TSTP Solution File: SYN069+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 08:23:17 EDT 2022
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 118 ( 34 unt; 9 typ; 0 def)
% Number of atoms : 864 ( 232 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1249 ( 316 ~; 245 |; 38 &; 642 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 235 ( 0 ^ 223 !; 12 ?; 235 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_f,type,
big_f: $i > $o ).
thf(tp_big_g,type,
big_g: $i > $o ).
thf(tp_big_h,type,
big_h: $i > $i > $o ).
thf(tp_big_j,type,
big_j: $i > $i > $o ).
thf(tp_big_k,type,
big_k: $i > $o ).
thf(tp_big_l,type,
big_l: $i > $o ).
thf(tp_sK1_Y,type,
sK1_Y: $i > $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(tp_sK3_Y,type,
sK3_Y: $i > $i ).
thf(1,axiom,
? [X: $i] :
( ( big_f @ X )
& ! [Y: $i] :
( ( big_h @ X @ Y )
=> ( big_l @ Y ) )
& ! [Y1: $i] :
( ( ( big_g @ Y1 )
& ( big_h @ X @ Y1 ) )
=> ( big_j @ X @ Y1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel45_3) ).
thf(2,axiom,
~ ? [Y: $i] :
( ( big_l @ Y )
& ( big_k @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel45_2) ).
thf(3,axiom,
! [X: $i] :
( ( ( big_f @ X )
& ! [Y: $i] :
( ( ( big_g @ Y )
& ( big_h @ X @ Y ) )
=> ( big_j @ X @ Y ) ) )
=> ! [Y1: $i] :
( ( big_g @ Y1 )
& ( big_h @ X @ Y1 )
& ( big_k @ Y1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel45_1) ).
thf(4,conjecture,
? [X: $i] :
( ( big_f @ X )
& ~ ? [Y: $i] :
( ( big_g @ Y )
& ( big_h @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel45) ).
thf(5,negated_conjecture,
( ( ? [X: $i] :
( ( big_f @ X )
& ~ ? [Y: $i] :
( ( big_g @ Y )
& ( big_h @ X @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ? [X: $i] :
( ( big_f @ X )
& ~ ? [Y: $i] :
( ( big_g @ Y )
& ( big_h @ X @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ? [X: $i] :
( ( big_f @ X )
& ! [Y: $i] :
( ( big_h @ X @ Y )
=> ( big_l @ Y ) )
& ! [Y1: $i] :
( ( ( big_g @ Y1 )
& ( big_h @ X @ Y1 ) )
=> ( big_j @ X @ Y1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ~ ? [Y: $i] :
( ( big_l @ Y )
& ( big_k @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( ( big_f @ X )
& ! [Y: $i] :
( ( ( big_g @ Y )
& ( big_h @ X @ Y ) )
=> ( big_j @ X @ Y ) ) )
=> ! [Y1: $i] :
( ( big_g @ Y1 )
& ( big_h @ X @ Y1 )
& ( big_k @ Y1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ? [X: $i] :
( ( big_f @ X )
& ~ ? [Y: $i] :
( ( big_g @ Y )
& ( big_h @ X @ Y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [X: $i] :
( ~ ( big_f @ X )
| ( ( big_g @ ( sK1_Y @ X ) )
& ( big_h @ X @ ( sK1_Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [SY9: $i] :
( ~ ( big_g @ SY9 )
| ~ ( big_h @ sK2_X @ SY9 )
| ( big_j @ sK2_X @ SY9 ) )
& ! [SY10: $i] :
( ~ ( big_h @ sK2_X @ SY10 )
| ( big_l @ SY10 ) )
& ( big_f @ sK2_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(13,plain,
( ( ! [Y: $i] :
( ~ ( big_k @ Y )
| ~ ( big_l @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( ( big_g @ ( sK3_Y @ X ) )
& ( big_h @ X @ ( sK3_Y @ X ) )
& ~ ( big_j @ X @ ( sK3_Y @ X ) ) )
| ~ ( big_f @ X )
| ( ! [Y1: $i] : ( big_g @ Y1 )
& ! [Y1: $i] : ( big_h @ X @ Y1 )
& ! [Y1: $i] : ( big_k @ Y1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( ( big_g @ ( sK3_Y @ X ) )
& ( big_h @ X @ ( sK3_Y @ X ) )
& ~ ( big_j @ X @ ( sK3_Y @ X ) ) )
| ~ ( big_f @ X )
| ( ! [Y1: $i] : ( big_g @ Y1 )
& ! [Y1: $i] : ( big_h @ X @ Y1 )
& ! [Y1: $i] : ( big_k @ Y1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [Y: $i] :
( ~ ( big_k @ Y )
| ~ ( big_l @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [SY9: $i] :
( ~ ( big_g @ SY9 )
| ~ ( big_h @ sK2_X @ SY9 )
| ( big_j @ sK2_X @ SY9 ) )
& ! [SY10: $i] :
( ~ ( big_h @ sK2_X @ SY10 )
| ( big_l @ SY10 ) )
& ( big_f @ sK2_X ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [X: $i] :
( ~ ( big_f @ X )
| ( ( big_g @ ( sK1_Y @ X ) )
& ( big_h @ X @ ( sK1_Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( big_g @ ( sK3_Y @ SX0 ) )
| ~ ( big_h @ SX0 @ ( sK3_Y @ SX0 ) ) )
