TSTP Solution File: NUM416^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM416^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 10:43:44 EDT 2023
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM416^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.10 % Command : do_cvc5 %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Aug 25 15:10:42 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.38 %----Proving TH0
% 0.14/0.39 %------------------------------------------------------------------------------
% 0.14/0.39 % File : NUM416^1 : TPTP v8.1.2. Released v3.6.0.
% 0.14/0.39 % Domain : Number Theory
% 0.14/0.39 % Problem : 10 * (10 * 10) = (10 + 10) * (5 * 10)
% 0.14/0.39 % Version : [Ben08] axioms : Especial.
% 0.14/0.39 % English :
% 0.14/0.39
% 0.14/0.39 % Refs : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% 0.14/0.39 % Source : [Ben08]
% 0.14/0.39 % Names : CHURCH_NUM_2 [Ben08]
% 0.14/0.39
% 0.14/0.39 % Status : Theorem
% 0.14/0.39 % Rating : 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v5.1.0, 0.60 v4.1.0, 0.33 v3.7.0
% 0.14/0.39 % Syntax : Number of formulae : 29 ( 15 unt; 14 typ; 14 def)
% 0.14/0.39 % Number of atoms : 31 ( 15 equ; 0 cnn)
% 0.14/0.39 % Maximal formula atoms : 1 ( 2 avg)
% 0.14/0.39 % Number of connectives : 75 ( 0 ~; 0 |; 0 &; 75 @)
% 0.14/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.14/0.39 % Maximal formula depth : 1 ( 1 avg)
% 0.14/0.39 % Number of types : 1 ( 0 usr)
% 0.14/0.39 % Number of type conns : 91 ( 91 >; 0 *; 0 +; 0 <<)
% 0.14/0.39 % Number of symbols : 19 ( 18 usr; 4 con; 0-4 aty)
% 0.14/0.39 % Number of variables : 33 ( 33 ^; 0 !; 0 ?; 33 :)
% 0.14/0.39 % SPC : TH0_THM_EQU_NAR
% 0.14/0.39
% 0.14/0.39 % Comments :
% 0.14/0.39 %------------------------------------------------------------------------------
% 0.14/0.39 %----Include church numerals definitions
% 0.14/0.39 %------------------------------------------------------------------------------
% 0.14/0.39 thf(zero,type,
% 0.14/0.39 zero: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(one,type,
% 0.14/0.39 one: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(two,type,
% 0.14/0.39 two: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(three,type,
% 0.14/0.39 three: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(four,type,
% 0.14/0.39 four: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(five,type,
% 0.14/0.39 five: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(six,type,
% 0.14/0.39 six: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(seven,type,
% 0.14/0.39 seven: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(eight,type,
% 0.14/0.39 eight: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(nine,type,
% 0.14/0.39 nine: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(ten,type,
% 0.14/0.39 ten: ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(succ,type,
% 0.14/0.39 succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(plus,type,
% 0.14/0.39 plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(mult,type,
% 0.14/0.39 mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(zero_ax,definition,
% 0.14/0.39 ( zero
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : Y ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(one_ax,definition,
% 0.14/0.39 ( one
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(two_ax,definition,
% 0.14/0.39 ( two
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ Y ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(three_ax,definition,
% 0.14/0.39 ( three
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ Y ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(four_ax,definition,
% 0.14/0.39 ( four
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(five_ax,definition,
% 0.14/0.39 ( five
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(six_ax,definition,
% 0.14/0.39 ( six
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(seven_ax,definition,
% 0.14/0.39 ( seven
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(eight_ax,definition,
% 0.14/0.39 ( eight
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(nine_ax,definition,
% 0.14/0.39 ( nine
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ten_ax,definition,
% 0.14/0.39 ( ten
% 0.14/0.39 = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(succ_ax,definition,
% 0.14/0.39 ( succ
% 0.14/0.39 = ( ^ [N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( X @ ( N @ X @ Y ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(plus_ax,definition,
% 0.14/0.39 ( plus
% 0.14/0.39 = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(mult_ax,definition,
% 0.14/0.39 ( mult
% 0.14/0.39 = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ) ).
