TSTP Solution File: SYN056+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN056+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 : n021.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 08:23:04 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 130 ( 79 unt; 8 typ; 0 def)
% Number of atoms : 773 ( 186 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 947 ( 270 ~; 236 |; 16 &; 398 @)
% ( 7 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 182 ( 0 ^ 178 !; 4 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_p,type,
big_p: $i > $o ).
thf(tp_big_q,type,
big_q: $i > $o ).
thf(tp_big_r,type,
big_r: $i > $o ).
thf(tp_big_s,type,
big_s: $i > $o ).
thf(tp_sK1_Y,type,
sK1_Y: $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(tp_sK3_X,type,
sK3_X: $i ).
thf(tp_sK4_Y,type,
sK4_Y: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( ( big_p @ X )
& ( big_q @ Y ) )
=> ( ( big_r @ X )
<=> ( big_s @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_2) ).
thf(2,axiom,
( ? [X: $i] : ( big_p @ X )
<=> ? [Y: $i] : ( big_q @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_1) ).
thf(3,conjecture,
( ! [X: $i] :
( ( big_p @ X )
=> ( big_r @ X ) )
<=> ! [Y: $i] :
( ( big_q @ Y )
=> ( big_s @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26) ).
thf(4,negated_conjecture,
( ( ! [X: $i] :
( ( big_p @ X )
=> ( big_r @ X ) )
<=> ! [Y: $i] :
( ( big_q @ Y )
=> ( big_s @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [X: $i] :
( ( big_p @ X )
=> ( big_r @ X ) )
<=> ! [Y: $i] :
( ( big_q @ Y )
=> ( big_s @ Y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i] :
( ( ( big_p @ X )
& ( big_q @ Y ) )
=> ( ( big_r @ X )
<=> ( big_s @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ? [X: $i] : ( big_p @ X )
<=> ? [Y: $i] : ( big_q @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ! [X: $i] :
( ( big_p @ X )
=> ( big_r @ X ) )
=> ! [Y: $i] :
( ( big_q @ Y )
=> ( big_s @ Y ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(9,plain,
( ( ! [Y: $i] :
( ( big_q @ Y )
=> ( big_s @ Y ) )
=> ! [X: $i] :
( ( big_p @ X )
=> ( big_r @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(10,plain,
( ( ~ ( ! [X: $i] :
( ( big_p @ X )
=> ( big_r @ X ) )
=> ! [Y: $i] :
( ( big_q @ Y )
=> ( big_s @ Y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ! [Y: $i] :
( ( big_q @ Y )
=> ( big_s @ Y ) )
=> ! [X: $i] :
( ( big_p @ X )
=> ( big_r @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i] :
( ~ ( big_p @ X )
| ( big_r @ X ) )
& ( big_q @ sK1_Y )
& ~ ( big_s @ sK1_Y ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ! [Y: $i] :
( ~ ( big_q @ Y )
| ( big_s @ Y ) )
& ( big_p @ sK2_X )
& ~ ( big_r @ sK2_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_p @ X )
| ~ ( big_q @ Y )
| ~ ( big_r @ X )
| ( big_s @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( big_p @ X )
| ~ ( big_q @ Y )
| ~ ( big_s @ Y )
| ( big_r @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(15,plain,
( ( ( ! [X: $i] :
~ ( big_p @ X )
| ( big_q @ sK4_Y ) )
& ( ! [Y: $i] :
~ ( big_q @ Y )
| ( big_p @ sK3_X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(16,plain,
( ( ( ! [X: $i] :
~ ( big_p @ X )
| ( big_q @ sK4_Y ) )
& ( ! [Y: $i] :
~ ( big_q @ Y )
| ( big_p @ sK3_X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_p @ X )
| ~ ( big_q @ Y )
| ~ ( big_r @ X )
| ( big_s @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( big_p @ X )
| ~ ( big_q @ Y )
| ~ ( big_s @ Y )
| ( big_r @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [X: $i] :
( ~ ( big_p @ X )
| ( big_r @ X ) )
& ( big_q @ sK1_Y )
& ~ ( big_s @ sK1_Y ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) )
| ~ ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_r @ SX0 ) )
| ~ ~ ( ~ ( big_q @ sK1_Y )
| ~ ~ ( big_s @ sK1_Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) )
| ~ ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_r @ SX0 ) )
| ~ ~ ( ~ ( big_q @ sK1_Y )
| ~ ~ ( big_s @ sK1_Y ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_r @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ~ ( ~ ( big_q @ sK1_Y )
| ~ ~ ( big_s @ sK1_Y ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(31,plain,
( ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(33,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(35,plain,
