%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV146^5 : 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 : n019.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 10:49:38 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 1
% Syntax : Number of formulae : 137 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 873 ( 275 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 2506 ( 683 ~; 474 |; 67 &;1184 @)
% ( 0 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 490 ( 0 ^; 490 !; 0 ?; 490 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_SY101,type,
sK10_SY101: ( a > $o ) > a ).
thf(tp_sK11_SY99,type,
sK11_SY99: ( a > $o ) > a ).
thf(tp_sK12_SY102,type,
sK12_SY102: ( a > $o ) > a ).
thf(tp_sK13_SY99,type,
sK13_SY99: ( a > $o ) > a ).
thf(tp_sK14_SY105,type,
sK14_SY105: ( a > $o ) > a ).
thf(tp_sK15_SY102,type,
sK15_SY102: ( a > $o ) > a ).
thf(tp_sK16_SY106,type,
sK16_SY106: ( a > $o ) > a ).
thf(tp_sK17_SY107,type,
sK17_SY107: ( a > $o ) > a ).
thf(tp_sK18_SY108,type,
sK18_SY108: ( a > $o ) > a ).
thf(tp_sK1_Xr,type,
sK1_Xr: a > a > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: a ).
thf(tp_sK3_SY43,type,
sK3_SY43: a ).
thf(tp_sK4_SY48,type,
sK4_SY48: a > $o ).
thf(tp_sK5_SX0,type,
sK5_SX0: a ).
thf(tp_sK6_SY56,type,
sK6_SY56: a ).
thf(tp_sK7_SY70,type,
sK7_SY70: a ).
thf(tp_sK8_SY91,type,
sK8_SY91: a > $o ).
thf(tp_sK9_SY98,type,
sK9_SY98: ( a > $o ) > a ).
thf(1,conjecture,
! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
& ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xy @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM525_pme) ).
thf(2,negated_conjecture,
( ( ! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
& ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xy @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
& ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xy @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY22: a,SY23: a] :
( ( sK1_Xr @ SY22 @ SY23 )
=> ! [SY24: a > $o] :
( ( ! [SY25: a] :
( ( sK1_Xr @ SY22 @ SY25 )
=> ( SY24 @ SY25 ) )
& ! [SY26: a,SY27: a] :
( ( ( SY24 @ SY26 )
& ( sK1_Xr @ SY26 @ SY27 ) )
=> ( SY24 @ SY27 ) ) )
=> ( SY24 @ SY23 ) ) )
& ! [SY28: a,SY29: a,SY30: a] :
( ( ! [SY31: a > $o] :
( ( ! [SY32: a] :
( ( sK1_Xr @ SY28 @ SY32 )
=> ( SY31 @ SY32 ) )
& ! [SY33: a,SY34: a] :
( ( ( SY31 @ SY33 )
& ( sK1_Xr @ SY33 @ SY34 ) )
=> ( SY31 @ SY34 ) ) )
=> ( SY31 @ SY29 ) )
& ! [SY35: a > $o] :
( ( ! [SY36: a] :
( ( sK1_Xr @ SY29 @ SY36 )
=> ( SY35 @ SY36 ) )
& ! [SY37: a,SY38: a] :
( ( ( SY35 @ SY37 )
& ( sK1_Xr @ SY37 @ SY38 ) )
=> ( SY35 @ SY38 ) ) )
=> ( SY35 @ SY30 ) ) )
=> ! [SY39: a > $o] :
( ( ! [SY40: a] :
( ( sK1_Xr @ SY28 @ SY40 )
=> ( SY39 @ SY40 ) )
& ! [SY41: a,SY42: a] :
( ( ( SY39 @ SY41 )
& ( sK1_Xr @ SY41 @ SY42 ) )
=> ( SY39 @ SY42 ) ) )
=> ( SY39 @ SY30 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY22: a,SY23: a] :
( ( sK1_Xr @ SY22 @ SY23 )
=> ! [SY24: a > $o] :
( ( ! [SY25: a] :
( ( sK1_Xr @ SY22 @ SY25 )
=> ( SY24 @ SY25 ) )
& ! [SY26: a,SY27: a] :
( ( ( SY24 @ SY26 )
& ( sK1_Xr @ SY26 @ SY27 ) )
=> ( SY24 @ SY27 ) ) )
=> ( SY24 @ SY23 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ! [SY28: a,SY29: a,SY30: a] :
( ( ! [SY31: a > $o] :
( ( ! [SY32: a] :
( ( sK1_Xr @ SY28 @ SY32 )
=> ( SY31 @ SY32 ) )
& ! [SY33: a,SY34: a] :
( ( ( SY31 @ SY33 )
& ( sK1_Xr @ SY33 @ SY34 ) )
=> ( SY31 @ SY34 ) ) )
=> ( SY31 @ SY29 ) )
& ! [SY35: a > $o] :
