%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV044^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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 10:49:26 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 99 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 699 ( 165 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1743 ( 251 ~; 205 |; 31 &;1164 @)
% ( 0 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 389 ( 0 ^; 389 !; 0 ?; 389 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_sK1_Xs,type,
sK1_Xs: b > $o ).
thf(tp_sK2_SY18,type,
sK2_SY18: b > a > a > $o ).
thf(tp_sK3_SX0,type,
sK3_SX0: b > a ).
thf(tp_sK4_SY56,type,
sK4_SY56: b > a ).
thf(tp_sK5_SY60,type,
sK5_SY60: b ).
thf(tp_sK6_SX0,type,
sK6_SX0: b > a ).
thf(tp_sK7_SY70,type,
sK7_SY70: b > a ).
thf(tp_sK8_SY75,type,
sK8_SY75: b > a ).
thf(tp_sK9_SY81,type,
sK9_SY81: b ).
thf(1,conjecture,
! [Xs: b > $o,Xp: b > a > a > $o] :
( ! [Xx: b] :
( ( Xs @ Xx )
=> ( ! [Xx0: a,Xy: a] :
( ( Xp @ Xx @ Xx0 @ Xy )
=> ( Xp @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xx0 @ Xy )
& ( Xp @ Xx @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xx0 @ Xz ) ) ) )
=> ( ! [Xx: b > a,Xy: b > a] :
( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xx0 ) ) ) )
& ! [Xx: b > a,Xy: b > a,Xz: b > a] :
( ( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
& ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xx0 ) ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xx0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM506_pme) ).
thf(2,negated_conjecture,
( ( ! [Xs: b > $o,Xp: b > a > a > $o] :
( ! [Xx: b] :
( ( Xs @ Xx )
=> ( ! [Xx0: a,Xy: a] :
( ( Xp @ Xx @ Xx0 @ Xy )
=> ( Xp @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xx0 @ Xy )
& ( Xp @ Xx @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xx0 @ Xz ) ) ) )
=> ( ! [Xx: b > a,Xy: b > a] :
( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xx0 ) ) ) )
& ! [Xx: b > a,Xy: b > a,Xz: b > a] :
( ( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
& ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xx0 ) ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xx0 ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xs: b > $o,Xp: b > a > a > $o] :
( ! [Xx: b] :
( ( Xs @ Xx )
=> ( ! [Xx0: a,Xy: a] :
( ( Xp @ Xx @ Xx0 @ Xy )
=> ( Xp @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xx0 @ Xy )
& ( Xp @ Xx @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xx0 @ Xz ) ) ) )
=> ( ! [Xx: b > a,Xy: b > a] :
( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xx0 ) ) ) )
& ! [Xx: b > a,Xy: b > a,Xz: b > a] :
( ( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
& ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xx0 ) ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xx0 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY18: b > a > a > $o] :
( ! [SY19: b] :
( ( sK1_Xs @ SY19 )
=> ( ! [Xx0: a,Xy: a] :
( ( SY18 @ SY19 @ Xx0 @ Xy )
=> ( SY18 @ SY19 @ Xy @ Xx0 ) )
& ! [Xx0: a,Xy: a,Xz: a] :
( ( ( SY18 @ SY19 @ Xx0 @ Xy )
& ( SY18 @ SY19 @ Xy @ Xz ) )
=> ( SY18 @ SY19 @ Xx0 @ Xz ) ) ) )
=> ( ! [SY25: b > a,SY26: b > a] :
( ! [SY27: b] :
( ( sK1_Xs @ SY27 )
=> ( SY18 @ SY27 @ ( SY25 @ SY27 ) @ ( SY26 @ SY27 ) ) )
=> ! [SY28: b] :
( ( sK1_Xs @ SY28 )
=> ( SY18 @ SY28 @ ( SY26 @ SY28 ) @ ( SY25 @ SY28 ) ) ) )
& ! [SY29: b > a,SY30: b > a,SY31: b > a] :
( ( ! [SY32: b] :
( ( sK1_Xs @ SY32 )
=> ( SY18 @ SY32 @ ( SY29 @ SY32 ) @ ( SY30 @ SY32 ) ) )
