TSTP Solution File: SEU997^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU997^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 : Tue Jul 19 14:11:11 EDT 2022
% Result : Theorem 44.88s 44.70s
% Output : Proof 44.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 67 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 471 ( 162 equ; 0 cnn)
% Maximal formula atoms : 42 ( 7 avg)
% Number of connectives : 877 ( 151 ~; 38 |; 20 &; 587 @)
% ( 0 <=>; 80 =>; 1 <=; 0 <~>)
% Maximal formula depth : 50 ( 5 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 11 con; 0-2 aty)
% Number of variables : 223 ( 0 ^ 223 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
thf(cCD_LATTICE_THM_pme,conjecture,
! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
( ( X1 @ X5 @ X5 )
= X5 )
=> ~ ! [X5: a] :
( ( X2 @ X5 @ X5 )
= X5 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
= ( X1 @ X6 @ X5 ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X2 @ X5 @ X6 )
= ( X2 @ X6 @ X5 ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
= X6 ) )
=> ~ ! [X5: a,X6: a] :
( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
= X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
= ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
= ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ( X2 @ X3 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
( ( X1 @ X3 @ X5 )
= X3 ) )
=> ~ ! [X5: a] :
( ( X2 @ X4 @ X5 )
= X4 ) )
=> ~ ! [X5: a] :
( ( X1 @ X4 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
~ ! [X6: a] :
( ( ( X1 @ X5 @ X6 )
= X3 )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ( ( X1 @ X5 @ X6 )
= X3 )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) )
=> ( ( X1 @ X5 @ X7 )
!= X3 ) )
=> ( ( X2 @ X5 @ X7 )
!= X4 ) )
=> ( X6 = X7 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
( ( X1 @ X5 @ X5 )
= X5 )
=> ~ ! [X5: a] :
( ( X2 @ X5 @ X5 )
= X5 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
= ( X1 @ X6 @ X5 ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X2 @ X5 @ X6 )
= ( X2 @ X6 @ X5 ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
= X6 ) )
=> ~ ! [X5: a,X6: a] :
( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
= X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
= ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
= ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ( X2 @ X3 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
( ( X1 @ X3 @ X5 )
= X3 ) )
=> ~ ! [X5: a] :
( ( X2 @ X4 @ X5 )
= X4 ) )
=> ~ ! [X5: a] :
( ( X1 @ X4 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
~ ! [X6: a] :
( ( ( X1 @ X5 @ X6 )
= X3 )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ( ( X1 @ X5 @ X6 )
= X3 )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) )
=> ( ( X1 @ X5 @ X7 )
!= X3 ) )
=> ( ( X2 @ X5 @ X7 )
!= X4 ) )
=> ( X6 = X7 ) ) ),
inference(assume_negation,[status(cth)],[cCD_LATTICE_THM_pme]) ).
thf(nax1,axiom,
( p1
<= ! [X6: a > a > a,X8: a > a > a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
( ( X6 @ X5 @ X5 )
= X5 )
=> ~ ! [X5: a] :
( ( X8 @ X5 @ X5 )
= X5 ) )
=> ~ ! [X5: a,X7: a,X9: a] :
( ( X6 @ ( X6 @ X5 @ X7 ) @ X9 )
