TSTP Solution File: NUM727^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM727^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : Mon Jul 18 13:55:45 EDT 2022
% Result : Theorem 36.87s 37.24s
% Output : Proof 36.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 67 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 515 ( 38 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 463 ( 41 ~; 33 |; 0 &; 380 @)
% ( 0 <=>; 8 =>; 1 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 24 con; 0-2 aty)
% Number of variables : 25 ( 0 ^ 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(satz39,conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ) ).
thf(h0,negated_conjecture,
( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ),
inference(assume_negation,[status(cth)],[satz39]) ).
thf(ax939,axiom,
( ~ p4
| p33 ),
file('<stdin>',ax939) ).
thf(ax926,axiom,
( ~ p33
| p46 ),
file('<stdin>',ax926) ).
thf(ax972,axiom,
p4,
file('<stdin>',ax972) ).
thf(pax5,axiom,
( p5
=> ! [X5: nat,X6: nat] :
( ( fts @ X5 @ X6 )
= ( fts @ X6 @ X5 ) ) ),
file('<stdin>',pax5) ).
thf(ax919,axiom,
( ~ p4
| p53 ),
file('<stdin>',ax919) ).
thf(pax6,axiom,
( p6
=> ! [X5: nat,X6: nat,X7: nat] :
( ( fts @ ( fts @ X5 @ X6 ) @ X7 )
= ( fts @ X5 @ ( fts @ X6 @ X7 ) ) ) ),
file('<stdin>',pax6) ).
thf(ax704,axiom,
( ~ p46
| p275 ),
file('<stdin>',ax704) ).
thf(nax1,axiom,
( p1
<= ( ( fts @ ( fnum @ fx ) @ ( fden @ fz ) )
= ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) ) ),
file('<stdin>',nax1) ).
thf(ax971,axiom,
p5,
file('<stdin>',ax971) ).
thf(ax975,axiom,
~ p1,
file('<stdin>',ax975) ).
thf(ax564,axiom,
( ~ p53
| p421 ),
file('<stdin>',ax564) ).
thf(pax275,axiom,
( p275
=> ( ( ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) )
= ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) ) )
=> ( ( fts @ ( fnum @ fz ) @ ( fden @ fx ) )
= ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) ) ) ),
file('<stdin>',pax275) ).
thf(ax970,axiom,
p6,
file('<stdin>',ax970) ).
thf(pax421,axiom,
( p421
=> ! [X1: nat] :
( ( ( fts @ ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) ) @ X1 )
= ( fts @ ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) ) @ X1 ) )
=> ( ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) )
= ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) ) ) ) ),
file('<stdin>',pax421) ).
thf(pax3,axiom,
( p3
=> ( ( fts @ ( fnum @ fy ) @ ( fden @ fz ) )
= ( fts @ ( fnum @ fz ) @ ( fden @ fy ) ) ) ),
file('<stdin>',pax3) ).
thf(pax2,axiom,
( p2
=> ( ( fts @ ( fnum @ fx ) @ ( fden @ fy ) )
= ( fts @ ( fnum @ fy ) @ ( fden @ fx ) ) ) ),
file('<stdin>',pax2) ).
thf(ax973,axiom,
p3,
file('<stdin>',ax973) ).
thf(ax974,axiom,
p2,
file('<stdin>',ax974) ).
thf(c_0_18,plain,
( ~ p4
| p33 ),
inference(fof_simplification,[status(thm)],[ax939]) ).
thf(c_0_19,plain,
( ~ p33
| p46 ),
inference(fof_simplification,[status(thm)],[ax926]) ).
thf(c_0_20,plain,
( p33
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,plain,
p4,
inference(split_conjunct,[status(thm)],[ax972]) ).
thf(c_0_22,plain,
! [X566: nat,X567: nat] :
( ~ p5
| ( ( fts @ X566 @ X567 )
= ( fts @ X567 @ X566 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_23,plain,
( ~ p4
| p53 ),
inference(fof_simplification,[status(thm)],[ax919]) ).
thf(c_0_24,plain,
! [X560: nat,X561: nat,X562: nat] :
( ~ p6
| ( ( fts @ ( fts @ X560 @ X561 ) @ X562 )
= ( fts @ X560 @ ( fts @ X561 @ X562 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])]) ).
thf(c_0_25,plain,
( ~ p46
| p275 ),
inference(fof_simplification,[status(thm)],[ax704]) ).
thf(c_0_26,plain,
( p46
| ~ p33 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,plain,
p33,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_28,plain,
( ( ( fts @ ( fnum @ fx ) @ ( fden @ fz ) )
!= ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) )
| p1 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).
thf(c_0_29,plain,
! [X2: nat,X1: nat] :
( ( ( fts @ X1 @ X2 )
= ( fts @ X2 @ X1 ) )
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_30,plain,
p5,
inference(split_conjunct,[status(thm)],[ax971]) ).
thf(c_0_31,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax975]) ).
thf(c_0_32,plain,
( ~ p53
| p421 ),
inference(fof_simplification,[status(thm)],[ax564]) ).
thf(c_0_33,plain,
( p53
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_34,plain,
( ~ p275
| ( ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) )
!= ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) ) )
| ( ( fts @ ( fnum @ fz ) @ ( fden @ fx ) )
= ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) ) ),
inference(fof_nnf,[status(thm)],[pax275]) ).