& ! [SY33: b] :
( ( sK1_Xs @ SY33 )
=> ( SY18 @ SY33 @ ( SY30 @ SY33 ) @ ( SY31 @ SY33 ) ) ) )
=> ! [SY34: b] :
( ( sK1_Xs @ SY34 )
=> ( SY18 @ SY34 @ ( SY29 @ SY34 ) @ ( SY31 @ SY34 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY35: b] :
( ( sK1_Xs @ SY35 )
=> ( ! [SY36: a,SY37: a] :
( ( sK2_SY18 @ SY35 @ SY36 @ SY37 )
=> ( sK2_SY18 @ SY35 @ SY37 @ SY36 ) )
& ! [SY38: a,SY39: a,SY40: a] :
( ( ( sK2_SY18 @ SY35 @ SY38 @ SY39 )
& ( sK2_SY18 @ SY35 @ SY39 @ SY40 ) )
=> ( sK2_SY18 @ SY35 @ SY38 @ SY40 ) ) ) )
=> ( ! [SY41: b > a,SY42: b > a] :
( ! [SY43: b] :
( ( sK1_Xs @ SY43 )
=> ( sK2_SY18 @ SY43 @ ( SY41 @ SY43 ) @ ( SY42 @ SY43 ) ) )
=> ! [SY44: b] :
( ( sK1_Xs @ SY44 )
=> ( sK2_SY18 @ SY44 @ ( SY42 @ SY44 ) @ ( SY41 @ SY44 ) ) ) )
& ! [SY45: b > a,SY46: b > a,SY47: b > a] :
( ( ! [SY48: b] :
( ( sK1_Xs @ SY48 )
=> ( sK2_SY18 @ SY48 @ ( SY45 @ SY48 ) @ ( SY46 @ SY48 ) ) )
& ! [SY49: b] :
( ( sK1_Xs @ SY49 )
=> ( sK2_SY18 @ SY49 @ ( SY46 @ SY49 ) @ ( SY47 @ SY49 ) ) ) )
=> ! [SY50: b] :
( ( sK1_Xs @ SY50 )
=> ( sK2_SY18 @ SY50 @ ( SY45 @ SY50 ) @ ( SY47 @ SY50 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY35: b] :
( ( sK1_Xs @ SY35 )
=> ( ! [SY36: a,SY37: a] :
( ( sK2_SY18 @ SY35 @ SY36 @ SY37 )
=> ( sK2_SY18 @ SY35 @ SY37 @ SY36 ) )
& ! [SY38: a,SY39: a,SY40: a] :
( ( ( sK2_SY18 @ SY35 @ SY38 @ SY39 )
& ( sK2_SY18 @ SY35 @ SY39 @ SY40 ) )
=> ( sK2_SY18 @ SY35 @ SY38 @ SY40 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY41: b > a,SY42: b > a] :
( ! [SY43: b] :
( ( sK1_Xs @ SY43 )
=> ( sK2_SY18 @ SY43 @ ( SY41 @ SY43 ) @ ( SY42 @ SY43 ) ) )
=> ! [SY44: b] :
( ( sK1_Xs @ SY44 )
=> ( sK2_SY18 @ SY44 @ ( SY42 @ SY44 ) @ ( SY41 @ SY44 ) ) ) )
& ! [SY45: b > a,SY46: b > a,SY47: b > a] :
( ( ! [SY48: b] :
( ( sK1_Xs @ SY48 )
=> ( sK2_SY18 @ SY48 @ ( SY45 @ SY48 ) @ ( SY46 @ SY48 ) ) )
& ! [SY49: b] :
( ( sK1_Xs @ SY49 )
=> ( sK2_SY18 @ SY49 @ ( SY46 @ SY49 ) @ ( SY47 @ SY49 ) ) ) )
=> ! [SY50: b] :
( ( sK1_Xs @ SY50 )
=> ( sK2_SY18 @ SY50 @ ( SY45 @ SY50 ) @ ( SY47 @ SY50 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY41: b > a,SY42: b > a] :
( ! [SY43: b] :
( ( sK1_Xs @ SY43 )
=> ( sK2_SY18 @ SY43 @ ( SY41 @ SY43 ) @ ( SY42 @ SY43 ) ) )
=> ! [SY44: b] :
( ( sK1_Xs @ SY44 )
=> ( sK2_SY18 @ SY44 @ ( SY42 @ SY44 ) @ ( SY41 @ SY44 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ! [SY45: b > a,SY46: b > a,SY47: b > a] :
( ( ! [SY48: b] :
( ( sK1_Xs @ SY48 )
=> ( sK2_SY18 @ SY48 @ ( SY45 @ SY48 ) @ ( SY46 @ SY48 ) ) )
& ! [SY49: b] :
( ( sK1_Xs @ SY49 )
=> ( sK2_SY18 @ SY49 @ ( SY46 @ SY49 ) @ ( SY47 @ SY49 ) ) ) )
=> ! [SY50: b] :
( ( sK1_Xs @ SY50 )
=> ( sK2_SY18 @ SY50 @ ( SY45 @ SY50 ) @ ( SY47 @ SY50 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ~ ! [SY41: b > a,SY42: b > a] :
( ! [SY43: b] :
( ( sK1_Xs @ SY43 )
=> ( sK2_SY18 @ SY43 @ ( SY41 @ SY43 ) @ ( SY42 @ SY43 ) ) )
=> ! [SY44: b] :
( ( sK1_Xs @ SY44 )
=> ( sK2_SY18 @ SY44 @ ( SY42 @ SY44 ) @ ( SY41 @ SY44 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SY45: b > a,SY46: b > a,SY47: b > a] :
( ( ! [SY48: b] :
( ( sK1_Xs @ SY48 )
=> ( sK2_SY18 @ SY48 @ ( SY45 @ SY48 ) @ ( SY46 @ SY48 ) ) )
& ! [SY49: b] :
( ( sK1_Xs @ SY49 )
=> ( sK2_SY18 @ SY49 @ ( SY46 @ SY49 ) @ ( SY47 @ SY49 ) ) ) )
=> ! [SY50: b] :
( ( sK1_Xs @ SY50 )
=> ( sK2_SY18 @ SY50 @ ( SY45 @ SY50 ) @ ( SY47 @ SY50 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [SY35: b] :
( ( sK1_Xs @ SY35 )
