TSTP Solution File: NUM342+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM342+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 : 600s
% DateTime : Mon Jul 18 13:26:49 EDT 2022
% Result : Theorem 29.92s 30.22s
% Output : Refutation 29.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : NUM342+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n015.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 : 600
% 0.13/0.35 % DateTime : Thu Jul 7 09:41:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.87/1.16 ============================== Prover9 ===============================
% 0.87/1.16 Prover9 (32) version 2009-11A, November 2009.
% 0.87/1.16 Process 29011 was started by sandbox2 on n015.cluster.edu,
% 0.87/1.16 Thu Jul 7 09:41:35 2022
% 0.87/1.16 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28858_n015.cluster.edu".
% 0.87/1.16 ============================== end of head ===========================
% 0.87/1.16
% 0.87/1.16 ============================== INPUT =================================
% 0.87/1.16
% 0.87/1.16 % Reading from file /tmp/Prover9_28858_n015.cluster.edu
% 0.87/1.16
% 0.87/1.16 set(prolog_style_variables).
% 0.87/1.16 set(auto2).
% 0.87/1.16 % set(auto2) -> set(auto).
% 0.87/1.16 % set(auto) -> set(auto_inference).
% 0.87/1.16 % set(auto) -> set(auto_setup).
% 0.87/1.16 % set(auto_setup) -> set(predicate_elim).
% 0.87/1.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.87/1.16 % set(auto) -> set(auto_limits).
% 0.87/1.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.87/1.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.87/1.16 % set(auto) -> set(auto_denials).
% 0.87/1.16 % set(auto) -> set(auto_process).
% 0.87/1.16 % set(auto2) -> assign(new_constants, 1).
% 0.87/1.16 % set(auto2) -> assign(fold_denial_max, 3).
% 0.87/1.16 % set(auto2) -> assign(max_weight, "200.000").
% 0.87/1.16 % set(auto2) -> assign(max_hours, 1).
% 0.87/1.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.87/1.16 % set(auto2) -> assign(max_seconds, 0).
% 0.87/1.16 % set(auto2) -> assign(max_minutes, 5).
% 0.87/1.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.87/1.16 % set(auto2) -> set(sort_initial_sos).
% 0.87/1.16 % set(auto2) -> assign(sos_limit, -1).
% 0.87/1.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.87/1.16 % set(auto2) -> assign(max_megs, 400).
% 0.87/1.16 % set(auto2) -> assign(stats, some).
% 0.87/1.16 % set(auto2) -> clear(echo_input).
% 0.87/1.16 % set(auto2) -> set(quiet).
% 0.87/1.16 % set(auto2) -> clear(print_initial_clauses).
% 0.87/1.16 % set(auto2) -> clear(print_given).
% 0.87/1.16 assign(lrs_ticks,-1).
% 0.87/1.16 assign(sos_limit,10000).
% 0.87/1.16 assign(order,kbo).
% 0.87/1.16 set(lex_order_vars).
% 0.87/1.16 clear(print_given).
% 0.87/1.16
% 0.87/1.16 % formulas(sos). % not echoed (402 formulas)
% 0.87/1.16
% 0.87/1.16 ============================== end of input ==========================
% 0.87/1.16
% 0.87/1.16 % From the command line: assign(max_seconds, 300).
