TSTP Solution File: KLE018+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE018+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 02:21:45 EDT 2022
% Result : Theorem 29.59s 29.94s
% Output : Refutation 29.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE018+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 16:16:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.13 ============================== Prover9 ===============================
% 0.46/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.13 Process 3569 was started by sandbox on n013.cluster.edu,
% 0.46/1.13 Thu Jun 16 16:16:44 2022
% 0.46/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3406_n013.cluster.edu".
% 0.46/1.13 ============================== end of head ===========================
% 0.46/1.13
% 0.46/1.13 ============================== INPUT =================================
% 0.46/1.13
% 0.46/1.13 % Reading from file /tmp/Prover9_3406_n013.cluster.edu
% 0.46/1.13
% 0.46/1.13 set(prolog_style_variables).
% 0.46/1.13 set(auto2).
% 0.46/1.13 % set(auto2) -> set(auto).
% 0.46/1.13 % set(auto) -> set(auto_inference).
% 0.46/1.13 % set(auto) -> set(auto_setup).
% 0.46/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.13 % set(auto) -> set(auto_limits).
% 0.46/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.13 % set(auto) -> set(auto_denials).
% 0.46/1.13 % set(auto) -> set(auto_process).
% 0.46/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.13 % set(auto2) -> assign(stats, some).
% 0.46/1.13 % set(auto2) -> clear(echo_input).
% 0.46/1.13 % set(auto2) -> set(quiet).
% 0.46/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.13 % set(auto2) -> clear(print_given).
% 0.46/1.13 assign(lrs_ticks,-1).
% 0.46/1.13 assign(sos_limit,10000).
% 0.46/1.13 assign(order,kbo).
% 0.46/1.13 set(lex_order_vars).
% 0.46/1.13 clear(print_given).
% 0.46/1.13
% 0.46/1.13 % formulas(sos). % not echoed (17 formulas)
% 0.46/1.13
% 0.46/1.13 ============================== end of input ==========================
% 0.46/1.13
% 0.46/1.13 % From the command line: assign(max_seconds, 300).
% 0.46/1.13
% 0.46/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.13
% 0.46/1.13 % Formulas that are not ordinary clauses:
% 0.46/1.13 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 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].
% 0.46/1.13 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 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].
% 0.46/1.13 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 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].
% 0.46/1.13 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].
% 0.46/1.13 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.13 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].
% 4.00/4.31 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 4.00/4.31 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 4.00/4.31 17 -(all X0 all X1 all X2 (test(X0) & test(X1) & test(X2) -> (leq(multiplication(X0,c(X1)),X2) -> leq(X0,addition(X1,X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.00/4.31
% 4.00/4.31 ============================== end of process non-clausal formulas ===
% 4.00/4.31
% 4.00/4.31 ============================== PROCESS INITIAL CLAUSES ===============
% 4.00/4.31
% 4.00/4.31 ============================== PREDICATE ELIMINATION =================
% 4.00/4.31 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 4.00/4.31 19 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 4.00/4.31 20 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 4.00/4.31 21 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 4.00/4.31 22 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 4.00/4.31 23 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 4.00/4.31 Derived: complement(f1(c1),c1). [resolve(18,a,19,a)].
% 4.00/4.31 Derived: complement(f1(c2),c2). [resolve(18,a,20,a)].
% 4.00/4.31 Derived: complement(f1(c3),c3). [resolve(18,a,21,a)].
% 4.00/4.31 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,22,a)].
% 4.00/4.31 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,23,a)].
% 4.00/4.31 24 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 4.00/4.31 Derived: c(c1) != A | complement(c1,A). [resolve(24,a,19,a)].
% 4.00/4.31 Derived: c(c2) != A | complement(c2,A). [resolve(24,a,20,a)].
% 4.00/4.31 Derived: c(c3) != A | complement(c3,A). [resolve(24,a,21,a)].
% 4.00/4.31 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(24,a,22,a)].
% 4.00/4.31 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(24,a,23,a)].
% 4.00/4.31 25 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 4.00/4.31 Derived: c(c1) = A | -complement(c1,A). [resolve(25,a,19,a)].
% 4.00/4.31 Derived: c(c2) = A | -complement(c2,A). [resolve(25,a,20,a)].
% 4.00/4.31 Derived: c(c3) = A | -complement(c3,A). [resolve(25,a,21,a)].
% 4.00/4.31 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(25,a,22,a)].
% 4.00/4.31 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(25,a,23,a)].