=> ( ! [SY36: a,SY37: a] :
( ( sK2_SY18 @ SY35 @ SY36 @ SY37 )
=> ( sK2_SY18 @ SY35 @ SY37 @ SY36 ) )
& ! [SY38: a,SY39: a,SY40: a] :
( ( ( sK2_SY18 @ SY35 @ SY38 @ SY39 )
& ( sK2_SY18 @ SY35 @ SY39 @ SY40 ) )
=> ( sK2_SY18 @ SY35 @ SY38 @ SY40 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(13,plain,
( ( ~ ! [SY41: b > a,SY42: b > a] :
( ! [SY43: b] :
( ( sK1_Xs @ SY43 )
=> ( sK2_SY18 @ SY43 @ ( SY41 @ SY43 ) @ ( SY42 @ SY43 ) ) )
=> ! [SY44: b] :
( ( sK1_Xs @ SY44 )
=> ( sK2_SY18 @ SY44 @ ( SY42 @ SY44 ) @ ( SY41 @ SY44 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [SX0: b > a,SX1: b > a] :
( ~ ! [SX2: b] :
( ~ ( sK1_Xs @ SX2 )
| ( sK2_SY18 @ SX2 @ ( SX0 @ SX2 ) @ ( SX1 @ SX2 ) ) )
| ! [SX2: b] :
( ~ ( sK1_Xs @ SX2 )
| ( sK2_SY18 @ SX2 @ ( SX1 @ SX2 ) @ ( SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: b] :
( ~ ( sK1_Xs @ SX0 )
| ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ( sK2_SY18 @ SX0 @ SX1 @ SX2 )
| ( sK2_SY18 @ SX0 @ SX2 @ SX1 ) )
| ~ ! [SX1: a,SX2: a,SX3: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SX0 @ SX1 @ SX2 )
| ~ ( sK2_SY18 @ SX0 @ SX2 @ SX3 ) )
| ( sK2_SY18 @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: b > a,SX1: b > a] :
( ~ ! [SX2: b] :
( ~ ( sK1_Xs @ SX2 )
| ( sK2_SY18 @ SX2 @ ( SX0 @ SX2 ) @ ( SX1 @ SX2 ) ) )
| ! [SX2: b] :
( ~ ( sK1_Xs @ SX2 )
| ( sK2_SY18 @ SX2 @ ( SX1 @ SX2 ) @ ( SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: b] :
( ( ~ ( sK1_Xs @ SV1 )
| ~ ( ~ ! [SY51: a,SY52: a] :
( ~ ( sK2_SY18 @ SV1 @ SY51 @ SY52 )
| ( sK2_SY18 @ SV1 @ SY52 @ SY51 ) )
| ~ ! [SY53: a,SY54: a,SY55: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SY53 @ SY54 )
| ~ ( sK2_SY18 @ SV1 @ SY54 @ SY55 ) )
| ( sK2_SY18 @ SV1 @ SY53 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY56: b > a] :
( ~ ! [SY57: b] :
( ~ ( sK1_Xs @ SY57 )
| ( sK2_SY18 @ SY57 @ ( sK3_SX0 @ SY57 ) @ ( SY56 @ SY57 ) ) )
| ! [SY58: b] :
( ~ ( sK1_Xs @ SY58 )
| ( sK2_SY18 @ SY58 @ ( SY56 @ SY58 ) @ ( sK3_SX0 @ SY58 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(19,plain,
! [SV1: b] :
( ( ( ~ ( sK1_Xs @ SV1 ) )
= $true )
| ( ( ~ ( ~ ! [SY51: a,SY52: a] :
( ~ ( sK2_SY18 @ SV1 @ SY51 @ SY52 )
| ( sK2_SY18 @ SV1 @ SY52 @ SY51 ) )
| ~ ! [SY53: a,SY54: a,SY55: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SY53 @ SY54 )
| ~ ( sK2_SY18 @ SV1 @ SY54 @ SY55 ) )
| ( sK2_SY18 @ SV1 @ SY53 @ SY55 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SY59: b] :
( ~ ( sK1_Xs @ SY59 )
| ( sK2_SY18 @ SY59 @ ( sK3_SX0 @ SY59 ) @ ( sK4_SY56 @ SY59 ) ) )
| ! [SY60: b] :
( ~ ( sK1_Xs @ SY60 )
| ( sK2_SY18 @ SY60 @ ( sK4_SY56 @ SY60 ) @ ( sK3_SX0 @ SY60 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(21,plain,
! [SV1: b] :
( ( ( sK1_Xs @ SV1 )
= $false )
| ( ( ~ ( ~ ! [SY51: a,SY52: a] :
( ~ ( sK2_SY18 @ SV1 @ SY51 @ SY52 )
| ( sK2_SY18 @ SV1 @ SY52 @ SY51 ) )
| ~ ! [SY53: a,SY54: a,SY55: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SY53 @ SY54 )
| ~ ( sK2_SY18 @ SV1 @ SY54 @ SY55 ) )
| ( sK2_SY18 @ SV1 @ SY53 @ SY55 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ! [SY59: b] :
( ~ ( sK1_Xs @ SY59 )
| ( sK2_SY18 @ SY59 @ ( sK3_SX0 @ SY59 ) @ ( sK4_SY56 @ SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ! [SY60: b] :
( ~ ( sK1_Xs @ SY60 )
| ( sK2_SY18 @ SY60 @ ( sK4_SY56 @ SY60 ) @ ( sK3_SX0 @ SY60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: b] :
( ( ( ~ ! [SY51: a,SY52: a] :
( ~ ( sK2_SY18 @ SV1 @ SY51 @ SY52 )
