TSTP Solution File: KLE017+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 : Sun Jul 17 02:21:44 EDT 2022
% Result : Theorem 1.51s 1.81s
% Output : Refutation 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 16 10:15:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.44/0.97 ============================== Prover9 ===============================
% 0.44/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.44/0.97 Process 4541 was started by sandbox on n021.cluster.edu,
% 0.44/0.97 Thu Jun 16 10:16:00 2022
% 0.44/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4387_n021.cluster.edu".
% 0.44/0.97 ============================== end of head ===========================
% 0.44/0.97
% 0.44/0.97 ============================== INPUT =================================
% 0.44/0.97
% 0.44/0.97 % Reading from file /tmp/Prover9_4387_n021.cluster.edu
% 0.44/0.97
% 0.44/0.97 set(prolog_style_variables).
% 0.44/0.97 set(auto2).
% 0.44/0.97 % set(auto2) -> set(auto).
% 0.44/0.97 % set(auto) -> set(auto_inference).
% 0.44/0.97 % set(auto) -> set(auto_setup).
% 0.44/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.44/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/0.97 % set(auto) -> set(auto_limits).
% 0.44/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/0.97 % set(auto) -> set(auto_denials).
% 0.44/0.97 % set(auto) -> set(auto_process).
% 0.44/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.44/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.44/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.44/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.44/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.44/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.44/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.44/0.97 % set(auto2) -> assign(stats, some).
% 0.44/0.97 % set(auto2) -> clear(echo_input).
% 0.44/0.97 % set(auto2) -> set(quiet).
% 0.44/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.44/0.97 % set(auto2) -> clear(print_given).
% 0.44/0.97 assign(lrs_ticks,-1).
% 0.44/0.97 assign(sos_limit,10000).
% 0.44/0.97 assign(order,kbo).
% 0.44/0.97 set(lex_order_vars).
% 0.44/0.97 clear(print_given).
% 0.44/0.97
% 0.44/0.97 % formulas(sos). % not echoed (17 formulas)
% 0.44/0.97
% 0.44/0.97 ============================== end of input ==========================
% 0.44/0.97
% 0.44/0.97 % From the command line: assign(max_seconds, 300).
% 0.44/0.97
% 0.44/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/0.97
% 0.44/0.97 % Formulas that are not ordinary clauses:
% 0.44/0.97 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.97 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 17 -(all X0 all X1 all X2 (test(X0) & test(X1) & test(X2) -> (leq(X2,multiplication(X0,X1)) <-> leq(X2,X0) & leq(X2,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.51/1.81
% 1.51/1.81 ============================== end of process non-clausal formulas ===
% 1.51/1.81
% 1.51/1.81 ============================== PROCESS INITIAL CLAUSES ===============
% 1.51/1.81
% 1.51/1.81 ============================== PREDICATE ELIMINATION =================
% 1.51/1.81 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 1.51/1.81 19 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 20 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 21 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 22 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 1.51/1.81 23 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 1.51/1.81 Derived: complement(f1(c1),c1). [resolve(18,a,19,a)].
% 1.51/1.81 Derived: complement(f1(c2),c2). [resolve(18,a,20,a)].
% 1.51/1.81 Derived: complement(f1(c3),c3). [resolve(18,a,21,a)].
% 1.51/1.81 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,22,a)].
% 1.51/1.81 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,23,a)].
% 1.51/1.81 24 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 1.51/1.81 Derived: c(c1) != A | complement(c1,A). [resolve(24,a,19,a)].
% 1.51/1.81 Derived: c(c2) != A | complement(c2,A). [resolve(24,a,20,a)].
% 1.51/1.81 Derived: c(c3) != A | complement(c3,A). [resolve(24,a,21,a)].
% 1.51/1.81 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(24,a,22,a)].
% 1.51/1.81 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(24,a,23,a)].
% 1.51/1.81 25 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 1.51/1.81 Derived: c(c1) = A | -complement(c1,A). [resolve(25,a,19,a)].
% 1.51/1.81 Derived: c(c2) = A | -complement(c2,A). [resolve(25,a,20,a)].
% 1.51/1.81 Derived: c(c3) = A | -complement(c3,A). [resolve(25,a,21,a)].
% 1.51/1.81 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(25,a,22,a)].
% 1.51/1.81 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(25,a,23,a)].
% 1.51/1.81
% 1.51/1.81 ============================== end predicate elimination =============
% 1.51/1.81
% 1.51/1.81 Auto_denials: (non-Horn, no changes).