( ( ! [SY36: a] :
( ( sK1_Xr @ SY29 @ SY36 )
=> ( SY35 @ SY36 ) )
& ! [SY37: a,SY38: a] :
( ( ( SY35 @ SY37 )
& ( sK1_Xr @ SY37 @ SY38 ) )
=> ( SY35 @ SY38 ) ) )
=> ( SY35 @ SY30 ) ) )
=> ! [SY39: a > $o] :
( ( ! [SY40: a] :
( ( sK1_Xr @ SY28 @ SY40 )
=> ( SY39 @ SY40 ) )
& ! [SY41: a,SY42: a] :
( ( ( SY39 @ SY41 )
& ( sK1_Xr @ SY41 @ SY42 ) )
=> ( SY39 @ SY42 ) ) )
=> ( SY39 @ SY30 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ! [SY22: a,SY23: a] :
( ( sK1_Xr @ SY22 @ SY23 )
=> ! [SY24: a > $o] :
( ( ! [SY25: a] :
( ( sK1_Xr @ SY22 @ SY25 )
=> ( SY24 @ SY25 ) )
& ! [SY26: a,SY27: a] :
( ( ( SY24 @ SY26 )
& ( sK1_Xr @ SY26 @ SY27 ) )
=> ( SY24 @ SY27 ) ) )
=> ( SY24 @ SY23 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY28: a,SY29: a,SY30: a] :
( ( ! [SY31: a > $o] :
( ( ! [SY32: a] :
( ( sK1_Xr @ SY28 @ SY32 )
=> ( SY31 @ SY32 ) )
& ! [SY33: a,SY34: a] :
( ( ( SY31 @ SY33 )
& ( sK1_Xr @ SY33 @ SY34 ) )
=> ( SY31 @ SY34 ) ) )
=> ( SY31 @ SY29 ) )
& ! [SY35: a > $o] :
( ( ! [SY36: a] :
( ( sK1_Xr @ SY29 @ SY36 )
=> ( SY35 @ SY36 ) )
& ! [SY37: a,SY38: a] :
( ( ( SY35 @ SY37 )
& ( sK1_Xr @ SY37 @ SY38 ) )
=> ( SY35 @ SY38 ) ) )
=> ( SY35 @ SY30 ) ) )
=> ! [SY39: a > $o] :
( ( ! [SY40: a] :
( ( sK1_Xr @ SY28 @ SY40 )
=> ( SY39 @ SY40 ) )
& ! [SY41: a,SY42: a] :
( ( ( SY39 @ SY41 )
& ( sK1_Xr @ SY41 @ SY42 ) )
=> ( SY39 @ SY42 ) ) )
=> ( SY39 @ SY30 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SY22: a,SY23: a] :
( ( sK1_Xr @ SY22 @ SY23 )
=> ! [SY24: a > $o] :
( ( ! [SY25: a] :
( ( sK1_Xr @ SY22 @ SY25 )
=> ( SY24 @ SY25 ) )
& ! [SY26: a,SY27: a] :
( ( ( SY24 @ SY26 )
& ( sK1_Xr @ SY26 @ SY27 ) )
=> ( SY24 @ SY27 ) ) )
=> ( SY24 @ SY23 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SX0: a,SX1: a] :
( ~ ( sK1_Xr @ SX0 @ SX1 )
| ! [SX2: a > $o] :
( ~ ~ ( ~ ! [SX3: a] :
( ~ ( sK1_Xr @ SX0 @ SX3 )
| ( SX2 @ SX3 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ~ ( ~ ( SX2 @ SX3 )
| ~ ( sK1_Xr @ SX3 @ SX4 ) )
| ( SX2 @ SX4 ) ) )
| ( SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( sK1_Xr @ SX0 @ SX1 )
| ! [SX2: a > $o] :
( ~ ~ ( ~ ! [SX3: a] :
( ~ ( sK1_Xr @ SX0 @ SX3 )
| ( SX2 @ SX3 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ~ ( ~ ( SX2 @ SX3 )
| ~ ( sK1_Xr @ SX3 @ SX4 ) )
| ( SX2 @ SX4 ) ) )
| ( SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY43: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY43 )
| ! [SY44: a > $o] :
( ~ ~ ( ~ ! [SY45: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY45 )
| ( SY44 @ SY45 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ~ ( ~ ( SY44 @ SX3 )
| ~ ( sK1_Xr @ SX3 @ SX4 ) )
| ( SY44 @ SX4 ) ) )
| ( SY44 @ SY43 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
( ( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY43 )
| ! [SY48: a > $o] :
( ~ ~ ( ~ ! [SY45: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY45 )
| ( SY48 @ SY45 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ~ ( ~ ( SY48 @ SX3 )
| ~ ( sK1_Xr @ SX3 @ SX4 ) )
| ( SY48 @ SX4 ) ) )
| ( SY48 @ sK3_SY43 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY43 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SY48: a > $o] :
( ~ ~ ( ~ ! [SY45: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY45 )
| ( SY48 @ SY45 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ~ ( ~ ( SY48 @ SX3 )
| ~ ( sK1_Xr @ SX3 @ SX4 ) )
| ( SY48 @ SX4 ) ) )
