TSTP Solution File: KLE034+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE034+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 58.14s 58.41s
% Output : Refutation 58.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE034+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 : n020.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 12:21:34 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.73/1.00 ============================== Prover9 ===============================
% 0.73/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.00 Process 15729 was started by sandbox2 on n020.cluster.edu,
% 0.73/1.00 Thu Jun 16 12:21:35 2022
% 0.73/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15576_n020.cluster.edu".
% 0.73/1.00 ============================== end of head ===========================
% 0.73/1.00
% 0.73/1.00 ============================== INPUT =================================
% 0.73/1.00
% 0.73/1.00 % Reading from file /tmp/Prover9_15576_n020.cluster.edu
% 0.73/1.00
% 0.73/1.00 set(prolog_style_variables).
% 0.73/1.00 set(auto2).
% 0.73/1.00 % set(auto2) -> set(auto).
% 0.73/1.00 % set(auto) -> set(auto_inference).
% 0.73/1.00 % set(auto) -> set(auto_setup).
% 0.73/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.00 % set(auto) -> set(auto_limits).
% 0.73/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.00 % set(auto) -> set(auto_denials).
% 0.73/1.00 % set(auto) -> set(auto_process).
% 0.73/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.00 % set(auto2) -> assign(stats, some).
% 0.73/1.00 % set(auto2) -> clear(echo_input).
% 0.73/1.00 % set(auto2) -> set(quiet).
% 0.73/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.00 % set(auto2) -> clear(print_given).
% 0.73/1.00 assign(lrs_ticks,-1).
% 0.73/1.00 assign(sos_limit,10000).
% 0.73/1.00 assign(order,kbo).
% 0.73/1.00 set(lex_order_vars).
% 0.73/1.00 clear(print_given).
% 0.73/1.00
% 0.73/1.00 % formulas(sos). % not echoed (17 formulas)
% 0.73/1.00
% 0.73/1.00 ============================== end of input ==========================
% 0.73/1.00
% 0.73/1.00 % From the command line: assign(max_seconds, 300).
% 0.73/1.00
% 0.73/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.00
% 0.73/1.00 % Formulas that are not ordinary clauses:
% 0.73/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 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].
% 0.73/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 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].
% 0.73/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 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].
% 0.73/1.00 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].
% 0.73/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 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].
% 2.71/3.02 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.71/3.02 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.71/3.02 17 -(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].
% 2.71/3.02
% 2.71/3.02 ============================== end of process non-clausal formulas ===
% 2.71/3.02
% 2.71/3.02 ============================== PROCESS INITIAL CLAUSES ===============
% 2.71/3.02
% 2.71/3.02 ============================== PREDICATE ELIMINATION =================
% 2.71/3.02 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.71/3.02 19 test(c4) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.71/3.02 20 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.71/3.02 21 test(c5) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.71/3.02 22 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.71/3.02 23 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.71/3.02 Derived: complement(f1(c4),c4). [resolve(18,a,19,a)].
% 2.71/3.02 Derived: complement(f1(c3),c3). [resolve(18,a,20,a)].
% 2.71/3.02 Derived: complement(f1(c5),c5). [resolve(18,a,21,a)].
% 2.71/3.02 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,22,a)].
% 2.71/3.02 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,23,a)].
% 2.71/3.02 24 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.71/3.02 Derived: c(c4) != A | complement(c4,A). [resolve(24,a,19,a)].
% 2.71/3.02 Derived: c(c3) != A | complement(c3,A). [resolve(24,a,20,a)].
% 2.71/3.02 Derived: c(c5) != A | complement(c5,A). [resolve(24,a,21,a)].
% 2.71/3.02 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(24,a,22,a)].
% 2.71/3.02 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(24,a,23,a)].
% 2.71/3.02 25 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.71/3.02 Derived: c(c4) = A | -complement(c4,A). [resolve(25,a,19,a)].
% 2.71/3.02 Derived: c(c3) = A | -complement(c3,A). [resolve(25,a,20,a)].
% 2.71/3.02 Derived: c(c5) = A | -complement(c5,A). [resolve(25,a,21,a)].
% 2.71/3.02 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(25,a,22,a)].
% 2.71/3.02 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(25,a,23,a)].
% 2.71/3.02
% 2.71/3.02 ============================== end predicate elimination =============
% 2.71/3.02
% 2.71/3.02 Auto_denials: (non-Horn, no changes).
% 2.71/3.02
% 2.71/3.02 Term ordering decisions:
% 2.71/3.02 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.
