TSTP Solution File: KLE034+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE034+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 02:21:53 EDT 2022
% Result : Theorem 2.49s 2.77s
% Output : Refutation 2.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE034+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 11:54:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/0.97 ============================== Prover9 ===============================
% 0.71/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.71/0.97 Process 31882 was started by sandbox on n005.cluster.edu,
% 0.71/0.97 Thu Jun 16 11:54:09 2022
% 0.71/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31729_n005.cluster.edu".
% 0.71/0.97 ============================== end of head ===========================
% 0.71/0.97
% 0.71/0.97 ============================== INPUT =================================
% 0.71/0.97
% 0.71/0.97 % Reading from file /tmp/Prover9_31729_n005.cluster.edu
% 0.71/0.97
% 0.71/0.97 set(prolog_style_variables).
% 0.71/0.97 set(auto2).
% 0.71/0.97 % set(auto2) -> set(auto).
% 0.71/0.97 % set(auto) -> set(auto_inference).
% 0.71/0.97 % set(auto) -> set(auto_setup).
% 0.71/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.71/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/0.97 % set(auto) -> set(auto_limits).
% 0.71/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/0.97 % set(auto) -> set(auto_denials).
% 0.71/0.97 % set(auto) -> set(auto_process).
% 0.71/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.71/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.71/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.71/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.71/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.71/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.71/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.71/0.97 % set(auto2) -> assign(stats, some).
% 0.71/0.97 % set(auto2) -> clear(echo_input).
% 0.71/0.97 % set(auto2) -> set(quiet).
% 0.71/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.71/0.97 % set(auto2) -> clear(print_given).
% 0.71/0.97 assign(lrs_ticks,-1).
% 0.71/0.97 assign(sos_limit,10000).
% 0.71/0.97 assign(order,kbo).
% 0.71/0.97 set(lex_order_vars).
% 0.71/0.97 clear(print_given).
% 0.71/0.97
% 0.71/0.97 % formulas(sos). % not echoed (19 formulas)
% 0.71/0.97
% 0.71/0.97 ============================== end of input ==========================
% 0.71/0.97
% 0.71/0.97 % From the command line: assign(max_seconds, 300).
% 0.71/0.97
% 0.71/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/0.97
% 0.71/0.97 % Formulas that are not ordinary clauses:
% 0.71/0.97 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 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].
% 0.71/0.97 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 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].
% 0.71/0.97 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 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].
% 0.71/0.97 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].
% 0.71/0.97 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 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].
% 1.90/2.15 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 1.90/2.15 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 1.90/2.15 17 (all X0 all X1 (test(X0) & test(X1) -> c(addition(X0,X1)) = multiplication(c(X0),c(X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption].
% 1.90/2.15 18 (all X0 all X1 (test(X0) & test(X1) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption].
% 1.90/2.15 19 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X2) & test(X4) & leq(multiplication(multiplication(X2,X0),c(X3)),zero) & leq(multiplication(multiplication(X3,X1),c(X4)),zero) -> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.90/2.15
% 1.90/2.15 ============================== end of process non-clausal formulas ===
% 1.90/2.15
% 1.90/2.15 ============================== PROCESS INITIAL CLAUSES ===============
% 1.90/2.15
% 1.90/2.15 ============================== PREDICATE ELIMINATION =================
% 1.90/2.15 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 1.90/2.15 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 1.90/2.15 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 1.90/2.15 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 1.90/2.15 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 1.90/2.15 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 1.90/2.15 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 1.90/2.15 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 1.90/2.15 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 1.90/2.15 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 1.90/2.15 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 1.90/2.16 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 1.90/2.16 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 1.90/2.16 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 1.90/2.16 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 1.90/2.16 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 1.90/2.16 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 1.90/2.16 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 1.90/2.16
% 1.90/2.16 ============================== end predicate elimination =============
% 1.90/2.16
% 1.90/2.16 Auto_denials: (non-Horn, no changes).
% 1.90/2.16
% 1.90/2.16 Term ordering decisions:
% 1.90/2.16 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. c=1. f1=1.
% 1.90/2.16
% 1.90/2.16 ============================== end of process initial clauses ========
% 1.90/2.16
% 1.90/2.16 ============================== CLAUSES FOR SEARCH ====================
% 1.90/2.16
% 1.90/2.16 ============================== end of clauses for search =============
% 1.90/2.16
% 1.90/2.16 ============================== SEARCH ================================
% 1.90/2.16
% 1.90/2.16 % Starting search at 0.02 seconds.
% 1.90/2.16
% 1.90/2.16 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 86 (0.00 of 0.70 sec).