| ( SY48 @ sK3_SY43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( sK1_Xr @ sK2_SX0 @ sK3_SY43 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SY52: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY52 )
| ( sK4_SY48 @ SY52 ) )
| ~ ! [SY53: a,SY54: a] :
( ~ ~ ( ~ ( sK4_SY48 @ SY53 )
| ~ ( sK1_Xr @ SY53 @ SY54 ) )
| ( sK4_SY48 @ SY54 ) ) )
| ( sK4_SY48 @ sK3_SY43 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ! [SY52: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY52 )
| ( sK4_SY48 @ SY52 ) )
| ~ ! [SY53: a,SY54: a] :
( ~ ~ ( ~ ( sK4_SY48 @ SY53 )
| ~ ( sK1_Xr @ SY53 @ SY54 ) )
| ( sK4_SY48 @ SY54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(19,plain,
( ( sK4_SY48 @ sK3_SY43 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ~ ! [SY52: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY52 )
| ( sK4_SY48 @ SY52 ) )
| ~ ! [SY53: a,SY54: a] :
( ~ ~ ( ~ ( sK4_SY48 @ SY53 )
| ~ ( sK1_Xr @ SY53 @ SY54 ) )
| ( sK4_SY48 @ SY54 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SY52: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY52 )
| ( sK4_SY48 @ SY52 ) )
| ~ ! [SY53: a,SY54: a] :
( ~ ~ ( ~ ( sK4_SY48 @ SY53 )
| ~ ( sK1_Xr @ SY53 @ SY54 ) )
| ( sK4_SY48 @ SY54 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
( ( ~ ! [SY52: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY52 )
| ( sK4_SY48 @ SY52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(23,plain,
( ( ~ ! [SY53: a,SY54: a] :
( ~ ~ ( ~ ( sK4_SY48 @ SY53 )
| ~ ( sK1_Xr @ SY53 @ SY54 ) )
| ( sK4_SY48 @ SY54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [SY52: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY52 )
| ( sK4_SY48 @ SY52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [SY53: a,SY54: a] :
( ~ ~ ( ~ ( sK4_SY48 @ SY53 )
| ~ ( sK1_Xr @ SY53 @ SY54 ) )
| ( sK4_SY48 @ SY54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: a] :
( ( ~ ( sK1_Xr @ sK2_SX0 @ SV1 )
| ( sK4_SY48 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: a] :
( ( ! [SY55: a] :
( ~ ~ ( ~ ( sK4_SY48 @ SV2 )
| ~ ( sK1_Xr @ SV2 @ SY55 ) )
| ( sK4_SY48 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: a] :
( ( ( ~ ( sK1_Xr @ sK2_SX0 @ SV1 ) )
= $true )
| ( ( sK4_SY48 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: a,SV2: a] :
( ( ~ ~ ( ~ ( sK4_SY48 @ SV2 )
| ~ ( sK1_Xr @ SV2 @ SV3 ) )
| ( sK4_SY48 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: a] :
( ( ( sK1_Xr @ sK2_SX0 @ SV1 )
= $false )
| ( ( sK4_SY48 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: a,SV2: a] :
( ( ( ~ ~ ( ~ ( sK4_SY48 @ SV2 )
| ~ ( sK1_Xr @ SV2 @ SV3 ) ) )
= $true )
| ( ( sK4_SY48 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV3: a,SV2: a] :
( ( ( ~ ( ~ ( sK4_SY48 @ SV2 )
| ~ ( sK1_Xr @ SV2 @ SV3 ) ) )
= $false )
| ( ( sK4_SY48 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV3: a,SV2: a] :
( ( ( ~ ( sK4_SY48 @ SV2 )
| ~ ( sK1_Xr @ SV2 @ SV3 ) )
= $true )
| ( ( sK4_SY48 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(34,plain,
! [SV3: a,SV2: a] :
( ( ( ~ ( sK4_SY48 @ SV2 ) )
= $true )
| ( ( ~ ( sK1_Xr @ SV2 @ SV3 ) )
= $true )
| ( ( sK4_SY48 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(35,plain,
! [SV3: a,SV2: a] :
( ( ( sK4_SY48 @ SV2 )
= $false )
| ( ( ~ ( sK1_Xr @ SV2 @ SV3 ) )
= $true )
| ( ( sK4_SY48 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(36,plain,
! [SV3: a,SV2: a] :
( ( ( sK1_Xr @ SV2 @ SV3 )
= $false )
| ( ( sK4_SY48 @ SV2 )
= $false )
| ( ( sK4_SY48 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,36,30,19]) ).
