%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV127^5 : 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 : n026.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 10:49:36 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 1
% Syntax : Number of formulae : 89 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 1109 ( 373 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 2752 ( 387 ~; 515 |; 41 &;1719 @)
% ( 0 <=>; 90 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 447 ( 447 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 473 ( 0 ^; 473 !; 0 ?; 473 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_SY113,type,
sK10_SY113: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(tp_sK11_SY114,type,
sK11_SY114: ( a > a > $o ) > ( a > a > $o ) > ( a > a > $o ) > a ).
thf(tp_sK12_SY116,type,
sK12_SY116: ( a > a > $o ) > ( a > a > $o ) > ( a > a > $o ) > a ).
thf(tp_sK13_SY118,type,
sK13_SY118: ( a > a > $o ) > ( a > a > $o ) > ( a > a > $o ) > a ).
thf(tp_sK14_SY119,type,
sK14_SY119: ( a > a > $o ) > ( a > a > $o ) > ( a > a > $o ) > a ).
thf(tp_sK1_P,type,
sK1_P: ( a > a > $o ) > $o ).
thf(tp_sK2_SY17,type,
sK2_SY17: a > a > $o ).
thf(tp_sK3_SY33,type,
sK3_SY33: a > a > $o ).
thf(tp_sK4_SY48,type,
sK4_SY48: a ).
thf(tp_sK5_SY62,type,
sK5_SY62: a ).
thf(tp_sK6_SX0,type,
sK6_SX0: a > a > $o ).
thf(tp_sK7_SY87,type,
sK7_SY87: ( a > a > $o ) > a ).
thf(tp_sK8_SY97,type,
sK8_SY97: ( a > a > $o ) > a ).
thf(tp_sK9_SY111,type,
sK9_SY111: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(1,conjecture,
! [P: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ! [Xp0: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( P @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) )
| ! [Xp0: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( P @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( P @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( R @ Xx0 @ Xy0 )
| ( S @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( P @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM252A_pme) ).
thf(2,negated_conjecture,
( ( ! [P: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ! [Xp0: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( P @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) )
| ! [Xp0: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( P @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( P @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( R @ Xx0 @ Xy0 )
| ( S @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( P @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [P: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ! [Xp0: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( P @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) )
| ! [Xp0: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( P @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( P @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( R @ Xx0 @ Xy0 )
| ( S @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( P @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY17: a > a > $o,SY18: a > a > $o,SY19: a,SY20: a] :
( ! [SY21: a > a > $o] :
( ( ! [SY22: a,SY23: a] :
( ( ! [SY24: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( SY17 @ Xx1 @ Xy1 )
=> ( SY24 @ Xx1 @ Xy1 ) )
& ( sK1_P @ SY24 ) )
=> ( SY24 @ SY22 @ SY23 ) )
| ! [SY27: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( SY18 @ Xx1 @ Xy1 )
=> ( SY27 @ Xx1 @ Xy1 ) )
& ( sK1_P @ SY27 ) )
=> ( SY27 @ SY22 @ SY23 ) ) )
=> ( SY21 @ SY22 @ SY23 ) )
& ( sK1_P @ SY21 ) )
=> ( SY21 @ SY19 @ SY20 ) )
=> ! [SY30: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( SY17 @ Xx0 @ Xy0 )
| ( SY18 @ Xx0 @ Xy0 ) )
=> ( SY30 @ Xx0 @ Xy0 ) )
& ( sK1_P @ SY30 ) )
=> ( SY30 @ SY19 @ SY20 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY33: a > a > $o,SY34: a,SY35: a] :
( ! [SY36: a > a > $o] :
( ( ! [SY37: a,SY38: a] :
( ( ! [SY39: a > a > $o] :
( ( ! [SY40: a,SY41: a] :
( ( sK2_SY17 @ SY40 @ SY41 )
=> ( SY39 @ SY40 @ SY41 ) )
& ( sK1_P @ SY39 ) )