% 4.00/4.31
% 4.00/4.31 ============================== end predicate elimination =============
% 4.00/4.31
% 4.00/4.31 Auto_denials: (non-Horn, no changes).
% 4.00/4.31
% 4.00/4.31 Term ordering decisions:
% 4.00/4.31 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. c=1. f1=1.
% 4.00/4.31
% 4.00/4.31 ============================== end of process initial clauses ========
% 4.00/4.31
% 4.00/4.31 ============================== CLAUSES FOR SEARCH ====================
% 4.00/4.31
% 4.00/4.31 ============================== end of clauses for search =============
% 4.00/4.31
% 4.00/4.31 ============================== SEARCH ================================
% 4.00/4.31
% 4.00/4.31 % Starting search at 0.01 seconds.
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=62.000, iters=3358
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=60.000, iters=3438
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=53.000, iters=3464
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=48.000, iters=3390
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=44.000, iters=3390
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=40.000, iters=3345
% 4.00/4.31
% 4.00/4.31 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 68 (0.00 of 1.69 sec).
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=38.000, iters=3378
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=37.000, iters=3356
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=36.000, iters=3389
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=34.000, iters=3391
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=33.000, iters=3360
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=32.000, iters=3343
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=31.000, iters=3345
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=30.000, iters=3334
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=29.000, iters=3341
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=28.000, iters=3335
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=27.000, iters=3393
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=26.000, iters=3385
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=25.000, iters=3407
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=24.000, iters=3339
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=23.000, iters=3339
% 4.00/4.31
% 4.00/4.31 Low Water (keep): wt=22.000, iters=3375
% 4.00/4.31
% 4.00/4.31 Low Water (displace): id=5736, wt=107.000
% 4.00/4.31
% 4.00/4.31 Low Water (displace): id=4816, wt=88.000
% 4.00/4.31
% 4.00/4.31 Low Water (displace): id=4456, wt=85.000
% 4.00/4.31
% 4.00/4.31 Low Water (displace): id=5476, wt=82.000
% 4.00/4.31
% 4.00/4.31 Low Water (displace): id=5708, wt=81.000
% 4.00/4.31
% 4.00/4.31 Low Water (displace): id=4811, wt=80.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=5709, wt=79.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=5372, wt=74.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=4815, wt=72.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=5429, wt=68.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=5405, wt=67.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=4534, wt=66.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=6312, wt=64.000
% 29.59/29.94
% 29.59/29.94 Low Water (keep): wt=21.000, iters=3340
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=11707, wt=18.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=11715, wt=17.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=11731, wt=16.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=11803, wt=15.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=11960, wt=14.000
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=12037, wt=13.000
% 29.59/29.94
% 29.59/29.94 Low Water (keep): wt=20.000, iters=3370
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=13907, wt=12.000
% 29.59/29.94
% 29.59/29.94 Low Water (keep): wt=19.000, iters=3340
% 29.59/29.94
% 29.59/29.94 Low Water (keep): wt=18.000, iters=3339
% 29.59/29.94
% 29.59/29.94 Low Water (displace): id=16941, wt=10.000
% 29.59/29.94
% 29.59/29.94 Low Water (keep): wt=17.000, iters=3340
% 29.59/29.94
% 29.59/29.94 Low Water (keep): wt=16.000, iters=3341
% 29.59/29.94
% 29.59/29.94 Low Water (keep): wt=15.000, iters=3342
% 29.59/29.94
% 29.59/29.94 ============================== PROOF =================================
% 29.59/29.94 % SZS status Theorem
% 29.59/29.94 % SZS output start Refutation
% 29.59/29.94
% 29.59/29.94 % Proof 1 at 28.08 (+ 0.65) seconds.
% 29.59/29.94 % Length of proof is 190.
% 29.59/29.94 % Level of proof is 26.
% 29.59/29.94 % Maximum clause weight is 28.000.
% 29.59/29.94 % Given clauses 2872.
% 29.59/29.94
% 29.59/29.94 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 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].
% 29.59/29.94 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 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].
% 29.59/29.94 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 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].
% 29.59/29.94 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].
% 29.59/29.94 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 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].