thf(38,plain,
( ( ~ ! [SY28: a,SY29: a,SY30: a] :
( ( ! [SY31: a > $o] :
( ( ! [SY32: a] :
( ( sK1_Xr @ SY28 @ SY32 )
=> ( SY31 @ SY32 ) )
& ! [SY33: a,SY34: a] :
( ( ( SY31 @ SY33 )
& ( sK1_Xr @ SY33 @ SY34 ) )
=> ( SY31 @ SY34 ) ) )
=> ( SY31 @ SY29 ) )
& ! [SY35: a > $o] :
( ( ! [SY36: a] :
( ( sK1_Xr @ SY29 @ SY36 )
=> ( SY35 @ SY36 ) )
& ! [SY37: a,SY38: a] :
( ( ( SY35 @ SY37 )
& ( sK1_Xr @ SY37 @ SY38 ) )
=> ( SY35 @ SY38 ) ) )
=> ( SY35 @ SY30 ) ) )
=> ! [SY39: a > $o] :
( ( ! [SY40: a] :
( ( sK1_Xr @ SY28 @ SY40 )
=> ( SY39 @ SY40 ) )
& ! [SY41: a,SY42: a] :
( ( ( SY39 @ SY41 )
& ( sK1_Xr @ SY41 @ SY42 ) )
=> ( SY39 @ SY42 ) ) )
=> ( SY39 @ SY30 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(39,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ! [SX3: a > $o] :
( ~ ~ ( ~ ! [SX4: a] :
( ~ ( sK1_Xr @ SX0 @ SX4 )
| ( SX3 @ SX4 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SX3 @ SX5 ) ) )
| ( SX3 @ SX1 ) )
| ~ ! [SX3: a > $o] :
( ~ ~ ( ~ ! [SX4: a] :
( ~ ( sK1_Xr @ SX1 @ SX4 )
| ( SX3 @ SX4 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SX3 @ SX5 ) ) )
| ( SX3 @ SX2 ) ) )
| ! [SX3: a > $o] :
( ~ ~ ( ~ ! [SX4: a] :
( ~ ( sK1_Xr @ SX0 @ SX4 )
| ( SX3 @ SX4 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SX3 @ SX5 ) ) )
| ( SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ! [SX3: a > $o] :
( ~ ~ ( ~ ! [SX4: a] :
( ~ ( sK1_Xr @ SX0 @ SX4 )
| ( SX3 @ SX4 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SX3 @ SX5 ) ) )
| ( SX3 @ SX1 ) )
| ~ ! [SX3: a > $o] :
( ~ ~ ( ~ ! [SX4: a] :
( ~ ( sK1_Xr @ SX1 @ SX4 )
| ( SX3 @ SX4 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SX3 @ SX5 ) ) )
| ( SX3 @ SX2 ) ) )
| ! [SX3: a > $o] :
( ~ ~ ( ~ ! [SX4: a] :
( ~ ( sK1_Xr @ SX0 @ SX4 )
| ( SX3 @ SX4 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SX3 @ SX5 ) ) )
| ( SX3 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [SY56: a,SY57: a] :
( ~ ~ ( ~ ! [SY58: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY58 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY58 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY58 @ SX5 ) ) )
| ( SY58 @ SY56 ) )
| ~ ! [SX3: a > $o] :
( ~ ~ ( ~ ! [SX4: a] :
( ~ ( sK1_Xr @ SY56 @ SX4 )
| ( SX3 @ SX4 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SX3 @ SX5 ) ) )
| ( SX3 @ SY57 ) ) )
| ! [SY66: a > $o] :
( ~ ~ ( ~ ! [SY67: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY67 )
| ( SY66 @ SY67 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY66 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY66 @ SX5 ) ) )
| ( SY66 @ SY57 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( ! [SY70: a] :
( ~ ~ ( ~ ! [SY71: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY71 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY71 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY71 @ SX5 ) ) )
| ( SY71 @ sK6_SY56 ) )
| ~ ! [SY75: a > $o] :
( ~ ~ ( ~ ! [SY76: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY76 )
| ( SY75 @ SY76 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY75 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY75 @ SX5 ) ) )
| ( SY75 @ SY70 ) ) )
| ! [SY66: a > $o] :
( ~ ~ ( ~ ! [SY67: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY67 )
| ( SY66 @ SY67 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY66 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY66 @ SX5 ) ) )
| ( SY66 @ SY70 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( ~ ~ ( ~ ! [SY71: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY71 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY71 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY71 @ SX5 ) ) )
| ( SY71 @ sK6_SY56 ) )
| ~ ! [SY87: a > $o] :
( ~ ~ ( ~ ! [SY76: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY76 )
| ( SY87 @ SY76 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY87 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY87 @ SX5 ) ) )
| ( SY87 @ sK7_SY70 ) ) )
| ! [SY91: a > $o] :
( ~ ~ ( ~ ! [SY67: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY67 )
| ( SY91 @ SY67 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY91 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY91 @ SX5 ) ) )