=> ( SY39 @ SY37 @ SY38 ) )
| ! [SY27: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( SY33 @ Xx1 @ Xy1 )
=> ( SY27 @ Xx1 @ Xy1 ) )
& ( sK1_P @ SY27 ) )
=> ( SY27 @ SY37 @ SY38 ) ) )
=> ( SY36 @ SY37 @ SY38 ) )
& ( sK1_P @ SY36 ) )
=> ( SY36 @ SY34 @ SY35 ) )
=> ! [SY45: a > a > $o] :
( ( ! [SY46: a,SY47: a] :
( ( ( sK2_SY17 @ SY46 @ SY47 )
| ( SY33 @ SY46 @ SY47 ) )
=> ( SY45 @ SY46 @ SY47 ) )
& ( sK1_P @ SY45 ) )
=> ( SY45 @ SY34 @ SY35 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY48: a,SY49: a] :
( ! [SY50: a > a > $o] :
( ( ! [SY51: a,SY52: a] :
( ( ! [SY39: a > a > $o] :
( ( ! [SY40: a,SY41: a] :
( ( sK2_SY17 @ SY40 @ SY41 )
=> ( SY39 @ SY40 @ SY41 ) )
& ( sK1_P @ SY39 ) )
=> ( SY39 @ SY51 @ SY52 ) )
| ! [SY56: a > a > $o] :
( ( ! [SY57: a,SY58: a] :
( ( sK3_SY33 @ SY57 @ SY58 )
=> ( SY56 @ SY57 @ SY58 ) )
& ( sK1_P @ SY56 ) )
=> ( SY56 @ SY51 @ SY52 ) ) )
=> ( SY50 @ SY51 @ SY52 ) )
& ( sK1_P @ SY50 ) )
=> ( SY50 @ SY48 @ SY49 ) )
=> ! [SY59: a > a > $o] :
( ( ! [SY60: a,SY61: a] :
( ( ( sK2_SY17 @ SY60 @ SY61 )
| ( sK3_SY33 @ SY60 @ SY61 ) )
=> ( SY59 @ SY60 @ SY61 ) )
& ( sK1_P @ SY59 ) )
=> ( SY59 @ SY48 @ SY49 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY62: a] :
( ! [SY63: a > a > $o] :
( ( ! [SY51: a,SY52: a] :
( ( ! [SY39: a > a > $o] :
( ( ! [SY40: a,SY41: a] :
( ( sK2_SY17 @ SY40 @ SY41 )
=> ( SY39 @ SY40 @ SY41 ) )
& ( sK1_P @ SY39 ) )
=> ( SY39 @ SY51 @ SY52 ) )
| ! [SY56: a > a > $o] :
( ( ! [SY57: a,SY58: a] :
( ( sK3_SY33 @ SY57 @ SY58 )
=> ( SY56 @ SY57 @ SY58 ) )
& ( sK1_P @ SY56 ) )
=> ( SY56 @ SY51 @ SY52 ) ) )
=> ( SY63 @ SY51 @ SY52 ) )
& ( sK1_P @ SY63 ) )
=> ( SY63 @ sK4_SY48 @ SY62 ) )
=> ! [SY72: a > a > $o] :
( ( ! [SY60: a,SY61: a] :
( ( ( sK2_SY17 @ SY60 @ SY61 )
| ( sK3_SY33 @ SY60 @ SY61 ) )
=> ( SY72 @ SY60 @ SY61 ) )
& ( sK1_P @ SY72 ) )
=> ( SY72 @ sK4_SY48 @ SY62 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY75: a > a > $o] :
( ( ! [SY51: a,SY52: a] :
( ( ! [SY39: a > a > $o] :
( ( ! [SY40: a,SY41: a] :
( ( sK2_SY17 @ SY40 @ SY41 )
=> ( SY39 @ SY40 @ SY41 ) )
& ( sK1_P @ SY39 ) )
=> ( SY39 @ SY51 @ SY52 ) )
| ! [SY56: a > a > $o] :
( ( ! [SY57: a,SY58: a] :
( ( sK3_SY33 @ SY57 @ SY58 )
=> ( SY56 @ SY57 @ SY58 ) )
& ( sK1_P @ SY56 ) )
=> ( SY56 @ SY51 @ SY52 ) ) )
=> ( SY75 @ SY51 @ SY52 ) )
& ( sK1_P @ SY75 ) )
=> ( SY75 @ sK4_SY48 @ sK5_SY62 ) )
=> ! [SY84: a > a > $o] :
( ( ! [SY60: a,SY61: a] :
( ( ( sK2_SY17 @ SY60 @ SY61 )
| ( sK3_SY33 @ SY60 @ SY61 ) )
=> ( SY84 @ SY60 @ SY61 ) )
& ( sK1_P @ SY84 ) )
=> ( SY84 @ sK4_SY48 @ sK5_SY62 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY75: a > a > $o] :
( ( ! [SY51: a,SY52: a] :
( ( ! [SY39: a > a > $o] :
( ( ! [SY40: a,SY41: a] :
( ( sK2_SY17 @ SY40 @ SY41 )
=> ( SY39 @ SY40 @ SY41 ) )
& ( sK1_P @ SY39 ) )
=> ( SY39 @ SY51 @ SY52 ) )
| ! [SY56: a > a > $o] :
( ( ! [SY57: a,SY58: a] :
( ( sK3_SY33 @ SY57 @ SY58 )
=> ( SY56 @ SY57 @ SY58 ) )
& ( sK1_P @ SY56 ) )
=> ( SY56 @ SY51 @ SY52 ) ) )
=> ( SY75 @ SY51 @ SY52 ) )
& ( sK1_P @ SY75 ) )
=> ( SY75 @ sK4_SY48 @ sK5_SY62 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY84: a > a > $o] :
( ( ! [SY60: a,SY61: a] :
( ( ( sK2_SY17 @ SY60 @ SY61 )
| ( sK3_SY33 @ SY60 @ SY61 ) )
=> ( SY84 @ SY60 @ SY61 ) )
& ( sK1_P @ SY84 ) )
=> ( SY84 @ sK4_SY48 @ sK5_SY62 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SY84: a > a > $o] :
( ( ! [SY60: a,SY61: a] :
( ( ( sK2_SY17 @ SY60 @ SY61 )
| ( sK3_SY33 @ SY60 @ SY61 ) )
=> ( SY84 @ SY60 @ SY61 ) )
& ( sK1_P @ SY84 ) )
=> ( SY84 @ sK4_SY48 @ sK5_SY62 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY75: a > a > $o] :
( ( ! [SY51: a,SY52: a] :
( ( ! [SY39: a > a > $o] :
( ( ! [SY40: a,SY41: a] :
( ( sK2_SY17 @ SY40 @ SY41 )
=> ( SY39 @ SY40 @ SY41 ) )
& ( sK1_P @ SY39 ) )
=> ( SY39 @ SY51 @ SY52 ) )
| ! [SY56: a > a > $o] :
( ( ! [SY57: a,SY58: a] :
( ( sK3_SY33 @ SY57 @ SY58 )
=> ( SY56 @ SY57 @ SY58 ) )
& ( sK1_P @ SY56 ) )
=> ( SY56 @ SY51 @ SY52 ) ) )
=> ( SY75 @ SY51 @ SY52 ) )
& ( sK1_P @ SY75 ) )