% 29.59/29.94 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 29.59/29.94 17 -(all X0 all X1 all X2 (test(X0) & test(X1) & test(X2) -> (leq(multiplication(X0,c(X1)),X2) -> leq(X0,addition(X1,X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 29.59/29.94 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 29.59/29.94 19 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 29.59/29.94 20 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 29.59/29.94 21 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 29.59/29.94 23 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 29.59/29.94 24 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 29.59/29.94 25 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 29.59/29.94 26 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 29.59/29.94 27 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 29.59/29.94 28 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 29.59/29.94 29 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 29.59/29.94 30 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 29.59/29.94 31 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 29.59/29.94 32 leq(multiplication(c1,c(c2)),c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 29.59/29.94 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 29.59/29.94 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 29.59/29.94 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([33(2)]),flip(a)].
% 29.59/29.94 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 29.59/29.94 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 29.59/29.94 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 29.59/29.94 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 29.59/29.94 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 29.59/29.94 41 -leq(c1,addition(c2,c3)) # label(goals) # label(negated_conjecture). [clausify(17)].
% 29.59/29.94 42 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 29.59/29.94 43 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 29.59/29.94 44 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 29.59/29.94 45 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 29.59/29.94 46 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 29.59/29.94 47 -complement(A,B) | addition(A,B) = one. [copy(46),rewrite([33(2)])].
% 29.59/29.94 48 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 29.59/29.94 49 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(A,B) != one. [copy(48),rewrite([33(8)])].
% 29.59/29.94 50 complement(f1(c1),c1). [resolve(18,a,19,a)].
% 29.59/29.94 51 complement(f1(c2),c2). [resolve(18,a,20,a)].
% 29.59/29.94 52 complement(f1(c3),c3). [resolve(18,a,21,a)].
% 29.59/29.94 54 complement(f1(A),A) | -complement(B,A). [resolve(18,a,23,a)].
% 29.59/29.94 55 c(c1) != A | complement(c1,A). [resolve(24,a,19,a)].
% 29.59/29.94 56 c(c2) != A | complement(c2,A). [resolve(24,a,20,a)].
% 29.59/29.94 57 c(c3) != A | complement(c3,A). [resolve(24,a,21,a)].
% 29.59/29.94 61 c(c2) = A | -complement(c2,A). [resolve(25,a,20,a)].
% 29.59/29.94 62 c(c3) = A | -complement(c3,A). [resolve(25,a,21,a)].
% 29.59/29.94 68 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),27(a,1)),rewrite([33(1),33(2),35(2,R),27(1),33(3)])].
% 29.59/29.94 69 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(26(a,1),38(a,2,2)),rewrite([30(3),33(3)])].
% 29.59/29.94 70 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(28(a,1),38(a,1,1)),rewrite([33(4)]),flip(a)].
% 29.59/29.94 71 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(29(a,1),40(a,1,1)),rewrite([33(4)]),flip(a)].
% 29.59/29.94 72 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)])].
% 29.59/29.94 74 addition(c3,multiplication(c1,c(c2))) = c3. [resolve(42,a,32,a),rewrite([33(6)])].
% 29.59/29.94 76 addition(c1,addition(c2,c3)) != addition(c2,c3). [ur(43,a,41,a)].
% 29.59/29.94 78 leq(multiplication(A,B),multiplication(A,C)) | multiplication(A,addition(B,C)) != multiplication(A,C). [para(38(a,1),43(b,1))].
% 29.59/29.94 79 leq(multiplication(A,B),multiplication(C,B)) | multiplication(addition(A,C),B) != multiplication(C,B). [para(40(a,1),43(b,1))].
% 29.59/29.94 81 complement(one,zero). [resolve(49,d,26,a),rewrite([28(6),30(9)]),xx(b),xx(c)].
% 29.59/29.94 86 addition(c1,f1(c1)) = one. [resolve(50,a,47,a),rewrite([33(4)])].
% 29.59/29.94 89 addition(c2,f1(c2)) = one. [resolve(51,a,47,a),rewrite([33(4)])].
% 29.59/29.94 92 addition(c3,f1(c3)) = one. [resolve(52,a,47,a),rewrite([33(4)])].
% 29.59/29.94 98 complement(c1,c(c1)). [resolve(55,a,29,a(flip)),rewrite([29(5)])].
% 29.59/29.94 100 complement(c2,c(c2)). [resolve(56,a,29,a(flip)),rewrite([29(5)])].
% 29.59/29.94 101 complement(c2,addition(zero,c(c2))). [resolve(56,a,26,a(flip)),rewrite([33(5)])].
% 29.59/29.94 102 complement(c3,c(c3)). [resolve(57,a,29,a(flip)),rewrite([29(5)])].