| ( SY91 @ sK7_SY70 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(44,plain,
( ( ~ ~ ( ~ ! [SY71: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY71 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY71 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY71 @ SX5 ) ) )
| ( SY71 @ sK6_SY56 ) )
| ~ ! [SY87: a > $o] :
( ~ ~ ( ~ ! [SY76: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY76 )
| ( SY87 @ SY76 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY87 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY87 @ SX5 ) ) )
| ( SY87 @ sK7_SY70 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [SY91: a > $o] :
( ~ ~ ( ~ ! [SY67: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY67 )
| ( SY91 @ SY67 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY91 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY91 @ SX5 ) ) )
| ( SY91 @ sK7_SY70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(46,plain,
( ( ~ ( ~ ! [SY71: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY71 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY71 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY71 @ SX5 ) ) )
| ( SY71 @ sK6_SY56 ) )
| ~ ! [SY87: a > $o] :
( ~ ~ ( ~ ! [SY76: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY76 )
| ( SY87 @ SY76 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY87 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY87 @ SX5 ) ) )
| ( SY87 @ sK7_SY70 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( ~ ~ ( ~ ! [SY95: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY95 )
| ( sK8_SY91 @ SY95 ) )
| ~ ! [SY96: a,SY97: a] :
( ~ ~ ( ~ ( sK8_SY91 @ SY96 )
| ~ ( sK1_Xr @ SY96 @ SY97 ) )
| ( sK8_SY91 @ SY97 ) ) )
| ( sK8_SY91 @ sK7_SY70 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(48,plain,
( ( ~ ! [SY71: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY71 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY71 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY71 @ SX5 ) ) )
| ( SY71 @ sK6_SY56 ) )
| ~ ! [SY87: a > $o] :
( ~ ~ ( ~ ! [SY76: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY76 )
| ( SY87 @ SY76 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY87 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY87 @ SX5 ) ) )
| ( SY87 @ sK7_SY70 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ~ ( ~ ! [SY95: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY95 )
| ( sK8_SY91 @ SY95 ) )
| ~ ! [SY96: a,SY97: a] :
( ~ ~ ( ~ ( sK8_SY91 @ SY96 )
| ~ ( sK1_Xr @ SY96 @ SY97 ) )
| ( sK8_SY91 @ SY97 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( sK8_SY91 @ sK7_SY70 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
( ( ~ ! [SY71: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY71 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY71 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY71 @ SX5 ) ) )
| ( SY71 @ sK6_SY56 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
( ( ~ ! [SY87: a > $o] :
( ~ ~ ( ~ ! [SY76: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY76 )
| ( SY87 @ SY76 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY87 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY87 @ SX5 ) ) )
| ( SY87 @ sK7_SY70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( ~ ( ~ ! [SY95: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY95 )
| ( sK8_SY91 @ SY95 ) )
| ~ ! [SY96: a,SY97: a] :
( ~ ~ ( ~ ( sK8_SY91 @ SY96 )
| ~ ( sK1_Xr @ SY96 @ SY97 ) )
| ( sK8_SY91 @ SY97 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( ! [SY71: a > $o] :
( ~ ~ ( ~ ! [SY59: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY59 )
| ( SY71 @ SY59 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY71 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY71 @ SX5 ) ) )
| ( SY71 @ sK6_SY56 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
( ( ! [SY87: a > $o] :
( ~ ~ ( ~ ! [SY76: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY76 )
| ( SY87 @ SY76 ) )
| ~ ! [SX4: a,SX5: a] :
( ~ ~ ( ~ ( SY87 @ SX4 )
| ~ ( sK1_Xr @ SX4 @ SX5 ) )
| ( SY87 @ SX5 ) ) )
| ( SY87 @ sK7_SY70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(56,plain,
( ( ~ ! [SY95: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY95 )
