%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL368+2 : TPTP v9.3.1. Released v9.1.0.
% 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 : n005.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 10:28:36 AM UTC 2026
% Result : Theorem 61.52s 10.59s
% Output : CNFRefutation 61.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 134 ( 39 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 1165 ( 15 ~; 16 |; 2 &;1130 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 290 ( 0 ^; 290 !; 0 ?; 290 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_is_a_theorem,type,
is_a_theorem: $i > $o ).
thf(tp_n,type,
n: $i > $i ).
thf(tp_u,type,
u: $i ).
thf(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ A @ ( implies @ B @ A ) ) @ ( implies @ ( implies @ C @ ( implies @ D @ ( implies @ E @ D ) ) ) @ F ) ) @ F ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ G @ H ) @ ( implies @ ( implies @ H @ I ) @ ( implies @ G @ I ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ J ) @ J ) @ J ) @ K ) ) @ K ) @ ( implies @ ( implies @ L @ ( implies @ ( n @ L ) @ M ) ) @ N ) ) @ N ) @ O ) ) @ O ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f2) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( ( is_a_theorem @ ( implies @ X @ Y ) )
& ( is_a_theorem @ X ) )
=> ( is_a_theorem @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(3,conjecture,
is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3) ).
thf(4,negated_conjecture,
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ A @ ( implies @ B @ A ) ) @ ( implies @ ( implies @ C @ ( implies @ D @ ( implies @ E @ D ) ) ) @ F ) ) @ F ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ G @ H ) @ ( implies @ ( implies @ H @ I ) @ ( implies @ G @ I ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ J ) @ J ) @ J ) @ K ) ) @ K ) @ ( implies @ ( implies @ L @ ( implies @ ( n @ L ) @ M ) ) @ N ) ) @ N ) @ O ) ) @ O ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ ( implies @ X @ Y ) )
& ( is_a_theorem @ X ) )
=> ( is_a_theorem @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ A @ ( implies @ B @ A ) ) @ ( implies @ ( implies @ C @ ( implies @ D @ ( implies @ E @ D ) ) ) @ F ) ) @ F ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ G @ H ) @ ( implies @ ( implies @ H @ I ) @ ( implies @ G @ I ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ J ) @ J ) @ J ) @ K ) ) @ K ) @ ( implies @ ( implies @ L @ ( implies @ ( n @ L ) @ M ) ) @ N ) ) @ N ) @ O ) ) @ O ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ~ ( is_a_theorem @ ( implies @ SV1 @ SY17 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV2: $i] :
( ( ! [SY18: $i,SY19: $i,SY20: $i,SY21: $i,SY22: $i,SY23: $i,SY24: $i,SY25: $i,SY26: $i,SY27: $i,SY28: $i,SY29: $i,SY30: $i,SY31: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SY18 @ SV2 ) ) @ ( implies @ ( implies @ SY19 @ ( implies @ SY20 @ ( implies @ SY21 @ SY20 ) ) ) @ SY22 ) ) @ SY22 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SY23 @ SY24 ) @ ( implies @ ( implies @ SY24 @ SY25 ) @ ( implies @ SY23 @ SY25 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY26 ) @ SY26 ) @ SY26 ) @ SY27 ) ) @ SY27 ) @ ( implies @ ( implies @ SY28 @ ( implies @ ( n @ SY28 ) @ SY29 ) ) @ SY30 ) ) @ SY30 ) @ SY31 ) ) @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY32: $i,SY33: $i,SY34: $i,SY35: $i,SY36: $i,SY37: $i,SY38: $i,SY39: $i,SY40: $i,SY41: $i,SY42: $i,SY43: $i,SY44: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SY32 @ ( implies @ SY33 @ ( implies @ SY34 @ SY33 ) ) ) @ SY35 ) ) @ SY35 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SY36 @ SY37 ) @ ( implies @ ( implies @ SY37 @ SY38 ) @ ( implies @ SY36 @ SY38 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY39 ) @ SY39 ) @ SY39 ) @ SY40 ) ) @ SY40 ) @ ( implies @ ( implies @ SY41 @ ( implies @ ( n @ SY41 ) @ SY42 ) ) @ SY43 ) ) @ SY43 ) @ SY44 ) ) @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
| ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i,SY48: $i,SY49: $i,SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SY45 @ ( implies @ SY46 @ SY45 ) ) ) @ SY47 ) ) @ SY47 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SY48 @ SY49 ) @ ( implies @ ( implies @ SY49 @ SY50 ) @ ( implies @ SY48 @ SY50 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY51 ) @ SY51 ) @ SY51 ) @ SY52 ) ) @ SY52 ) @ ( implies @ ( implies @ SY53 @ ( implies @ ( n @ SY53 ) @ SY54 ) ) @ SY55 ) ) @ SY55 ) @ SY56 ) ) @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV3 ) ) )
= $true )
| ( ( ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY57: $i,SY58: $i,SY59: $i,SY60: $i,SY61: $i,SY62: $i,SY63: $i,SY64: $i,SY65: $i,SY66: $i,SY67: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SY57 @ SV6 ) ) ) @ SY58 ) ) @ SY58 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SY59 @ SY60 ) @ ( implies @ ( implies @ SY60 @ SY61 ) @ ( implies @ SY59 @ SY61 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY62 ) @ SY62 ) @ SY62 ) @ SY63 ) ) @ SY63 ) @ ( implies @ ( implies @ SY64 @ ( implies @ ( n @ SY64 ) @ SY65 ) ) @ SY66 ) ) @ SY66 ) @ SY67 ) ) @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV3: $i,SV1: $i] :
( ( ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
= $false )
| ( ( ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i,SY71: $i,SY72: $i,SY73: $i,SY74: $i,SY75: $i,SY76: $i,SY77: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SY68 ) ) @ SY68 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SY69 @ SY70 ) @ ( implies @ ( implies @ SY70 @ SY71 ) @ ( implies @ SY69 @ SY71 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY72 ) @ SY72 ) @ SY72 ) @ SY73 ) ) @ SY73 ) @ ( implies @ ( implies @ SY74 @ ( implies @ ( n @ SY74 ) @ SY75 ) ) @ SY76 ) ) @ SY76 ) @ SY77 ) ) @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV3: $i,SV1: $i] :
( ( ( is_a_theorem @ SV1 )
= $false )
| ( ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
= $false )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY78: $i,SY79: $i,SY80: $i,SY81: $i,SY82: $i,SY83: $i,SY84: $i,SY85: $i,SY86: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SY78 @ SY79 ) @ ( implies @ ( implies @ SY79 @ SY80 ) @ ( implies @ SY78 @ SY80 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY81 ) @ SY81 ) @ SY81 ) @ SY82 ) ) @ SY82 ) @ ( implies @ ( implies @ SY83 @ ( implies @ ( n @ SY83 ) @ SY84 ) ) @ SY85 ) ) @ SY85 ) @ SY86 ) ) @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY87: $i,SY88: $i,SY89: $i,SY90: $i,SY91: $i,SY92: $i,SY93: $i,SY94: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SY87 ) @ ( implies @ ( implies @ SY87 @ SY88 ) @ ( implies @ SV9 @ SY88 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY89 ) @ SY89 ) @ SY89 ) @ SY90 ) ) @ SY90 ) @ ( implies @ ( implies @ SY91 @ ( implies @ ( n @ SY91 ) @ SY92 ) ) @ SY93 ) ) @ SY93 ) @ SY94 ) ) @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY95: $i,SY96: $i,SY97: $i,SY98: $i,SY99: $i,SY100: $i,SY101: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SY95 ) @ ( implies @ SV9 @ SY95 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY96 ) @ SY96 ) @ SY96 ) @ SY97 ) ) @ SY97 ) @ ( implies @ ( implies @ SY98 @ ( implies @ ( n @ SY98 ) @ SY99 ) ) @ SY100 ) ) @ SY100 ) @ SY101 ) ) @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i,SY105: $i,SY106: $i,SY107: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SV11 ) @ ( implies @ SV9 @ SV11 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SY102 ) @ SY102 ) @ SY102 ) @ SY103 ) ) @ SY103 ) @ ( implies @ ( implies @ SY104 @ ( implies @ ( n @ SY104 ) @ SY105 ) ) @ SY106 ) ) @ SY106 ) @ SY107 ) ) @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(29,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY108: $i,SY109: $i,SY110: $i,SY111: $i,SY112: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SV11 ) @ ( implies @ SV9 @ SV11 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SV12 ) @ SV12 ) @ SV12 ) @ SY108 ) ) @ SY108 ) @ ( implies @ ( implies @ SY109 @ ( implies @ ( n @ SY109 ) @ SY110 ) ) @ SY111 ) ) @ SY111 ) @ SY112 ) ) @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SV11 ) @ ( implies @ SV9 @ SV11 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SV12 ) @ SV12 ) @ SV12 ) @ SV13 ) ) @ SV13 ) @ ( implies @ ( implies @ SY113 @ ( implies @ ( n @ SY113 ) @ SY114 ) ) @ SY115 ) ) @ SY115 ) @ SY116 ) ) @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV14: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY117: $i,SY118: $i,SY119: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SV11 ) @ ( implies @ SV9 @ SV11 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SV12 ) @ SV12 ) @ SV12 ) @ SV13 ) ) @ SV13 ) @ ( implies @ ( implies @ SV14 @ ( implies @ ( n @ SV14 ) @ SY117 ) ) @ SY118 ) ) @ SY118 ) @ SY119 ) ) @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(32,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY120: $i,SY121: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SV11 ) @ ( implies @ SV9 @ SV11 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SV12 ) @ SV12 ) @ SV12 ) @ SV13 ) ) @ SV13 ) @ ( implies @ ( implies @ SV14 @ ( implies @ ( n @ SV14 ) @ SV15 ) ) @ SY120 ) ) @ SY120 ) @ SY121 ) ) @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV16: $i,SV15: $i,SV14: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY122: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SV11 ) @ ( implies @ SV9 @ SV11 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SV12 ) @ SV12 ) @ SV12 ) @ SV13 ) ) @ SV13 ) @ ( implies @ ( implies @ SV14 @ ( implies @ ( n @ SV14 ) @ SV15 ) ) @ SV16 ) ) @ SV16 ) @ SY122 ) ) @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV17: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV2 @ ( implies @ SV4 @ SV2 ) ) @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ ( implies @ SV7 @ SV6 ) ) ) @ SV8 ) ) @ SV8 ) @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ ( implies @ SV9 @ SV10 ) @ ( implies @ ( implies @ SV10 @ SV11 ) @ ( implies @ SV9 @ SV11 ) ) ) @ ( implies @ ( implies @ ( implies @ ( n @ SV12 ) @ SV12 ) @ SV12 ) @ SV13 ) ) @ SV13 ) @ ( implies @ ( implies @ SV14 @ ( implies @ ( n @ SV14 ) @ SV15 ) ) @ SV16 ) ) @ SV16 ) @ SV17 ) ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,34,24]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL368+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 12:16:44 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 61.52/10.59
% 61.52/10.59 No.of.Axioms: 2
% 61.52/10.59
% 61.52/10.59 Length.of.Defs: 0
% 61.52/10.59
% 61.52/10.59 Contains.Choice.Funs: false
% 61.52/10.59 ..
% 61.52/10.59
% 61.52/10.59 ********************************
% 61.52/10.59 * All subproblems solved! *
% 61.52/10.59 ********************************
% 61.52/10.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 61.52/10.59
% 61.52/10.59 %**** Beginning of derivation protocol ****
% 61.52/10.59 % SZS output start CNFRefutation
% See solution above
% 61.52/10.59
% 61.52/10.59 %**** End of derivation protocol ****
% 61.52/10.59 %**** no. of clauses in derivation: 36 ****
% 61.52/10.59 %**** clause counter: 35 ****
% 61.52/10.59
% 61.52/10.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------