= ( X6 @ X5 @ ( X6 @ X7 @ X9 ) ) ) )
=> ~ ! [X5: a,X7: a,X9: a] :
( ( X8 @ ( X8 @ X5 @ X7 ) @ X9 )
= ( X8 @ X5 @ ( X8 @ X7 @ X9 ) ) ) )
=> ~ ! [X5: a,X7: a] :
( ( X6 @ X5 @ X7 )
= ( X6 @ X7 @ X5 ) ) )
=> ~ ! [X5: a,X7: a] :
( ( X8 @ X5 @ X7 )
= ( X8 @ X7 @ X5 ) ) )
=> ~ ! [X5: a,X7: a] :
( ( X6 @ ( X8 @ X5 @ X7 ) @ X7 )
= X7 ) )
=> ~ ! [X5: a,X7: a] :
( ( X8 @ ( X6 @ X5 @ X7 ) @ X7 )
= X7 ) )
=> ~ ! [X5: a,X7: a,X9: a] :
( ( X8 @ X5 @ ( X6 @ X7 @ X9 ) )
= ( X6 @ ( X8 @ X5 @ X7 ) @ ( X8 @ X5 @ X9 ) ) ) )
=> ~ ! [X5: a,X7: a,X9: a] :
( ( X6 @ X5 @ ( X8 @ X7 @ X9 ) )
= ( X8 @ ( X6 @ X5 @ X7 ) @ ( X6 @ X5 @ X9 ) ) ) )
=> ~ ! [X5: a] :
( ( X8 @ X3 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
( ( X6 @ X3 @ X5 )
= X3 ) )
=> ~ ! [X5: a] :
( ( X8 @ X4 @ X5 )
= X4 ) )
=> ~ ! [X5: a] :
( ( X6 @ X4 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
~ ! [X7: a] :
( ( ( X6 @ X5 @ X7 )
= X3 )
=> ( ( X8 @ X5 @ X7 )
!= X4 ) ) )
=> ! [X5: a,X7: a,X9: a] :
( ~ ( ~ ( ~ ( ( ( X6 @ X5 @ X7 )
= X3 )
=> ( ( X8 @ X5 @ X7 )
!= X4 ) )
=> ( ( X6 @ X5 @ X9 )
!= X3 ) )
=> ( ( X8 @ X5 @ X9 )
!= X4 ) )
=> ( X7 = X9 ) ) ) ),
file('<stdin>',nax1) ).
thf(ax101,axiom,
~ p1,
file('<stdin>',ax101) ).
thf(c_0_2,plain,
! [X3219: a,X3220: a,X3221: a,X3222: a,X3223: a,X3224: a,X3225: a,X3226: a,X3227: a,X3228: a,X3229: a,X3230: a,X3231: a,X3232: a,X3233: a,X3234: a,X3235: a,X3236: a,X3237: a,X3238: a,X3239: a,X3240: a,X3241: a,X3242: a,X3243: a,X3244: a,X3245: a] :
( ( ( ( esk1613_0 @ X3219 @ X3219 )
= X3219 )
| p1 )
& ( ( ( esk1614_0 @ X3220 @ X3220 )
= X3220 )
| p1 )
& ( ( ( esk1613_0 @ ( esk1613_0 @ X3221 @ X3222 ) @ X3223 )
= ( esk1613_0 @ X3221 @ ( esk1613_0 @ X3222 @ X3223 ) ) )
| p1 )
& ( ( ( esk1614_0 @ ( esk1614_0 @ X3224 @ X3225 ) @ X3226 )
= ( esk1614_0 @ X3224 @ ( esk1614_0 @ X3225 @ X3226 ) ) )
| p1 )
& ( ( ( esk1613_0 @ X3227 @ X3228 )
= ( esk1613_0 @ X3228 @ X3227 ) )
| p1 )
& ( ( ( esk1614_0 @ X3229 @ X3230 )
= ( esk1614_0 @ X3230 @ X3229 ) )
| p1 )
& ( ( ( esk1613_0 @ ( esk1614_0 @ X3231 @ X3232 ) @ X3232 )
= X3232 )
| p1 )
& ( ( ( esk1614_0 @ ( esk1613_0 @ X3233 @ X3234 ) @ X3234 )
= X3234 )
| p1 )
& ( ( ( esk1614_0 @ X3235 @ ( esk1613_0 @ X3236 @ X3237 ) )
= ( esk1613_0 @ ( esk1614_0 @ X3235 @ X3236 ) @ ( esk1614_0 @ X3235 @ X3237 ) ) )
| p1 )
& ( ( ( esk1613_0 @ X3238 @ ( esk1614_0 @ X3239 @ X3240 ) )
= ( esk1614_0 @ ( esk1613_0 @ X3238 @ X3239 ) @ ( esk1613_0 @ X3238 @ X3240 ) ) )
| p1 )
& ( ( ( esk1614_0 @ esk1615_0 @ X3241 )
= X3241 )
| p1 )
& ( ( ( esk1613_0 @ esk1615_0 @ X3242 )
= esk1615_0 )
| p1 )
& ( ( ( esk1614_0 @ esk1616_0 @ X3243 )
= esk1616_0 )
| p1 )
& ( ( ( esk1613_0 @ esk1616_0 @ X3244 )
= X3244 )
| p1 )
& ( ( ( esk1613_0 @ X3245 @ ( esk1617_1 @ X3245 ) )
= esk1615_0 )
| p1 )
& ( ( ( esk1614_0 @ X3245 @ ( esk1617_1 @ X3245 ) )
= esk1616_0 )
| p1 )
& ( ( ( esk1613_0 @ esk1618_0 @ esk1619_0 )
= esk1615_0 )
| p1 )
& ( ( ( esk1614_0 @ esk1618_0 @ esk1619_0 )
= esk1616_0 )
| p1 )
& ( ( ( esk1613_0 @ esk1618_0 @ esk1620_0 )
= esk1615_0 )
| p1 )
& ( ( ( esk1614_0 @ esk1618_0 @ esk1620_0 )
= esk1616_0 )
| p1 )
& ( ( esk1619_0 != esk1620_0 )
| p1 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])]) ).