% 2.71/3.02
% 2.71/3.02 ============================== end of process initial clauses ========
% 2.71/3.02
% 2.71/3.02 ============================== CLAUSES FOR SEARCH ====================
% 2.71/3.02
% 2.71/3.02 ============================== end of clauses for search =============
% 2.71/3.02
% 2.71/3.02 ============================== SEARCH ================================
% 2.71/3.02
% 2.71/3.02 % Starting search at 0.01 seconds.
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=62.000, iters=3383
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=60.000, iters=3465
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=53.000, iters=3434
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=48.000, iters=3360
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=44.000, iters=3395
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=42.000, iters=3340
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=40.000, iters=3364
% 2.71/3.02
% 2.71/3.02 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 65 (0.00 of 1.01 sec).
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=38.000, iters=3358
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=37.000, iters=3333
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=36.000, iters=3378
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=34.000, iters=3342
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=33.000, iters=3340
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=32.000, iters=3354
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=31.000, iters=3345
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=30.000, iters=3336
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=29.000, iters=3342
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=28.000, iters=3342
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=27.000, iters=3410
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=26.000, iters=3353
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=25.000, iters=3443
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=24.000, iters=3346
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=23.000, iters=3347
% 2.71/3.02
% 2.71/3.02 Low Water (keep): wt=22.000, iters=3333
% 2.71/3.02
% 2.71/3.02 Low Water (displace): id=5904, wt=107.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5102, wt=88.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=4733, wt=85.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5715, wt=82.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5876, wt=81.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5097, wt=80.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5877, wt=79.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5609, wt=74.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5101, wt=72.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5668, wt=68.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=5642, wt=67.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=4819, wt=66.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=6277, wt=64.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=11678, wt=19.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=11680, wt=18.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=11688, wt=16.000
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=21.000, iters=3353
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=11866, wt=14.000
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=12019, wt=13.000
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=20.000, iters=3335
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=14066, wt=12.000
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=19.000, iters=3333
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=18.000, iters=3333
% 58.14/58.41
% 58.14/58.41 Low Water (displace): id=17657, wt=10.000
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=17.000, iters=3333
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=16.000, iters=3346
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=15.000, iters=3335
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=14.000, iters=3333
% 58.14/58.41
% 58.14/58.41 Low Water (keep): wt=13.000, iters=3333
% 58.14/58.41
% 58.14/58.41 ============================== PROOF =================================
% 58.14/58.41 % SZS status Theorem
% 58.14/58.41 % SZS output start Refutation
% 58.14/58.41
% 58.14/58.41 % Proof 1 at 55.84 (+ 1.58) seconds.
% 58.14/58.41 % Length of proof is 59.
% 58.14/58.41 % Level of proof is 8.
% 58.14/58.41 % Maximum clause weight is 19.000.
% 58.14/58.41 % Given clauses 7562.
% 58.14/58.41
% 58.14/58.41 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 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].
% 58.14/58.41 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 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].
% 58.14/58.41 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].
% 58.14/58.41 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 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].
% 58.14/58.41 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 58.14/58.41 17 -(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].
% 58.14/58.41 19 test(c4) # label(goals) # label(negated_conjecture). [clausify(17)].
% 58.14/58.41 24 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 58.14/58.41 25 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 58.14/58.41 26 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 58.14/58.41 28 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 58.14/58.41 29 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 58.14/58.41 30 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 58.14/58.41 31 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 58.14/58.41 32 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 58.14/58.41 33 leq(multiplication(multiplication(c3,c1),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 58.14/58.41 34 leq(multiplication(multiplication(c4,c2),c(c5)),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 58.14/58.41 37 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 58.14/58.41 38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 58.14/58.41 39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(38),flip(a)].
% 58.14/58.41 40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 58.14/58.42 41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(40),flip(a)].
% 58.14/58.42 42 -leq(multiplication(multiplication(multiplication(c3,c1),c2),c(c5)),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 58.14/58.42 43 -leq(multiplication(c3,multiplication(c1,multiplication(c2,c(c5)))),zero). [copy(42),rewrite([37(5),37(8),37(7)])].
% 58.14/58.42 44 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 58.14/58.42 45 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 58.14/58.42 46 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 58.14/58.42 48 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 58.14/58.42 49 -complement(A,B) | addition(A,B) = one. [copy(48),rewrite([32(2)])].
% 58.14/58.42 57 c(c4) != A | complement(c4,A). [resolve(24,a,19,a)].
% 58.14/58.42 62 c(c4) = A | -complement(c4,A). [resolve(25,a,19,a)].
% 58.14/58.42 67 leq(multiplication(c4,multiplication(c2,c(c5))),zero). [back_rewrite(34),rewrite([37(6)])].