% 1.51/1.81
% 1.51/1.81 Term ordering decisions:
% 1.51/1.81 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. c=1. f1=1.
% 1.51/1.81
% 1.51/1.81 ============================== end of process initial clauses ========
% 1.51/1.81
% 1.51/1.81 ============================== CLAUSES FOR SEARCH ====================
% 1.51/1.81
% 1.51/1.81 ============================== end of clauses for search =============
% 1.51/1.81
% 1.51/1.81 ============================== SEARCH ================================
% 1.51/1.81
% 1.51/1.81 % Starting search at 0.01 seconds.
% 1.51/1.81
% 1.51/1.81 Low Water (keep): wt=29.000, iters=3627
% 1.51/1.81
% 1.51/1.81 Low Water (keep): wt=28.000, iters=3506
% 1.51/1.81
% 1.51/1.81 ============================== PROOF =================================
% 1.51/1.81 % SZS status Theorem
% 1.51/1.81 % SZS output start Refutation
% 1.51/1.81
% 1.51/1.81 % Proof 1 at 0.83 (+ 0.02) seconds.
% 1.51/1.81 % Length of proof is 103.
% 1.51/1.81 % Level of proof is 16.
% 1.51/1.81 % Maximum clause weight is 20.000.
% 1.51/1.81 % Given clauses 449.
% 1.51/1.81
% 1.51/1.81 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.81 17 -(all X0 all X1 all X2 (test(X0) & test(X1) & test(X2) -> (leq(X2,multiplication(X0,X1)) <-> leq(X2,X0) & leq(X2,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.51/1.81 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 1.51/1.81 19 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 20 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 21 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 24 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 1.51/1.81 26 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 1.51/1.81 27 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 1.51/1.81 28 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.51/1.81 29 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.51/1.81 30 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 1.51/1.81 32 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.51/1.81 33 leq(c3,multiplication(c1,c2)) | leq(c3,c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 34 leq(c3,multiplication(c1,c2)) | leq(c3,c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 35 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 1.51/1.81 36 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(35),rewrite([32(2)]),flip(a)].
% 1.51/1.81 37 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 1.51/1.81 38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 1.51/1.81 39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(38),flip(a)].
% 1.51/1.81 40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 1.51/1.81 41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(40),flip(a)].
% 1.51/1.81 42 -leq(c3,multiplication(c1,c2)) | -leq(c3,c1) | -leq(c3,c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 1.51/1.81 43 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 1.51/1.81 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 1.51/1.81 45 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 1.51/1.81 46 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 1.51/1.81 47 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 1.51/1.81 48 -complement(A,B) | addition(A,B) = one. [copy(47),rewrite([32(2)])].
% 1.51/1.81 51 complement(f1(c1),c1). [resolve(18,a,19,a)].
% 1.51/1.81 52 complement(f1(c2),c2). [resolve(18,a,20,a)].
% 1.51/1.81 53 complement(f1(c3),c3). [resolve(18,a,21,a)].
% 1.51/1.81 58 c(c3) != A | complement(c3,A). [resolve(24,a,21,a)].
% 1.51/1.81 69 addition(A,addition(A,B)) = addition(A,B). [para(36(a,1),27(a,1)),rewrite([32(1),32(2),36(2,R),27(1),32(3)])].
% 1.51/1.81 70 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(26(a,1),39(a,2,2)),rewrite([30(3),32(3)])].
% 1.51/1.81 71 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(28(a,1),39(a,1,1)),rewrite([32(4)]),flip(a)].
% 1.51/1.81 72 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(29(a,1),41(a,1,1)),rewrite([32(4)]),flip(a)].
% 1.51/1.81 73 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(37(a,1),41(a,1,1)),rewrite([32(6)])].
% 1.51/1.81 75 addition(c3,multiplication(c1,c2)) = multiplication(c1,c2) | leq(c3,c2). [resolve(43,a,34,a)].
% 1.51/1.81 76 addition(c3,multiplication(c1,c2)) = multiplication(c1,c2) | leq(c3,c1). [resolve(43,a,33,a)].
% 1.51/1.81 87 addition(c1,f1(c1)) = one. [resolve(51,a,48,a),rewrite([32(4)])].
% 1.51/1.81 90 addition(c2,f1(c2)) = one. [resolve(52,a,48,a),rewrite([32(4)])].
