TSTP Solution File: NUM726^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM726^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 : 300s
% DateTime : Thu Aug 31 10:47:13 EDT 2023
% Result : Theorem 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM726^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 16:54:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 % File : NUM726^1 : TPTP v8.1.2. Released v3.7.0.
% 0.22/0.53 % Domain : Number Theory
% 0.22/0.53 % Problem : Landau theorem 38
% 0.22/0.53 % Version : Especial.
% 0.22/0.53 % English : ts (num y) (den x) = ts (num x) (den y)
% 0.22/0.53
% 0.22/0.53 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.22/0.53 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.22/0.53 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.53 % Source : [Bro09]
% 0.22/0.53 % Names : satz38 [Lan30]
% 0.22/0.53
% 0.22/0.53 % Status : Theorem
% 0.22/0.53 % : Without extensionality : Theorem
% 0.22/0.53 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.22/0.53 % Syntax : Number of formulae : 9 ( 2 unt; 7 typ; 0 def)
% 0.22/0.53 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.22/0.53 % Maximal formula atoms : 1 ( 1 avg)
% 0.22/0.53 % Number of connectives : 16 ( 0 ~; 0 |; 0 &; 16 @)
% 0.22/0.53 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.22/0.53 % Maximal formula depth : 1 ( 1 avg)
% 0.22/0.53 % Number of types : 2 ( 2 usr)
% 0.22/0.53 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.22/0.53 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.22/0.53 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.22/0.53 % SPC : TH0_THM_EQU_NAR
% 0.22/0.53
% 0.22/0.53 % Comments :
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 thf(frac_type,type,
% 0.22/0.53 frac: $tType ).
% 0.22/0.53
% 0.22/0.53 thf(x,type,
% 0.22/0.53 x: frac ).
% 0.22/0.53
% 0.22/0.53 thf(y,type,
% 0.22/0.53 y: frac ).
% 0.22/0.53
% 0.22/0.53 thf(nat_type,type,
% 0.22/0.53 nat: $tType ).
% 0.22/0.53
% 0.22/0.53 thf(ts,type,
% 0.22/0.53 ts: nat > nat > nat ).
% 0.22/0.53
% 0.22/0.53 thf(num,type,
% 0.22/0.53 num: frac > nat ).
% 0.22/0.53
% 0.22/0.53 thf(den,type,
% 0.22/0.53 den: frac > nat ).
% 0.22/0.53
% 0.22/0.53 thf(e,axiom,
% 0.22/0.53 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 0.22/0.53 = ( ts @ ( num @ y ) @ ( den @ x ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(satz38,conjecture,
% 0.22/0.53 ( ( ts @ ( num @ y ) @ ( den @ x ) )
% 0.22/0.53 = ( ts @ ( num @ x ) @ ( den @ y ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.BeDy2cMe3e/cvc5---1.0.5_2802.p...
% 0.22/0.53 (declare-sort $$unsorted 0)
% 0.22/0.53 (declare-sort tptp.frac 0)
% 0.22/0.53 (declare-fun tptp.x () tptp.frac)
% 0.22/0.53 (declare-fun tptp.y () tptp.frac)
% 0.22/0.53 (declare-sort tptp.nat 0)
% 0.22/0.53 (declare-fun tptp.ts (tptp.nat tptp.nat) tptp.nat)
% 0.22/0.53 (declare-fun tptp.num (tptp.frac) tptp.nat)
% 0.22/0.53 (declare-fun tptp.den (tptp.frac) tptp.nat)
% 0.22/0.53 (assert (= (@ (@ tptp.ts (@ tptp.num tptp.x)) (@ tptp.den tptp.y)) (@ (@ tptp.ts (@ tptp.num tptp.y)) (@ tptp.den tptp.x))))
% 0.22/0.53 (assert (not (= (@ (@ tptp.ts (@ tptp.num tptp.y)) (@ tptp.den tptp.x)) (@ (@ tptp.ts (@ tptp.num tptp.x)) (@ tptp.den tptp.y)))))
% 0.22/0.53 (set-info :filename cvc5---1.0.5_2802)
% 0.22/0.53 (check-sat-assuming ( true ))
% 0.22/0.53 ------- get file name : TPTP file name is NUM726^1
% 0.22/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2802.smt2...
% 0.22/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.53 % SZS status Theorem for NUM726^1
% 0.22/0.53 % SZS output start Proof for NUM726^1
% 0.22/0.53 (
% 0.22/0.53 (let ((_let_1 (@ (@ tptp.ts (@ tptp.num tptp.x)) (@ tptp.den tptp.y)))) (let ((_let_2 (@ (@ tptp.ts (@ tptp.num tptp.y)) (@ tptp.den tptp.x)))) (let ((_let_3 (not (= _let_2 _let_1)))) (let ((_let_4 (= _let_1 _let_2))) (SCOPE (SCOPE (CONTRA (ASSUME :args (_let_4)) (SYMM (ASSUME :args (_let_3)))) :args (_let_4 _let_3 true)))))))
% 0.22/0.53 )
% 0.22/0.53 % SZS output end Proof for NUM726^1
% 0.22/0.53 % cvc5---1.0.5 exiting
% 0.22/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------