| ( sK2_SY18 @ SV1 @ SY52 @ SY51 ) )
| ~ ! [SY53: a,SY54: a,SY55: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SY53 @ SY54 )
| ~ ( sK2_SY18 @ SV1 @ SY54 @ SY55 ) )
| ( sK2_SY18 @ SV1 @ SY53 @ SY55 ) ) )
= $false )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SY59: b] :
( ~ ( sK1_Xs @ SY59 )
| ( sK2_SY18 @ SY59 @ ( sK3_SX0 @ SY59 ) @ ( sK4_SY56 @ SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( sK1_Xs @ sK5_SY60 )
| ( sK2_SY18 @ sK5_SY60 @ ( sK4_SY56 @ sK5_SY60 ) @ ( sK3_SX0 @ sK5_SY60 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(27,plain,
! [SV1: b] :
( ( ( ~ ! [SY51: a,SY52: a] :
( ~ ( sK2_SY18 @ SV1 @ SY51 @ SY52 )
| ( sK2_SY18 @ SV1 @ SY52 @ SY51 ) ) )
= $false )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: b] :
( ( ( ~ ! [SY53: a,SY54: a,SY55: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SY53 @ SY54 )
| ~ ( sK2_SY18 @ SV1 @ SY54 @ SY55 ) )
| ( sK2_SY18 @ SV1 @ SY53 @ SY55 ) ) )
= $false )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV2: b] :
( ( ~ ( sK1_Xs @ SV2 )
| ( sK2_SY18 @ SV2 @ ( sK3_SX0 @ SV2 ) @ ( sK4_SY56 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ( sK1_Xs @ sK5_SY60 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( sK2_SY18 @ sK5_SY60 @ ( sK4_SY56 @ sK5_SY60 ) @ ( sK3_SX0 @ sK5_SY60 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(32,plain,
! [SV1: b] :
( ( ( ! [SY51: a,SY52: a] :
( ~ ( sK2_SY18 @ SV1 @ SY51 @ SY52 )
| ( sK2_SY18 @ SV1 @ SY52 @ SY51 ) ) )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(33,plain,
! [SV1: b] :
( ( ( ! [SY53: a,SY54: a,SY55: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SY53 @ SY54 )
| ~ ( sK2_SY18 @ SV1 @ SY54 @ SY55 ) )
| ( sK2_SY18 @ SV1 @ SY53 @ SY55 ) ) )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV2: b] :
( ( ( ~ ( sK1_Xs @ SV2 ) )
= $true )
| ( ( sK2_SY18 @ SV2 @ ( sK3_SX0 @ SV2 ) @ ( sK4_SY56 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( sK1_Xs @ sK5_SY60 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(36,plain,
! [SV3: a,SV1: b] :
( ( ( ! [SY61: a] :
( ~ ( sK2_SY18 @ SV1 @ SV3 @ SY61 )
| ( sK2_SY18 @ SV1 @ SY61 @ SV3 ) ) )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: a,SV1: b] :
( ( ( ! [SY62: a,SY63: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SV4 @ SY62 )
| ~ ( sK2_SY18 @ SV1 @ SY62 @ SY63 ) )
| ( sK2_SY18 @ SV1 @ SV4 @ SY63 ) ) )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: b] :
( ( ( sK1_Xs @ SV2 )
= $false )
| ( ( sK2_SY18 @ SV2 @ ( sK3_SX0 @ SV2 ) @ ( sK4_SY56 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV5: a,SV3: a,SV1: b] :
( ( ( ~ ( sK2_SY18 @ SV1 @ SV3 @ SV5 )
| ( sK2_SY18 @ SV1 @ SV5 @ SV3 ) )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: a,SV4: a,SV1: b] :
( ( ( ! [SY64: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SV4 @ SV6 )
| ~ ( sK2_SY18 @ SV1 @ SV6 @ SY64 ) )
| ( sK2_SY18 @ SV1 @ SV4 @ SY64 ) ) )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV5: a,SV3: a,SV1: b] :
( ( ( ~ ( sK2_SY18 @ SV1 @ SV3 @ SV5 ) )
= $true )
| ( ( sK2_SY18 @ SV1 @ SV5 @ SV3 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV7: a,SV6: a,SV4: a,SV1: b] :
( ( ( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SV4 @ SV6 )
| ~ ( sK2_SY18 @ SV1 @ SV6 @ SV7 ) )
| ( sK2_SY18 @ SV1 @ SV4 @ SV7 ) )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV5: a,SV3: a,SV1: b] :
( ( ( sK2_SY18 @ SV1 @ SV3 @ SV5 )
= $false )
| ( ( sK2_SY18 @ SV1 @ SV5 @ SV3 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV7: a,SV6: a,SV4: a,SV1: b] :
