TSTP Solution File: KLE013+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 02:21:43 EDT 2022
% Result : Theorem 63.00s 63.30s
% Output : Refutation 63.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 08:10:17 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.76/1.01 ============================== Prover9 ===============================
% 0.76/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.01 Process 30079 was started by sandbox2 on n022.cluster.edu,
% 0.76/1.01 Thu Jun 16 08:10:18 2022
% 0.76/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29926_n022.cluster.edu".
% 0.76/1.01 ============================== end of head ===========================
% 0.76/1.01
% 0.76/1.01 ============================== INPUT =================================
% 0.76/1.01
% 0.76/1.01 % Reading from file /tmp/Prover9_29926_n022.cluster.edu
% 0.76/1.01
% 0.76/1.01 set(prolog_style_variables).
% 0.76/1.01 set(auto2).
% 0.76/1.01 % set(auto2) -> set(auto).
% 0.76/1.01 % set(auto) -> set(auto_inference).
% 0.76/1.01 % set(auto) -> set(auto_setup).
% 0.76/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.01 % set(auto) -> set(auto_limits).
% 0.76/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.01 % set(auto) -> set(auto_denials).
% 0.76/1.01 % set(auto) -> set(auto_process).
% 0.76/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.01 % set(auto2) -> assign(stats, some).
% 0.76/1.01 % set(auto2) -> clear(echo_input).
% 0.76/1.01 % set(auto2) -> set(quiet).
% 0.76/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.01 % set(auto2) -> clear(print_given).
% 0.76/1.01 assign(lrs_ticks,-1).
% 0.76/1.01 assign(sos_limit,10000).
% 0.76/1.01 assign(order,kbo).
% 0.76/1.01 set(lex_order_vars).
% 0.76/1.01 clear(print_given).
% 0.76/1.01
% 0.76/1.01 % formulas(sos). % not echoed (17 formulas)
% 0.76/1.01
% 0.76/1.01 ============================== end of input ==========================
% 0.76/1.01
% 0.76/1.01 % From the command line: assign(max_seconds, 300).
% 0.76/1.01
% 0.76/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.01
% 0.76/1.01 % Formulas that are not ordinary clauses:
% 0.76/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 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].
% 0.76/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 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].
% 0.76/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 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].
% 0.76/1.01 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].
% 0.76/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.01 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].
% 2.88/3.16 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.88/3.16 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.88/3.16 17 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(X0,X1),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.88/3.16
% 2.88/3.16 ============================== end of process non-clausal formulas ===
% 2.88/3.16
% 2.88/3.16 ============================== PROCESS INITIAL CLAUSES ===============
% 2.88/3.16
% 2.88/3.16 ============================== PREDICATE ELIMINATION =================
% 2.88/3.16 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.88/3.16 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.88/3.16 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.88/3.16 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.88/3.16 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.88/3.16 Derived: complement(f1(c2),c2). [resolve(18,a,19,a)].
% 2.88/3.16 Derived: complement(f1(c1),c1). [resolve(18,a,20,a)].
% 2.88/3.16 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 2.88/3.16 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 2.88/3.16 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.88/3.16 Derived: c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 2.88/3.16 Derived: c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 2.88/3.16 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 2.88/3.16 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 2.88/3.16 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.88/3.16 Derived: c(c2) = A | -complement(c2,A). [resolve(24,a,19,a)].
% 2.88/3.16 Derived: c(c1) = A | -complement(c1,A). [resolve(24,a,20,a)].
% 2.88/3.16 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.88/3.16 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.88/3.16 25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.88/3.16 26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.88/3.16
% 2.88/3.16 ============================== end predicate elimination =============
% 2.88/3.16
% 2.88/3.16 Auto_denials: (non-Horn, no changes).
% 2.88/3.16
% 2.88/3.16 Term ordering decisions:
% 2.88/3.16 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 2.88/3.16
% 2.88/3.16 ============================== end of process initial clauses ========
% 2.88/3.16
% 2.88/3.16 ============================== CLAUSES FOR SEARCH ====================
% 2.88/3.16
% 2.88/3.16 ============================== end of clauses for search =============
% 2.88/3.16
% 2.88/3.16 ============================== SEARCH ================================
% 2.88/3.16
% 2.88/3.16 % Starting search at 0.01 seconds.
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=82.000, iters=3367
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=74.000, iters=3466
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=68.000, iters=3436
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=67.000, iters=3381
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=64.000, iters=3361
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=60.000, iters=3424
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=58.000, iters=3366
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=54.000, iters=3485
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=53.000, iters=3420
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=52.000, iters=3417
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=48.000, iters=3350
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=46.000, iters=3339
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=44.000, iters=3340
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=42.000, iters=3343
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=38.000, iters=5698
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=32.000, iters=5007
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=28.000, iters=4145
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=25.000, iters=3537
% 2.88/3.16
% 2.88/3.16 Low Water (keep): wt=24.000, iters=3362
% 2.88/3.16
% 2.88/3.16 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 106 (0.00 of 1.61 sec).