| ~ ~ ( big_j @ SX0 @ ( sK3_Y @ SX0 ) ) )
| ~ ( big_f @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SX1: $i] : ( big_h @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_g @ SX0 )
| ~ ( big_h @ sK2_X @ SX0 )
| ( big_j @ sK2_X @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( big_h @ sK2_X @ SX0 )
| ( big_l @ SX0 ) )
| ~ ( big_f @ sK2_X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [SX0: $i] :
( ~ ( big_f @ SX0 )
| ~ ( ~ ( big_g @ ( sK1_Y @ SX0 ) )
| ~ ( big_h @ SX0 @ ( sK1_Y @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: $i] :
( ( ~ ( big_k @ SV1 )
| ~ ( big_l @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: $i] :
( ( ~ ( ~ ~ ( ~ ( big_g @ ( sK3_Y @ SV2 ) )
| ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) )
| ~ ~ ( big_j @ SV2 @ ( sK3_Y @ SV2 ) ) )
| ~ ( big_f @ SV2 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_g @ SX0 )
| ~ ( big_h @ sK2_X @ SX0 )
| ( big_j @ sK2_X @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( big_h @ sK2_X @ SX0 )
| ( big_l @ SX0 ) )
| ~ ( big_f @ sK2_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i] :
( ( ~ ( big_f @ SV3 )
| ~ ( ~ ( big_g @ ( sK1_Y @ SV3 ) )
| ~ ( big_h @ SV3 @ ( sK1_Y @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( ~ ( big_k @ SV1 ) )
= $true )
| ( ( ~ ( big_l @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( big_g @ ( sK3_Y @ SV2 ) )
| ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) )
| ~ ~ ( big_j @ SV2 @ ( sK3_Y @ SV2 ) ) )
| ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_g @ SX0 )
| ~ ( big_h @ sK2_X @ SX0 )
| ( big_j @ sK2_X @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( big_h @ sK2_X @ SX0 )
| ( big_l @ SX0 ) )
| ~ ( big_f @ sK2_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
! [SV3: $i] :
( ( ( ~ ( big_f @ SV3 ) )
= $true )
| ( ( ~ ( ~ ( big_g @ ( sK1_Y @ SV3 ) )
| ~ ( big_h @ SV3 @ ( sK1_Y @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( big_k @ SV1 )
= $false )
| ( ( ~ ( big_l @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( big_g @ ( sK3_Y @ SV2 ) )
| ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) )
| ~ ~ ( big_j @ SV2 @ ( sK3_Y @ SV2 ) ) ) )
= $true )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [SX0: $i] :
( ~ ( big_g @ SX0 )
| ~ ( big_h @ sK2_X @ SX0 )
| ( big_j @ sK2_X @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_h @ sK2_X @ SX0 )
| ( big_l @ SX0 ) )
| ~ ( big_f @ sK2_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( big_f @ SV3 )
= $false )
| ( ( ~ ( ~ ( big_g @ ( sK1_Y @ SV3 ) )
| ~ ( big_h @ SV3 @ ( sK1_Y @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV1: $i] :
( ( ( big_l @ SV1 )
= $false )
| ( ( big_k @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( big_g @ ( sK3_Y @ SV2 ) )
| ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) )
| ~ ~ ( big_j @ SV2 @ ( sK3_Y @ SV2 ) ) )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV4: $i] :
( ( ~ ( big_g @ SV4 )
| ~ ( big_h @ sK2_X @ SV4 )
| ( big_j @ sK2_X @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_h @ sK2_X @ SX0 )
| ( big_l @ SX0 ) )
| ~ ( big_f @ sK2_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV3: $i] :
( ( ( ~ ( big_g @ ( sK1_Y @ SV3 ) )
| ~ ( big_h @ SV3 @ ( sK1_Y @ SV3 ) ) )
= $false )
| ( ( big_f @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( big_g @ ( sK3_Y @ SV2 ) )
| ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) ) )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( ~ ~ ( big_j @ SV2 @ ( sK3_Y @ SV2 ) ) )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV4: $i] :
( ( ( ~ ( big_g @ SV4 )
| ~ ( big_h @ sK2_X @ SV4 ) )
= $true )
| ( ( big_j @ sK2_X @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_h @ sK2_X @ SX0 )
| ( big_l @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( big_f @ sK2_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV3: $i] :
( ( ( ~ ( big_g @ ( sK1_Y @ SV3 ) ) )
= $false )
| ( ( big_f @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(47,plain,
