TSTP Solution File: KLE105+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE105+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 02:22:15 EDT 2022
% Result : Theorem 46.89s 47.13s
% Output : Refutation 46.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE105+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n011.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 08:08:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.79/1.06 ============================== Prover9 ===============================
% 0.79/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.06 Process 18966 was started by sandbox on n011.cluster.edu,
% 0.79/1.06 Thu Jun 16 08:08:36 2022
% 0.79/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18811_n011.cluster.edu".
% 0.79/1.06 ============================== end of head ===========================
% 0.79/1.06
% 0.79/1.06 ============================== INPUT =================================
% 0.79/1.06
% 0.79/1.06 % Reading from file /tmp/Prover9_18811_n011.cluster.edu
% 0.79/1.06
% 0.79/1.06 set(prolog_style_variables).
% 0.79/1.06 set(auto2).
% 0.79/1.06 % set(auto2) -> set(auto).
% 0.79/1.06 % set(auto) -> set(auto_inference).
% 0.79/1.06 % set(auto) -> set(auto_setup).
% 0.79/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.06 % set(auto) -> set(auto_limits).
% 0.79/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.06 % set(auto) -> set(auto_denials).
% 0.79/1.06 % set(auto) -> set(auto_process).
% 0.79/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.06 % set(auto2) -> assign(stats, some).
% 0.79/1.06 % set(auto2) -> clear(echo_input).
% 0.79/1.06 % set(auto2) -> set(quiet).
% 0.79/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.06 % set(auto2) -> clear(print_given).
% 0.79/1.06 assign(lrs_ticks,-1).
% 0.79/1.06 assign(sos_limit,10000).
% 0.79/1.06 assign(order,kbo).
% 0.79/1.06 set(lex_order_vars).
% 0.79/1.06 clear(print_given).
% 0.79/1.06
% 0.79/1.06 % formulas(sos). % not echoed (27 formulas)
% 0.79/1.06
% 0.79/1.06 ============================== end of input ==========================
% 0.79/1.06
% 0.79/1.06 % From the command line: assign(max_seconds, 300).
% 0.79/1.06
% 0.79/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.06
% 0.79/1.06 % Formulas that are not ordinary clauses:
% 0.79/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 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].
% 0.79/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 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].
% 0.79/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 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].
% 0.79/1.06 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].
% 0.79/1.06 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 18 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 4.90/5.17 27 -(all X0 all X1 all X2 (addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) -> addition(domain(X1),backward_box(X0,domain(X2))) = backward_box(X0,domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.90/5.17
% 4.90/5.17 ============================== end of process non-clausal formulas ===
% 4.90/5.17
% 4.90/5.17 ============================== PROCESS INITIAL CLAUSES ===============
% 4.90/5.17
% 4.90/5.17 ============================== PREDICATE ELIMINATION =================
% 4.90/5.17 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 4.90/5.17 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 4.90/5.17
% 4.90/5.17 ============================== end predicate elimination =============
% 4.90/5.17
% 4.90/5.17 Auto_denials:
% 4.90/5.17 % copying label goals to answer in negative clause
% 4.90/5.17
% 4.90/5.17 Term ordering decisions:
% 4.90/5.17 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. forward_diamond=1. backward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1.
% 4.90/5.17
% 4.90/5.17 ============================== end of process initial clauses ========
% 4.90/5.17
% 4.90/5.17 ============================== CLAUSES FOR SEARCH ====================
% 4.90/5.17
% 4.90/5.17 ============================== end of clauses for search =============
% 4.90/5.17
% 4.90/5.17 ============================== SEARCH ================================
% 4.90/5.17
% 4.90/5.17 % Starting search at 0.01 seconds.
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=41.000, iters=3380
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=39.000, iters=3403
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=36.000, iters=3366
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=31.000, iters=3336
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=30.000, iters=3345
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=29.000, iters=3349
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=28.000, iters=3335
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=27.000, iters=3387
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=26.000, iters=3333
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=25.000, iters=3337
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=21.000, iters=4348
% 4.90/5.17
% 4.90/5.17 Low Water (keep): wt=20.000, iters=3970
% 4.90/5.17
% 4.90/5.17 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.76 sec).
% 4.90/5.17
% 4.90/5.17 Low Water (displace): id=6299, wt=49.000
% 4.90/5.17
% 4.90/5.17 Low Water (displace): id=3733, wt=48.000
% 4.90/5.17
% 4.90/5.17 Low Water (displace): id=7006, wt=47.000
% 4.90/5.17
% 4.90/5.17 Low Water (displace): id=4707, wt=46.000
% 4.90/5.17
% 4.90/5.17 Low Water (displace): id=7007, wt=45.000
% 4.90/5.17
% 4.90/5.17 Low Water (displace): id=5991, wt=44.000
% 4.90/5.17
% 4.90/5.17 Low Water (displace): id=4435, wt=43.000
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=15462, wt=19.000
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=15463, wt=18.000
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=15469, wt=17.000
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=15534, wt=16.000
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=15537, wt=15.000
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=15546, wt=14.000
% 46.89/47.13
% 46.89/47.13 Low Water (keep): wt=19.000, iters=3336
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=16741, wt=13.000
% 46.89/47.13
% 46.89/47.13 Low Water (keep): wt=18.000, iters=3333
% 46.89/47.13
% 46.89/47.13 Low Water (keep): wt=17.000, iters=3335
% 46.89/47.13
% 46.89/47.13 Low Water (keep): wt=16.000, iters=3333
% 46.89/47.13
% 46.89/47.13 Low Water (displace): id=29374, wt=12.000
% 46.89/47.13
% 46.89/47.13 Low Water (keep): wt=15.000, iters=3336
% 46.89/47.13
% 46.89/47.13 ============================== PROOF =================================
% 46.89/47.13 % SZS status Theorem
% 46.89/47.13 % SZS output start Refutation
% 46.89/47.13
% 46.89/47.13 % Proof 1 at 44.36 (+ 1.71) seconds: goals.