thf(c_0_3,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax101]) ).
thf(c_0_4,plain,
! [X1: a,X2: a] :
( ( ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ X2 )
= X2 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
! [X2: a,X1: a] :
( ( ( esk1613_0 @ X1 @ X2 )
= ( esk1613_0 @ X2 @ X1 ) )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_7,plain,
! [X1: a,X2: a,X3: a] :
( ( ( esk1613_0 @ X1 @ ( esk1614_0 @ X2 @ X3 ) )
= ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ ( esk1613_0 @ X1 @ X3 ) ) )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,plain,
( ( ( esk1613_0 @ esk1618_0 @ esk1620_0 )
= esk1615_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,plain,
! [X1: a] :
( ( ( esk1614_0 @ esk1615_0 @ X1 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_10,plain,
! [X1: a,X2: a] :
( ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ X2 )
= X2 ),
inference(sr,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_11,plain,
! [X2: a,X1: a] :
( ( esk1613_0 @ X1 @ X2 )
= ( esk1613_0 @ X2 @ X1 ) ),
inference(sr,[status(thm)],[c_0_6,c_0_5]) ).
thf(c_0_12,plain,
! [X1: a] :
( ( ( esk1614_0 @ esk1616_0 @ X1 )
= esk1616_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_13,plain,
( ( ( esk1613_0 @ esk1618_0 @ esk1619_0 )
= esk1615_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_14,plain,
! [X1: a,X2: a] :
( ( ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ X2 )
= X2 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_15,plain,
! [X2: a,X1: a] :
( ( ( esk1614_0 @ X1 @ X2 )
= ( esk1614_0 @ X2 @ X1 ) )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_16,plain,
! [X1: a,X2: a,X3: a] :
( ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ ( esk1613_0 @ X1 @ X3 ) )
= ( esk1613_0 @ X1 @ ( esk1614_0 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_7,c_0_5]) ).
thf(c_0_17,plain,
( ( esk1613_0 @ esk1618_0 @ esk1620_0 )
= esk1615_0 ),
inference(sr,[status(thm)],[c_0_8,c_0_5]) ).
thf(c_0_18,plain,
! [X1: a] :
( ( esk1614_0 @ esk1615_0 @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_9,c_0_5]) ).
thf(c_0_19,plain,
! [X1: a] :
( ( ( esk1614_0 @ X1 @ ( esk1617_1 @ X1 ) )
= esk1616_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_20,plain,
! [X2: a,X1: a] :
( ( esk1613_0 @ X1 @ ( esk1614_0 @ X2 @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_21,plain,
! [X1: a] :
( ( esk1614_0 @ esk1616_0 @ X1 )
= esk1616_0 ),
inference(sr,[status(thm)],[c_0_12,c_0_5]) ).
thf(c_0_22,plain,
( ( esk1613_0 @ esk1618_0 @ esk1619_0 )
= esk1615_0 ),
inference(sr,[status(thm)],[c_0_13,c_0_5]) ).