% 29.59/29.94 103 complement(c3,addition(zero,c(c3))). [resolve(57,a,26,a(flip)),rewrite([33(5)])].
% 29.59/29.94 115 leq(A,addition(A,B)). [resolve(68,a,43,b)].
% 29.59/29.94 121 addition(zero,one) = one. [resolve(81,a,47,a),rewrite([33(3)])].
% 29.59/29.94 124 complement(f1(c(c1)),c(c1)). [resolve(98,a,54,b)].
% 29.59/29.94 125 addition(c1,c(c1)) = one. [resolve(98,a,47,a)].
% 29.59/29.94 126 multiplication(c1,c(c1)) = zero. [resolve(98,a,45,a)].
% 29.59/29.94 127 multiplication(c(c1),c1) = zero. [resolve(98,a,44,a)].
% 29.59/29.94 130 complement(f1(c(c2)),c(c2)). [resolve(100,a,54,b)].
% 29.59/29.94 131 addition(c2,c(c2)) = one. [resolve(100,a,47,a)].
% 29.59/29.94 132 multiplication(c2,c(c2)) = zero. [resolve(100,a,45,a)].
% 29.59/29.94 133 multiplication(c(c2),c2) = zero. [resolve(100,a,44,a)].
% 29.59/29.94 138 complement(f1(c(c3)),c(c3)). [resolve(102,a,54,b)].
% 29.59/29.94 139 addition(c3,c(c3)) = one. [resolve(102,a,47,a)].
% 29.59/29.94 140 multiplication(c3,c(c3)) = zero. [resolve(102,a,45,a)].
% 29.59/29.94 141 multiplication(c(c3),c3) = zero. [resolve(102,a,44,a)].
% 29.59/29.94 144 leq(multiplication(A,B),multiplication(A,addition(B,C))). [para(38(a,1),115(a,2))].
% 29.59/29.94 147 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(70(a,2),35(a,2,2)),rewrite([33(2)]),flip(a)].
% 29.59/29.94 148 multiplication(addition(A,multiplication(A,B)),C) = multiplication(A,multiplication(addition(B,one),C)). [para(70(a,1),36(a,1,1))].
% 29.59/29.94 151 multiplication(A,addition(B,addition(C,one))) = addition(A,multiplication(A,addition(B,C))). [para(70(a,1),38(a,1,2)),rewrite([35(4,R),38(3),33(1)]),flip(a)].
% 29.59/29.94 174 addition(A,multiplication(addition(B,one),C)) = addition(C,addition(A,multiplication(B,C))). [para(71(a,2),35(a,2,2)),rewrite([33(2)]),flip(a)].
% 29.59/29.94 192 leq(multiplication(A,multiplication(B,C)),multiplication(D,C)) | multiplication(addition(D,multiplication(A,B)),C) != multiplication(D,C). [para(72(a,1),43(b,1))].
% 29.59/29.94 205 addition(one,c1) = one. [para(86(a,1),68(a,1,2)),rewrite([33(3),86(7)])].
% 29.59/29.94 227 addition(A,multiplication(A,c1)) = A. [para(205(a,1),38(a,2,2)),rewrite([28(2),28(5)])].
% 29.59/29.94 228 addition(A,multiplication(c1,A)) = A. [para(205(a,1),40(a,2,1)),rewrite([29(2),29(5)])].
% 29.59/29.94 234 addition(one,c2) = one. [para(89(a,1),68(a,1,2)),rewrite([33(3),89(7)])].
% 29.59/29.94 259 addition(A,multiplication(c2,A)) = A. [para(234(a,1),40(a,2,1)),rewrite([29(2),29(5)])].
% 29.59/29.94 264 addition(one,c3) = one. [para(92(a,1),68(a,1,2)),rewrite([33(3),92(7)])].
% 29.59/29.94 286 addition(A,multiplication(A,c3)) = A. [para(264(a,1),38(a,2,2)),rewrite([28(2),28(5)])].
% 29.59/29.94 287 addition(A,multiplication(c3,A)) = A. [para(264(a,1),40(a,2,1)),rewrite([29(2),29(5)])].
% 29.59/29.94 312 addition(zero,c(c2)) = c(c2). [resolve(101,a,61,b),flip(a)].
% 29.59/29.94 316 addition(zero,c(c3)) = c(c3). [resolve(103,a,62,b),flip(a)].
% 29.59/29.94 326 addition(c(c1),f1(c(c1))) = one. [resolve(124,a,47,a),rewrite([33(6)])].
