TSTP Solution File: KLE012+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE012+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 3.14s 3.46s
% Output : Refutation 3.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE012+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 14:00:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.46/1.01 ============================== Prover9 ===============================
% 0.46/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.01 Process 5442 was started by sandbox2 on n014.cluster.edu,
% 0.46/1.01 Thu Jun 16 14:00:06 2022
% 0.46/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5288_n014.cluster.edu".
% 0.46/1.01 ============================== end of head ===========================
% 0.46/1.01
% 0.46/1.01 ============================== INPUT =================================
% 0.46/1.01
% 0.46/1.01 % Reading from file /tmp/Prover9_5288_n014.cluster.edu
% 0.46/1.01
% 0.46/1.01 set(prolog_style_variables).
% 0.46/1.01 set(auto2).
% 0.46/1.01 % set(auto2) -> set(auto).
% 0.46/1.01 % set(auto) -> set(auto_inference).
% 0.46/1.01 % set(auto) -> set(auto_setup).
% 0.46/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.01 % set(auto) -> set(auto_limits).
% 0.46/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.01 % set(auto) -> set(auto_denials).
% 0.46/1.01 % set(auto) -> set(auto_process).
% 0.46/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.01 % set(auto2) -> assign(stats, some).
% 0.46/1.01 % set(auto2) -> clear(echo_input).
% 0.46/1.01 % set(auto2) -> set(quiet).
% 0.46/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.01 % set(auto2) -> clear(print_given).
% 0.46/1.01 assign(lrs_ticks,-1).
% 0.46/1.01 assign(sos_limit,10000).
% 0.46/1.01 assign(order,kbo).
% 0.46/1.01 set(lex_order_vars).
% 0.46/1.01 clear(print_given).
% 0.46/1.01
% 0.46/1.01 % formulas(sos). % not echoed (17 formulas)
% 0.46/1.01
% 0.46/1.01 ============================== end of input ==========================
% 0.46/1.01
% 0.46/1.01 % From the command line: assign(max_seconds, 300).
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.01
% 0.46/1.01 % Formulas that are not ordinary clauses:
% 0.46/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 0.46/1.01 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].
% 0.46/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 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].
% 2.83/3.17 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.83/3.17 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.83/3.17 17 -(all X0 all X1 (test(X1) & test(X0) -> multiplication(X0,X1) = multiplication(X1,X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.83/3.17
% 2.83/3.17 ============================== end of process non-clausal formulas ===
% 2.83/3.17
% 2.83/3.17 ============================== PROCESS INITIAL CLAUSES ===============
% 2.83/3.17
% 2.83/3.17 ============================== PREDICATE ELIMINATION =================
% 2.83/3.17 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.83/3.17 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.83/3.17 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.83/3.17 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.83/3.17 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.83/3.17 Derived: complement(f1(c2),c2). [resolve(18,a,19,a)].
% 2.83/3.17 Derived: complement(f1(c1),c1). [resolve(18,a,20,a)].
% 2.83/3.17 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 2.83/3.17 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 2.83/3.17 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.83/3.17 Derived: c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 2.83/3.17 Derived: c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 2.83/3.17 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 2.83/3.17 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 2.83/3.17 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.83/3.17 Derived: c(c2) = A | -complement(c2,A). [resolve(24,a,19,a)].
% 2.83/3.17 Derived: c(c1) = A | -complement(c1,A). [resolve(24,a,20,a)].
% 2.83/3.17 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.83/3.17 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.83/3.17 25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.83/3.17 26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.83/3.17
% 2.83/3.17 ============================== end predicate elimination =============
% 2.83/3.17
% 2.83/3.17 Auto_denials: (non-Horn, no changes).
% 2.83/3.17
% 2.83/3.17 Term ordering decisions:
% 2.83/3.17 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 2.83/3.17
% 2.83/3.17 ============================== end of process initial clauses ========
% 2.83/3.17
% 2.83/3.17 ============================== CLAUSES FOR SEARCH ====================
% 2.83/3.17
% 2.83/3.17 ============================== end of clauses for search =============
% 2.83/3.17
% 2.83/3.17 ============================== SEARCH ================================
% 2.83/3.17
% 2.83/3.17 % Starting search at 0.01 seconds.
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=82.000, iters=3367
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=74.000, iters=3466
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=68.000, iters=3436
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=67.000, iters=3381
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=64.000, iters=3361
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=60.000, iters=3424
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=58.000, iters=3366
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=54.000, iters=3485
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=53.000, iters=3420
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=52.000, iters=3417
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=48.000, iters=3350
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=46.000, iters=3339
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=44.000, iters=3340
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=42.000, iters=3343
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=40.000, iters=3346
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=39.000, iters=3362
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=37.000, iters=3342
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=36.000, iters=3393
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=35.000, iters=3384
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=34.000, iters=3343
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=33.000, iters=3360
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=32.000, iters=3342
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=31.000, iters=3360
% 2.83/3.17
% 2.83/3.17 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 94 (0.00 of 1.69 sec).