thf(c_0_23,plain,
! [X1: a] :
( ( ( esk1613_0 @ X1 @ ( esk1617_1 @ X1 ) )
= esk1615_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_24,plain,
! [X1: a,X2: a,X3: a] :
( ( ( esk1614_0 @ X1 @ ( esk1613_0 @ X2 @ X3 ) )
= ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ ( esk1614_0 @ X1 @ X3 ) ) )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_25,plain,
( ( ( esk1614_0 @ esk1618_0 @ esk1620_0 )
= esk1616_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_26,plain,
! [X1: a] :
( ( ( esk1613_0 @ esk1616_0 @ X1 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_27,plain,
! [X1: a,X2: a] :
( ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ X2 )
= X2 ),
inference(sr,[status(thm)],[c_0_14,c_0_5]) ).
thf(c_0_28,plain,
! [X2: a,X1: a] :
( ( esk1614_0 @ X1 @ X2 )
= ( esk1614_0 @ X2 @ X1 ) ),
inference(sr,[status(thm)],[c_0_15,c_0_5]) ).
thf(c_0_29,plain,
! [X1: a] :
( ( ( esk1613_0 @ esk1615_0 @ X1 )
= esk1615_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_30,plain,
! [X1: a] :
( ( esk1613_0 @ esk1618_0 @ ( esk1614_0 @ esk1620_0 @ X1 ) )
= ( esk1613_0 @ esk1618_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
thf(c_0_31,plain,
! [X1: a] :
( ( esk1614_0 @ X1 @ ( esk1617_1 @ X1 ) )
= esk1616_0 ),
inference(sr,[status(thm)],[c_0_19,c_0_5]) ).
thf(c_0_32,plain,
! [X1: a] :
( ( esk1613_0 @ X1 @ esk1616_0 )
= X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_33,plain,
( ( ( esk1614_0 @ esk1618_0 @ esk1619_0 )
= esk1616_0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_34,plain,
! [X1: a] :
( ( esk1613_0 @ esk1618_0 @ ( esk1614_0 @ esk1619_0 @ X1 ) )
= ( esk1613_0 @ esk1618_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_18]) ).
thf(c_0_35,plain,
! [X1: a] :
( ( esk1613_0 @ X1 @ ( esk1617_1 @ X1 ) )
= esk1615_0 ),
inference(sr,[status(thm)],[c_0_23,c_0_5]) ).
thf(c_0_36,plain,
! [X1: a,X2: a,X3: a] :
( ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ ( esk1614_0 @ X1 @ X3 ) )
= ( esk1614_0 @ X1 @ ( esk1613_0 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_24,c_0_5]) ).
thf(c_0_37,plain,
( ( esk1614_0 @ esk1618_0 @ esk1620_0 )
= esk1616_0 ),
inference(sr,[status(thm)],[c_0_25,c_0_5]) ).
thf(c_0_38,plain,
! [X1: a] :
( ( esk1613_0 @ esk1616_0 @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_26,c_0_5]) ).
thf(c_0_39,plain,
! [X2: a,X1: a] :
( ( esk1614_0 @ X1 @ ( esk1613_0 @ X2 @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_40,plain,
! [X1: a] :
( ( esk1613_0 @ esk1615_0 @ X1 )
= esk1615_0 ),
inference(sr,[status(thm)],[c_0_29,c_0_5]) ).
thf(c_0_41,plain,
( ( esk1613_0 @ esk1618_0 @ ( esk1617_1 @ esk1620_0 ) )
= esk1618_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
thf(c_0_42,plain,
( ( esk1614_0 @ esk1618_0 @ esk1619_0 )
= esk1616_0 ),
inference(sr,[status(thm)],[c_0_33,c_0_5]) ).
thf(c_0_43,plain,
( ( esk1613_0 @ esk1618_0 @ ( esk1617_1 @ esk1619_0 ) )
= esk1618_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_32]) ).
thf(c_0_44,plain,
! [X1: a,X2: a] :
( ( esk1613_0 @ X1 @ ( esk1614_0 @ ( esk1617_1 @ X1 ) @ X2 ) )
= ( esk1613_0 @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_35]),c_0_18]) ).
thf(c_0_45,plain,
! [X1: a] :
( ( esk1614_0 @ esk1618_0 @ ( esk1613_0 @ esk1620_0 @ X1 ) )
= ( esk1614_0 @ esk1618_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
thf(c_0_46,plain,
! [X1: a] :
( ( esk1614_0 @ X1 @ esk1615_0 )
= X1 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_47,plain,
( ( esk1614_0 @ esk1618_0 @ ( esk1617_1 @ esk1620_0 ) )
= ( esk1617_1 @ esk1620_0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_41]),c_0_28]) ).