| ( sK8_SY91 @ SY95 ) )
| ~ ! [SY96: a,SY97: a] :
( ~ ~ ( ~ ( sK8_SY91 @ SY96 )
| ~ ( sK1_Xr @ SY96 @ SY97 ) )
| ( sK8_SY91 @ SY97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV4: a > $o] :
( ( ~ ~ ( ~ ! [SY98: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY98 )
| ( SV4 @ SY98 ) )
| ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
| ( SV4 @ sK6_SY56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV5: a > $o] :
( ( ~ ~ ( ~ ! [SY101: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY101 )
| ( SV5 @ SY101 ) )
| ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
| ( SV5 @ sK7_SY70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(59,plain,
( ( ~ ! [SY95: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY95 )
| ( sK8_SY91 @ SY95 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
( ( ~ ! [SY96: a,SY97: a] :
( ~ ~ ( ~ ( sK8_SY91 @ SY96 )
| ~ ( sK1_Xr @ SY96 @ SY97 ) )
| ( sK8_SY91 @ SY97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ! [SY98: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY98 )
| ( SV4 @ SY98 ) )
| ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV5: a > $o] :
( ( ( ~ ~ ( ~ ! [SY101: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY101 )
| ( SV5 @ SY101 ) )
| ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
( ( ! [SY95: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY95 )
| ( sK8_SY91 @ SY95 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(64,plain,
( ( ! [SY96: a,SY97: a] :
( ~ ~ ( ~ ( sK8_SY91 @ SY96 )
| ~ ( sK1_Xr @ SY96 @ SY97 ) )
| ( sK8_SY91 @ SY97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ! [SY98: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY98 )
| ( SV4 @ SY98 ) )
| ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV5: a > $o] :
( ( ( ~ ( ~ ! [SY101: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY101 )
| ( SV5 @ SY101 ) )
| ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV6: a] :
( ( ~ ( sK1_Xr @ sK5_SX0 @ SV6 )
| ( sK8_SY91 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV7: a] :
( ( ! [SY104: a] :
( ~ ~ ( ~ ( sK8_SY91 @ SV7 )
| ~ ( sK1_Xr @ SV7 @ SY104 ) )
| ( sK8_SY91 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV4: a > $o] :
( ( ( ~ ! [SY98: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY98 )
| ( SV4 @ SY98 ) )
| ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV5: a > $o] :
( ( ( ~ ! [SY101: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY101 )
| ( SV5 @ SY101 ) )
| ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV6: a] :
( ( ( ~ ( sK1_Xr @ sK5_SX0 @ SV6 ) )
= $true )
| ( ( sK8_SY91 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV8: a,SV7: a] :
( ( ~ ~ ( ~ ( sK8_SY91 @ SV7 )
| ~ ( sK1_Xr @ SV7 @ SV8 ) )
| ( sK8_SY91 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV4: a > $o] :
( ( ( ~ ! [SY98: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY98 )
| ( SV4 @ SY98 ) ) )
= $true )
| ( ( ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV5: a > $o] :
( ( ( ~ ! [SY101: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY101 )
| ( SV5 @ SY101 ) ) )
= $true )
| ( ( ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV6: a] :
( ( ( sK1_Xr @ sK5_SX0 @ SV6 )
= $false )
| ( ( sK8_SY91 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV8: a,SV7: a] :
( ( ( ~ ~ ( ~ ( sK8_SY91 @ SV7 )
| ~ ( sK1_Xr @ SV7 @ SV8 ) ) )
= $true )
| ( ( sK8_SY91 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV4: a > $o] :
( ( ( ! [SY98: a] :
( ~ ( sK1_Xr @ sK5_SX0 @ SY98 )
| ( SV4 @ SY98 ) ) )
= $false )
| ( ( ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV5: a > $o] :
( ( ( ! [SY101: a] :
( ~ ( sK1_Xr @ sK6_SY56 @ SY101 )
| ( SV5 @ SY101 ) ) )
= $false )
| ( ( ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV8: a,SV7: a] :
( ( ( ~ ( ~ ( sK8_SY91 @ SV7 )
| ~ ( sK1_Xr @ SV7 @ SV8 ) ) )
= $false )
| ( ( sK8_SY91 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV4: a > $o] :
( ( ( ~ ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
| ( SV4 @ ( sK9_SY98 @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(81,plain,
! [SV5: a > $o] :
( ( ( ~ ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