( ( ! [SX0: $i] :
( ~ ( big_p @ SX0 )
| ( big_r @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ( ~ ( big_q @ sK1_Y )
| ~ ~ ( big_s @ sK1_Y ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(37,plain,
( ( ( ! [SX0: $i] :
~ ( big_p @ SX0 ) )
= $true )
| ( ( big_q @ sK4_Y )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ( ! [SX0: $i] :
~ ( big_q @ SX0 ) )
= $true )
| ( ( big_p @ sK3_X )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV1: $i] :
( ( ! [SY6: $i] :
( ~ ( big_p @ SV1 )
| ~ ( big_q @ SY6 )
| ~ ( big_r @ SV1 )
| ( big_s @ SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV2: $i] :
( ( ! [SY7: $i] :
( ~ ( big_p @ SV2 )
| ~ ( big_q @ SY7 )
| ~ ( big_s @ SY7 )
| ( big_r @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV3: $i] :
( ( ~ ( big_p @ SV3 )
| ( big_r @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( ~ ( big_q @ sK1_Y )
| ~ ~ ( big_s @ sK1_Y ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV4: $i] :
( ( ( ~ ( big_p @ SV4 ) )
= $true )
| ( ( big_q @ sK4_Y )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV5: $i] :
( ( ( ~ ( big_q @ SV5 ) )
= $true )
| ( ( big_p @ sK3_X )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( big_p @ SV1 )
| ~ ( big_q @ SV6 )
| ~ ( big_r @ SV1 )
| ( big_s @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( big_p @ SV2 )
| ~ ( big_q @ SV7 )
| ~ ( big_s @ SV7 )
| ( big_r @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV3: $i] :
( ( ( ~ ( big_p @ SV3 ) )
= $true )
| ( ( big_r @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,plain,
( ( ~ ( big_q @ sK1_Y ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(49,plain,
( ( ~ ~ ( big_s @ sK1_Y ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(50,plain,
! [SV4: $i] :
( ( ( big_p @ SV4 )
= $false )
| ( ( big_q @ sK4_Y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( big_q @ SV5 )
= $false )
| ( ( big_p @ sK3_X )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( big_p @ SV1 )
| ~ ( big_q @ SV6 ) )
= $true )
| ( ( ~ ( big_r @ SV1 )
| ( big_s @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( big_p @ SV2 )
| ~ ( big_q @ SV7 ) )
= $true )
| ( ( ~ ( big_s @ SV7 )
| ( big_r @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV3: $i] :
( ( ( big_p @ SV3 )
= $false )
| ( ( big_r @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(55,plain,
( ( big_q @ sK1_Y )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(56,plain,
( ( ~ ( big_s @ sK1_Y ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(57,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( big_p @ SV1 ) )
= $true )
| ( ( ~ ( big_q @ SV6 ) )
= $true )
| ( ( ~ ( big_r @ SV1 )
| ( big_s @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( big_p @ SV2 ) )
= $true )
| ( ( ~ ( big_q @ SV7 ) )
= $true )
| ( ( ~ ( big_s @ SV7 )
| ( big_r @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
( ( big_s @ sK1_Y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV6: $i,SV1: $i] :
( ( ( big_p @ SV1 )
= $false )
| ( ( ~ ( big_q @ SV6 ) )
= $true )
| ( ( ~ ( big_r @ SV1 )
| ( big_s @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV7: $i,SV2: $i] :
( ( ( big_p @ SV2 )
= $false )
| ( ( ~ ( big_q @ SV7 ) )
= $true )
| ( ( ~ ( big_s @ SV7 )
| ( big_r @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV1: $i,SV6: $i] :
( ( ( big_q @ SV6 )
= $false )
| ( ( big_p @ SV1 )
= $false )
| ( ( ~ ( big_r @ SV1 )
| ( big_s @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV2: $i,SV7: $i] :
( ( ( big_q @ SV7 )
= $false )
| ( ( big_p @ SV2 )
= $false )
| ( ( ~ ( big_s @ SV7 )
| ( big_r @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( big_r @ SV1 ) )
= $true )
| ( ( big_s @ SV6 )
= $true )
| ( ( big_p @ SV1 )
= $false )
| ( ( big_q @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( big_s @ SV7 ) )
= $true )
| ( ( big_r @ SV2 )
= $true )
| ( ( big_p @ SV2 )
= $false )
| ( ( big_q @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV6: $i,SV1: $i] :
( ( ( big_r @ SV1 )
= $false )
| ( ( big_s @ SV6 )
= $true )
| ( ( big_p @ SV1 )
= $false )
| ( ( big_q @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV2: $i,SV7: $i] :
( ( ( big_s @ SV7 )
= $false )
| ( ( big_r @ SV2 )
= $true )
| ( ( big_p @ SV2 )
= $false )
| ( ( big_q @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,67,66,59,55,54,51]) ).