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=49.000, iters=3333
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=45.000, iters=3368
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=41.000, iters=3370
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=40.000, iters=3373
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=39.000, iters=3341
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=38.000, iters=3525
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=35.000, iters=3433
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=34.000, iters=3413
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=33.000, iters=3382
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=32.000, iters=3361
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=31.000, iters=3380
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=29.000, iters=3370
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=28.000, iters=3363
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=27.000, iters=3335
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=26.000, iters=3341
% 1.90/2.16
% 1.90/2.16 Low Water (keep): wt=25.000, iters=3340
% 2.49/2.77
% 2.49/2.77 Low Water (keep): wt=24.000, iters=3347
% 2.49/2.77
% 2.49/2.77 Low Water (keep): wt=23.000, iters=3353
% 2.49/2.77
% 2.49/2.77 Low Water (keep): wt=22.000, iters=3345
% 2.49/2.77
% 2.49/2.77 Low Water (keep): wt=21.000, iters=3338
% 2.49/2.77
% 2.49/2.77 Low Water (keep): wt=20.000, iters=3371
% 2.49/2.77
% 2.49/2.77 ============================== PROOF =================================
% 2.49/2.77 % SZS status Theorem
% 2.49/2.77 % SZS output start Refutation
% 2.49/2.77
% 2.49/2.77 % Proof 1 at 1.77 (+ 0.05) seconds.
% 2.49/2.77 % Length of proof is 90.
% 2.49/2.77 % Level of proof is 14.
% 2.49/2.77 % Maximum clause weight is 19.000.
% 2.49/2.77 % Given clauses 1013.
% 2.49/2.77
% 2.49/2.77 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 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].
% 2.49/2.77 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 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].
% 2.49/2.77 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].
% 2.49/2.77 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 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].
% 2.49/2.77 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 17 (all X0 all X1 (test(X0) & test(X1) -> c(addition(X0,X1)) = multiplication(c(X0),c(X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 18 (all X0 all X1 (test(X0) & test(X1) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption].
% 2.49/2.77 19 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X2) & test(X4) & leq(multiplication(multiplication(X2,X0),c(X3)),zero) & leq(multiplication(multiplication(X3,X1),c(X4)),zero) -> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.49/2.77 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.49/2.77 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.49/2.77 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.49/2.77 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.49/2.77 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.49/2.77 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.49/2.77 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.49/2.77 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.49/2.77 28 test(c4) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.49/2.77 31 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.49/2.77 32 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.49/2.77 33 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.49/2.77 34 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.49/2.77 35 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.49/2.77 36 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.49/2.77 38 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.49/2.77 39 leq(multiplication(multiplication(c3,c1),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.49/2.77 40 leq(multiplication(multiplication(c4,c2),c(c5)),zero) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.49/2.77 43 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.49/2.77 44 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.49/2.77 45 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(44),flip(a)].
% 2.49/2.77 46 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.49/2.77 47 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(46),flip(a)].
% 2.49/2.77 48 -leq(multiplication(multiplication(multiplication(c3,c1),c2),c(c5)),zero) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.49/2.77 49 -leq(multiplication(c3,multiplication(c1,multiplication(c2,c(c5)))),zero). [copy(48),rewrite([43(5),43(8),43(7)])].
% 2.49/2.77 50 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.49/2.77 51 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.49/2.77 52 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 2.49/2.77 53 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(52),flip(c)].
% 2.49/2.77 54 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 2.49/2.77 55 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(54),flip(c)].
% 2.49/2.77 56 multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 2.49/2.77 57 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 2.49/2.77 58 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 2.49/2.77 62 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 2.49/2.77 63 -test(A) | c(A) != B | addition(A,B) = one. [copy(62),rewrite([38(4)])].
% 2.49/2.77 64 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 2.49/2.77 65 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 2.49/2.77 67 leq(multiplication(c4,multiplication(c2,c(c5))),zero). [back_rewrite(40),rewrite([43(6)])].
% 2.49/2.77 68 leq(multiplication(c3,multiplication(c1,c(c4))),zero). [back_rewrite(39),rewrite([43(6)])].
% 2.49/2.77 69 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(53,a,b),rewrite([32(5)])].
% 2.49/2.77 74 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(31(a,1),45(a,2,2)),rewrite([35(3),38(3)])].
% 2.49/2.77 75 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(33(a,1),45(a,1,1)),rewrite([38(4)]),flip(a)].
% 2.49/2.77 77 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(43(a,1),47(a,1,1)),rewrite([38(6)])].
% 2.49/2.77 80 multiplication(c3,multiplication(c1,multiplication(c2,c(c5)))) != zero. [ur(51,a,49,a),rewrite([38(10),74(10)])].
% 2.49/2.77 95 -test(A) | addition(c(A),c(c4)) = c(multiplication(c4,A)). [resolve(55,a,28,a),rewrite([38(5)])].
% 2.49/2.77 103 multiplication(c4,f1(c4)) = zero. [resolve(56,b,28,a)].
% 2.49/2.77 111 addition(c4,f1(c4)) = one. [resolve(58,b,28,a)].
% 2.49/2.77 127 c(c4) != A | addition(A,c4) = one. [resolve(63,a,28,a),rewrite([38(5)])].
% 2.49/2.77 131 test(one). [resolve(65,c,31,a),rewrite([35(3),33(6)]),xx(a),xx(b)].
% 2.49/2.77 145 multiplication(c4,multiplication(c2,c(c5))) = zero. [resolve(67,a,50,a),rewrite([38(8),74(8)])].
