TSTP Solution File: NUM785^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM785^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 10:47:58 EDT 2023
% Result : Theorem 0.22s 0.55s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : NUM785^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Aug 25 17:23:26 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 0.22/0.55 %------------------------------------------------------------------------------
% 0.22/0.55 % File : NUM785^1 : TPTP v8.1.2. Released v3.7.0.
% 0.22/0.55 % Domain : Number Theory
% 0.22/0.55 % Problem : Landau theorem 81d
% 0.22/0.55 % Version : Especial.
% 0.22/0.55 % English : ~(more x0 y0)
% 0.22/0.55
% 0.22/0.55 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.22/0.55 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.22/0.55 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.55 % Source : [Bro09]
% 0.22/0.55 % Names : satz81d [Lan30]
% 0.22/0.55
% 0.22/0.55 % Status : Theorem
% 0.22/0.55 % : Without extensionality : Theorem
% 0.22/0.55 % Rating : 0.09 v8.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.22/0.55 % Syntax : Number of formulae : 10 ( 1 unt; 6 typ; 0 def)
% 0.22/0.55 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.22/0.55 % Maximal formula atoms : 6 ( 2 avg)
% 0.22/0.55 % Number of connectives : 36 ( 11 ~; 0 |; 0 &; 18 @)
% 0.22/0.55 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.22/0.55 % Maximal formula depth : 13 ( 7 avg)
% 0.22/0.55 % Number of types : 2 ( 1 usr)
% 0.22/0.55 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.22/0.55 % Number of symbols : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.22/0.55 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.22/0.55 % SPC : TH0_THM_NEQ_NAR
% 0.22/0.55
% 0.22/0.55 % Comments :
% 0.22/0.55 %------------------------------------------------------------------------------
% 0.22/0.55 thf(rat_type,type,
% 0.22/0.55 rat: $tType ).
% 0.22/0.55
% 0.22/0.55 thf(x0,type,
% 0.22/0.55 x0: rat ).
% 0.22/0.55
% 0.22/0.55 thf(y0,type,
% 0.22/0.55 y0: rat ).
% 0.22/0.55
% 0.22/0.55 thf(less,type,
% 0.22/0.55 less: rat > rat > $o ).
% 0.22/0.55
% 0.22/0.55 thf(is,type,
% 0.22/0.55 is: rat > rat > $o ).
% 0.22/0.55
% 0.22/0.55 thf(l,axiom,
% 0.22/0.55 ( ~ ( less @ x0 @ y0 )
% 0.22/0.55 => ( is @ x0 @ y0 ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(more,type,
% 0.22/0.55 more: rat > rat > $o ).
% 0.22/0.55
% 0.22/0.55 thf(et,axiom,
% 0.22/0.55 ! [Xa: $o] :
% 0.22/0.55 ( ~ ~ Xa
% 0.22/0.55 => Xa ) ).
% 0.22/0.55
% 0.22/0.55 thf(satz81b,axiom,
% 0.22/0.55 ! [Xx0: rat,Xy0: rat] :
% 0.22/0.55 ~ ( ( ( is @ Xx0 @ Xy0 )
% 0.22/0.55 => ~ ( more @ Xx0 @ Xy0 ) )
% 0.22/0.55 => ~ ~ ( ( ( more @ Xx0 @ Xy0 )
% 0.22/0.55 => ~ ( less @ Xx0 @ Xy0 ) )
% 0.22/0.55 => ~ ( ( less @ Xx0 @ Xy0 )
% 0.22/0.55 => ~ ( is @ Xx0 @ Xy0 ) ) ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(satz81d,conjecture,
% 0.22/0.55 ~ ( more @ x0 @ y0 ) ).
% 0.22/0.55
% 0.22/0.55 %------------------------------------------------------------------------------
% 0.22/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.0MIw8Au7uC/cvc5---1.0.5_9061.p...
% 0.22/0.55 (declare-sort $$unsorted 0)
% 0.22/0.55 (declare-sort tptp.rat 0)
% 0.22/0.55 (declare-fun tptp.x0 () tptp.rat)
% 0.22/0.55 (declare-fun tptp.y0 () tptp.rat)
% 0.22/0.55 (declare-fun tptp.less (tptp.rat tptp.rat) Bool)
% 0.22/0.55 (declare-fun tptp.is (tptp.rat tptp.rat) Bool)
% 0.22/0.55 (assert (=> (not (@ (@ tptp.less tptp.x0) tptp.y0)) (@ (@ tptp.is tptp.x0) tptp.y0)))
% 0.22/0.55 (declare-fun tptp.more (tptp.rat tptp.rat) Bool)
% 0.22/0.55 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.22/0.55 (assert (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (let ((_let_1 (@ (@ tptp.is Xx0) Xy0))) (let ((_let_2 (@ (@ tptp.less Xx0) Xy0))) (let ((_let_3 (@ (@ tptp.more Xx0) Xy0))) (not (=> (=> _let_1 (not _let_3)) (not (not (=> (=> _let_3 (not _let_2)) (not (=> _let_2 (not _let_1)))))))))))))
% 0.22/0.55 (assert (not (not (@ (@ tptp.more tptp.x0) tptp.y0))))
% 0.22/0.55 (set-info :filename cvc5---1.0.5_9061)
% 0.22/0.55 (check-sat-assuming ( true ))
% 0.22/0.55 ------- get file name : TPTP file name is NUM785^1
% 0.22/0.55 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9061.smt2...