% 0.87/1.16
% 0.87/1.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.87/1.16
% 0.87/1.16 % Formulas that are not ordinary clauses:
% 0.87/1.16 1 (all X all Y all Z (rdn_positive_less(rdnn(X),rdnn(Y)) & rdn_positive_less(rdnn(Y),rdnn(Z)) -> rdn_positive_less(rdnn(X),rdnn(Z)))) # label(rdn_positive_less_transitivity) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 2 (all Ds all Os all Db all Ob (rdn_positive_less(Os,Ob) -> rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)))) # label(rdn_positive_less_multi_digit_high) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 3 (all Ds all O all Db (rdn_positive_less(rdnn(Ds),rdnn(Db)) & rdn_non_zero(O) -> rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)))) # label(rdn_positive_less_multi_digit_low) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 4 (all D all Db all Ob (rdn_non_zero(Ob) -> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)))) # label(rdn_extra_digits_positive_less) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 5 (all X (rdn_non_zero_digit(rdnn(X)) -> rdn_non_zero(rdnn(X)))) # label(rdn_non_zero_by_digit) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 6 (all D all O (rdn_non_zero(O) -> rdn_non_zero(rdn(rdnn(D),O)))) # label(rdn_non_zero_by_structure) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 7 (all X all Y all RDN_X all RDN_Y (rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) & rdn_positive_less(RDN_X,RDN_Y) -> less(X,Y))) # label(less_entry_point_pos_pos) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 8 (all X all Y all RDN_X all RDN_Y (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) -> less(X,Y))) # label(less_entry_point_neg_pos) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 9 (all X all Y all RDN_X all RDN_Y (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_positive_less(RDN_Y,RDN_X) -> less(X,Y))) # label(less_entry_point_neg_neg) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 10 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 11 (all X all Y (less_or_equal(X,Y) <-> less(X,Y) | X = Y)) # label(less_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 12 (all X all Y all Z (sum(X,n1,Y) & less(Z,Y) -> less_or_equal(Z,X))) # label(less_successor) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 13 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z) & rdn_translate(Z,rdn_pos(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_pos_pos) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 14 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z) & rdn_translate(Z,rdn_neg(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_neg_neg) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 15 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_positive_less(RDN_X,RDN_Y) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y) & rdn_translate(Z,rdn_neg(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_pos_neg_1) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 16 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_neg(RDN_Y)) & rdn_positive_less(RDN_Y,RDN_X) & rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X) & rdn_translate(Z,rdn_pos(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_pos_neg_2) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 17 (all POS_X all NEG_X all RDN_X (rdn_translate(POS_X,rdn_pos(RDN_X)) & rdn_translate(NEG_X,rdn_neg(RDN_X)) -> sum(POS_X,NEG_X,n0))) # label(sum_entry_point_posx_negx) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 18 (all X all Y all Z all RDN_X all RDN_Y (rdn_translate(X,rdn_neg(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) & sum(Y,X,Z) -> sum(X,Y,Z))) # label(sum_entry_point_neg_pos) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 19 (all X all Y all Z1 all Z2 (sum(X,Y,Z1) & sum(X,Y,Z2) -> Z1 = Z2)) # label(unique_sum) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 20 (all X1 all X2 all Y all Z (sum(X1,Y,Z) & sum(X2,Y,Z) -> X1 = X2)) # label(unique_LHS) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 21 (all X all Y1 all Y2 all Z (sum(X,Y1,Z) & sum(X,Y2,Z) -> Y1 = Y2)) # label(unique_RHS) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 22 (all X all Y all Z (sum(Y,Z,X) <-> difference(X,Y,Z))) # label(minus_entry_point) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 23 (all C all D1 all D2 all RD all ID (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)) -> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)))) # label(add_digit_digit_digit) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 24 (all C all D1 all D2 all ID all RD all IC1 all IC2 (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0)) -> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))))) # label(add_digit_digit_rdn) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 25 (all C all D1 all D2 all O2 all RD all RO all ID all IC1 all IC2 all NC (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(NC),rdnn(n0)) & rdn_add_with_carry(rdnn(NC),rdnn(n0),O2,RO) & rdn_non_zero(O2) & rdn_non_zero(RO) -> rdn_add_with_carry(rdnn(C),rdnn(D1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO)))) # label(add_digit_rdn_rdn) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.16 26 (all C all D1 all O1 all D2 all O2 all RD all RO all ID all IC1 all IC2 all RC (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2)) & rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(RC),rdnn(n0)) & rdn_add_with_carry(rdnn(RC),O1,O2,RO) & rdn_non_zero(O1) & rdn_non_zero(O2) & rdn_non_zero(RO) -> rdn_add_with_carry(rdnn(C),rdn(rdnn(D1),O1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO)))) # label(add_rdn_rdn_rdn) # label(axiom) # label(non_clause). [assumption].
% 29.92/30.22 27 (all C all D1 all O1 all D2 all RD all RO (rdn_add_with_carry(rdnn(C),rdnn(D2),rdn(rdnn(D1),O1),rdn(rdnn(RD),RO)) -> rdn_add_with_carry(rdnn(C),rdn(rdnn(D1),O1),rdnn(D2),rdn(rdnn(RD),RO)))) # label(add_rdn_digit_rdn) # label(axiom) # label(non_clause). [assumption].