=> ( SY75 @ sK4_SY48 @ sK5_SY62 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ! [SY84: a > a > $o] :
( ( ! [SY60: a,SY61: a] :
( ( ( sK2_SY17 @ SY60 @ SY61 )
| ( sK3_SY33 @ SY60 @ SY61 ) )
=> ( SY84 @ SY60 @ SY61 ) )
& ( sK1_P @ SY84 ) )
=> ( SY84 @ sK4_SY48 @ sK5_SY62 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ( ( sK2_SY17 @ SX1 @ SX2 )
| ( sK3_SY33 @ SX1 @ SX2 ) )
| ( SX0 @ SX1 @ SX2 ) )
| ~ ( sK1_P @ SX0 ) )
| ( SX0 @ sK4_SY48 @ sK5_SY62 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ( ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SX1 @ SX2 ) )
| ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SX1 @ SX2 ) ) )
| ( SX0 @ SX1 @ SX2 ) )
| ~ ( sK1_P @ SX0 ) )
| ( SX0 @ sK4_SY48 @ sK5_SY62 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ( ( sK2_SY17 @ SX1 @ SX2 )
| ( sK3_SY33 @ SX1 @ SX2 ) )
| ( SX0 @ SX1 @ SX2 ) )
| ~ ( sK1_P @ SX0 ) )
| ( SX0 @ sK4_SY48 @ sK5_SY62 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: a > a > $o] :
( ( ~ ~ ( ~ ! [SY87: a,SY88: a] :
( ~ ( ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) )
| ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) ) )
| ( SV1 @ SY87 @ SY88 ) )
| ~ ( sK1_P @ SV1 ) )
| ( SV1 @ sK4_SY48 @ sK5_SY62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ! [SY95: a,SY96: a] :
( ~ ( ( sK2_SY17 @ SY95 @ SY96 )
| ( sK3_SY33 @ SY95 @ SY96 ) )
| ( sK6_SX0 @ SY95 @ SY96 ) )
| ~ ( sK1_P @ sK6_SX0 ) )
| ( sK6_SX0 @ sK4_SY48 @ sK5_SY62 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(19,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY87: a,SY88: a] :
( ~ ( ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) )
| ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) ) )
| ( SV1 @ SY87 @ SY88 ) )
| ~ ( sK1_P @ SV1 ) ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( ~ ! [SY95: a,SY96: a] :
( ~ ( ( sK2_SY17 @ SY95 @ SY96 )
| ( sK3_SY33 @ SY95 @ SY96 ) )
| ( sK6_SX0 @ SY95 @ SY96 ) )
| ~ ( sK1_P @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( sK6_SX0 @ sK4_SY48 @ sK5_SY62 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( ~ ! [SY87: a,SY88: a] :
( ~ ( ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) )
| ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) ) )
| ( SV1 @ SY87 @ SY88 ) )
| ~ ( sK1_P @ SV1 ) ) )
= $false )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ~ ! [SY95: a,SY96: a] :
( ~ ( ( sK2_SY17 @ SY95 @ SY96 )
| ( sK3_SY33 @ SY95 @ SY96 ) )
| ( sK6_SX0 @ SY95 @ SY96 ) )
| ~ ( sK1_P @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: a > a > $o] :
( ( ( ~ ! [SY87: a,SY88: a] :
( ~ ( ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) )
| ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) ) )
| ( SV1 @ SY87 @ SY88 ) )
| ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ! [SY95: a,SY96: a] :
( ~ ( ( sK2_SY17 @ SY95 @ SY96 )
| ( sK3_SY33 @ SY95 @ SY96 ) )
| ( sK6_SX0 @ SY95 @ SY96 ) )
| ~ ( sK1_P @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: a > a > $o] :
( ( ( ~ ! [SY87: a,SY88: a] :
( ~ ( ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) )
| ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) ) )
| ( SV1 @ SY87 @ SY88 ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ! [SY95: a,SY96: a] :
( ~ ( ( sK2_SY17 @ SY95 @ SY96 )
| ( sK3_SY33 @ SY95 @ SY96 ) )
| ( sK6_SX0 @ SY95 @ SY96 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ( sK1_P @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY87: a,SY88: a] :
( ~ ( ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) )
| ! [SX3: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SX3 ) )
| ( SX3 @ SY87 @ SY88 ) ) )
| ( SV1 @ SY87 @ SY88 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [SY95: a,SY96: a] :
( ~ ( ( sK2_SY17 @ SY95 @ SY96 )
| ( sK3_SY33 @ SY95 @ SY96 ) )
| ( sK6_SX0 @ SY95 @ SY96 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( sK1_P @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY97: a] :
( ~ ( ! [SY98: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SY98 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY98 ) )
| ( SY98 @ ( sK7_SY87 @ SV1 ) @ SY97 ) )