thf(c_0_35,plain,
! [X1: nat,X2: nat,X5: nat] :
( ( ( fts @ ( fts @ X1 @ X2 ) @ X5 )
= ( fts @ X1 @ ( fts @ X2 @ X5 ) ) )
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_36,plain,
p6,
inference(split_conjunct,[status(thm)],[ax970]) ).
thf(c_0_37,plain,
( p275
| ~ p46 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_38,plain,
p46,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
thf(c_0_39,plain,
( p1
| ( ( fts @ ( fnum @ fx ) @ ( fden @ fz ) )
!= ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_40,plain,
! [X2: nat,X1: nat] :
( ( fts @ X1 @ X2 )
= ( fts @ X2 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
thf(c_0_41,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_42,plain,
! [X258: nat] :
( ~ p421
| ( ( fts @ ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) ) @ X258 )
!= ( fts @ ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) ) @ X258 ) )
| ( ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) )
= ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax421])])]) ).
thf(c_0_43,plain,
( p421
| ~ p53 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_44,plain,
p53,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_21])]) ).
thf(c_0_45,plain,
( ( ( fts @ ( fnum @ fz ) @ ( fden @ fx ) )
= ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) )
| ~ p275
| ( ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) )
!= ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_46,plain,
! [X1: nat,X2: nat,X5: nat] :
( ( fts @ ( fts @ X1 @ X2 ) @ X5 )
= ( fts @ X1 @ ( fts @ X2 @ X5 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_47,plain,
p275,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
thf(c_0_48,plain,
( fts @ ( fden @ fx ) @ ( fnum @ fz ) )
!= ( fts @ ( fden @ fz ) @ ( fnum @ fx ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_40]),c_0_41]) ).
thf(c_0_49,plain,
! [X1: nat] :
( ( ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) )
= ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) ) )
| ~ p421
| ( ( fts @ ( fts @ ( fts @ ( fnum @ fx ) @ ( fden @ fz ) ) @ ( fden @ fx ) ) @ X1 )
!= ( fts @ ( fts @ ( fts @ ( fnum @ fz ) @ ( fden @ fx ) ) @ ( fden @ fx ) ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_50,plain,
p421,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
thf(c_0_51,plain,
( fts @ ( fden @ fx ) @ ( fts @ ( fden @ fx ) @ ( fnum @ fz ) ) )
!= ( fts @ ( fden @ fx ) @ ( fts @ ( fden @ fz ) @ ( fnum @ fx ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_46]),c_0_40]),c_0_47])]),c_0_48]) ).
thf(c_0_52,plain,
( ~ p3
| ( ( fts @ ( fnum @ fy ) @ ( fden @ fz ) )
= ( fts @ ( fnum @ fz ) @ ( fden @ fy ) ) ) ),
inference(fof_nnf,[status(thm)],[pax3]) ).
thf(c_0_53,plain,
( ~ p2
| ( ( fts @ ( fnum @ fx ) @ ( fden @ fy ) )
= ( fts @ ( fnum @ fy ) @ ( fden @ fx ) ) ) ),
inference(fof_nnf,[status(thm)],[pax2]) ).
thf(c_0_54,plain,
! [X1: nat] :
( ( fts @ ( fden @ fx ) @ ( fts @ ( fden @ fx ) @ ( fts @ ( fnum @ fz ) @ X1 ) ) )
!= ( fts @ ( fden @ fx ) @ ( fts @ ( fden @ fz ) @ ( fts @ ( fnum @ fx ) @ X1 ) ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_40]),c_0_40]),c_0_40]),c_0_46]),c_0_40]),c_0_40]),c_0_40]),c_0_46]),c_0_46]),c_0_40]),c_0_46]),c_0_40]),c_0_46]),c_0_46]),c_0_50])]),c_0_51]) ).
thf(c_0_55,plain,
( ( ( fts @ ( fnum @ fy ) @ ( fden @ fz ) )
= ( fts @ ( fnum @ fz ) @ ( fden @ fy ) ) )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_56,plain,
p3,
inference(split_conjunct,[status(thm)],[ax973]) ).
thf(c_0_57,plain,
( ( ( fts @ ( fnum @ fx ) @ ( fden @ fy ) )
= ( fts @ ( fnum @ fy ) @ ( fden @ fx ) ) )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_58,plain,
p2,
inference(split_conjunct,[status(thm)],[ax974]) ).
thf(c_0_59,plain,
! [X1: nat] :
( ( fts @ ( fden @ fx ) @ ( fts @ ( fden @ fx ) @ ( fts @ X1 @ ( fnum @ fz ) ) ) )
!= ( fts @ ( fden @ fx ) @ ( fts @ ( fden @ fz ) @ ( fts @ ( fnum @ fx ) @ X1 ) ) ) ),
inference(spm,[status(thm)],[c_0_54,c_0_40]) ).
thf(c_0_60,plain,
( ( fts @ ( fden @ fy ) @ ( fnum @ fz ) )
= ( fts @ ( fden @ fz ) @ ( fnum @ fy ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_40]),c_0_40]),c_0_56])]) ).
thf(c_0_61,plain,
( ( fts @ ( fden @ fy ) @ ( fnum @ fx ) )
= ( fts @ ( fden @ fx ) @ ( fnum @ fy ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_40]),c_0_40]),c_0_58])]) ).
thf(c_0_62,plain,
$false,
inference(ar,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_40]),c_0_61]),c_0_40,c_0_46]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM727^1 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 08:11:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 36.87/37.24 % SZS status Theorem
% 36.87/37.24 % Mode: mode485
% 36.87/37.24 % Inferences: 48
% 36.87/37.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------