TSTP Solution File: NUM636^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 10:45:54 EDT 2023
% Result : Timeout 299.71s 300.19s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Fri Aug 25 14:37:25 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 35.62/35.93 %------------------------------------------------------------------------------
% 35.62/35.93 % File : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% 35.62/35.93 % Domain : Number Theory
% 35.62/35.93 % Problem : Landau theorem 2
% 35.62/35.93 % Version : Especial.
% 35.62/35.93 % English : ~(suc x = x)
% 35.62/35.93
% 35.62/35.93 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 35.62/35.93 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 35.62/35.93 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 35.62/35.93 % Source : [Bro09]
% 35.62/35.93 % Names : satz2 [Lan30]
% 35.62/35.93
% 35.62/35.93 % Status : Theorem
% 35.62/35.93 % : Without extensionality : Theorem
% 35.62/35.93 % Rating : 0.62 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 35.62/35.93 % Syntax : Number of formulae : 13 ( 4 unt; 7 typ; 0 def)
% 35.62/35.93 % Number of atoms : 10 ( 4 equ; 0 cnn)
% 35.62/35.93 % Maximal formula atoms : 4 ( 1 avg)
% 35.62/35.93 % Number of connectives : 31 ( 4 ~; 0 |; 0 &; 21 @)
% 35.62/35.93 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 35.62/35.93 % Maximal formula depth : 9 ( 5 avg)
% 35.62/35.93 % Number of types : 3 ( 2 usr)
% 35.62/35.93 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 35.62/35.93 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 35.62/35.93 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 35.62/35.93 % SPC : TH0_THM_EQU_NAR
% 35.62/35.93
% 35.62/35.93 % Comments :
% 35.62/35.93 %------------------------------------------------------------------------------
% 35.62/35.93 thf(nat_type,type,
% 35.62/35.93 nat: $tType ).
% 35.62/35.93
% 35.62/35.93 thf(x,type,
% 35.62/35.93 x: nat ).
% 35.62/35.93
% 35.62/35.93 thf(suc,type,
% 35.62/35.93 suc: nat > nat ).
% 35.62/35.93
% 35.62/35.93 thf(set_type,type,
% 35.62/35.93 set: $tType ).
% 35.62/35.93
% 35.62/35.93 thf(esti,type,
% 35.62/35.93 esti: nat > set > $o ).
% 35.62/35.93
% 35.62/35.93 thf(setof,type,
% 35.62/35.93 setof: ( nat > $o ) > set ).
% 35.62/35.93
% 35.62/35.93 thf(estie,axiom,
% 35.62/35.93 ! [Xp: nat > $o,Xs: nat] :
% 35.62/35.93 ( ( esti @ Xs @ ( setof @ Xp ) )
% 35.62/35.93 => ( Xp @ Xs ) ) ).
% 35.62/35.93
% 35.62/35.93 thf(n_1,type,
% 35.62/35.93 n_1: nat ).
% 35.62/35.93
% 35.62/35.93 thf(ax5,axiom,
% 35.62/35.93 ! [Xs: set] :
% 35.62/35.93 ( ( esti @ n_1 @ Xs )
% 35.62/35.93 => ( ! [Xx: nat] :
% 35.62/35.93 ( ( esti @ Xx @ Xs )
% 35.62/35.93 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 35.62/35.93 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 35.62/35.93
% 35.62/35.93 thf(estii,axiom,
% 35.62/35.93 ! [Xp: nat > $o,Xs: nat] :
% 35.62/35.93 ( ( Xp @ Xs )
% 35.62/35.93 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 35.62/35.93
% 35.62/35.93 thf(ax3,axiom,
% 35.62/35.93 ! [Xx: nat] :
% 35.62/35.93 ( ( suc @ Xx )
% 35.62/35.93 != n_1 ) ).
% 35.62/35.93
% 35.62/35.93 thf(satz1,axiom,
% 35.62/35.93 ! [Xx: nat,Xy: nat] :
% 35.62/35.93 ( ( Xx != Xy )
% 35.62/35.93 => ( ( suc @ Xx )
% 35.62/35.93 != ( suc @ Xy ) ) ) ).
% 35.62/35.93
% 35.62/35.93 thf(satz2,conjecture,
% 35.62/35.93 ( ( suc @ x )
% 35.62/35.93 != x ) ).
% 35.62/35.93
% 35.62/35.93 %------------------------------------------------------------------------------
% 35.62/35.93 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.sP2IHNJ0bH/cvc5---1.0.5_4382.p...
% 35.62/35.93 (declare-sort $$unsorted 0)
% 35.62/35.93 (declare-sort tptp.nat 0)
% 35.62/35.93 (declare-fun tptp.x () tptp.nat)
% 35.62/35.93 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 35.62/35.93 (declare-sort tptp.set 0)
% 35.62/35.93 (declare-fun tptp.esti (tptp.nat tptp.set) Bool)
% 35.62/35.93 (declare-fun tptp.setof ((-> tptp.nat Bool)) tptp.set)
% 35.62/35.93 (assert (forall ((Xp (-> tptp.nat Bool)) (Xs tptp.nat)) (=> (@ (@ tptp.esti Xs) (@ tptp.setof Xp)) (@ Xp Xs))))
% 35.62/35.93 (declare-fun tptp.n_1 () tptp.nat)
% 35.62/35.93 (assert (forall ((Xs tptp.set)) (=> (@ (@ tptp.esti tptp.n_1) Xs) (=> (forall ((Xx tptp.nat)) (=> (@ (@ tptp.esti Xx) Xs) (@ (@ tptp.esti (@ tptp.suc Xx)) Xs))) (forall ((Xx tptp.nat)) (@ (@ tptp.esti Xx) Xs))))))
% 35.62/35.93 (assert (forall ((Xp (-> tptp.nat Bool)) (Xs tptp.nat)) (=> (@ Xp Xs) (@ (@ tptp.esti Xs) (@ tptp.setof Xp)))))
% 35.62/35.93 (assert (forall ((Xx tptp.nat)) (not (= (@ tptp.suc Xx) tptp.n_1))))
% 35.62/35.93 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (not (= Xx Xy)) (not (= (@ tptp.suc Xx) (@ tptp.suc Xy))))))
% 35.62/35.93 (assert (not (not (= (@ tptp.suc tptp.x) tptp.x))))
% 35.62/35.93 (set-info :filename cvc5---1.0.5_4382)
% 35.62/35.93 (check-sat-assuming ( true ))
% 35.62/35.93 ------- get file name : TPTP file name is NUM636^1
% 35.62/35.93 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4382.smt2...
% 35.62/35.93 --- Run --ho-elim --full-saturate-quant at 10...
% 35.62/35.93 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 35.62/35.93 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 35.62/35.93 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 35.62/35.93 --- Run --no-ho-ma/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 6441 Alarm clock ( read result; case "$result" in
% 299.71/300.19 unsat)
% 299.71/300.19 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.71/300.19 ;;
% 299.71/300.19 sat)
% 299.71/300.19 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.71/300.19 ;;
% 299.71/300.19 esac; exit 1 )
% 299.71/300.20 Alarm clock
% 299.71/300.20 % cvc5---1.0.5 exiting
% 299.71/300.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------