! [SV3: $i] :
( ( ( ~ ( big_h @ SV3 @ ( sK1_Y @ SV3 ) ) )
= $false )
| ( ( big_f @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(48,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( big_g @ ( sK3_Y @ SV2 ) )
| ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) ) )
= $true )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(49,plain,
! [SV2: $i] :
( ( ( ~ ( big_j @ SV2 @ ( sK3_Y @ SV2 ) ) )
= $true )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(50,plain,
! [SV4: $i] :
( ( ( ~ ( big_g @ SV4 ) )
= $true )
| ( ( ~ ( big_h @ sK2_X @ SV4 ) )
= $true )
| ( ( big_j @ sK2_X @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(51,plain,
( ( ! [SX0: $i] :
( ~ ( big_h @ sK2_X @ SX0 )
| ( big_l @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(52,plain,
( ( big_f @ sK2_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(53,plain,
! [SV3: $i] :
( ( ( big_g @ ( sK1_Y @ SV3 ) )
= $true )
| ( ( big_f @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(54,plain,
! [SV3: $i] :
( ( ( big_h @ SV3 @ ( sK1_Y @ SV3 ) )
= $true )
| ( ( big_f @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(55,plain,
! [SV2: $i] :
( ( ( ~ ( big_g @ ( sK3_Y @ SV2 ) )
| ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( big_g @ SV4 )
= $false )
| ( ( ~ ( big_h @ sK2_X @ SV4 ) )
= $true )
| ( ( big_j @ sK2_X @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV5: $i] :
( ( ~ ( big_h @ sK2_X @ SV5 )
| ( big_l @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV2: $i] :
( ( ( ~ ( big_g @ ( sK3_Y @ SV2 ) ) )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV2: $i] :
( ( ( ~ ( big_h @ SV2 @ ( sK3_Y @ SV2 ) ) )
= $false )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(61,plain,
! [SV2: $i] :
( ( ( big_f @ SV2 )
= $false )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV4: $i] :
( ( ( big_h @ sK2_X @ SV4 )
= $false )
| ( ( big_g @ SV4 )
= $false )
| ( ( big_j @ sK2_X @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( ~ ( big_h @ sK2_X @ SV5 ) )
= $true )
| ( ( big_l @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(65,plain,
! [SV2: $i] :
( ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( ~ ( big_f @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(66,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) )
= $false )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( big_h @ sK2_X @ SV5 )
= $false )
| ( ( big_l @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV2: $i] :
( ( ( big_f @ SV2 )
= $false )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV2: $i] :
( ( ( big_f @ SV2 )
= $false )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) ) )
= $false )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_k @ SX1 ) )
= $false )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) )
= $false )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
| ~ ! [SX1: $i] : ( big_k @ SX1 ) )
= $false )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) ) )
= $true )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV2: $i] :
( ( ( ! [SX1: $i] : ( big_k @ SX1 ) )
= $true )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) ) )
= $false )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_k @ SX1 ) )
= $false )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(78,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) ) )
= $false )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_k @ SX1 ) )
= $false )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $false )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV2: $i,SV6: $i] :
( ( ( big_k @ SV6 )
= $true )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) ) )
= $true )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(83,plain,
! [SV2: $i] :
( ( ( ! [SX1: $i] : ( big_k @ SX1 ) )
= $true )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(84,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) ) )
= $true )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(85,plain,