( ( ( ~ ~ ( ~ ( sK2_SY18 @ SV1 @ SV4 @ SV6 )
| ~ ( sK2_SY18 @ SV1 @ SV6 @ SV7 ) ) )
= $true )
| ( ( sK2_SY18 @ SV1 @ SV4 @ SV7 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV7: a,SV6: a,SV4: a,SV1: b] :
( ( ( ~ ( ~ ( sK2_SY18 @ SV1 @ SV4 @ SV6 )
| ~ ( sK2_SY18 @ SV1 @ SV6 @ SV7 ) ) )
= $false )
| ( ( sK2_SY18 @ SV1 @ SV4 @ SV7 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV7: a,SV6: a,SV4: a,SV1: b] :
( ( ( ~ ( sK2_SY18 @ SV1 @ SV4 @ SV6 )
| ~ ( sK2_SY18 @ SV1 @ SV6 @ SV7 ) )
= $true )
| ( ( sK2_SY18 @ SV1 @ SV4 @ SV7 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(47,plain,
! [SV7: a,SV6: a,SV4: a,SV1: b] :
( ( ( ~ ( sK2_SY18 @ SV1 @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ( sK2_SY18 @ SV1 @ SV6 @ SV7 ) )
= $true )
| ( ( sK2_SY18 @ SV1 @ SV4 @ SV7 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV7: a,SV6: a,SV4: a,SV1: b] :
( ( ( sK2_SY18 @ SV1 @ SV4 @ SV6 )
= $false )
| ( ( ~ ( sK2_SY18 @ SV1 @ SV6 @ SV7 ) )
= $true )
| ( ( sK2_SY18 @ SV1 @ SV4 @ SV7 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV4: a,SV7: a,SV6: a,SV1: b] :
( ( ( sK2_SY18 @ SV1 @ SV6 @ SV7 )
= $false )
| ( ( sK2_SY18 @ SV1 @ SV4 @ SV6 )
= $false )
| ( ( sK2_SY18 @ SV1 @ SV4 @ SV7 )
= $true )
| ( ( sK1_Xs @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,49,43,38,35]) ).
thf(51,plain,
( ( ! [SY35: b] :
( ( sK1_Xs @ SY35 )
=> ( ! [SY36: a,SY37: a] :
( ( sK2_SY18 @ SY35 @ SY36 @ SY37 )
=> ( sK2_SY18 @ SY35 @ SY37 @ SY36 ) )
& ! [SY38: a,SY39: a,SY40: a] :
( ( ( sK2_SY18 @ SY35 @ SY38 @ SY39 )
& ( sK2_SY18 @ SY35 @ SY39 @ SY40 ) )
=> ( sK2_SY18 @ SY35 @ SY38 @ SY40 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(52,plain,
( ( ~ ! [SY45: b > a,SY46: b > a,SY47: b > a] :
( ( ! [SY48: b] :
( ( sK1_Xs @ SY48 )
=> ( sK2_SY18 @ SY48 @ ( SY45 @ SY48 ) @ ( SY46 @ SY48 ) ) )
& ! [SY49: b] :
( ( sK1_Xs @ SY49 )
=> ( sK2_SY18 @ SY49 @ ( SY46 @ SY49 ) @ ( SY47 @ SY49 ) ) ) )
=> ! [SY50: b] :
( ( sK1_Xs @ SY50 )
=> ( sK2_SY18 @ SY50 @ ( SY45 @ SY50 ) @ ( SY47 @ SY50 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(53,plain,
( ( ! [SX0: b] :
( ~ ( sK1_Xs @ SX0 )
| ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ( sK2_SY18 @ SX0 @ SX1 @ SX2 )
| ( sK2_SY18 @ SX0 @ SX2 @ SX1 ) )
| ~ ! [SX1: a,SX2: a,SX3: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SX0 @ SX1 @ SX2 )
| ~ ( sK2_SY18 @ SX0 @ SX2 @ SX3 ) )
| ( sK2_SY18 @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(54,plain,
( ( ~ ! [SX0: b > a,SX1: b > a,SX2: b > a] :
( ~ ~ ( ~ ! [SX3: b] :
( ~ ( sK1_Xs @ SX3 )
| ( sK2_SY18 @ SX3 @ ( SX0 @ SX3 ) @ ( SX1 @ SX3 ) ) )
| ~ ! [SX3: b] :
( ~ ( sK1_Xs @ SX3 )
| ( sK2_SY18 @ SX3 @ ( SX1 @ SX3 ) @ ( SX2 @ SX3 ) ) ) )
| ! [SX3: b] :
( ~ ( sK1_Xs @ SX3 )
| ( sK2_SY18 @ SX3 @ ( SX0 @ SX3 ) @ ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(55,plain,
! [SV8: b] :
( ( ~ ( sK1_Xs @ SV8 )
| ~ ( ~ ! [SY65: a,SY66: a] :
( ~ ( sK2_SY18 @ SV8 @ SY65 @ SY66 )
| ( sK2_SY18 @ SV8 @ SY66 @ SY65 ) )
| ~ ! [SY67: a,SY68: a,SY69: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SY67 @ SY68 )
| ~ ( sK2_SY18 @ SV8 @ SY68 @ SY69 ) )
| ( sK2_SY18 @ SV8 @ SY67 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(56,plain,
( ( ! [SX0: b > a,SX1: b > a,SX2: b > a] :
( ~ ~ ( ~ ! [SX3: b] :
( ~ ( sK1_Xs @ SX3 )
| ( sK2_SY18 @ SX3 @ ( SX0 @ SX3 ) @ ( SX1 @ SX3 ) ) )
| ~ ! [SX3: b] :
( ~ ( sK1_Xs @ SX3 )