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=30.000, iters=3402
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=29.000, iters=3385
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=28.000, iters=3355
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=27.000, iters=3461
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=26.000, iters=3343
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=25.000, iters=3359
% 2.83/3.17
% 2.83/3.17 Low Water (keep): wt=24.000, iters=3333
% 2.83/3.17
% 2.83/3.17 Low Water (displace): id=5768, wt=107.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5784, wt=88.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5445, wt=85.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5785, wt=82.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5026, wt=81.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5779, wt=80.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5028, wt=79.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5404, wt=75.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=6071, wt=74.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5783, wt=72.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=6122, wt=68.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=6103, wt=67.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=5516, wt=66.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=6158, wt=64.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=11673, wt=18.000
% 3.14/3.46
% 3.14/3.46 Low Water (keep): wt=23.000, iters=3341
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=11793, wt=17.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=11833, wt=16.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=11847, wt=15.000
% 3.14/3.46
% 3.14/3.46 Low Water (displace): id=11879, wt=14.000
% 3.14/3.46
% 3.14/3.46 ============================== PROOF =================================
% 3.14/3.46 % SZS status Theorem
% 3.14/3.46 % SZS output start Refutation
% 3.14/3.46
% 3.14/3.46 % Proof 1 at 2.41 (+ 0.05) seconds.
% 3.14/3.46 % Length of proof is 102.
% 3.14/3.46 % Level of proof is 16.
% 3.14/3.46 % Maximum clause weight is 17.000.
% 3.14/3.46 % Given clauses 653.
% 3.14/3.46
% 3.14/3.46 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 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].
% 3.14/3.46 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 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].
% 3.14/3.46 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 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].
% 3.14/3.46 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].
% 3.14/3.46 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 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].
% 3.14/3.46 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 3.14/3.46 17 -(all X0 all X1 (test(X1) & test(X0) -> multiplication(X0,X1) = multiplication(X1,X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.14/3.46 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 3.14/3.46 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.14/3.46 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.14/3.46 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 3.14/3.46 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 3.14/3.46 27 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 3.14/3.46 28 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 3.14/3.46 29 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 3.14/3.46 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 3.14/3.46 31 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 3.14/3.46 32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 3.14/3.46 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 3.14/3.46 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 3.14/3.46 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([33(2)]),flip(a)].
% 3.14/3.46 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 3.14/3.46 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 3.14/3.46 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 3.14/3.46 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 3.14/3.46 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 3.14/3.47 41 multiplication(c2,c1) != multiplication(c1,c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.14/3.47 42 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 3.14/3.47 43 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 3.14/3.47 44 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 3.14/3.47 45 -complement(A,B) | addition(A,B) = one. [copy(44),rewrite([33(2)])].
% 3.14/3.47 48 complement(f1(c2),c2). [resolve(18,a,19,a)].
% 3.14/3.47 49 complement(f1(c1),c1). [resolve(18,a,20,a)].
% 3.14/3.47 51 complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 3.14/3.47 52 c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 3.14/3.47 53 c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 3.14/3.47 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)])].
% 3.14/3.47 64 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(27(a,1),38(a,2,2)),rewrite([31(3),33(3)])].
% 3.14/3.47 65 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(29(a,1),38(a,1,1)),rewrite([33(4)]),flip(a)].
% 3.14/3.47 66 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(30(a,1),40(a,1,1)),rewrite([33(4)]),flip(a)].
% 3.14/3.47 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)])].
% 3.14/3.47 75 addition(c2,f1(c2)) = one. [resolve(48,a,45,a),rewrite([33(4)])].
% 3.14/3.47 78 addition(c1,f1(c1)) = one. [resolve(49,a,45,a),rewrite([33(4)])].
% 3.14/3.47 84 complement(c2,c(c2)). [resolve(52,a,30,a(flip)),rewrite([30(5)])].
% 3.14/3.47 86 complement(c1,c(c1)). [resolve(53,a,30,a(flip)),rewrite([30(5)])].
% 3.14/3.47 106 addition(c2,c(c2)) = one. [resolve(84,a,45,a)].
% 3.14/3.47 107 multiplication(c2,c(c2)) = zero. [resolve(84,a,43,a)].
% 3.14/3.47 111 complement(f1(c(c1)),c(c1)). [resolve(86,a,51,b)].
% 3.14/3.47 112 addition(c1,c(c1)) = one. [resolve(86,a,45,a)].
% 3.14/3.47 113 multiplication(c1,c(c1)) = zero. [resolve(86,a,43,a)].
% 3.14/3.47 114 multiplication(c(c1),c1) = zero. [resolve(86,a,42,a)].