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5772, wt=107.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5788, wt=88.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5449, wt=85.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5789, wt=82.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5030, wt=81.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5783, wt=80.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5032, wt=79.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5408, wt=75.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=6075, wt=74.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=5787, wt=72.000
% 2.88/3.16
% 2.88/3.16 Low Water (displace): id=6126, wt=68.000
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=6107, wt=67.000
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=5520, wt=66.000
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=6162, wt=64.000
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=11655, wt=17.000
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=23.000, iters=3353
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=11790, wt=16.000
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=11795, wt=15.000
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=11826, wt=14.000
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=22.000, iters=3334
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=21.000, iters=3333
% 63.00/63.30
% 63.00/63.30 Low Water (displace): id=15051, wt=13.000
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=20.000, iters=3346
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=19.000, iters=3342
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=18.000, iters=3335
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=17.000, iters=3400
% 63.00/63.30
% 63.00/63.30 Low Water (keep): wt=16.000, iters=3333
% 63.00/63.30
% 63.00/63.30 ============================== PROOF =================================
% 63.00/63.30 % SZS status Theorem
% 63.00/63.30 % SZS output start Refutation
% 63.00/63.30
% 63.00/63.30 % Proof 1 at 60.84 (+ 1.44) seconds.
% 63.00/63.30 % Length of proof is 97.
% 63.00/63.30 % Level of proof is 14.
% 63.00/63.30 % Maximum clause weight is 23.000.
% 63.00/63.30 % Given clauses 3886.
% 63.00/63.30
% 63.00/63.30 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 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].
% 63.00/63.30 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 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].
% 63.00/63.30 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 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].
% 63.00/63.30 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].
% 63.00/63.30 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 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].
% 63.00/63.30 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 63.00/63.30 17 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(X0,X1),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 63.00/63.30 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 63.00/63.30 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 63.00/63.30 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 63.00/63.30 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 63.00/63.30 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 63.00/63.30 27 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 63.00/63.30 28 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 63.00/63.30 29 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 63.00/63.30 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 63.00/63.30 31 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 63.00/63.30 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 63.00/63.30 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 63.00/63.30 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([33(2)]),flip(a)].
% 63.00/63.30 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 63.00/63.30 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 63.00/63.30 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 63.00/63.30 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 63.00/63.30 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 63.00/63.30 41 addition(addition(c1,c2),multiplication(c(c1),c(c2))) != one # label(goals) # label(negated_conjecture). [clausify(17)].
% 63.00/63.30 43 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 63.00/63.30 44 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 63.00/63.30 45 -complement(A,B) | addition(A,B) = one. [copy(44),rewrite([33(2)])].
% 63.00/63.30 48 complement(f1(c2),c2). [resolve(18,a,19,a)].
% 63.00/63.30 49 complement(f1(c1),c1). [resolve(18,a,20,a)].
% 63.00/63.30 51 complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 63.00/63.30 52 c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 63.00/63.30 53 c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 63.00/63.30 63 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),28(a,1)),rewrite([33(1),33(2),35(2,R),28(1),33(3)])].
% 63.00/63.30 64 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(27(a,1),38(a,2,2)),rewrite([31(3),33(3)])].
% 63.00/63.30 65 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(29(a,1),38(a,1,1)),rewrite([33(4)]),flip(a)].
% 63.00/63.30 66 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(30(a,1),40(a,1,1)),rewrite([33(4)]),flip(a)].
% 63.00/63.30 67 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(36(a,1),40(a,1,1)),rewrite([33(6)])].
% 63.00/63.30 76 addition(c2,f1(c2)) = one. [resolve(48,a,45,a),rewrite([33(4)])].
% 63.00/63.30 79 addition(c1,f1(c1)) = one. [resolve(49,a,45,a),rewrite([33(4)])].
% 63.00/63.30 85 complement(c2,c(c2)). [resolve(52,a,30,a(flip)),rewrite([30(5)])].
% 63.00/63.30 87 complement(c1,c(c1)). [resolve(53,a,30,a(flip)),rewrite([30(5)])].
% 63.00/63.30 107 addition(c2,c(c2)) = one. [resolve(85,a,45,a)].
% 63.00/63.30 108 multiplication(c2,c(c2)) = zero. [resolve(85,a,43,a)].
% 63.00/63.30 112 complement(f1(c(c1)),c(c1)). [resolve(87,a,51,b)].
% 63.00/63.30 113 addition(c1,c(c1)) = one. [resolve(87,a,45,a)].