% 29.59/29.94 331 multiplication(c1,multiplication(c(c1),A)) = zero. [para(126(a,1),36(a,1,1)),rewrite([31(2)]),flip(a)].
% 29.59/29.94 332 multiplication(c1,addition(A,c(c1))) = multiplication(c1,A). [para(126(a,1),38(a,1,1)),rewrite([69(4),33(6)]),flip(a)].
% 29.59/29.94 335 multiplication(addition(A,multiplication(B,c1)),c(c1)) = multiplication(A,c(c1)). [para(126(a,1),72(a,1,1,2)),rewrite([30(2),69(5)]),flip(a)].
% 29.59/29.94 340 multiplication(c(c1),multiplication(c1,A)) = zero. [para(127(a,1),36(a,1,1)),rewrite([31(2)]),flip(a)].
% 29.59/29.94 347 addition(c(c2),f1(c(c2))) = one. [resolve(130,a,47,a),rewrite([33(6)])].
% 29.59/29.94 357 multiplication(addition(c2,multiplication(A,B)),c(c2)) = multiplication(A,multiplication(B,c(c2))). [para(132(a,1),72(a,1,2)),rewrite([33(6),69(6)]),flip(a)].
% 29.59/29.94 369 multiplication(c(c2),multiplication(c2,A)) = zero. [para(133(a,1),36(a,1,1)),rewrite([31(2)]),flip(a)].
% 29.59/29.94 376 addition(c(c3),f1(c(c3))) = one. [resolve(138,a,47,a),rewrite([33(6)])].
% 29.59/29.94 403 multiplication(c3,addition(A,c(c3))) = multiplication(c3,A). [para(140(a,1),38(a,1,1)),rewrite([69(4),33(6)]),flip(a)].
% 29.59/29.94 406 multiplication(addition(A,multiplication(B,c3)),c(c3)) = multiplication(A,c(c3)). [para(140(a,1),72(a,1,1,2)),rewrite([30(2),69(5)]),flip(a)].
% 29.59/29.94 412 multiplication(addition(A,multiplication(B,c(c3))),c3) = multiplication(A,c3). [para(141(a,1),72(a,1,1,2)),rewrite([30(2),69(4)]),flip(a)].
% 29.59/29.94 490 addition(A,addition(B,multiplication(A,c1))) = addition(A,B). [para(227(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 29.59/29.94 506 addition(A,addition(B,multiplication(c2,A))) = addition(A,B). [para(259(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 29.59/29.94 508 addition(A,addition(B,multiplication(A,c3))) = addition(A,B). [para(286(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 29.59/29.94 513 addition(A,addition(B,multiplication(c3,A))) = addition(A,B). [para(287(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 29.59/29.94 586 leq(multiplication(A,B),multiplication(A,addition(C,multiplication(B,D)))) | multiplication(A,addition(C,multiplication(B,addition(D,one)))) != multiplication(A,addition(C,multiplication(B,D))). [para(147(a,2),78(b,1,2))].
% 29.59/29.94 587 leq(multiplication(A,B),multiplication(addition(C,multiplication(A,D)),B)) | multiplication(addition(C,multiplication(A,addition(D,one))),B) != multiplication(addition(C,multiplication(A,D)),B). [para(147(a,2),79(b,1,1))].
% 29.59/29.94 597 addition(one,c(c1)) = one. [para(326(a,1),68(a,1,2)),rewrite([33(4),326(10)])].
% 29.59/29.94 687 addition(A,multiplication(A,c(c1))) = A. [para(597(a,1),38(a,2,2)),rewrite([28(2),28(6)])].
% 29.59/29.94 688 addition(A,multiplication(c(c1),A)) = A. [para(597(a,1),40(a,2,1)),rewrite([29(2),29(6)])].
% 29.59/29.94 755 multiplication(c1,addition(A,multiplication(c(c1),B))) = multiplication(c1,A). [para(331(a,1),38(a,1,1)),rewrite([69(4),33(7)]),flip(a)].
% 29.59/29.94 760 multiplication(c(c1),addition(A,multiplication(c1,B))) = multiplication(c(c1),A). [para(340(a,1),38(a,1,1)),rewrite([69(5),33(8)]),flip(a)].
% 29.59/29.94 772 leq(multiplication(A,c(c2)),A). [para(347(a,1),144(a,2,2)),rewrite([28(5)])].
% 29.59/29.94 808 leq(multiplication(A,multiplication(B,c(c2))),multiplication(A,B)). [para(36(a,1),772(a,1))].