| ! [SY101: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY101 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY101 ) )
| ( SY101 @ ( sK7_SY87 @ SV1 ) @ SY97 ) ) )
| ( SV1 @ ( sK7_SY87 @ SV1 ) @ SY97 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(33,plain,
! [SV2: a] :
( ( ! [SY104: a] :
( ~ ( ( sK2_SY17 @ SV2 @ SY104 )
| ( sK3_SY33 @ SV2 @ SY104 ) )
| ( sK6_SX0 @ SV2 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( ! [SY105: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SY105 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY105 ) )
| ( SY105 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) )
| ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
| ( SV1 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(35,plain,
! [SV3: a,SV2: a] :
( ( ~ ( ( sK2_SY17 @ SV2 @ SV3 )
| ( sK3_SY33 @ SV2 @ SV3 ) )
| ( sK6_SX0 @ SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( ! [SY105: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SY105 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY105 ) )
| ( SY105 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) )
| ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV1: a > a > $o] :
( ( ( SV1 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV3: a,SV2: a] :
( ( ( ~ ( ( sK2_SY17 @ SV2 @ SV3 )
| ( sK3_SY33 @ SV2 @ SV3 ) ) )
= $true )
| ( ( sK6_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY105: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SY105 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY105 ) )
| ( SY105 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) )
| ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV1: a > a > $o] :
( ( ( sK1_P @ SV1 )
= $false )
| ( ( SV1 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $false )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV3: a,SV2: a] :
( ( ( ( sK2_SY17 @ SV2 @ SV3 )
| ( sK3_SY33 @ SV2 @ SV3 ) )
= $false )
| ( ( sK6_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY105: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK2_SY17 @ SX4 @ SX5 )
| ( SY105 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY105 ) )
| ( SY105 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV3: a,SV2: a] :
( ( ( sK2_SY17 @ SV2 @ SV3 )
= $false )
| ( ( sK6_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
! [SV3: a,SV2: a] :
( ( ( sK3_SY33 @ SV2 @ SV3 )
= $false )
| ( ( sK6_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY111: a,SY112: a] :
( ~ ( sK2_SY17 @ SY111 @ SY112 )
| ( SV4 @ SY111 @ SY112 ) )
| ~ ( sK1_P @ SV4 ) )
| ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY111: a,SY112: a] :
( ~ ( sK2_SY17 @ SY111 @ SY112 )
| ( SV4 @ SY111 @ SY112 ) )
| ~ ( sK1_P @ SV4 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ( ~ ! [SY111: a,SY112: a] :
( ~ ( sK2_SY17 @ SY111 @ SY112 )
| ( SV4 @ SY111 @ SY112 ) )
| ~ ( sK1_P @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ! [SY111: a,SY112: a] :
( ~ ( sK2_SY17 @ SY111 @ SY112 )
| ( SV4 @ SY111 @ SY112 ) )
| ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(49,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ! [SY111: a,SY112: a] :
( ~ ( sK2_SY17 @ SY111 @ SY112 )
| ( SV4 @ SY111 @ SY112 ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ! [SY111: a,SY112: a] :
( ~ ( sK2_SY17 @ SY111 @ SY112 )
| ( SV4 @ SY111 @ SY112 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV4: a > a > $o,SV1: a > a > $o] :
( ( ( ! [SY113: a] :
( ~ ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ SY113 )
| ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ SY113 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(52,plain,
! [SV4: a > a > $o,SV1: a > a > $o] :
( ( ( ~ ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
| ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(53,plain,
! [SV4: a > a > $o,SV1: a > a > $o] :
( ( ( ~ ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(54,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV4: a > a > $o,SV1: a > a > $o] :
( ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( ~ ( sK1_P @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( sK1_P @ SV4 )
= $false )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV1: a > a > $o,SV4: a > a > $o] :
( ( ( sK1_P @ SV4 )
= $false )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( ! [SY108: a > a > $o] :
( ~ ~ ( ~ ! [SX4: a,SX5: a] :
( ~ ( sK3_SY33 @ SX4 @ SX5 )
| ( SY108 @ SX4 @ SX5 ) )
| ~ ( sK1_P @ SY108 ) )
| ( SY108 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY114: a,SY115: a] :
( ~ ( sK3_SY33 @ SY114 @ SY115 )
| ( SV5 @ SY114 @ SY115 ) )
| ~ ( sK1_P @ SV5 ) )
| ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV6: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY116: a,SY117: a] :
( ~ ( sK3_SY33 @ SY116 @ SY117 )
| ( SV6 @ SY116 @ SY117 ) )
| ~ ( sK1_P @ SV6 ) )
| ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY114: a,SY115: a] :
( ~ ( sK3_SY33 @ SY114 @ SY115 )
| ( SV5 @ SY114 @ SY115 ) )
| ~ ( sK1_P @ SV5 ) ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV6: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY116: a,SY117: a] :
( ~ ( sK3_SY33 @ SY116 @ SY117 )
| ( SV6 @ SY116 @ SY117 ) )
| ~ ( sK1_P @ SV6 ) ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( ~ ! [SY114: a,SY115: a] :
( ~ ( sK3_SY33 @ SY114 @ SY115 )
| ( SV5 @ SY114 @ SY115 ) )
| ~ ( sK1_P @ SV5 ) ) )
= $false )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV6: a > a > $o] :
( ( ( ~ ( ~ ! [SY116: a,SY117: a] :
( ~ ( sK3_SY33 @ SY116 @ SY117 )
| ( SV6 @ SY116 @ SY117 ) )
| ~ ( sK1_P @ SV6 ) ) )
= $false )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ! [SY114: a,SY115: a] :
( ~ ( sK3_SY33 @ SY114 @ SY115 )
| ( SV5 @ SY114 @ SY115 ) )
| ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(65,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV6: a > a > $o] :
( ( ( ~ ! [SY116: a,SY117: a] :
( ~ ( sK3_SY33 @ SY116 @ SY117 )
| ( SV6 @ SY116 @ SY117 ) )
| ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(66,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ! [SY114: a,SY115: a] :
( ~ ( sK3_SY33 @ SY114 @ SY115 )
| ( SV5 @ SY114 @ SY115 ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV6: a > a > $o] :
( ( ( ~ ! [SY116: a,SY117: a] :
( ~ ( sK3_SY33 @ SY116 @ SY117 )
| ( SV6 @ SY116 @ SY117 ) ) )
= $true )
| ( ( ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV5: a > a > $o] :
( ( ( ! [SY114: a,SY115: a] :
( ~ ( sK3_SY33 @ SY114 @ SY115 )
| ( SV5 @ SY114 @ SY115 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(69,plain,
! [SV4: a > a > $o,SV1: a > a > $o,SV6: a > a > $o] :
( ( ( ! [SY116: a,SY117: a] :
( ~ ( sK3_SY33 @ SY116 @ SY117 )
| ( SV6 @ SY116 @ SY117 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV5: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ! [SY118: a] :
( ~ ( sK3_SY33 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ SY118 )
| ( SV5 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ SY118 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(71,plain,
! [SV6: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ! [SY119: a] :
( ~ ( sK3_SY33 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ SY119 )
| ( SV6 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ SY119 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(72,plain,
! [SV5: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ( sK3_SY33 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) )
| ( SV5 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(73,plain,
! [SV6: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ( sK3_SY33 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) )
| ( SV6 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(74,plain,
! [SV5: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ( sK3_SY33 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(75,plain,
! [SV1: a > a > $o,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( SV5 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) )
= $false )
| ( ( ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV6: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( ~ ( sK3_SY33 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) ) )