% 63.00/63.30 114 multiplication(c1,c(c1)) = zero. [resolve(87,a,43,a)].
% 63.00/63.30 130 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(65(a,2),35(a,2,2)),rewrite([33(2)]),flip(a)].
% 63.00/63.30 157 addition(one,c2) = one. [para(76(a,1),63(a,1,2)),rewrite([33(3),76(7)])].
% 63.00/63.30 166 addition(A,multiplication(A,c2)) = A. [para(157(a,1),38(a,2,2)),rewrite([29(2),29(5)])].
% 63.00/63.30 167 addition(A,multiplication(c2,A)) = A. [para(157(a,1),40(a,2,1)),rewrite([30(2),30(5)])].
% 63.00/63.30 174 addition(A,addition(multiplication(A,B),multiplication(C,multiplication(D,addition(B,one))))) = multiplication(addition(A,multiplication(C,D)),addition(B,one)). [para(65(a,1),67(a,1,2)),rewrite([35(7,R)])].
% 63.00/63.30 181 addition(one,c1) = one. [para(79(a,1),63(a,1,2)),rewrite([33(3),79(7)])].
% 63.00/63.30 230 multiplication(c2,addition(A,c(c2))) = multiplication(c2,A). [para(108(a,1),38(a,1,1)),rewrite([64(4),33(6)]),flip(a)].
% 63.00/63.30 231 multiplication(addition(A,c2),c(c2)) = multiplication(A,c(c2)). [para(108(a,1),40(a,1,1)),rewrite([64(5),33(5)]),flip(a)].
% 63.00/63.30 234 multiplication(addition(c2,multiplication(A,B)),c(c2)) = multiplication(A,multiplication(B,c(c2))). [para(108(a,1),67(a,1,2)),rewrite([33(6),64(6)]),flip(a)].
% 63.00/63.30 250 addition(c(c1),f1(c(c1))) = one. [resolve(112,a,45,a),rewrite([33(6)])].
% 63.00/63.30 254 multiplication(c1,addition(A,c(c1))) = multiplication(c1,A). [para(114(a,1),38(a,1,1)),rewrite([64(4),33(6)]),flip(a)].
% 63.00/63.30 332 addition(A,addition(B,multiplication(A,c2))) = addition(A,B). [para(166(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 63.00/63.30 335 addition(A,addition(B,multiplication(c2,A))) = addition(A,B). [para(167(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 63.00/63.30 388 addition(one,c(c1)) = one. [para(250(a,1),63(a,1,2)),rewrite([33(4),250(10)])].
% 63.00/63.30 397 addition(A,multiplication(c(c1),A)) = A. [para(388(a,1),40(a,2,1)),rewrite([30(2),30(6)])].
% 63.00/63.30 484 addition(A,addition(B,multiplication(c(c1),A))) = addition(A,B). [para(397(a,1),35(a,2,2)),rewrite([33(4),33(6)])].
% 63.00/63.30 566 multiplication(c2,c2) = c2. [para(107(a,1),230(a,1,2)),rewrite([29(3)]),flip(a)].
% 63.00/63.30 571 multiplication(c2,multiplication(c2,A)) = multiplication(c2,A). [para(566(a,1),36(a,1,1)),flip(a)].
% 63.00/63.30 572 multiplication(c2,addition(A,c2)) = multiplication(c2,addition(A,one)). [para(566(a,1),38(a,1,1)),rewrite([65(4,R),33(7)]),flip(a)].
% 63.00/63.30 573 multiplication(addition(A,c2),c2) = multiplication(addition(A,one),c2). [para(566(a,1),40(a,1,1)),rewrite([66(4,R),33(6)]),flip(a)].
% 63.00/63.30 626 multiplication(c2,addition(A,multiplication(c2,B))) = multiplication(c2,addition(B,A)). [para(571(a,1),38(a,1,1)),rewrite([38(5),33(7)]),flip(a)].
% 63.00/63.30 647 multiplication(c1,c1) = c1. [para(113(a,1),254(a,1,2)),rewrite([29(3)]),flip(a)].
% 63.00/63.30 677 multiplication(addition(A,multiplication(B,c1)),c1) = multiplication(addition(B,A),c1). [para(647(a,1),67(a,1,1,2)),rewrite([40(5)]),flip(a)].
% 63.00/63.30 996 addition(multiplication(A,c(c2)),multiplication(addition(A,c2),B)) = multiplication(addition(A,c2),addition(B,c(c2))). [para(231(a,1),38(a,1,1)),rewrite([33(12)])].
% 63.00/63.30 1115 addition(A,multiplication(addition(A,B),c2)) = addition(A,multiplication(B,c2)). [para(40(a,1),332(a,1,2)),rewrite([33(1)])].
% 63.00/63.30 1121 addition(one,addition(c2,c(c1))) = one. [para(388(a,1),332(a,2)),rewrite([30(6),33(5)])].