| ( sK2_SY18 @ SX3 @ ( SX1 @ SX3 ) @ ( SX2 @ SX3 ) ) ) )
| ! [SX3: b] :
( ~ ( sK1_Xs @ SX3 )
| ( sK2_SY18 @ SX3 @ ( SX0 @ SX3 ) @ ( SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV8: b] :
( ( ( ~ ( sK1_Xs @ SV8 ) )
= $true )
| ( ( ~ ( ~ ! [SY65: a,SY66: a] :
( ~ ( sK2_SY18 @ SV8 @ SY65 @ SY66 )
| ( sK2_SY18 @ SV8 @ SY66 @ SY65 ) )
| ~ ! [SY67: a,SY68: a,SY69: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SY67 @ SY68 )
| ~ ( sK2_SY18 @ SV8 @ SY68 @ SY69 ) )
| ( sK2_SY18 @ SV8 @ SY67 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [SY70: b > a,SY71: b > a] :
( ~ ~ ( ~ ! [SY72: b] :
( ~ ( sK1_Xs @ SY72 )
| ( sK2_SY18 @ SY72 @ ( sK6_SX0 @ SY72 ) @ ( SY70 @ SY72 ) ) )
| ~ ! [SX3: b] :
( ~ ( sK1_Xs @ SX3 )
| ( sK2_SY18 @ SX3 @ ( SY70 @ SX3 ) @ ( SY71 @ SX3 ) ) ) )
| ! [SY74: b] :
( ~ ( sK1_Xs @ SY74 )
| ( sK2_SY18 @ SY74 @ ( sK6_SX0 @ SY74 ) @ ( SY71 @ SY74 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(59,plain,
! [SV8: b] :
( ( ( sK1_Xs @ SV8 )
= $false )
| ( ( ~ ( ~ ! [SY65: a,SY66: a] :
( ~ ( sK2_SY18 @ SV8 @ SY65 @ SY66 )
| ( sK2_SY18 @ SV8 @ SY66 @ SY65 ) )
| ~ ! [SY67: a,SY68: a,SY69: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SY67 @ SY68 )
| ~ ( sK2_SY18 @ SV8 @ SY68 @ SY69 ) )
| ( sK2_SY18 @ SV8 @ SY67 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
( ( ! [SY75: b > a] :
( ~ ~ ( ~ ! [SY76: b] :
( ~ ( sK1_Xs @ SY76 )
| ( sK2_SY18 @ SY76 @ ( sK6_SX0 @ SY76 ) @ ( sK7_SY70 @ SY76 ) ) )
| ~ ! [SY77: b] :
( ~ ( sK1_Xs @ SY77 )
| ( sK2_SY18 @ SY77 @ ( sK7_SY70 @ SY77 ) @ ( SY75 @ SY77 ) ) ) )
| ! [SY74: b] :
( ~ ( sK1_Xs @ SY74 )
| ( sK2_SY18 @ SY74 @ ( sK6_SX0 @ SY74 ) @ ( SY75 @ SY74 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(61,plain,
! [SV8: b] :
( ( ( ~ ! [SY65: a,SY66: a] :
( ~ ( sK2_SY18 @ SV8 @ SY65 @ SY66 )
| ( sK2_SY18 @ SV8 @ SY66 @ SY65 ) )
| ~ ! [SY67: a,SY68: a,SY69: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SY67 @ SY68 )
| ~ ( sK2_SY18 @ SV8 @ SY68 @ SY69 ) )
| ( sK2_SY18 @ SV8 @ SY67 @ SY69 ) ) )
= $false )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
( ( ~ ~ ( ~ ! [SY76: b] :
( ~ ( sK1_Xs @ SY76 )
| ( sK2_SY18 @ SY76 @ ( sK6_SX0 @ SY76 ) @ ( sK7_SY70 @ SY76 ) ) )
| ~ ! [SY80: b] :
( ~ ( sK1_Xs @ SY80 )
| ( sK2_SY18 @ SY80 @ ( sK7_SY70 @ SY80 ) @ ( sK8_SY75 @ SY80 ) ) ) )
| ! [SY81: b] :
( ~ ( sK1_Xs @ SY81 )
| ( sK2_SY18 @ SY81 @ ( sK6_SX0 @ SY81 ) @ ( sK8_SY75 @ SY81 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(63,plain,
! [SV8: b] :
( ( ( ~ ! [SY65: a,SY66: a] :
( ~ ( sK2_SY18 @ SV8 @ SY65 @ SY66 )
| ( sK2_SY18 @ SV8 @ SY66 @ SY65 ) ) )
= $false )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(64,plain,
! [SV8: b] :
( ( ( ~ ! [SY67: a,SY68: a,SY69: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SY67 @ SY68 )
| ~ ( sK2_SY18 @ SV8 @ SY68 @ SY69 ) )
| ( sK2_SY18 @ SV8 @ SY67 @ SY69 ) ) )
= $false )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
( ( ~ ~ ( ~ ! [SY76: b] :
( ~ ( sK1_Xs @ SY76 )
| ( sK2_SY18 @ SY76 @ ( sK6_SX0 @ SY76 ) @ ( sK7_SY70 @ SY76 ) ) )
| ~ ! [SY80: b] :
( ~ ( sK1_Xs @ SY80 )
| ( sK2_SY18 @ SY80 @ ( sK7_SY70 @ SY80 ) @ ( sK8_SY75 @ SY80 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
( ( ! [SY81: b] :
( ~ ( sK1_Xs @ SY81 )
| ( sK2_SY18 @ SY81 @ ( sK6_SX0 @ SY81 ) @ ( sK8_SY75 @ SY81 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV8: b] :
( ( ( ! [SY65: a,SY66: a] :
( ~ ( sK2_SY18 @ SV8 @ SY65 @ SY66 )
| ( sK2_SY18 @ SV8 @ SY66 @ SY65 ) ) )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV8: b] :