% 29.92/30.22 28 -(exists X exists Y (sum(X,Y,n8) & difference(X,Y,n0))) # label(sum_and_difference) # label(negated_conjecture) # label(non_clause). [assumption].
% 29.92/30.22
% 29.92/30.22 ============================== end of process non-clausal formulas ===
% 29.92/30.22
% 29.92/30.22 ============================== PROCESS INITIAL CLAUSES ===============
% 29.92/30.22
% 29.92/30.22 ============================== PREDICATE ELIMINATION =================
% 29.92/30.22 29 less_or_equal(A,B) | -less(A,B) # label(less_or_equal) # label(axiom). [clausify(11)].
% 29.92/30.22 30 -less_or_equal(A,B) | less(A,B) | B = A # label(less_or_equal) # label(axiom). [clausify(11)].
% 29.92/30.22 31 less_or_equal(A,B) | B != A # label(less_or_equal) # label(axiom). [clausify(11)].
% 29.92/30.22 32 -sum(A,n1,B) | -less(C,B) | less_or_equal(C,A) # label(less_successor) # label(axiom). [clausify(12)].
% 29.92/30.22 Derived: -sum(A,n1,B) | -less(C,B) | less(C,A) | A = C. [resolve(32,c,30,a)].
% 29.92/30.22
% 29.92/30.22 ============================== end predicate elimination =============
% 29.92/30.22
% 29.92/30.22 Auto_denials: (non-Horn, no changes).
% 29.92/30.22
% 29.92/30.22 Term ordering decisions:
% 29.92/30.22 Function symbol KB weights: n1=1. n0=1. n2=1. n3=1. n4=1. n5=1. n6=1. n7=1. n8=1. n9=1. n10=1. n100=1. n101=1. n102=1. n103=1. n104=1. n105=1. n106=1. n107=1. n108=1. n109=1. n11=1. n110=1. n111=1. n112=1. n113=1. n114=1. n115=1. n116=1. n117=1. n118=1. n119=1. n12=1. n120=1. n121=1. n122=1. n123=1. n124=1. n125=1. n126=1. n127=1. n13=1. n14=1. n15=1. n16=1. n17=1. n18=1. n19=1. n20=1. n21=1. n22=1. n23=1. n24=1. n25=1. n26=1. n27=1. n28=1. n29=1. n30=1. n31=1. n32=1. n33=1. n34=1. n35=1. n36=1. n37=1. n38=1. n39=1. n40=1. n41=1. n42=1. n43=1. n44=1. n45=1. n46=1. n47=1. n48=1. n49=1. n50=1. n51=1. n52=1. n53=1. n54=1. n55=1. n56=1. n57=1. n58=1. n59=1. n60=1. n61=1. n62=1. n63=1. n64=1. n65=1. n66=1. n67=1. n68=1. n69=1. n70=1. n71=1. n72=1. n73=1. n74=1. n75=1. n76=1. n77=1. n78=1. n79=1. n80=1. n81=1. n82=1. n83=1. n84=1. n85=1. n86=1. n87=1. n88=1. n89=1. n90=1. n91=1. n92=1. n93=1. n94=1. n95=1. n96=1. n97=1. n98=1. n99=1. nn1=1. nn10=1. nn100=1. nn101=1. nn102=1. nn103=1. nn104=1. nn105=1. nn106=1. nn107=1. nn108=1. nn109=1. nn11=1. nn110=1. nn111=1. nn112=1. nn113=1. nn114=1. nn115=1. nn116=1. nn117=1. nn118=1. nn119=1. nn12=1. nn120=1. nn121=1. nn122=1. nn123=1. nn124=1. nn125=1. nn126=1. nn127=1. nn128=1. nn13=1. nn14=1. nn15=1. nn16=1. nn17=1. nn18=1. nn19=1. nn2=1. nn20=1. nn21=1. nn22=1. nn23=1. nn24=1. nn25=1. nn26=1. nn27=1. nn28=1. nn29=1. nn3=1. nn30=1. nn31=1. nn32=1. nn33=1. nn34=1. nn35=1. nn36=1. nn37=1. nn38=1. nn39=1. nn4=1. nn40=1. nn41=1. nn42=1. nn43=1. nn44=1. nn45=1. nn46=1. nn47=1. nn48=1. nn49=1. nn5=1. nn50=1. nn51=1. nn52=1. nn53=1. nn54=1. nn55=1. nn56=1. nn57=1. nn58=1. nn59=1. nn6=1. nn60=1. nn61=1. nn62=1. nn63=1. nn64=1. nn65=1. nn66=1. nn67=1. nn68=1. nn69=1. nn7=1. nn70=1. nn71=1. nn72=1. nn73=1. nn74=1. nn75=1. nn76=1. nn77=1. nn78=1. nn79=1. nn8=1. nn80=1. nn81=1. nn82=1. nn83=1. nn84=1. nn85=1. nn86=1. nn87=1. nn88=1. nn89=1. nn9=1. nn90=1. nn91=1. nn92=1. nn93=1. nn94=1. nn95=1. nn96=1. nn97=1. nn98=1. nn99=1. rdn=1. rdnn=1. rdn_neg=1. rdn_pos=1.