% 29.59/29.94 850 multiplication(A,addition(zero,addition(one,c(c3)))) = addition(A,multiplication(A,c(c3))). [para(316(a,1),151(a,2,2,2)),rewrite([33(5)])].
% 29.59/29.94 870 multiplication(c(c2),addition(A,multiplication(c2,B))) = multiplication(c(c2),A). [para(369(a,1),38(a,1,1)),rewrite([69(5),33(8)]),flip(a)].
% 29.59/29.94 874 multiplication(c(c2),multiplication(addition(one,multiplication(c2,A)),B)) = multiplication(c(c2),B). [para(369(a,1),148(a,1,1,2)),rewrite([33(4),312(4),33(9)]),flip(a)].
% 29.59/29.94 902 addition(one,c(c3)) = one. [para(376(a,1),68(a,1,2)),rewrite([33(4),376(10)])].
% 29.59/29.94 909 addition(A,multiplication(A,c(c3))) = A. [back_rewrite(850),rewrite([902(5),121(3),28(2)]),flip(a)].
% 29.59/29.94 1120 addition(A,addition(B,multiplication(A,c(c1)))) = addition(A,B). [para(687(a,1),35(a,2,2)),rewrite([33(4),33(6)])].
% 29.59/29.94 1145 addition(A,addition(B,multiplication(c(c1),A))) = addition(A,B). [para(688(a,1),35(a,2,2)),rewrite([33(4),33(6)])].
% 29.59/29.94 1223 addition(A,addition(B,multiplication(A,c(c3)))) = addition(A,B). [para(909(a,1),35(a,2,2)),rewrite([33(4),33(6)])].
% 29.59/29.94 1981 multiplication(c1,c1) = c1. [para(125(a,1),332(a,1,2)),rewrite([28(3)]),flip(a)].
% 29.59/29.94 2002 multiplication(c1,multiplication(c1,A)) = multiplication(c1,A). [para(1981(a,1),36(a,1,1)),flip(a)].
% 29.59/29.94 2005 multiplication(addition(A,multiplication(B,c1)),c1) = multiplication(addition(B,A),c1). [para(1981(a,1),72(a,1,1,2)),rewrite([40(5)]),flip(a)].
% 29.59/29.94 2020 multiplication(c1,addition(A,multiplication(c1,B))) = multiplication(c1,addition(B,A)). [para(2002(a,1),38(a,1,1)),rewrite([38(5),33(7)]),flip(a)].
% 29.59/29.94 2306 multiplication(c3,c3) = c3. [para(139(a,1),403(a,1,2)),rewrite([28(3)]),flip(a)].
% 29.59/29.94 2416 multiplication(addition(A,multiplication(B,c3)),c3) = multiplication(addition(B,A),c3). [para(2306(a,1),72(a,1,1,2)),rewrite([40(5)]),flip(a)].
% 29.59/29.94 2610 leq(multiplication(c1,multiplication(c(c2),A)),multiplication(c3,A)). [para(74(a,1),192(b,1,1)),xx(b)].
% 29.59/29.94 8866 addition(A,multiplication(addition(A,B),c1)) = addition(A,multiplication(B,c1)). [para(40(a,1),490(a,1,2)),rewrite([33(1)])].
% 29.59/29.94 8876 addition(one,addition(c1,c3)) = one. [para(264(a,1),490(a,2)),rewrite([29(5),33(4)])].
% 29.59/29.94 9407 addition(A,addition(B,multiplication(addition(C,c3),A))) = addition(B,multiplication(addition(C,one),A)). [para(174(a,2),513(a,2)),rewrite([33(5),35(5,R),40(4)])].
% 29.59/29.94 16199 leq(multiplication(A,c1),multiplication(A,addition(B,one))). [para(228(a,1),586(b,1,2)),rewrite([33(7),35(7),33(6),228(6),33(4),33(14),35(14),33(13),228(13),33(11)]),xx(b)].
% 29.59/29.94 16201 leq(multiplication(A,c3),multiplication(A,addition(B,one))). [para(287(a,1),586(b,1,2)),rewrite([33(7),35(7),33(6),287(6),33(4),33(14),35(14),33(13),287(13),33(11)]),xx(b)].
% 29.59/29.94 16213 leq(multiplication(A,c1),addition(A,multiplication(A,B))). [para(70(a,1),16199(a,2))].
% 29.59/29.94 16239 leq(multiplication(A,c3),addition(A,multiplication(A,B))). [para(70(a,1),16201(a,2))].