( ( ( ! [SY67: a,SY68: a,SY69: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SY67 @ SY68 )
| ~ ( sK2_SY18 @ SV8 @ SY68 @ SY69 ) )
| ( sK2_SY18 @ SV8 @ SY67 @ SY69 ) ) )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( ~ ( ~ ! [SY76: b] :
( ~ ( sK1_Xs @ SY76 )
| ( sK2_SY18 @ SY76 @ ( sK6_SX0 @ SY76 ) @ ( sK7_SY70 @ SY76 ) ) )
| ~ ! [SY80: b] :
( ~ ( sK1_Xs @ SY80 )
| ( sK2_SY18 @ SY80 @ ( sK7_SY70 @ SY80 ) @ ( sK8_SY75 @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( ~ ( sK1_Xs @ sK9_SY81 )
| ( sK2_SY18 @ sK9_SY81 @ ( sK6_SX0 @ sK9_SY81 ) @ ( sK8_SY75 @ sK9_SY81 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(71,plain,
! [SV9: a,SV8: b] :
( ( ( ! [SY82: a] :
( ~ ( sK2_SY18 @ SV8 @ SV9 @ SY82 )
| ( sK2_SY18 @ SV8 @ SY82 @ SV9 ) ) )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV10: a,SV8: b] :
( ( ( ! [SY83: a,SY84: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SV10 @ SY83 )
| ~ ( sK2_SY18 @ SV8 @ SY83 @ SY84 ) )
| ( sK2_SY18 @ SV8 @ SV10 @ SY84 ) ) )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(73,plain,
( ( ~ ! [SY76: b] :
( ~ ( sK1_Xs @ SY76 )
| ( sK2_SY18 @ SY76 @ ( sK6_SX0 @ SY76 ) @ ( sK7_SY70 @ SY76 ) ) )
| ~ ! [SY80: b] :
( ~ ( sK1_Xs @ SY80 )
| ( sK2_SY18 @ SY80 @ ( sK7_SY70 @ SY80 ) @ ( sK8_SY75 @ SY80 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
( ( ~ ( sK1_Xs @ sK9_SY81 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(75,plain,
( ( sK2_SY18 @ sK9_SY81 @ ( sK6_SX0 @ sK9_SY81 ) @ ( sK8_SY75 @ sK9_SY81 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(76,plain,
! [SV11: a,SV9: a,SV8: b] :
( ( ( ~ ( sK2_SY18 @ SV8 @ SV9 @ SV11 )
| ( sK2_SY18 @ SV8 @ SV11 @ SV9 ) )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV12: a,SV10: a,SV8: b] :
( ( ( ! [SY85: a] :
( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SV10 @ SV12 )
| ~ ( sK2_SY18 @ SV8 @ SV12 @ SY85 ) )
| ( sK2_SY18 @ SV8 @ SV10 @ SY85 ) ) )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(78,plain,
( ( ~ ! [SY76: b] :
( ~ ( sK1_Xs @ SY76 )
| ( sK2_SY18 @ SY76 @ ( sK6_SX0 @ SY76 ) @ ( sK7_SY70 @ SY76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
( ( ~ ! [SY80: b] :
( ~ ( sK1_Xs @ SY80 )
| ( sK2_SY18 @ SY80 @ ( sK7_SY70 @ SY80 ) @ ( sK8_SY75 @ SY80 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(80,plain,
( ( sK1_Xs @ sK9_SY81 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(81,plain,
! [SV11: a,SV9: a,SV8: b] :
( ( ( ~ ( sK2_SY18 @ SV8 @ SV9 @ SV11 ) )
= $true )
| ( ( sK2_SY18 @ SV8 @ SV11 @ SV9 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV13: a,SV12: a,SV10: a,SV8: b] :
( ( ( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SV10 @ SV12 )
| ~ ( sK2_SY18 @ SV8 @ SV12 @ SV13 ) )
| ( sK2_SY18 @ SV8 @ SV10 @ SV13 ) )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(83,plain,
( ( ! [SY76: b] :
( ~ ( sK1_Xs @ SY76 )
| ( sK2_SY18 @ SY76 @ ( sK6_SX0 @ SY76 ) @ ( sK7_SY70 @ SY76 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(84,plain,
( ( ! [SY80: b] :
( ~ ( sK1_Xs @ SY80 )
| ( sK2_SY18 @ SY80 @ ( sK7_SY70 @ SY80 ) @ ( sK8_SY75 @ SY80 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV11: a,SV9: a,SV8: b] :
( ( ( sK2_SY18 @ SV8 @ SV9 @ SV11 )
= $false )
| ( ( sK2_SY18 @ SV8 @ SV11 @ SV9 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV13: a,SV12: a,SV10: a,SV8: b] :
( ( ( ~ ~ ( ~ ( sK2_SY18 @ SV8 @ SV10 @ SV12 )
| ~ ( sK2_SY18 @ SV8 @ SV12 @ SV13 ) ) )
= $true )