thf(69,plain,
( ( ( ! [X: $i] :
~ ( big_p @ X )
| ( big_q @ sK4_Y ) )
& ( ! [Y: $i] :
~ ( big_q @ Y )
| ( big_p @ sK3_X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_p @ X )
| ~ ( big_q @ Y )
| ~ ( big_r @ X )
| ( big_s @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( big_p @ X )
| ~ ( big_q @ Y )
| ~ ( big_s @ Y )
| ( big_r @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(71,plain,
( ( ! [Y: $i] :
( ~ ( big_q @ Y )
| ( big_s @ Y ) )
& ( big_p @ sK2_X )
& ~ ( big_r @ sK2_X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(72,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( big_q @ SX0 )
| ( big_s @ SX0 ) )
| ~ ~ ( ~ ( big_p @ sK2_X )
| ~ ~ ( big_r @ sK2_X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(73,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(74,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) )
| ~ ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(75,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_q @ SX0 )
| ( big_s @ SX0 ) )
| ~ ~ ( ~ ( big_p @ sK2_X )
| ~ ~ ( big_r @ sK2_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(76,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
( ( ~ ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) )
| ~ ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
( ( ~ ! [SX0: $i] :
( ~ ( big_q @ SX0 )
| ( big_s @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(79,plain,
( ( ~ ~ ( ~ ( big_p @ sK2_X )
| ~ ~ ( big_r @ sK2_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(82,plain,
( ( ~ ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(83,plain,
( ( ~ ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ( big_q @ SX0 )
| ( big_s @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(85,plain,
( ( ~ ( ~ ( big_p @ sK2_X )
| ~ ~ ( big_r @ sK2_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_r @ SX0 )
| ( big_s @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_p @ SX0 )
| ~ ( big_q @ SX1 )
| ~ ( big_s @ SX1 )
| ( big_r @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(88,plain,
( ( ! [SX0: $i] :
~ ( big_p @ SX0 )
| ( big_q @ sK4_Y ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(89,plain,
( ( ! [SX0: $i] :
~ ( big_q @ SX0 )
| ( big_p @ sK3_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(90,plain,
! [SV8: $i] :
( ( ~ ( big_q @ SV8 )
| ( big_s @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(91,plain,
( ( ~ ( big_p @ sK2_X )
| ~ ~ ( big_r @ sK2_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV9: $i] :
( ( ! [SY8: $i] :
( ~ ( big_p @ SV9 )
| ~ ( big_q @ SY8 )
| ~ ( big_r @ SV9 )
| ( big_s @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV10: $i] :
( ( ! [SY9: $i] :
( ~ ( big_p @ SV10 )
| ~ ( big_q @ SY9 )
| ~ ( big_s @ SY9 )
| ( big_r @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(94,plain,
( ( ( ! [SX0: $i] :
~ ( big_p @ SX0 ) )
= $true )
| ( ( big_q @ sK4_Y )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
( ( ( ! [SX0: $i] :
~ ( big_q @ SX0 ) )
= $true )
| ( ( big_p @ sK3_X )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV8: $i] :
( ( ( ~ ( big_q @ SV8 ) )
= $true )
| ( ( big_s @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(97,plain,
( ( ~ ( big_p @ sK2_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(98,plain,
( ( ~ ~ ( big_r @ sK2_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(99,plain,
! [SV11: $i,SV9: $i] :
( ( ~ ( big_p @ SV9 )
| ~ ( big_q @ SV11 )
| ~ ( big_r @ SV9 )
| ( big_s @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV12: $i,SV10: $i] :
( ( ~ ( big_p @ SV10 )
| ~ ( big_q @ SV12 )
| ~ ( big_s @ SV12 )
| ( big_r @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV13: $i] :
( ( ( ~ ( big_p @ SV13 ) )
= $true )
| ( ( big_q @ sK4_Y )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV14: $i] :
( ( ( ~ ( big_q @ SV14 ) )
= $true )