% 29.59/29.94 16251 leq(multiplication(c1,A),multiplication(addition(B,one),A)). [para(228(a,1),587(b,1,1)),rewrite([33(7),35(7),33(6),228(6),33(4),33(14),35(14),33(13),228(13),33(11)]),xx(b)].
% 29.59/29.94 16305 leq(multiplication(addition(A,B),c1),addition(A,multiplication(B,c1))). [para(335(a,1),16213(a,2,2)),rewrite([2005(5),33(1),33(10),35(10,R),1120(10)])].
% 29.59/29.94 16486 leq(multiplication(addition(A,B),c3),addition(A,multiplication(B,c3))). [para(406(a,1),16239(a,2,2)),rewrite([2416(5),33(1),33(10),35(10,R),1223(10)])].
% 29.59/29.94 16489 leq(multiplication(c1,A),addition(A,multiplication(B,A))). [para(71(a,1),16251(a,2))].
% 29.59/29.94 18406 leq(multiplication(addition(A,B),c1),addition(B,multiplication(A,c1))). [para(33(a,1),16305(a,1,1))].
% 29.59/29.94 18429 leq(c1,addition(one,multiplication(addition(c1,c3),c1))). [para(8876(a,1),16305(a,1,1)),rewrite([29(3)])].
% 29.59/29.94 18483 addition(one,multiplication(addition(c1,c3),c1)) = one. [resolve(18429,a,42,a),rewrite([9407(9),33(4),205(4),29(4),205(3)]),flip(a)].
% 29.59/29.94 18486 addition(A,multiplication(A,multiplication(addition(c1,c3),c1))) = A. [para(18483(a,1),38(a,2,2)),rewrite([28(2),28(9)])].
% 29.59/29.94 18758 leq(multiplication(c1,addition(A,B)),addition(A,multiplication(c1,B))). [para(760(a,1),16489(a,2,2)),rewrite([2020(5),33(2),33(10),35(10,R),1145(10)])].
% 29.59/29.94 19287 leq(multiplication(addition(A,B),c3),addition(B,multiplication(A,c3))). [para(33(a,1),16486(a,1,1))].
% 29.59/29.94 19295 leq(c3,addition(c1,multiplication(c(c1),c3))). [para(125(a,1),16486(a,1,1)),rewrite([29(3)])].
% 29.59/29.94 19364 addition(c1,multiplication(c(c1),c3)) = addition(c1,c3). [resolve(19295,a,42,a),rewrite([1145(8),33(3)]),flip(a)].
% 29.59/29.94 19389 multiplication(c1,addition(c1,c3)) = c1. [para(19364(a,1),755(a,1,2)),rewrite([1981(8)])].
% 29.59/29.94 19392 multiplication(c1,multiplication(addition(c1,c3),A)) = multiplication(c1,A). [para(19389(a,1),36(a,1,1)),flip(a)].
% 29.59/29.94 20271 multiplication(c(c2),c(c2)) = c(c2). [para(874(a,1),357(a,2)),rewrite([870(8),28(5),131(4),29(4)]),flip(a)].
% 29.59/29.94 20282 leq(multiplication(c1,c(c2)),multiplication(c3,c(c2))). [para(20271(a,1),2610(a,1,2))].
% 29.59/29.94 20292 multiplication(addition(c1,c3),c(c2)) = multiplication(c3,c(c2)). [resolve(20282,a,42,a),rewrite([40(9)])].
% 29.59/29.94 21103 leq(c1,multiplication(addition(c1,c3),c1)). [para(18486(a,1),16489(a,2)),rewrite([19392(7),1981(3)])].
% 29.59/29.94 21109 multiplication(addition(c1,c3),c1) = c1. [resolve(21103,a,42,a),rewrite([8866(7),287(5)]),flip(a)].
% 29.59/29.94 21380 leq(multiplication(c1,addition(A,B)),addition(B,multiplication(c1,A))). [para(33(a,1),18758(a,1,2))].
% 29.59/29.94 21390 leq(c1,addition(c3,multiplication(c1,c(c3)))). [para(139(a,1),18758(a,1,2)),rewrite([28(3)])].
% 29.59/29.94 21470 addition(c3,multiplication(c1,c(c3))) = addition(c1,c3). [resolve(21390,a,42,a),rewrite([1223(8)]),flip(a)].