| ( ( sK2_SY18 @ SV8 @ SV10 @ SV13 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV14: b] :
( ( ~ ( sK1_Xs @ SV14 )
| ( sK2_SY18 @ SV14 @ ( sK6_SX0 @ SV14 ) @ ( sK7_SY70 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV15: b] :
( ( ~ ( sK1_Xs @ SV15 )
| ( sK2_SY18 @ SV15 @ ( sK7_SY70 @ SV15 ) @ ( sK8_SY75 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV13: a,SV12: a,SV10: a,SV8: b] :
( ( ( ~ ( ~ ( sK2_SY18 @ SV8 @ SV10 @ SV12 )
| ~ ( sK2_SY18 @ SV8 @ SV12 @ SV13 ) ) )
= $false )
| ( ( sK2_SY18 @ SV8 @ SV10 @ SV13 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV14: b] :
( ( ( ~ ( sK1_Xs @ SV14 ) )
= $true )
| ( ( sK2_SY18 @ SV14 @ ( sK6_SX0 @ SV14 ) @ ( sK7_SY70 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV15: b] :
( ( ( ~ ( sK1_Xs @ SV15 ) )
= $true )
| ( ( sK2_SY18 @ SV15 @ ( sK7_SY70 @ SV15 ) @ ( sK8_SY75 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(92,plain,
! [SV13: a,SV12: a,SV10: a,SV8: b] :
( ( ( ~ ( sK2_SY18 @ SV8 @ SV10 @ SV12 )
| ~ ( sK2_SY18 @ SV8 @ SV12 @ SV13 ) )
= $true )
| ( ( sK2_SY18 @ SV8 @ SV10 @ SV13 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(93,plain,
! [SV14: b] :
( ( ( sK1_Xs @ SV14 )
= $false )
| ( ( sK2_SY18 @ SV14 @ ( sK6_SX0 @ SV14 ) @ ( sK7_SY70 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV15: b] :
( ( ( sK1_Xs @ SV15 )
= $false )
| ( ( sK2_SY18 @ SV15 @ ( sK7_SY70 @ SV15 ) @ ( sK8_SY75 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV13: a,SV12: a,SV10: a,SV8: b] :
( ( ( ~ ( sK2_SY18 @ SV8 @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ( sK2_SY18 @ SV8 @ SV12 @ SV13 ) )
= $true )
| ( ( sK2_SY18 @ SV8 @ SV10 @ SV13 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV13: a,SV12: a,SV10: a,SV8: b] :
( ( ( sK2_SY18 @ SV8 @ SV10 @ SV12 )
= $false )
| ( ( ~ ( sK2_SY18 @ SV8 @ SV12 @ SV13 ) )
= $true )
| ( ( sK2_SY18 @ SV8 @ SV10 @ SV13 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(97,plain,
! [SV10: a,SV13: a,SV12: a,SV8: b] :
( ( ( sK2_SY18 @ SV8 @ SV12 @ SV13 )
= $false )
| ( ( sK2_SY18 @ SV8 @ SV10 @ SV12 )
= $false )
| ( ( sK2_SY18 @ SV8 @ SV10 @ SV13 )
= $true )
| ( ( sK1_Xs @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(98,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,97,94,93,85,80]) ).
thf(99,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[98,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV044^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.21 % Computer : n026.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 15:42:32 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.28
% 0.08/0.28 No.of.Axioms: 0
% 0.08/0.28
% 0.08/0.28 Length.of.Defs: 0
% 0.08/0.28
% 0.08/0.28 Contains.Choice.Funs: false
% 0.08/0.28 ....
% 0.08/0.28
% 0.08/0.28 ********************************
% 0.08/0.28 * All subproblems solved! *
% 0.08/0.28 ********************************
% 0.08/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:98,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.28
% 0.08/0.28 %**** Beginning of derivation protocol ****
% 0.08/0.28 % SZS output start CNFRefutation
% See solution above
% 0.08/0.28
% 0.08/0.28 %**** End of derivation protocol ****
% 0.08/0.28 %**** no. of clauses in derivation: 99 ****
% 0.08/0.28 %**** clause counter: 98 ****
% 0.08/0.28
% 0.08/0.28 % SZS status Theorem for /export/starexec/sandbox2/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:98,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------