| ( SV5 @ ( sK10_SY101 @ SV5 ) ) )
= $false )
| ( ( ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(82,plain,
! [SV8: a,SV7: a] :
( ( ( ~ ( sK8_SY91 @ SV7 )
| ~ ( sK1_Xr @ SV7 @ SV8 ) )
= $true )
| ( ( sK8_SY91 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(83,plain,
! [SV4: a > $o] :
( ( ( ~ ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(84,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(85,plain,
! [SV5: a > $o] :
( ( ( ~ ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) ) )
= $false )
| ( ( ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(86,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(87,plain,
! [SV8: a,SV7: a] :
( ( ( ~ ( sK8_SY91 @ SV7 ) )
= $true )
| ( ( ~ ( sK1_Xr @ SV7 @ SV8 ) )
= $true )
| ( ( sK8_SY91 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV4: a > $o] :
( ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( ~ ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV4: a > $o] :
( ( ( ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV5: a > $o] :
( ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( ~ ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(91,plain,
! [SV5: a > $o] :
( ( ( ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV8: a,SV7: a] :
( ( ( sK8_SY91 @ SV7 )
= $false )
| ( ( ~ ( sK1_Xr @ SV7 @ SV8 ) )
= $true )
| ( ( sK8_SY91 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV4: a > $o] :
( ( ( ! [SY99: a,SY100: a] :
( ~ ~ ( ~ ( SV4 @ SY99 )
| ~ ( sK1_Xr @ SY99 @ SY100 ) )
| ( SV4 @ SY100 ) ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV4: a > $o] :
( ( ( ! [SY105: a] :
( ~ ~ ( ~ ( SV4 @ ( sK11_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK11_SY99 @ SV4 ) @ SY105 ) )
| ( SV4 @ SY105 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(95,plain,
! [SV5: a > $o] :
( ( ( ! [SY102: a,SY103: a] :
( ~ ~ ( ~ ( SV5 @ SY102 )
| ~ ( sK1_Xr @ SY102 @ SY103 ) )
| ( SV5 @ SY103 ) ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV5: a > $o] :
( ( ( ! [SY106: a] :
( ~ ~ ( ~ ( SV5 @ ( sK12_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK12_SY102 @ SV5 ) @ SY106 ) )
| ( SV5 @ SY106 ) ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(97,plain,
! [SV8: a,SV7: a] :
( ( ( sK1_Xr @ SV7 @ SV8 )
= $false )
| ( ( sK8_SY91 @ SV7 )
= $false )
| ( ( sK8_SY91 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV4: a > $o] :
( ( ( ! [SY107: a] :
( ~ ~ ( ~ ( SV4 @ ( sK13_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK13_SY99 @ SV4 ) @ SY107 ) )
| ( SV4 @ SY107 ) ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[93]) ).
thf(99,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ( SV4 @ ( sK11_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK11_SY99 @ SV4 ) @ ( sK14_SY105 @ SV4 ) ) )
| ( SV4 @ ( sK14_SY105 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[94]) ).
thf(100,plain,
! [SV5: a > $o] :
( ( ( ! [SY108: a] :
( ~ ~ ( ~ ( SV5 @ ( sK15_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK15_SY102 @ SV5 ) @ SY108 ) )
| ( SV5 @ SY108 ) ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(101,plain,
! [SV5: a > $o] :
( ( ( ~ ~ ( ~ ( SV5 @ ( sK12_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK12_SY102 @ SV5 ) @ ( sK16_SY106 @ SV5 ) ) )
| ( SV5 @ ( sK16_SY106 @ SV5 ) ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[96]) ).
thf(102,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ( SV4 @ ( sK13_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK13_SY99 @ SV4 ) @ ( sK17_SY107 @ SV4 ) ) )
| ( SV4 @ ( sK17_SY107 @ SV4 ) ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(103,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ( SV4 @ ( sK11_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK11_SY99 @ SV4 ) @ ( sK14_SY105 @ SV4 ) ) ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(104,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK14_SY105 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(105,plain,
! [SV5: a > $o] :
( ( ( ~ ~ ( ~ ( SV5 @ ( sK15_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK15_SY102 @ SV5 ) @ ( sK18_SY108 @ SV5 ) ) )
| ( SV5 @ ( sK18_SY108 @ SV5 ) ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[100]) ).