% 29.59/29.94 21529 leq(c1,addition(multiplication(c3,c1),multiplication(c1,c(c3)))). [para(21470(a,1),18406(a,1,1)),rewrite([21109(5),33(9)])].
% 29.59/29.94 21530 addition(multiplication(c3,c1),multiplication(c1,c(c3))) = c1. [resolve(21529,a,42,a),rewrite([1223(10),287(5)]),flip(a)].
% 29.59/29.94 21535 multiplication(c3,multiplication(c1,c3)) = multiplication(c1,c3). [para(21530(a,1),412(a,1,1)),rewrite([36(8)]),flip(a)].
% 29.59/29.94 21558 multiplication(c3,addition(c(c3),multiplication(c1,c3))) = multiplication(c1,c3). [para(21535(a,1),403(a,2)),rewrite([33(7)])].
% 29.59/29.94 21769 leq(c3,addition(c(c2),multiplication(c2,c3))). [para(131(a,1),19287(a,1,1)),rewrite([29(3)])].
% 29.59/29.94 21785 addition(c(c2),multiplication(c2,c3)) = addition(c3,c(c2)). [resolve(21769,a,42,a),rewrite([506(8)]),flip(a)].
% 29.59/29.94 22962 multiplication(c1,multiplication(c3,c(c2))) = multiplication(c1,c(c2)). [para(20292(a,1),19392(a,1,2))].
% 29.59/29.94 23627 leq(c1,addition(c(c3),multiplication(c1,c3))). [para(139(a,1),21380(a,1,2)),rewrite([28(3)])].
% 29.59/29.94 23638 addition(c(c3),multiplication(c1,c3)) = addition(c1,c(c3)). [resolve(23627,a,42,a),rewrite([508(8)]),flip(a)].
% 29.59/29.94 23640 multiplication(c3,c1) = multiplication(c1,c3). [back_rewrite(21558),rewrite([23638(7),403(6)])].
% 29.59/29.94 23687 multiplication(c3,multiplication(c1,A)) = multiplication(c1,multiplication(c3,A)). [para(23640(a,1),36(a,1,1)),rewrite([36(4)]),flip(a)].
% 29.59/29.94 23695 leq(multiplication(c1,c(c2)),multiplication(c1,c3)). [para(23640(a,1),808(a,2)),rewrite([23687(6),22962(6)])].
% 29.59/29.94 23781 multiplication(c1,addition(c3,c(c2))) = multiplication(c1,c3). [resolve(23695,a,42,a),rewrite([33(8),38(8)])].
% 29.59/29.94 24076 addition(c2,addition(c3,c(c2))) = one. [para(21785(a,1),147(a,2,2)),rewrite([33(6),264(6),28(5),33(4),131(4)]),flip(a)].
% 29.59/29.94 24090 leq(c1,addition(c2,multiplication(c1,c3))). [para(24076(a,1),18758(a,1,2)),rewrite([28(3),23781(8)])].
% 29.59/29.94 24094 addition(c2,multiplication(c1,c3)) = addition(c1,c2). [resolve(24090,a,42,a),rewrite([508(7)]),flip(a)].
% 29.59/29.94 24097 $F. [para(24094(a,1),174(a,2,2)),rewrite([33(4),205(4),29(4),35(8),33(7),35(8,R),33(7)]),flip(a),unit_del(a,76)].
% 29.59/29.94
% 29.59/29.94 % SZS output end Refutation
% 29.59/29.94 ============================== end of proof ==========================
% 29.59/29.94
% 29.59/29.94 ============================== STATISTICS ============================
% 29.59/29.94
% 29.59/29.94 Given=2872. Generated=656165. Kept=24066. proofs=1.
% 29.59/29.94 Usable=2181. Sos=9626. Demods=1828. Limbo=1, Disabled=12300. Hints=0.
% 29.59/29.94 Megabytes=18.36.
% 29.59/29.94 User_CPU=28.09, System_CPU=0.65, Wall_clock=29.
% 29.59/29.94
% 29.59/29.94 ============================== end of statistics =====================
% 29.59/29.94
% 29.59/29.94 ============================== end of search =========================
% 29.59/29.94
% 29.59/29.94 THEOREM PROVED
% 29.59/29.94 % SZS status Theorem
% 29.59/29.94
% 29.59/29.94 Exiting with 1 proof.
% 29.59/29.94
% 29.59/29.94 Process 3569 exit (max_proofs) Thu Jun 16 16:17:13 2022
% 29.59/29.94 Prover9 interrupted
%------------------------------------------------------------------------------