% 29.92/30.22
% 29.92/30.22 ============================== end of process initial clauses ========
% 29.92/30.22
% 29.92/30.22 ============================== CLAUSES FOR SEARCH ====================
% 29.92/30.22
% 29.92/30.22 ============================== end of clauses for search =============
% 29.92/30.22
% 29.92/30.22 ============================== SEARCH ================================
% 29.92/30.22
% 29.92/30.22 % Starting search at 0.12 seconds.
% 29.92/30.22
% 29.92/30.22 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.35 sec).
% 29.92/30.22
% 29.92/30.22 Low Water (keep): wt=3.000, iters=3357
% 29.92/30.22
% 29.92/30.22 ============================== PROOF =================================
% 29.92/30.22 % SZS status Theorem
% 29.92/30.22 % SZS output start Refutation
% 29.92/30.22
% 29.92/30.22 % Proof 1 at 29.00 (+ 0.09) seconds.
% 29.92/30.22 % Length of proof is 28.
% 29.92/30.22 % Level of proof is 9.
% 29.92/30.22 % Maximum clause weight is 27.000.
% 29.92/30.22 % Given clauses 29025.
% 29.92/30.22
% 29.92/30.22 13 (all X all Y all Z all RDN_X all RDN_Y all RDN_Z (rdn_translate(X,rdn_pos(RDN_X)) & rdn_translate(Y,rdn_pos(RDN_Y)) & rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z) & rdn_translate(Z,rdn_pos(RDN_Z)) -> sum(X,Y,Z))) # label(sum_entry_point_pos_pos) # label(axiom) # label(non_clause). [assumption].
% 29.92/30.22 22 (all X all Y all Z (sum(Y,Z,X) <-> difference(X,Y,Z))) # label(minus_entry_point) # label(axiom) # label(non_clause). [assumption].
% 29.92/30.22 23 (all C all D1 all D2 all RD all ID (rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) & rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)) -> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)))) # label(add_digit_digit_digit) # label(axiom) # label(non_clause). [assumption].
% 29.92/30.22 28 -(exists X exists Y (sum(X,Y,n8) & difference(X,Y,n0))) # label(sum_and_difference) # label(negated_conjecture) # label(non_clause). [assumption].
% 29.92/30.22 33 rdn_translate(n0,rdn_pos(rdnn(n0))) # label(rdn0) # label(axiom). [assumption].
% 29.92/30.22 37 rdn_translate(n4,rdn_pos(rdnn(n4))) # label(rdn4) # label(axiom). [assumption].
% 29.92/30.22 41 rdn_translate(n8,rdn_pos(rdnn(n8))) # label(rdn8) # label(axiom). [assumption].
% 29.92/30.22 319 -rdn_translate(A,rdn_pos(B)) | -rdn_translate(C,rdn_pos(D)) | -rdn_add_with_carry(rdnn(n0),B,D,E) | -rdn_translate(F,rdn_pos(E)) | sum(A,C,F) # label(sum_entry_point_pos_pos) # label(axiom). [clausify(13)].
% 29.92/30.22 328 -sum(A,B,C) | difference(C,A,B) # label(minus_entry_point) # label(axiom). [clausify(22)].
% 29.92/30.22 330 -rdn_digit_add(rdnn(A),rdnn(B),rdnn(C),rdnn(n0)) | -rdn_digit_add(rdnn(C),rdnn(D),rdnn(E),rdnn(n0)) | rdn_add_with_carry(rdnn(D),rdnn(A),rdnn(B),rdnn(E)) # label(add_digit_digit_digit) # label(axiom). [clausify(23)].