% 63.00/63.30 7325 multiplication(addition(c1,c2),c1) = c1. [para(157(a,1),677(a,2,1)),rewrite([30(4),33(3),30(8)])].
% 63.00/63.30 7386 addition(addition(c1,c2),multiplication(A,B)) = addition(c1,addition(c2,multiplication(A,B))). [para(7325(a,1),174(a,1,2,1)),rewrite([33(7),181(7),29(6),35(7,R),35(6),33(5),35(6,R),33(5),63(7),33(13),181(13),29(12)]),flip(a)].
% 63.00/63.30 7399 addition(c1,addition(c2,multiplication(c(c1),c(c2)))) != one. [back_rewrite(41),rewrite([7386(9)])].
% 63.00/63.30 7698 addition(c1,multiplication(c(c1),c2)) = addition(c1,c2). [para(113(a,1),1115(a,1,2,1)),rewrite([30(4)]),flip(a)].
% 63.00/63.30 7703 addition(one,multiplication(c(c1),c2)) = one. [para(388(a,1),1115(a,1,2,1)),rewrite([30(4),157(3)]),flip(a)].
% 63.00/63.30 7774 addition(A,multiplication(c(c1),multiplication(c2,A))) = A. [para(7703(a,1),40(a,2,1)),rewrite([30(2),36(5),30(8)])].
% 63.00/63.30 7867 multiplication(c2,addition(multiplication(c2,c1),multiplication(c(c1),c2))) = c2. [para(7698(a,1),626(a,2,2)),rewrite([33(9),572(15),33(14),181(14),29(13)])].
% 63.00/63.30 7927 multiplication(c(c1),addition(one,multiplication(c2,c(c1)))) = c(c1). [para(7774(a,1),65(a,2)),rewrite([33(8)])].
% 63.00/63.30 8199 addition(multiplication(c2,c1),multiplication(c(c1),c2)) = c2. [para(7867(a,1),66(a,2,2)),rewrite([33(3),157(3),30(10),33(18),484(18),65(13,R),33(12),181(12),29(11)])].
% 63.00/63.30 8202 addition(c(c1),multiplication(c2,c1)) = addition(c2,c(c1)). [para(8199(a,1),130(a,2,2)),rewrite([33(8),157(8),29(7),33(6),33(10)])].
% 63.00/63.30 8273 addition(c1,addition(c2,c(c1))) = one. [para(8202(a,1),335(a,1,2)),rewrite([113(10)])].
% 63.00/63.30 8300 addition(one,multiplication(c2,c(c1))) = one. [para(7927(a,1),66(a,2,2)),rewrite([33(4),388(4),30(8),33(15),335(15),33(10),388(10)])].
% 63.00/63.30 8301 multiplication(addition(c2,c(c1)),c(c2)) = multiplication(c(c1),c(c2)). [para(7927(a,1),234(a,1,1,2)),rewrite([8300(15),30(13)])].
% 63.00/63.30 23712 addition(multiplication(A,c(c2)),multiplication(addition(A,one),c2)) = addition(A,c2). [para(107(a,1),996(a,2,2)),rewrite([573(7),29(12)])].
% 63.00/63.30 28570 addition(c2,multiplication(c(c1),c(c2))) = addition(c2,c(c1)). [para(8301(a,1),23712(a,1,1)),rewrite([33(11),1121(11),30(8),33(7),33(13),63(13)])].
% 63.00/63.30 28573 $F. [back_rewrite(7399),rewrite([28570(8),8273(6)]),xx(a)].
% 63.00/63.30
% 63.00/63.30 % SZS output end Refutation
% 63.00/63.30 ============================== end of proof ==========================
% 63.00/63.30
% 63.00/63.30 ============================== STATISTICS ============================
% 63.00/63.30
% 63.00/63.30 Given=3886. Generated=2626157. Kept=28541. proofs=1.
% 63.00/63.30 Usable=3635. Sos=9941. Demods=1657. Limbo=3, Disabled=14999. Hints=0.
% 63.00/63.30 Megabytes=21.78.
% 63.00/63.30 User_CPU=60.84, System_CPU=1.44, Wall_clock=62.
% 63.00/63.30
% 63.00/63.30 ============================== end of statistics =====================
% 63.00/63.30
% 63.00/63.30 ============================== end of search =========================
% 63.00/63.30
% 63.00/63.30 THEOREM PROVED
% 63.00/63.30 % SZS status Theorem
% 63.00/63.30
% 63.00/63.30 Exiting with 1 proof.
% 63.00/63.30
% 63.00/63.30 Process 30079 exit (max_proofs) Thu Jun 16 08:11:20 2022
% 63.00/63.30 Prover9 interrupted
%------------------------------------------------------------------------------