TSTP Solution File: NUM668^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM668^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 10:46:28 EDT 2023
% Result : Theorem 0.23s 0.55s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : NUM668^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n026.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Aug 25 12:25:03 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.52 %----Proving TH0
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 % File : NUM668^1 : TPTP v8.1.2. Released v3.7.0.
% 0.23/0.55 % Domain : Number Theory
% 0.23/0.55 % Problem : Landau theorem 18
% 0.23/0.55 % Version : Especial.
% 0.23/0.55 % English : ~(forall x_0:nat.~(pl x y = pl x x_0))
% 0.23/0.55
% 0.23/0.55 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.23/0.55 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.23/0.55 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.23/0.55 % Source : [Bro09]
% 0.23/0.55 % Names : satz18 [Lan30]
% 0.23/0.55
% 0.23/0.55 % Status : Theorem
% 0.23/0.55 % : Without extensionality : Theorem
% 0.23/0.55 % Rating : 0.15 v8.1.0, 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
% 0.23/0.55 % Syntax : Number of formulae : 5 ( 1 unt; 4 typ; 0 def)
% 0.23/0.55 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.23/0.55 % Maximal formula atoms : 1 ( 1 avg)
% 0.23/0.55 % Number of connectives : 6 ( 2 ~; 0 |; 0 &; 4 @)
% 0.23/0.55 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.23/0.55 % Maximal formula depth : 4 ( 4 avg)
% 0.23/0.55 % Number of types : 1 ( 1 usr)
% 0.23/0.55 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.23/0.55 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.23/0.55 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.23/0.55 % SPC : TH0_THM_EQU_NAR
% 0.23/0.55
% 0.23/0.55 % Comments :
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 thf(nat_type,type,
% 0.23/0.55 nat: $tType ).
% 0.23/0.55
% 0.23/0.55 thf(x,type,
% 0.23/0.55 x: nat ).
% 0.23/0.55
% 0.23/0.55 thf(y,type,
% 0.23/0.55 y: nat ).
% 0.23/0.55
% 0.23/0.55 thf(pl,type,
% 0.23/0.55 pl: nat > nat > nat ).
% 0.23/0.55
% 0.23/0.55 thf(satz18,conjecture,
% 0.23/0.55 ~ ! [Xx_0: nat] :
% 0.23/0.55 ( ( pl @ x @ y )
% 0.23/0.55 != ( pl @ x @ Xx_0 ) ) ).
% 0.23/0.55
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ka0DCQEmBx/cvc5---1.0.5_25939.p...
% 0.23/0.55 (declare-sort $$unsorted 0)
% 0.23/0.55 (declare-sort tptp.nat 0)
% 0.23/0.55 (declare-fun tptp.x () tptp.nat)
% 0.23/0.55 (declare-fun tptp.y () tptp.nat)
% 0.23/0.55 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.23/0.55 (assert (not (not (forall ((Xx_0 tptp.nat)) (let ((_let_1 (@ tptp.pl tptp.x))) (not (= (@ _let_1 tptp.y) (@ _let_1 Xx_0))))))))
% 0.23/0.55 (set-info :filename cvc5---1.0.5_25939)
% 0.23/0.55 (check-sat-assuming ( true ))
% 0.23/0.55 ------- get file name : TPTP file name is NUM668^1
% 0.23/0.55 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25939.smt2...
% 0.23/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.55 % SZS status Theorem for NUM668^1
% 0.23/0.55 % SZS output start Proof for NUM668^1
% 0.23/0.55 (
% 0.23/0.55 (let ((_let_1 (forall ((Xx_0 tptp.nat)) (let ((_let_1 (@ tptp.pl tptp.x))) (not (= (@ _let_1 tptp.y) (@ _let_1 Xx_0))))))) (let ((_let_2 (not (not _let_1)))) (let ((_let_3 (forall ((Xx_0 tptp.nat)) (let ((_let_1 (ho_3 k_2 tptp.x))) (not (= (ho_4 _let_1 Xx_0) (ho_4 _let_1 tptp.y))))))) (let ((_let_4 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_5 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_6 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_7 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_8 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_1 _let_3))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_8 :args (tptp.y QUANTIFIERS_INST_ENUM)) :args (_let_3))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_8 (PREPROCESS :args ((and _let_7 _let_6 _let_5 _let_4)))) :args ((and _let_3 _let_7 _let_6 _let_5 _let_4))) :args (0)) :args (false false _let_3)) :args (_let_2 true)))))))))))
% 0.23/0.56 )
% 0.23/0.56 % SZS output end Proof for NUM668^1
% 0.23/0.56 % cvc5---1.0.5 exiting
% 0.23/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------