ) > $o ) > a > $o,SV8: a > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK13_SY45 @ SV8 @ SV12 ) )
| ~ ( ~ ( sK13_SY45 @ SV8 @ SV12 @ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) ) )
| ~ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) @ sK3_SV2 ) ) )
= $false )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(115,plain,
! [SV5: ( a > $o ) > $o,SV10: ( a > $o ) > $o] :
( ( ( ~ ( SV10 @ ( sK11_SY35 @ SV5 @ SV10 ) )
| ~ ( sK11_SY35 @ SV5 @ SV10 @ sK3_SV2 ) )
= $false )
| ( ( sK1_SX0 @ SV10 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV5: ( a > $o ) > $o,SV11: ( a > $o ) > $o] :
( ( ( ~ ( SV11 @ ( sK12_SY35 @ SV5 @ SV11 ) )
| ~ ( sK12_SY35 @ SV5 @ SV11 @ sK3_SV2 ) )
= $false )
| ( ( sK1_SX0 @ SV11 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV12: ( ( a > $o ) > $o ) > a > $o,SV8: a > $o] :
( ( ( ~ ( sK1_SX0 @ ( sK13_SY45 @ SV8 @ SV12 ) ) )
= $false )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(118,plain,
! [SV12: ( ( a > $o ) > $o ) > a > $o,SV8: a > $o] :
( ( ( ~ ( ~ ( sK13_SY45 @ SV8 @ SV12 @ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) ) )
| ~ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) @ sK3_SV2 ) ) )
= $false )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(119,plain,
! [SV5: ( a > $o ) > $o,SV10: ( a > $o ) > $o] :
( ( ( ~ ( SV10 @ ( sK11_SY35 @ SV5 @ SV10 ) ) )
= $false )
| ( ( sK1_SX0 @ SV10 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV10: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK11_SY35 @ SV5 @ SV10 @ sK3_SV2 ) )
= $false )
| ( ( sK1_SX0 @ SV10 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV5: ( a > $o ) > $o,SV11: ( a > $o ) > $o] :
( ( ( ~ ( SV11 @ ( sK12_SY35 @ SV5 @ SV11 ) ) )
= $false )
| ( ( sK1_SX0 @ SV11 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV11: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK12_SY35 @ SV5 @ SV11 @ sK3_SV2 ) )
= $false )
| ( ( sK1_SX0 @ SV11 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(123,plain,
! [SV12: ( ( a > $o ) > $o ) > a > $o,SV8: a > $o] :
( ( ( sK1_SX0 @ ( sK13_SY45 @ SV8 @ SV12 ) )
= $true )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV12: ( ( a > $o ) > $o ) > a > $o,SV8: a > $o] :
( ( ( ~ ( sK13_SY45 @ SV8 @ SV12 @ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) ) )
| ~ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) @ sK3_SV2 ) )
= $true )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(125,plain,
! [SV5: ( a > $o ) > $o,SV10: ( a > $o ) > $o] :
( ( ( SV10 @ ( sK11_SY35 @ SV5 @ SV10 ) )
= $true )
| ( ( sK1_SX0 @ SV10 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(126,plain,
! [SV10: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( sK11_SY35 @ SV5 @ SV10 @ sK3_SV2 )
= $true )
| ( ( sK1_SX0 @ SV10 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( SV5 @ ( sK9_SY39 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(127,plain,
! [SV5: ( a > $o ) > $o,SV11: ( a > $o ) > $o] :
( ( ( SV11 @ ( sK12_SY35 @ SV5 @ SV11 ) )
= $true )
| ( ( sK1_SX0 @ SV11 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV11: ( a > $o ) > $o,SV5: ( a > $o ) > $o] :
( ( ( sK12_SY35 @ SV5 @ SV11 @ sK3_SV2 )
= $true )
| ( ( sK1_SX0 @ SV11 )
= $false )
| ( ( sK1_SX0 @ SV5 )
= $false )
| ( ( sK9_SY39 @ SV5 @ sK3_SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV12: ( ( a > $o ) > $o ) > a > $o,SV8: a > $o] :
( ( ( ~ ( sK13_SY45 @ SV8 @ SV12 @ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) ) ) )
= $true )
| ( ( ~ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) @ sK3_SV2 ) )
= $true )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV12: ( ( a > $o ) > $o ) > a > $o,SV8: a > $o] :
( ( ( sK13_SY45 @ SV8 @ SV12 @ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) ) )
= $false )
| ( ( ~ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) @ sK3_SV2 ) )
= $true )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(131,plain,
! [SV8: a > $o,SV12: ( ( a > $o ) > $o ) > a > $o] :
( ( ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) @ sK3_SV2 )
= $false )
| ( ( sK13_SY45 @ SV8 @ SV12 @ ( SV12 @ ( sK13_SY45 @ SV8 @ SV12 ) ) )
= $false )
| ( ( sK7_SY33 @ SV8 )
= $false )
| ( ( SV8 @ sK3_SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(132,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,131,128,127,126,125,123,110,97,75,67,65,50,29]) ).
thf(133,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO246^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n007.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 17:32:20 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.31
% 0.67/0.31 No.of.Axioms: 0
% 0.67/0.31
% 0.67/0.31 Length.of.Defs: 0
% 0.67/0.31
% 0.67/0.31 Contains.Choice.Funs: false
% 0.67/0.31 ...
% 0.67/0.31
% 0.67/0.31 ********************************
% 0.67/0.31 * All subproblems solved! *
% 0.67/0.31 ********************************
% 0.67/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:132,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.67/0.31
% 0.67/0.31 %**** Beginning of derivation protocol ****
% 0.67/0.31 % SZS output start CNFRefutation
% See solution above
% 0.67/0.31
% 0.67/0.31 %**** End of derivation protocol ****
% 0.67/0.31 %**** no. of clauses in derivation: 133 ****
% 0.67/0.31 %**** clause counter: 132 ****
% 0.67/0.31
% 0.67/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:132,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------