TSTP Solution File: ITP132^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP132^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 : Sun Jul 17 00:29:13 EDT 2022
% Result : Theorem 22.47s 22.42s
% Output : Proof 22.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 85 ( 31 ~; 23 |; 0 &; 30 @)
% ( 0 <=>; 0 =>; 1 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 18 con; 0-2 aty)
% Number of variables : 3 ( 3 ^ 0 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
( ( minus_minus_nat
@ ( groups1842438620at_nat
@ ^ [X1: nat] : ( times_times_nat @ ( p @ X1 ) @ X1 )
@ ( set_ord_atMost_nat @ n ) )
@ k )
= ( minus_minus_nat @ n @ k ) ) ).
thf(h0,negated_conjecture,
( minus_minus_nat
@ ( groups1842438620at_nat
@ ^ [X1: nat] : ( times_times_nat @ ( p @ X1 ) @ X1 )
@ ( set_ord_atMost_nat @ n ) )
@ k )
!= ( minus_minus_nat @ n @ k ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(ax328,axiom,
( ~ p43
| p612 ),
file('<stdin>',ax328) ).
thf(nax98,axiom,
( p98
<= ( fk = fk ) ),
file('<stdin>',nax98) ).
thf(ax12,axiom,
( ~ p924
| ~ p1
| ~ p923 ),
file('<stdin>',ax12) ).
thf(ax11,axiom,
( ~ p612
| p924 ),
file('<stdin>',ax11) ).
thf(ax904,axiom,
p43,
file('<stdin>',ax904) ).
thf(ax849,axiom,
( p90
| ~ p97
| ~ p98 ),
file('<stdin>',ax849) ).
thf(ax857,axiom,
~ p90,
file('<stdin>',ax857) ).
thf(ax946,axiom,
p1,
file('<stdin>',ax946) ).
thf(ax9,axiom,
( p923
| p97 ),
file('<stdin>',ax9) ).
thf(c_0_9,plain,
( ~ p43
| p612 ),
inference(fof_simplification,[status(thm)],[ax328]) ).
thf(c_0_10,plain,
( ( fk != fk )
| p98 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax98])]) ).
thf(c_0_11,plain,
( ~ p924
| ~ p1
| ~ p923 ),
inference(fof_simplification,[status(thm)],[ax12]) ).
thf(c_0_12,plain,
( ~ p612
| p924 ),
inference(fof_simplification,[status(thm)],[ax11]) ).
thf(c_0_13,plain,
( p612
| ~ p43 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
p43,
inference(split_conjunct,[status(thm)],[ax904]) ).
thf(c_0_15,plain,
( p90
| ~ p97
| ~ p98 ),
inference(fof_simplification,[status(thm)],[ax849]) ).
thf(c_0_16,plain,
( p98
| ( fk != fk ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
~ p90,
inference(fof_simplification,[status(thm)],[ax857]) ).
thf(c_0_18,plain,
( ~ p924
| ~ p1
| ~ p923 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_19,plain,
p1,
inference(split_conjunct,[status(thm)],[ax946]) ).
thf(c_0_20,plain,
( p924
| ~ p612 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_21,plain,
p612,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_22,plain,
( p90
| ~ p97
| ~ p98 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_23,plain,
p98,
inference(cn,[status(thm)],[c_0_16]) ).
thf(c_0_24,plain,
~ p90,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
( ~ p923
| ~ p924 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
thf(c_0_26,plain,
p924,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_27,plain,
( p923
| p97 ),
inference(split_conjunct,[status(thm)],[ax9]) ).
thf(c_0_28,plain,
~ p97,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),c_0_24]) ).
thf(c_0_29,plain,
~ p923,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
thf(c_0_30,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ( minus_minus_nat
@ ( groups1842438620at_nat
@ ^ [X1: nat] : ( times_times_nat @ ( p @ X1 ) @ X1 )
@ ( set_ord_atMost_nat @ n ) )
@ k )
= ( minus_minus_nat @ n @ k ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP132^1 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n019.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 : Fri Jun 3 00:44:25 EDT 2022
% 0.19/0.33 % CPUTime :
% 22.47/22.42 % SZS status Theorem
% 22.47/22.42 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 22.47/22.42 % Inferences: 109
% 22.47/22.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------