| ( ( big_p @ sK3_X )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV8: $i] :
( ( ( big_q @ SV8 )
= $false )
| ( ( big_s @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(104,plain,
( ( big_p @ sK2_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(105,plain,
( ( ~ ( big_r @ sK2_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV11: $i,SV9: $i] :
( ( ( ~ ( big_p @ SV9 )
| ~ ( big_q @ SV11 ) )
= $true )
| ( ( ~ ( big_r @ SV9 )
| ( big_s @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV12: $i,SV10: $i] :
( ( ( ~ ( big_p @ SV10 )
| ~ ( big_q @ SV12 ) )
= $true )
| ( ( ~ ( big_s @ SV12 )
| ( big_r @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV13: $i] :
( ( ( big_p @ SV13 )
= $false )
| ( ( big_q @ sK4_Y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV14: $i] :
( ( ( big_q @ SV14 )
= $false )
| ( ( big_p @ sK3_X )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(110,plain,
( ( big_r @ sK2_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV11: $i,SV9: $i] :
( ( ( ~ ( big_p @ SV9 ) )
= $true )
| ( ( ~ ( big_q @ SV11 ) )
= $true )
| ( ( ~ ( big_r @ SV9 )
| ( big_s @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV12: $i,SV10: $i] :
( ( ( ~ ( big_p @ SV10 ) )
= $true )
| ( ( ~ ( big_q @ SV12 ) )
= $true )
| ( ( ~ ( big_s @ SV12 )
| ( big_r @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV11: $i,SV9: $i] :
( ( ( big_p @ SV9 )
= $false )
| ( ( ~ ( big_q @ SV11 ) )
= $true )
| ( ( ~ ( big_r @ SV9 )
| ( big_s @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(114,plain,
! [SV12: $i,SV10: $i] :
( ( ( big_p @ SV10 )
= $false )
| ( ( ~ ( big_q @ SV12 ) )
= $true )
| ( ( ~ ( big_s @ SV12 )
| ( big_r @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV9: $i,SV11: $i] :
( ( ( big_q @ SV11 )
= $false )
| ( ( big_p @ SV9 )
= $false )
| ( ( ~ ( big_r @ SV9 )
| ( big_s @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV10: $i,SV12: $i] :
( ( ( big_q @ SV12 )
= $false )
| ( ( big_p @ SV10 )
= $false )
| ( ( ~ ( big_s @ SV12 )
| ( big_r @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV11: $i,SV9: $i] :
( ( ( ~ ( big_r @ SV9 ) )
= $true )
| ( ( big_s @ SV11 )
= $true )
| ( ( big_p @ SV9 )
= $false )
| ( ( big_q @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV10: $i,SV12: $i] :
( ( ( ~ ( big_s @ SV12 ) )
= $true )
| ( ( big_r @ SV10 )
= $true )
| ( ( big_p @ SV10 )
= $false )
| ( ( big_q @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(119,plain,
! [SV11: $i,SV9: $i] :
( ( ( big_r @ SV9 )
= $false )
| ( ( big_s @ SV11 )
= $true )
| ( ( big_p @ SV9 )
= $false )
| ( ( big_q @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(120,plain,
! [SV10: $i,SV12: $i] :
( ( ( big_s @ SV12 )
= $false )
| ( ( big_r @ SV10 )
= $true )
| ( ( big_p @ SV10 )
= $false )
| ( ( big_q @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(121,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[103,120,119,110,109,108,104]) ).
thf(122,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[121,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 21:59:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 2
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.12/0.40
% 0.12/0.40 ********************************
% 0.12/0.40 * All subproblems solved! *
% 0.12/0.40 ********************************
% 0.12/0.40 % 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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.41
% 0.18/0.41 %**** Beginning of derivation protocol ****
% 0.18/0.41 % SZS output start CNFRefutation
% See solution above
% 0.18/0.41
% 0.18/0.41 %**** End of derivation protocol ****
% 0.18/0.41 %**** no. of clauses in derivation: 122 ****
% 0.18/0.41 %**** clause counter: 121 ****
% 0.18/0.41
% 0.18/0.41 % 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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------