% 1.51/1.81 93 addition(c3,f1(c3)) = one. [resolve(53,a,48,a),rewrite([32(4)])].
% 1.51/1.81 103 complement(c3,c(c3)). [resolve(58,a,29,a(flip)),rewrite([29(5)])].
% 1.51/1.81 116 leq(A,addition(A,B)). [resolve(69,a,44,b)].
% 1.51/1.81 140 addition(c3,c(c3)) = one. [resolve(103,a,48,a)].
% 1.51/1.81 141 multiplication(c3,c(c3)) = zero. [resolve(103,a,46,a)].
% 1.51/1.81 142 multiplication(c(c3),c3) = zero. [resolve(103,a,45,a)].
% 1.51/1.81 145 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(39(a,1),116(a,2))].
% 1.51/1.81 146 leq(multiplication(A,B),multiplication(addition(A,C),B)). [para(41(a,1),116(a,2))].
% 1.51/1.81 148 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(71(a,2),36(a,2,2)),rewrite([32(2)]),flip(a)].
% 1.51/1.81 175 addition(A,multiplication(addition(B,one),C)) = addition(C,addition(A,multiplication(B,C))). [para(72(a,2),36(a,2,2)),rewrite([32(2)]),flip(a)].
% 1.51/1.81 193 leq(multiplication(A,multiplication(B,C)),multiplication(D,C)) | multiplication(addition(D,multiplication(A,B)),C) != multiplication(D,C). [para(73(a,1),44(b,1))].
% 1.51/1.81 195 leq(multiplication(A,multiplication(B,C)),multiplication(addition(D,multiplication(A,B)),C)). [para(73(a,1),116(a,2))].
% 1.51/1.81 206 addition(one,c1) = one. [para(87(a,1),69(a,1,2)),rewrite([32(3),87(7)])].
% 1.51/1.81 228 addition(A,multiplication(A,c1)) = A. [para(206(a,1),39(a,2,2)),rewrite([28(2),28(5)])].
% 1.51/1.81 229 addition(A,multiplication(c1,A)) = A. [para(206(a,1),41(a,2,1)),rewrite([29(2),29(5)])].
% 1.51/1.81 231 addition(c3,multiplication(c1,c2)) = multiplication(c1,c2) | addition(c2,c3) = c2. [resolve(75,b,43,a),rewrite([32(12)])].
% 1.51/1.81 234 addition(one,c2) = one. [para(90(a,1),69(a,1,2)),rewrite([32(3),90(7)])].
% 1.51/1.81 244 addition(c3,multiplication(c1,c2)) = multiplication(c1,c2) | addition(c1,c3) = c1. [resolve(76,b,43,a),rewrite([32(12)])].
% 1.51/1.81 247 addition(A,multiplication(c2,A)) = A. [para(234(a,1),41(a,2,1)),rewrite([29(2),29(5)])].
% 1.51/1.81 251 addition(one,c3) = one. [para(93(a,1),69(a,1,2)),rewrite([32(3),93(7)])].
% 1.51/1.81 378 multiplication(c3,addition(A,c(c3))) = multiplication(c3,A). [para(141(a,1),39(a,1,1)),rewrite([70(4),32(6)]),flip(a)].
% 1.51/1.81 386 multiplication(addition(A,c(c3)),c3) = multiplication(A,c3). [para(142(a,1),41(a,1,1)),rewrite([70(4),32(5)]),flip(a)].
% 1.51/1.81 476 addition(A,addition(B,multiplication(c1,A))) = addition(A,B). [para(229(a,1),36(a,2,2)),rewrite([32(3),32(5)])].
% 1.51/1.81 533 leq(multiplication(A,c3),A). [para(140(a,1),145(a,2,2)),rewrite([28(4)])].
% 1.51/1.81 2204 multiplication(c3,c3) = c3. [para(140(a,1),378(a,1,2)),rewrite([28(3)]),flip(a)].
% 1.51/1.81 2219 multiplication(c3,multiplication(c3,A)) = multiplication(c3,A). [para(2204(a,1),37(a,1,1)),flip(a)].
% 1.51/1.81 2359 leq(multiplication(A,c3),addition(A,c(c3))). [para(386(a,1),533(a,1))].
% 1.51/1.81 2711 leq(multiplication(A,multiplication(c1,B)),multiplication(A,B)). [para(228(a,1),193(b,1,1)),xx(b)].