% 3.14/3.47 129 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)].
% 3.14/3.47 156 addition(one,c2) = one. [para(75(a,1),63(a,1,2)),rewrite([33(3),75(7)])].
% 3.14/3.47 165 addition(A,multiplication(A,c2)) = A. [para(156(a,1),38(a,2,2)),rewrite([29(2),29(5)])].
% 3.14/3.47 166 addition(A,multiplication(c2,A)) = A. [para(156(a,1),40(a,2,1)),rewrite([30(2),30(5)])].
% 3.14/3.47 180 addition(one,c1) = one. [para(78(a,1),63(a,1,2)),rewrite([33(3),78(7)])].
% 3.14/3.47 200 addition(A,multiplication(c1,A)) = A. [para(180(a,1),40(a,2,1)),rewrite([30(2),30(5)])].
% 3.14/3.47 229 multiplication(c2,addition(A,c(c2))) = multiplication(c2,A). [para(107(a,1),38(a,1,1)),rewrite([64(4),33(6)]),flip(a)].
% 3.14/3.47 249 addition(c(c1),f1(c(c1))) = one. [resolve(111,a,45,a),rewrite([33(6)])].
% 3.14/3.47 252 multiplication(c1,multiplication(c(c1),A)) = zero. [para(113(a,1),36(a,1,1)),rewrite([32(2)]),flip(a)].
% 3.14/3.47 263 multiplication(addition(A,c(c1)),c1) = multiplication(A,c1). [para(114(a,1),40(a,1,1)),rewrite([64(4),33(5)]),flip(a)].
% 3.14/3.47 265 multiplication(addition(c(c1),multiplication(A,B)),c1) = multiplication(A,multiplication(B,c1)). [para(114(a,1),67(a,1,2)),rewrite([33(5),64(5)]),flip(a)].
% 3.14/3.47 328 addition(A,addition(B,multiplication(A,c2))) = addition(A,B). [para(165(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 3.14/3.47 336 addition(A,addition(B,multiplication(c1,A))) = addition(A,B). [para(200(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 3.14/3.47 384 addition(one,c(c1)) = one. [para(249(a,1),63(a,1,2)),rewrite([33(4),249(10)])].
% 3.14/3.47 393 addition(A,multiplication(c(c1),A)) = A. [para(384(a,1),40(a,2,1)),rewrite([30(2),30(6)])].
% 3.14/3.47 432 multiplication(c1,addition(A,multiplication(c(c1),B))) = multiplication(c1,A). [para(252(a,1),38(a,1,1)),rewrite([64(4),33(7)]),flip(a)].
% 3.14/3.47 480 addition(A,addition(B,multiplication(c(c1),A))) = addition(A,B). [para(393(a,1),35(a,2,2)),rewrite([33(4),33(6)])].
% 3.14/3.47 562 multiplication(c2,c2) = c2. [para(106(a,1),229(a,1,2)),rewrite([29(3)]),flip(a)].
% 3.14/3.47 567 multiplication(c2,multiplication(c2,A)) = multiplication(c2,A). [para(562(a,1),36(a,1,1)),flip(a)].
% 3.14/3.47 568 multiplication(c2,addition(A,c2)) = multiplication(c2,addition(A,one)). [para(562(a,1),38(a,1,1)),rewrite([65(4,R),33(7)]),flip(a)].
% 3.14/3.47 570 multiplication(addition(A,multiplication(B,c2)),c2) = multiplication(addition(B,A),c2). [para(562(a,1),67(a,1,1,2)),rewrite([40(5)]),flip(a)].
% 3.14/3.47 622 multiplication(c2,addition(A,multiplication(c2,B))) = multiplication(c2,addition(B,A)). [para(567(a,1),38(a,1,1)),rewrite([38(5),33(7)]),flip(a)].
% 3.14/3.47 1111 addition(A,multiplication(addition(A,B),c2)) = addition(A,multiplication(B,c2)). [para(40(a,1),328(a,1,2)),rewrite([33(1)])].
% 3.14/3.47 1263 addition(A,multiplication(addition(B,c1),A)) = addition(A,multiplication(B,A)). [para(40(a,1),336(a,1,2))].
% 3.14/3.47 7077 multiplication(addition(c2,c(c1)),c2) = c2. [para(384(a,1),570(a,2,1)),rewrite([30(5),33(4),30(9)])].
% 3.14/3.47 7773 addition(one,multiplication(c1,c2)) = one. [para(180(a,1),1111(a,1,2,1)),rewrite([30(4),156(3)]),flip(a)].
% 3.14/3.47 7774 addition(c1,multiplication(c(c1),c2)) = addition(c1,c2). [para(112(a,1),1111(a,1,2,1)),rewrite([30(4)]),flip(a)].