% 2.49/2.77 146 multiplication(c3,multiplication(c1,c(c4))) = zero. [resolve(68,a,50,a),rewrite([38(8),74(8)])].
% 2.49/2.77 150 multiplication(c(c4),c(c4)) = c(c4). [resolve(69,a,28,a)].
% 2.49/2.77 164 addition(one,f1(one)) = one. [resolve(131,a,58,b)].
% 2.49/2.77 165 f1(one) = zero. [resolve(131,a,57,b),rewrite([33(4)])].
% 2.49/2.77 169 addition(zero,one) = one. [back_rewrite(164),rewrite([165(3),38(3)])].
% 2.49/2.77 170 -test(zero) | c(zero) = one. [para(165(a,1),64(a,1)),rewrite([165(4)]),unit_del(c,131)].
% 2.49/2.77 175 test(zero). [resolve(169,a,65,c),rewrite([33(3),35(6)]),xx(a),xx(b)].
% 2.49/2.77 177 c(zero) = one. [back_unit_del(170),unit_del(a,175)].
% 2.49/2.77 241 multiplication(c4,addition(A,f1(c4))) = multiplication(c4,A). [para(103(a,1),45(a,1,1)),rewrite([74(4),38(6)]),flip(a)].
% 2.49/2.77 243 addition(zero,c4) = c4. [para(103(a,1),75(a,2,2)),rewrite([38(5),241(6),33(3),38(4)]),flip(a)].
% 2.49/2.77 246 multiplication(addition(c4,multiplication(A,B)),f1(c4)) = multiplication(A,multiplication(B,f1(c4))). [para(103(a,1),77(a,1,2)),rewrite([38(6),74(6)]),flip(a)].
% 2.49/2.77 705 addition(one,c(c4)) = one. [resolve(95,a,175,a),rewrite([177(2),35(7),177(6)])].
% 2.49/2.77 768 addition(A,multiplication(c(c4),A)) = A. [para(705(a,1),47(a,2,1)),rewrite([34(2),34(6)])].
% 2.49/2.77 787 multiplication(addition(c4,multiplication(A,B)),multiplication(c2,c(c5))) = multiplication(A,multiplication(B,multiplication(c2,c(c5)))). [para(145(a,1),77(a,1,2)),rewrite([38(8),74(8)]),flip(a)].
% 2.49/2.77 788 multiplication(c3,multiplication(c1,multiplication(c(c4),A))) = zero. [para(146(a,1),43(a,1,1)),rewrite([36(2),43(7)]),flip(a)].
% 2.49/2.77 813 multiplication(c(c4),multiplication(c(c4),A)) = multiplication(c(c4),A). [para(150(a,1),43(a,1,1)),flip(a)].
% 2.49/2.77 1473 addition(c4,c(c4)) = one. [resolve(127,a,768,a(flip)),rewrite([150(7),32(5),38(4)])].
% 2.49/2.77 6712 multiplication(c(c4),f1(c4)) = f1(c4). [para(150(a,1),246(a,1,1,2)),rewrite([1473(4),34(4),813(10)]),flip(a)].
% 2.49/2.77 6840 multiplication(c(c4),multiplication(f1(c4),A)) = multiplication(f1(c4),A). [para(6712(a,1),43(a,1,1)),flip(a)].
% 2.49/2.77 9827 multiplication(c3,multiplication(c1,f1(c4))) = zero. [para(6712(a,1),788(a,1,2,2))].
% 2.49/2.77 13411 multiplication(f1(c4),multiplication(c2,c(c5))) = multiplication(c2,c(c5)). [para(6712(a,1),787(a,1,1,2)),rewrite([111(4),34(6),6840(14)]),flip(a)].
% 2.49/2.77 13416 $F. [para(9827(a,1),787(a,1,1,2)),rewrite([38(3),243(3),145(6),43(11),13411(10)]),flip(a),unit_del(a,80)].
% 2.49/2.77
% 2.49/2.77 % SZS output end Refutation
% 2.49/2.77 ============================== end of proof ==========================
% 2.49/2.77
% 2.49/2.77 ============================== STATISTICS ============================
% 2.49/2.77
% 2.49/2.77 Given=1013. Generated=77628. Kept=13381. proofs=1.
% 2.49/2.77 Usable=792. Sos=9596. Demods=3228. Limbo=19, Disabled=3014. Hints=0.
% 2.49/2.77 Megabytes=13.13.
% 2.49/2.77 User_CPU=1.77, System_CPU=0.05, Wall_clock=2.
% 2.49/2.77
% 2.49/2.77 ============================== end of statistics =====================
% 2.49/2.77
% 2.49/2.77 ============================== end of search =========================
% 2.49/2.77
% 2.49/2.77 THEOREM PROVED
% 2.49/2.77 % SZS status Theorem
% 2.49/2.77
% 2.49/2.77 Exiting with 1 proof.
% 2.49/2.77
% 2.49/2.77 Process 31882 exit (max_proofs) Thu Jun 16 11:54:11 2022
% 2.49/2.77 Prover9 interrupted
%------------------------------------------------------------------------------