thf(c_0_48,plain,
! [X1: a] :
( ( esk1614_0 @ esk1618_0 @ ( esk1613_0 @ esk1619_0 @ X1 ) )
= ( esk1614_0 @ esk1618_0 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_42]),c_0_38]) ).
thf(c_0_49,plain,
( ( esk1614_0 @ esk1618_0 @ ( esk1617_1 @ esk1619_0 ) )
= ( esk1617_1 @ esk1619_0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_28]) ).
thf(c_0_50,plain,
! [X1: a] :
( ( esk1613_0 @ X1 @ ( esk1617_1 @ ( esk1617_1 @ X1 ) ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_31]),c_0_32]) ).
thf(c_0_51,plain,
( ( esk1617_1 @ esk1620_0 )
= esk1618_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_46]),c_0_47]) ).
thf(c_0_52,plain,
( ( esk1617_1 @ esk1619_0 )
= esk1618_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_35]),c_0_46]),c_0_49]) ).
thf(c_0_53,plain,
! [X1: a,X2: a] :
( ( esk1614_0 @ X1 @ ( esk1613_0 @ ( esk1617_1 @ X1 ) @ X2 ) )
= ( esk1614_0 @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_38]) ).
thf(c_0_54,plain,
( ( esk1613_0 @ esk1620_0 @ ( esk1617_1 @ esk1618_0 ) )
= esk1620_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_55,plain,
( ( esk1613_0 @ esk1619_0 @ ( esk1617_1 @ esk1618_0 ) )
= esk1619_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_52]) ).
thf(c_0_56,plain,
! [X1: a] :
( ( esk1614_0 @ X1 @ ( esk1617_1 @ ( esk1617_1 @ X1 ) ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_35]),c_0_46]) ).
thf(c_0_57,plain,
( ( esk1614_0 @ esk1620_0 @ ( esk1617_1 @ esk1618_0 ) )
= ( esk1617_1 @ esk1618_0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_54]),c_0_28]) ).
thf(c_0_58,plain,
( p1
| ( esk1619_0 != esk1620_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_59,plain,
( ( esk1614_0 @ esk1619_0 @ ( esk1617_1 @ esk1618_0 ) )
= ( esk1617_1 @ esk1618_0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_55]),c_0_28]) ).
thf(c_0_60,plain,
( ( esk1617_1 @ esk1618_0 )
= esk1620_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_51]),c_0_57]) ).
thf(c_0_61,plain,
esk1620_0 != esk1619_0,
inference(sr,[status(thm)],[c_0_58,c_0_5]) ).
thf(c_0_62,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_52]),c_0_59]),c_0_60]),c_0_61]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
( ( X1 @ X5 @ X5 )
= X5 )
=> ~ ! [X5: a] :
( ( X2 @ X5 @ X5 )
= X5 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
= ( X1 @ X6 @ X5 ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X2 @ X5 @ X6 )
= ( X2 @ X6 @ X5 ) ) )
=> ~ ! [X5: a,X6: a] :
( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
= X6 ) )
=> ~ ! [X5: a,X6: a] :
( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
= X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
= ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
= ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ( X2 @ X3 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
( ( X1 @ X3 @ X5 )
= X3 ) )
=> ~ ! [X5: a] :
( ( X2 @ X4 @ X5 )
= X4 ) )
=> ~ ! [X5: a] :
( ( X1 @ X4 @ X5 )
= X5 ) )
=> ~ ! [X5: a] :
~ ! [X6: a] :
( ( ( X1 @ X5 @ X6 )
= X3 )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ( ( X1 @ X5 @ X6 )
= X3 )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) )
=> ( ( X1 @ X5 @ X7 )
!= X3 ) )
=> ( ( X2 @ X5 @ X7 )
!= X4 ) )
=> ( X6 = X7 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU997^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 12:25:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 44.88/44.70 % SZS status Theorem
% 44.88/44.70 % Mode: mode459
% 44.88/44.70 % Inferences: 12
% 44.88/44.70 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------