% 58.14/58.42 68 leq(multiplication(c3,multiplication(c1,c(c4))),zero). [back_rewrite(33),rewrite([37(6)])].
% 58.14/58.42 73 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(26(a,1),39(a,2,2)),rewrite([30(3),32(3)])].
% 58.14/58.42 74 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(28(a,1),39(a,1,1)),rewrite([32(4)]),flip(a)].
% 58.14/58.42 76 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)])].
% 58.14/58.42 79 multiplication(c3,multiplication(c1,multiplication(c2,c(c5)))) != zero. [ur(45,a,43,a),rewrite([32(10),73(10)])].
% 58.14/58.42 101 complement(c4,c(c4)). [resolve(57,a,29,a(flip)),rewrite([29(5)])].
% 58.14/58.42 102 complement(c4,addition(zero,c(c4))). [resolve(57,a,26,a(flip)),rewrite([32(5)])].
% 58.14/58.42 118 multiplication(c4,multiplication(c2,c(c5))) = zero. [resolve(67,a,44,a),rewrite([32(8),73(8)])].
% 58.14/58.42 119 multiplication(c3,multiplication(c1,c(c4))) = zero. [resolve(68,a,44,a),rewrite([32(8),73(8)])].
% 58.14/58.42 133 addition(c4,c(c4)) = one. [resolve(101,a,49,a)].
% 58.14/58.42 135 multiplication(c(c4),c4) = zero. [resolve(101,a,46,a)].
% 58.14/58.42 156 multiplication(addition(A,multiplication(A,B)),C) = multiplication(A,multiplication(addition(B,one),C)). [para(74(a,1),37(a,1,1))].
% 58.14/58.42 321 addition(zero,c(c4)) = c(c4). [resolve(102,a,62,b),flip(a)].
% 58.14/58.42 356 multiplication(c(c4),multiplication(c4,A)) = zero. [para(135(a,1),37(a,1,1)),rewrite([31(2)]),flip(a)].
% 58.14/58.42 480 multiplication(addition(c4,multiplication(A,B)),multiplication(c2,c(c5))) = multiplication(A,multiplication(B,multiplication(c2,c(c5)))). [para(118(a,1),76(a,1,2)),rewrite([32(8),73(8)]),flip(a)].
% 58.14/58.42 487 multiplication(c3,multiplication(c1,multiplication(c(c4),A))) = zero. [para(119(a,1),37(a,1,1)),rewrite([31(2),37(7)]),flip(a)].
% 58.14/58.42 721 multiplication(c(c4),addition(A,multiplication(c4,B))) = multiplication(c(c4),A). [para(356(a,1),39(a,1,1)),rewrite([73(5),32(8)]),flip(a)].
% 58.14/58.42 725 multiplication(c(c4),multiplication(addition(one,multiplication(c4,A)),B)) = multiplication(c(c4),B). [para(356(a,1),156(a,1,1,2)),rewrite([32(4),321(4),32(9)]),flip(a)].
% 58.14/58.42 18706 multiplication(c(c4),multiplication(c2,c(c5))) = multiplication(c2,c(c5)). [para(725(a,1),480(a,2)),rewrite([721(8),28(5),133(4),29(6)]),flip(a)].
% 58.14/58.42 33115 $F. [para(18706(a,1),487(a,1,2,2)),unit_del(a,79)].
% 58.14/58.42
% 58.14/58.42 % SZS output end Refutation
% 58.14/58.42 ============================== end of proof ==========================
% 58.14/58.42
% 58.14/58.42 ============================== STATISTICS ============================
% 58.14/58.42
% 58.14/58.42 Given=7562. Generated=2673337. Kept=33083. proofs=1.
% 58.14/58.42 Usable=6218. Sos=9318. Demods=1806. Limbo=0, Disabled=17590. Hints=0.
% 58.14/58.42 Megabytes=22.74.
% 58.14/58.42 User_CPU=55.84, System_CPU=1.58, Wall_clock=57.
% 58.14/58.42
% 58.14/58.42 ============================== end of statistics =====================
% 58.14/58.42
% 58.14/58.42 ============================== end of search =========================
% 58.14/58.42
% 58.14/58.42 THEOREM PROVED
% 58.14/58.42 % SZS status Theorem
% 58.14/58.42
% 58.14/58.42 Exiting with 1 proof.
% 58.14/58.42
% 58.14/58.42 Process 15729 exit (max_proofs) Thu Jun 16 12:22:32 2022
% 58.14/58.42 Prover9 interrupted
%------------------------------------------------------------------------------