% 3.14/3.47 7776 addition(A,multiplication(c2,multiplication(A,c2))) = A. [para(166(a,1),1111(a,1,2,1)),rewrite([165(3),36(4)]),flip(a)].
% 3.14/3.47 7846 addition(A,multiplication(c1,multiplication(c2,A))) = A. [para(7773(a,1),40(a,2,1)),rewrite([30(2),36(4),30(7)])].
% 3.14/3.47 7877 addition(A,addition(B,multiplication(c2,multiplication(A,c2)))) = addition(A,B). [para(7776(a,1),35(a,2,2)),rewrite([33(5),33(7)])].
% 3.14/3.47 7938 addition(A,multiplication(c1,multiplication(c2,multiplication(A,c2)))) = A. [para(7846(a,1),1111(a,1,2,1)),rewrite([165(3),36(6),36(5)]),flip(a)].
% 3.14/3.47 7941 multiplication(c2,addition(multiplication(c2,c1),multiplication(c(c1),c2))) = c2. [para(7774(a,1),622(a,2,2)),rewrite([33(9),568(15),33(14),180(14),29(13)])].
% 3.14/3.47 8125 multiplication(c1,addition(one,multiplication(c2,multiplication(c1,c2)))) = c1. [para(7938(a,1),65(a,2)),rewrite([33(8)])].
% 3.14/3.47 8204 addition(one,multiplication(c2,multiplication(c1,c2))) = one. [para(8125(a,1),66(a,2,2)),rewrite([33(3),180(3),30(9),33(16),7877(16),33(10),180(10)])].
% 3.14/3.47 8208 addition(A,multiplication(A,multiplication(c2,multiplication(c1,c2)))) = A. [para(8204(a,1),38(a,2,2)),rewrite([29(2),29(9)])].
% 3.14/3.47 8259 addition(multiplication(c2,c1),multiplication(c(c1),c2)) = c2. [para(7941(a,1),66(a,2,2)),rewrite([33(3),156(3),30(10),33(18),480(18),65(13,R),33(12),180(12),29(11)])].
% 3.14/3.47 8262 addition(c(c1),multiplication(c2,c1)) = addition(c2,c(c1)). [para(8259(a,1),129(a,2,2)),rewrite([33(8),156(8),29(7),33(6),33(10)])].
% 3.14/3.47 8265 multiplication(c1,multiplication(c2,c1)) = multiplication(c1,c2). [para(8259(a,1),432(a,1,2)),flip(a)].
% 3.14/3.47 8274 multiplication(c1,multiplication(c2,multiplication(c1,A))) = multiplication(c1,multiplication(c2,A)). [para(8265(a,1),36(a,1,1)),rewrite([36(4),36(9)]),flip(a)].
% 3.14/3.47 8335 addition(c(c1),multiplication(c2,multiplication(c1,c2))) = addition(c2,c(c1)). [para(8262(a,1),1111(a,1,2,1)),rewrite([7077(8),33(4),36(11)]),flip(a)].
% 3.14/3.47 12197 multiplication(c2,multiplication(c1,c2)) = multiplication(c1,c2). [para(8208(a,1),1263(a,2)),rewrite([33(12),7776(12),8274(12),562(9),33(9),166(9)]),flip(a)].
% 3.14/3.47 12215 addition(c(c1),multiplication(c1,c2)) = addition(c2,c(c1)). [back_rewrite(8335),rewrite([12197(7)])].
% 3.14/3.47 12242 $F. [para(12197(a,1),265(a,1,1,2)),rewrite([12215(6),263(6),36(9),8265(9),12197(8)]),unit_del(a,41)].
% 3.14/3.47
% 3.14/3.47 % SZS output end Refutation
% 3.14/3.47 ============================== end of proof ==========================
% 3.14/3.47
% 3.14/3.47 ============================== STATISTICS ============================
% 3.14/3.47
% 3.14/3.47 Given=653. Generated=75227. Kept=12210. proofs=1.
% 3.14/3.47 Usable=557. Sos=9990. Demods=2562. Limbo=14, Disabled=1686. Hints=0.
% 3.14/3.47 Megabytes=13.97.
% 3.14/3.47 User_CPU=2.41, System_CPU=0.05, Wall_clock=2.
% 3.14/3.47
% 3.14/3.47 ============================== end of statistics =====================
% 3.14/3.47
% 3.14/3.47 ============================== end of search =========================
% 3.14/3.47
% 3.14/3.47 THEOREM PROVED
% 3.14/3.47 % SZS status Theorem
% 3.14/3.47
% 3.14/3.47 Exiting with 1 proof.
% 3.14/3.47
% 3.14/3.47 Process 5442 exit (max_proofs) Thu Jun 16 14:00:08 2022
% 3.14/3.47 Prover9 interrupted
%------------------------------------------------------------------------------