= $false )
| ( ( ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV1: a > a > $o,SV4: a > a > $o,SV6: a > a > $o] :
( ( ( SV6 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) )
= $false )
| ( ( ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV5: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( sK3_SY33 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( sK1_P @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV1: a > a > $o,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( sK1_P @ SV5 )
= $false )
| ( ( SV5 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) )
= $false )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV6: a > a > $o,SV1: a > a > $o,SV4: a > a > $o] :
( ( ( sK3_SY33 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( sK1_P @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV1: a > a > $o,SV4: a > a > $o,SV6: a > a > $o] :
( ( ( sK1_P @ SV6 )
= $false )
| ( ( SV6 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) )
= $false )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV1: a > a > $o,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( sK1_P @ SV5 )
= $false )
| ( ( sK3_SY33 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV5: a > a > $o,SV4: a > a > $o,SV1: a > a > $o] :
( ( ( sK1_P @ SV1 )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV5 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) )
= $false )
| ( ( sK1_P @ SV5 )
= $false )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV1: a > a > $o,SV4: a > a > $o,SV6: a > a > $o] :
( ( ( sK1_P @ SV6 )
= $false )
| ( ( sK3_SY33 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( ~ ( sK1_P @ SV1 ) )
= $true )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV6: a > a > $o,SV4: a > a > $o,SV1: a > a > $o] :
( ( ( sK1_P @ SV1 )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV6 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) )
= $false )
| ( ( sK1_P @ SV6 )
= $false )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV5: a > a > $o,SV4: a > a > $o,SV1: a > a > $o] :
( ( ( sK1_P @ SV1 )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( SV4 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $false )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV5 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK3_SY33 @ ( sK11_SY114 @ SV4 @ SV1 @ SV5 ) @ ( sK13_SY118 @ SV5 @ SV1 @ SV4 ) )
= $true )
| ( ( sK1_P @ SV5 )
= $false )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV6: a > a > $o,SV4: a > a > $o,SV1: a > a > $o] :
( ( ( sK1_P @ SV1 )
= $false )
| ( ( sK1_P @ SV4 )
= $false )
| ( ( sK2_SY17 @ ( sK9_SY111 @ SV1 @ SV4 ) @ ( sK10_SY113 @ SV4 @ SV1 ) )
= $true )
| ( ( SV4 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( SV6 @ ( sK7_SY87 @ SV1 ) @ ( sK8_SY97 @ SV1 ) )
= $true )
| ( ( sK3_SY33 @ ( sK12_SY116 @ SV4 @ SV1 @ SV6 ) @ ( sK14_SY119 @ SV6 @ SV1 @ SV4 ) )
= $true )
| ( ( sK1_P @ SV6 )
= $false )
| ( ( SV1 @ sK4_SY48 @ sK5_SY62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(88,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,87,86,85,83,44,43,40,31]) ).
thf(89,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV127^5 : 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
% 0.09/0.17 % Computer : n026.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
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:43:47 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
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 0
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 0
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 ...
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % 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:88,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 89 ****
% 0.09/0.23 %**** clause counter: 88 ****
% 0.09/0.23
% 0.09/0.23 % 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:88,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------