% 1.51/1.81 2813 leq(multiplication(c3,multiplication(c1,c3)),c3). [para(2204(a,1),2711(a,2))].
% 1.51/1.81 2820 multiplication(c3,addition(one,multiplication(c1,c3))) = c3. [resolve(2813,a,43,a),rewrite([32(7),71(7,R),32(6)])].
% 1.51/1.81 3008 leq(multiplication(c3,A),multiplication(addition(B,c3),A)). [para(2204(a,1),195(a,2,1,2)),rewrite([2219(4)])].
% 1.51/1.81 4228 addition(one,multiplication(c1,c3)) = one. [para(2820(a,1),72(a,2,2)),rewrite([32(3),251(3),29(7),32(12),476(12),32(8),251(8)])].
% 1.51/1.81 4231 leq(c3,addition(A,c3)). [para(2820(a,1),146(a,1)),rewrite([32(3),4228(8),28(5)])].
% 1.51/1.81 5875 addition(c2,c3) = c2. [para(231(a,1),175(a,2,2)),rewrite([32(9),206(9),29(9),32(8),229(13)]),merge(b)].
% 1.51/1.81 5880 leq(c3,c2). [para(5875(a,1),4231(a,2))].
% 1.51/1.81 5881 leq(multiplication(c3,A),multiplication(c2,A)). [para(5875(a,1),3008(a,2,1))].
% 1.51/1.81 5882 -leq(c3,multiplication(c1,c2)) | -leq(c3,c1). [back_unit_del(42),unit_del(c,5880)].
% 1.51/1.81 5891 leq(c3,multiplication(c2,c3)). [para(2204(a,1),5881(a,1))].
% 1.51/1.81 5902 addition(c1,c3) = c1. [para(244(a,1),148(a,2,2)),rewrite([32(10),234(10),28(9),32(8),71(13,R),32(12),234(12),28(11)]),merge(b)].
% 1.51/1.81 5903 multiplication(c2,c3) = c3. [resolve(5891,a,43,a),rewrite([247(5)]),flip(a)].
% 1.51/1.81 5914 leq(c3,c1). [para(5902(a,1),4231(a,2))].
% 1.51/1.81 5916 -leq(c3,multiplication(c1,c2)). [back_unit_del(5882),unit_del(b,5914)].
% 1.51/1.81 5931 leq(c3,addition(c2,c(c3))). [para(5903(a,1),2359(a,1))].
% 1.51/1.81 5940 addition(c3,multiplication(c1,c2)) != multiplication(c1,c2). [ur(44,a,5916,a)].
% 1.51/1.81 5950 addition(c2,c(c3)) = one. [resolve(5931,a,43,a),rewrite([36(6,R),32(5),140(5),32(3),234(3)]),flip(a)].
% 1.51/1.81 6111 multiplication(c3,c2) = c3. [para(5950(a,1),378(a,1,2)),rewrite([28(3)]),flip(a)].
% 1.51/1.81 6117 addition(c3,multiplication(A,c2)) = multiplication(addition(A,c3),c2). [para(6111(a,1),41(a,1,1)),rewrite([32(6)])].
% 1.51/1.81 6143 $F. [back_rewrite(5940),rewrite([6117(5),5902(3)]),xx(a)].
% 1.51/1.81
% 1.51/1.81 % SZS output end Refutation
% 1.51/1.81 ============================== end of proof ==========================
% 1.51/1.81
% 1.51/1.81 ============================== STATISTICS ============================
% 1.51/1.81
% 1.51/1.81 Given=449. Generated=24246. Kept=6112. proofs=1.
% 1.51/1.81 Usable=376. Sos=5173. Demods=1080. Limbo=26, Disabled=580. Hints=0.
% 1.51/1.81 Megabytes=7.65.
% 1.51/1.81 User_CPU=0.83, System_CPU=0.02, Wall_clock=1.
% 1.51/1.81
% 1.51/1.81 ============================== end of statistics =====================
% 1.51/1.81
% 1.51/1.81 ============================== end of search =========================
% 1.51/1.81
% 1.51/1.81 THEOREM PROVED
% 1.51/1.81 % SZS status Theorem
% 1.51/1.81
% 1.51/1.81 Exiting with 1 proof.
% 1.51/1.81
% 1.51/1.81 Process 4541 exit (max_proofs) Thu Jun 16 10:16:01 2022
% 1.51/1.81 Prover9 interrupted
%------------------------------------------------------------------------------