thf(106,plain,
! [SV5: a > $o] :
( ( ( ~ ~ ( ~ ( SV5 @ ( sK12_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK12_SY102 @ SV5 ) @ ( sK16_SY106 @ SV5 ) ) ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(107,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( sK16_SY106 @ SV5 ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(108,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ( SV4 @ ( sK13_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK13_SY99 @ SV4 ) @ ( sK17_SY107 @ SV4 ) ) ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(109,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK17_SY107 @ SV4 ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(110,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK11_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK11_SY99 @ SV4 ) @ ( sK14_SY105 @ SV4 ) ) ) )
= $true )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(111,plain,
! [SV5: a > $o] :
( ( ( ~ ~ ( ~ ( SV5 @ ( sK15_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK15_SY102 @ SV5 ) @ ( sK18_SY108 @ SV5 ) ) ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( sK18_SY108 @ SV5 ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(113,plain,
! [SV5: a > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK12_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK12_SY102 @ SV5 ) @ ( sK16_SY106 @ SV5 ) ) ) )
= $true )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(114,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK13_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK13_SY99 @ SV4 ) @ ( sK17_SY107 @ SV4 ) ) ) )
= $true )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(115,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK11_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK11_SY99 @ SV4 ) @ ( sK14_SY105 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV5: a > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK15_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK15_SY102 @ SV5 ) @ ( sK18_SY108 @ SV5 ) ) ) )
= $true )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(117,plain,
! [SV5: a > $o] :
( ( ( ~ ( SV5 @ ( sK12_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK12_SY102 @ SV5 ) @ ( sK16_SY106 @ SV5 ) ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK13_SY99 @ SV4 ) )
| ~ ( sK1_Xr @ ( sK13_SY99 @ SV4 ) @ ( sK17_SY107 @ SV4 ) ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK11_SY99 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV4: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK11_SY99 @ SV4 ) @ ( sK14_SY105 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV5: a > $o] :
( ( ( ~ ( SV5 @ ( sK15_SY102 @ SV5 ) )
| ~ ( sK1_Xr @ ( sK15_SY102 @ SV5 ) @ ( sK18_SY108 @ SV5 ) ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV5: a > $o] :
( ( ( ~ ( SV5 @ ( sK12_SY102 @ SV5 ) ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV5: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK12_SY102 @ SV5 ) @ ( sK16_SY106 @ SV5 ) ) )
= $false )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK13_SY99 @ SV4 ) ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(125,plain,
! [SV4: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK13_SY99 @ SV4 ) @ ( sK17_SY107 @ SV4 ) ) )
= $false )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(126,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK11_SY99 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(127,plain,
! [SV4: a > $o] :
( ( ( sK1_Xr @ ( sK11_SY99 @ SV4 ) @ ( sK14_SY105 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SY98 @ SV4 ) )
= $false )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(128,plain,
! [SV5: a > $o] :
( ( ( ~ ( SV5 @ ( sK15_SY102 @ SV5 ) ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV5: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK15_SY102 @ SV5 ) @ ( sK18_SY108 @ SV5 ) ) )
= $false )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(130,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( sK12_SY102 @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(131,plain,
! [SV5: a > $o] :
( ( ( sK1_Xr @ ( sK12_SY102 @ SV5 ) @ ( sK16_SY106 @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK10_SY101 @ SV5 ) )
= $false )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(132,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK13_SY99 @ SV4 ) )
= $true )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(133,plain,
! [SV4: a > $o] :
( ( ( sK1_Xr @ ( sK13_SY99 @ SV4 ) @ ( sK17_SY107 @ SV4 ) )
= $true )
| ( ( sK1_Xr @ sK5_SX0 @ ( sK9_SY98 @ SV4 ) )
= $true )
| ( ( SV4 @ sK6_SY56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(134,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( sK15_SY102 @ SV5 ) )
= $true )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(135,plain,
! [SV5: a > $o] :
( ( ( sK1_Xr @ ( sK15_SY102 @ SV5 ) @ ( sK18_SY108 @ SV5 ) )
= $true )
| ( ( sK1_Xr @ sK6_SY56 @ ( sK10_SY101 @ SV5 ) )
= $true )
| ( ( SV5 @ sK7_SY70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,135,134,133,132,131,130,127,126,112,109,107,104,97,75]) ).
thf(137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[136,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV146^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:41:31 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25
% 0.09/0.25 No.of.Axioms: 0
% 0.09/0.25
% 0.09/0.25 Length.of.Defs: 0
% 0.09/0.25
% 0.09/0.25 Contains.Choice.Funs: false
% 0.09/0.25 .....
% 0.09/0.25
% 0.09/0.25 ********************************
% 0.09/0.25 * All subproblems solved! *
% 0.09/0.25 ********************************
% 0.09/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:136,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.25
% 0.09/0.25 %**** Beginning of derivation protocol ****
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26
% 0.09/0.26 %**** End of derivation protocol ****
% 0.09/0.26 %**** no. of clauses in derivation: 137 ****
% 0.09/0.26 %**** clause counter: 136 ****
% 0.09/0.26
% 0.09/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:136,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------