% 0.22/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.55 % SZS status Theorem for NUM785^1
% 0.22/0.55 % SZS output start Proof for NUM785^1
% 0.22/0.55 (
% 0.22/0.55 (let ((_let_1 (@ (@ tptp.more tptp.x0) tptp.y0))) (let ((_let_2 (not (not _let_1)))) (let ((_let_3 (forall ((Xx0 tptp.rat) (Xy0 tptp.rat)) (let ((_let_1 (@ (@ tptp.is Xx0) Xy0))) (let ((_let_2 (@ (@ tptp.less Xx0) Xy0))) (let ((_let_3 (@ (@ tptp.more Xx0) Xy0))) (not (=> (=> _let_1 (not _let_3)) (not (not (=> (=> _let_3 (not _let_2)) (not (=> _let_2 (not _let_1)))))))))))))) (let ((_let_4 (=> (not (@ (@ tptp.less tptp.x0) tptp.y0)) (@ (@ tptp.is tptp.x0) tptp.y0)))) (let ((_let_5 (forall ((BOUND_VARIABLE_632 tptp.rat) (BOUND_VARIABLE_634 tptp.rat)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_632) BOUND_VARIABLE_634)) (not (ho_4 (ho_3 k_6 BOUND_VARIABLE_632) BOUND_VARIABLE_634)))))) (let ((_let_6 (ho_4 (ho_3 k_6 tptp.x0) tptp.y0))) (let ((_let_7 (not _let_6))) (let ((_let_8 (ho_4 (ho_3 k_2 tptp.x0) tptp.y0))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (0))) (let ((_let_12 (forall ((BOUND_VARIABLE_645 tptp.rat) (BOUND_VARIABLE_647 tptp.rat)) (or (not (ho_4 (ho_3 k_6 BOUND_VARIABLE_645) BOUND_VARIABLE_647)) (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_645) BOUND_VARIABLE_647)))))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_632 tptp.rat) (BOUND_VARIABLE_634 tptp.rat)) (or (not (@ (@ tptp.is BOUND_VARIABLE_632) BOUND_VARIABLE_634)) (not (@ (@ tptp.more BOUND_VARIABLE_632) BOUND_VARIABLE_634)))) (forall ((BOUND_VARIABLE_645 tptp.rat) (BOUND_VARIABLE_647 tptp.rat)) (or (not (@ (@ tptp.more BOUND_VARIABLE_645) BOUND_VARIABLE_647)) (not (@ (@ tptp.less BOUND_VARIABLE_645) BOUND_VARIABLE_647)))) (forall ((BOUND_VARIABLE_658 tptp.rat) (BOUND_VARIABLE_660 tptp.rat)) (or (not (@ (@ tptp.less BOUND_VARIABLE_658) BOUND_VARIABLE_660)) (not (@ (@ tptp.is BOUND_VARIABLE_658) BOUND_VARIABLE_660))))) (and _let_5 _let_12 (forall ((BOUND_VARIABLE_658 tptp.rat) (BOUND_VARIABLE_660 tptp.rat)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_658) BOUND_VARIABLE_660)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_658) BOUND_VARIABLE_660)))))))))))) (let ((_let_14 (not _let_10))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_1 _let_6))))))) (let ((_let_16 (ho_4 (ho_3 k_5 tptp.x0) tptp.y0))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_7 _let_17))) (let ((_let_19 (_let_12))) (let ((_let_20 (tptp.x0 tptp.y0 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_21 (forall ((u |u_(-> tptp.rat Bool)|) (e Bool) (i tptp.rat)) (not (forall ((v |u_(-> tptp.rat Bool)|)) (not (forall ((ii tptp.rat)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_22 (forall ((x |u_(-> tptp.rat Bool)|) (y |u_(-> tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_23 (forall ((u |u_(-> tptp.rat tptp.rat Bool)|) (e |u_(-> tptp.rat Bool)|) (i tptp.rat)) (not (forall ((v |u_(-> tptp.rat tptp.rat Bool)|)) (not (forall ((ii tptp.rat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_24 (forall ((x |u_(-> tptp.rat tptp.rat Bool)|) (y |u_(-> tptp.rat tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_25 (=> _let_17 _let_8))) (let ((_let_26 (_let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args _let_20) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_7 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_25)))) (PREPROCESS :args ((and _let_24 _let_23 _let_22 _let_21)))) :args ((and _let_25 _let_24 _let_23 _let_22 _let_21))) :args _let_11)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) (REFL :args (_let_8)) :args (or))) :args ((or _let_8 _let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_17 _let_7 (not _let_18)))) _let_15 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_19) :args _let_20) :args _let_19)) (AND_ELIM _let_13 :args (1)) :args (_let_18 false _let_12)) :args (_let_17 false _let_6 false _let_18)) :args (_let_8 true _let_16)) _let_15 :args (_let_14 false _let_8 false _let_6)) (AND_ELIM _let_13 :args _let_11) :args (false true _let_10 false _let_5)) :args (_let_4 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_3 _let_2 true)))))))))))))))))))))))))))))
% 0.22/0.56 )
% 0.22/0.56 % SZS output end Proof for NUM785^1
% 0.22/0.56 % cvc5---1.0.5 exiting
% 0.22/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------