! [SV2: $i] :
( ( ( ! [SX1: $i] : ( big_k @ SX1 ) )
= $true )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_g @ SX1 ) )
= $false )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV2: $i] :
( ( ( ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $false )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $false )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV2: $i,SV7: $i] :
( ( ( big_k @ SV7 )
= $true )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_g @ SX1 )
| ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $false )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV2: $i,SV8: $i] :
( ( ( big_k @ SV8 )
= $true )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV2: $i] :
( ( ( ! [SX1: $i] : ( big_g @ SX1 ) )
= $true )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(93,plain,
! [SV2: $i] :
( ( ( ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $true )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_g @ SX1 ) )
= $false )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(95,plain,
! [SV2: $i] :
( ( ( ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $false )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(96,plain,
! [SV2: $i] :
( ( ( ~ ! [SX1: $i] : ( big_g @ SX1 ) )
= $false )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(97,plain,
! [SV2: $i] :
( ( ( ~ ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $false )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(98,plain,
! [SV2: $i,SV9: $i] :
( ( ( big_g @ SV9 )
= $true )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV10: $i,SV2: $i] :
( ( ( big_h @ SV2 @ SV10 )
= $true )
| ( ( big_j @ SV2 @ ( sK3_Y @ SV2 ) )
= $false )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV2: $i] :
( ( ( ! [SX1: $i] : ( big_g @ SX1 ) )
= $true )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV2: $i] :
( ( ( ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $true )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV2: $i] :
( ( ( ! [SX1: $i] : ( big_g @ SX1 ) )
= $true )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
! [SV2: $i] :
( ( ( ! [SY12: $i] : ( big_h @ SV2 @ SY12 ) )
= $true )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV2: $i,SV11: $i] :
( ( ( big_g @ SV11 )
= $true )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV12: $i,SV2: $i] :
( ( ( big_h @ SV2 @ SV12 )
= $true )
| ( ( big_g @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV2: $i,SV13: $i] :
( ( ( big_g @ SV13 )
= $true )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV14: $i,SV2: $i] :
( ( ( big_h @ SV2 @ SV14 )
= $true )
| ( ( big_h @ SV2 @ ( sK3_Y @ SV2 ) )
= $true )
| ( ( big_f @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(108,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,107,106,105,104,99,98,91,89,81,67,62,54,53,52]) ).
thf(109,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% 0.00/0.09 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.29 % Computer : n003.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jul 11 18:11:00 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29
% 0.09/0.29 No.of.Axioms: 3
% 0.09/0.29
% 0.09/0.29 Length.of.Defs: 0
% 0.09/0.29
% 0.09/0.29 Contains.Choice.Funs: false
% 0.09/0.29 (rf:0,axioms:3,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.13/0.34
% 0.13/0.34 ********************************
% 0.13/0.34 * All subproblems solved! *
% 0.13/0.34 ********************************
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:108,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.34
% 0.13/0.34 %**** Beginning of derivation protocol ****
% 0.13/0.34 % SZS output start CNFRefutation
% See solution above
% 0.13/0.34
% 0.13/0.34 %**** End of derivation protocol ****
% 0.13/0.34 %**** no. of clauses in derivation: 109 ****
% 0.13/0.34 %**** clause counter: 108 ****
% 0.13/0.34
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:108,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------