% 0.14/0.39
% 0.14/0.39 %------------------------------------------------------------------------------
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 thf(thm,conjecture,
% 0.14/0.41 ( ( mult @ ten @ ( mult @ ten @ ten ) )
% 0.14/0.41 = ( mult @ ( plus @ ten @ ten ) @ ( mult @ five @ ten ) ) ) ).
% 0.14/0.41
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.pcn6F7m2vP/cvc5---1.0.5_12867.p...
% 0.14/0.41 (declare-sort $$unsorted 0)
% 0.14/0.41 (declare-fun tptp.zero ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.one ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.two ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.three ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.four ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.five ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.six ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.seven ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.eight ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.nine ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.ten ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.succ ((-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.plus ((-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (declare-fun tptp.mult ((-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.14/0.41 (assert (= tptp.zero (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) Y)))
% 0.14/0.41 (assert (= tptp.one (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))
% 0.14/0.41 (assert (= tptp.two (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))))
% 0.14/0.41 (assert (= tptp.three (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))))
% 0.14/0.41 (assert (= tptp.four (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X Y)))))))
% 0.14/0.41 (assert (= tptp.five (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))))
% 0.14/0.41 (assert (= tptp.six (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))
% 0.14/0.41 (assert (= tptp.seven (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))
% 0.14/0.41 (assert (= tptp.eight (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))
% 0.14/0.41 (assert (= tptp.nine (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))
% 0.14/0.41 (assert (= tptp.ten (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))
% 0.14/0.41 (assert (= tptp.succ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y)))))
% 0.14/0.41 (assert (= tptp.plus (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y)))))
% 0.14/0.41 (assert (= tptp.mult (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y))))
% 0.14/0.41 (assert (let ((_let_1 (@ tptp.mult tptp.ten))) (not (= (@ _let_1 (@ _let_1 tptp.ten)) (@ (@ tptp.mult (@ (@ tptp.plus tptp.ten) tptp.ten)) (@ (@ tptp.mult tptp.five) tptp.ten))))))
% 0.14/0.41 (set-info :filename cvc5---1.0.5_12867)
% 0.14/0.41 (check-sat-assuming ( true ))
% 0.14/0.41 ------- get file name : TPTP file name is NUM416^1
% 0.14/0.41 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12867.smt2...
% 0.14/0.41 --- Run --ho-elim --full-saturate-quant at 10...
% 0.14/0.41 % SZS status Theorem for NUM416^1
% 0.14/0.41 % SZS output start Proof for NUM416^1
% 0.14/0.41 (
% 0.14/0.41 (let ((_let_1 (@ tptp.mult tptp.ten))) (let ((_let_2 (not (= (@ _let_1 (@ _let_1 tptp.ten)) (@ (@ tptp.mult (@ (@ tptp.plus tptp.ten) tptp.ten)) (@ (@ tptp.mult tptp.five) tptp.ten)))))) (let ((_let_3 (= tptp.mult (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y))))) (let ((_let_4 (= tptp.plus (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y)))))) (let ((_let_5 (= tptp.succ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y)))))) (let ((_let_6 (= tptp.ten (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))) (let ((_let_7 (= tptp.nine (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) (let ((_let_8 (= tptp.eight (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (let ((_let_9 (= tptp.seven (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (let ((_let_10 (= tptp.six (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (let ((_let_11 (= tptp.five (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))))) (let ((_let_12 (= tptp.four (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X Y)))))))) (let ((_let_13 (= tptp.three (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))))) (let ((_let_14 (= tptp.two (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))))) (let ((_let_15 (= tptp.one (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))) (let ((_let_16 (= tptp.zero (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) Y)))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO (ASSUME :args (_let_3)) (ASSUME :args (_let_4)) (ASSUME :args (_let_5)) (ASSUME :args (_let_6)) (ASSUME :args (_let_7)) (ASSUME :args (_let_8)) (ASSUME :args (_let_9)) (ASSUME :args (_let_10)) (ASSUME :args (_let_11)) (ASSUME :args (_let_12)) (ASSUME :args (_let_13)) (ASSUME :args (_let_14)) (ASSUME :args (_let_15)) (ASSUME :args (_let_16))) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args (_let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 true)))))))))))))))))))
% 0.14/0.41 )
% 0.14/0.41 % SZS output end Proof for NUM416^1
% 0.14/0.41 % cvc5---1.0.5 exiting
% 0.14/0.41 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------