% 29.92/30.22 375 rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)) # label(rdn_digit_add_n4_n0_n4_n0) # label(axiom). [assumption].
% 29.92/30.22 379 rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)) # label(rdn_digit_add_n4_n4_n8_n0) # label(axiom). [assumption].
% 29.92/30.22 415 rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)) # label(rdn_digit_add_n8_n0_n8_n0) # label(axiom). [assumption].
% 29.92/30.22 435 -sum(A,B,n8) | -difference(A,B,n0) # label(sum_and_difference) # label(negated_conjecture). [clausify(28)].
% 29.92/30.22 440 -rdn_translate(A,rdn_pos(B)) | -rdn_add_with_carry(rdnn(n0),B,B,C) | -rdn_translate(D,rdn_pos(C)) | sum(A,A,D). [factor(319,a,b)].
% 29.92/30.22 441 -rdn_translate(A,rdn_pos(B)) | -rdn_translate(C,rdn_pos(D)) | -rdn_add_with_carry(rdnn(n0),B,D,B) | sum(A,C,A). [factor(319,a,d)].
% 29.92/30.22 448 -rdn_digit_add(rdnn(A),rdnn(B),rdnn(A),rdnn(n0)) | rdn_add_with_carry(rdnn(B),rdnn(A),rdnn(B),rdnn(A)). [factor(330,a,b)].
% 29.92/30.22 1246 -rdn_digit_add(rdnn(n8),rdnn(A),rdnn(B),rdnn(n0)) | rdn_add_with_carry(rdnn(A),rdnn(n4),rdnn(n4),rdnn(B)). [resolve(379,a,330,a)].
% 29.92/30.22 1400 rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)). [resolve(448,a,375,a)].
% 29.92/30.22 13101 rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)). [resolve(1246,a,415,a)].
% 29.92/30.22 14156 -rdn_translate(A,rdn_pos(rdnn(n4))) | -rdn_translate(B,rdn_pos(rdnn(n0))) | sum(A,B,A). [resolve(1400,a,441,c)].
% 29.92/30.22 17335 -rdn_translate(A,rdn_pos(rdnn(n4))) | -rdn_translate(B,rdn_pos(rdnn(n8))) | sum(A,A,B). [resolve(13101,a,440,b)].
% 29.92/30.22 25326 -rdn_translate(A,rdn_pos(rdnn(n0))) | sum(n4,A,n4). [resolve(14156,a,37,a)].
% 29.92/30.22 25328 sum(n4,n0,n4). [resolve(25326,a,33,a)].
% 29.92/30.22 25331 difference(n4,n4,n0). [resolve(25328,a,328,a)].
% 29.92/30.22 25336 -sum(n4,n4,n8). [resolve(25331,a,435,b)].
% 29.92/30.22 36917 -rdn_translate(A,rdn_pos(rdnn(n8))) | sum(n4,n4,A). [resolve(17335,a,37,a)].
% 29.92/30.22 36919 $F. [resolve(36917,a,41,a),unit_del(a,25336)].
% 29.92/30.22
% 29.92/30.22 % SZS output end Refutation
% 29.92/30.22 ============================== end of proof ==========================
% 29.92/30.22
% 29.92/30.22 ============================== STATISTICS ============================
% 29.92/30.22
% 29.92/30.22 Given=29025. Generated=108375. Kept=36886. proofs=1.
% 29.92/30.22 Usable=28971. Sos=7859. Demods=0. Limbo=0, Disabled=464. Hints=0.
% 29.92/30.22 Megabytes=86.03.
% 29.92/30.22 User_CPU=29.00, System_CPU=0.09, Wall_clock=29.
% 29.92/30.22
% 29.92/30.22 ============================== end of statistics =====================
% 29.92/30.22
% 29.92/30.22 ============================== end of search =========================
% 29.92/30.22
% 29.92/30.22 THEOREM PROVED
% 29.92/30.22 % SZS status Theorem
% 29.92/30.22
% 29.92/30.22 Exiting with 1 proof.
% 29.92/30.22
% 29.92/30.22 Process 29011 exit (max_proofs) Thu Jul 7 09:42:04 2022
% 29.96/30.22 Prover9 interrupted
%------------------------------------------------------------------------------