% 46.89/47.13 % Length of proof is 164.
% 46.89/47.13 % Level of proof is 28.
% 46.89/47.13 % Maximum clause weight is 35.000.
% 46.89/47.13 % Given clauses 2769.
% 46.89/47.13
% 46.89/47.13 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 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].
% 46.89/47.13 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 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].
% 46.89/47.13 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 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].
% 46.89/47.13 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].
% 46.89/47.13 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 18 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 46.89/47.13 27 -(all X0 all X1 all X2 (addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) -> addition(domain(X1),backward_box(X0,domain(X2))) = backward_box(X0,domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 46.89/47.13 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 46.89/47.13 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 46.89/47.13 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 46.89/47.13 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 46.89/47.13 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 46.89/47.13 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 46.89/47.13 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 46.89/47.13 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 46.89/47.13 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 46.89/47.13 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 46.89/47.13 40 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)].
% 46.89/47.13 41 c(A) = antidomain(antidomain(antidomain(A))). [copy(40),rewrite([37(2)])].
% 46.89/47.13 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 46.89/47.13 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 46.89/47.13 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 46.89/47.13 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 46.89/47.13 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 46.89/47.13 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 46.89/47.13 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 46.89/47.13 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 46.89/47.13 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 46.89/47.13 55 backward_box(A,B) = c(backward_diamond(A,c(B))) # label(backward_box) # label(axiom). [clausify(26)].
% 46.89/47.13 56 backward_box(A,B) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(B))))),A)))))). [copy(55),rewrite([41(2),52(5),41(10)])].
% 46.89/47.13 57 domain(c3) = addition(forward_diamond(c1,domain(c2)),domain(c3)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 46.89/47.13 58 addition(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = antidomain(antidomain(c3)). [copy(57),rewrite([37(2),37(6),50(8),37(14),42(16)]),flip(a)].
% 46.89/47.13 59 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 46.89/47.13 60 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(59),rewrite([42(2)]),flip(a)].
% 46.89/47.13 61 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 46.89/47.13 62 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 46.89/47.13 63 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(62),flip(a)].
% 46.89/47.13 64 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 46.89/47.13 65 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(64),flip(a)].
% 46.89/47.13 66 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 46.89/47.13 67 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(66),flip(a)].
% 46.89/47.13 68 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 46.89/47.13 69 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(68),flip(a)].
% 46.89/47.13 70 backward_box(c1,domain(c3)) != addition(domain(c2),backward_box(c1,domain(c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 46.89/47.13 71 addition(antidomain(antidomain(c2)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1))))))) != antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1)))))) # answer(goals). [copy(70),rewrite([37(3),56(5),37(17),37(21),56(23)]),flip(a)].
% 46.89/47.13 72 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 46.89/47.13 73 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 46.89/47.13 74 addition(A,addition(A,B)) = addition(A,B). [para(60(a,1),31(a,1)),rewrite([42(1),42(2),60(2,R),31(1),42(3)])].
% 46.89/47.13 75 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),61(a,1,1)),rewrite([35(2)]),flip(a)].
% 46.89/47.13 78 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),63(a,2,2)),rewrite([34(3),42(3)])].
% 46.89/47.13 79 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),63(a,1,1)),rewrite([42(4)]),flip(a)].
% 46.89/47.13 80 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),63(a,1,1)),rewrite([78(4)]),flip(a)].
% 46.89/47.13 81 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),63(a,1,1)),rewrite([78(3),42(3)]),flip(a)].
% 46.89/47.13 82 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),65(a,1,1)),rewrite([42(4)]),flip(a)].
% 46.89/47.13 83 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(36(a,1),65(a,1,1)),rewrite([78(3),42(3)]),flip(a)].
% 46.89/47.13 84 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),65(a,1,1)),rewrite([78(4),42(3)]),flip(a)].
% 46.89/47.13 92 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),67(a,1,1,1))].
% 46.89/47.13 97 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),69(a,1,1,1))].
% 46.89/47.13 100 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(61(a,1),69(a,1,1,1))].
% 46.89/47.13 101 addition(zero,antidomain(zero)) = one. [para(72(a,1),44(a,1,1)),rewrite([72(3)])].
% 46.89/47.13 102 addition(zero,coantidomain(zero)) = one. [para(73(a,1),46(a,1,1)),rewrite([73(3)])].
% 46.89/47.13 105 multiplication(A,antidomain(zero)) = A. [para(101(a,1),63(a,2,2)),rewrite([34(2),78(5),32(5)])].
% 46.89/47.13 109 multiplication(A,coantidomain(zero)) = A. [para(102(a,1),63(a,2,2)),rewrite([34(2),78(5),32(5)])].
% 46.89/47.13 111 addition(one,antidomain(A)) = one. [para(44(a,1),74(a,1,2)),rewrite([42(3),44(7)])].
% 46.89/47.13 112 addition(one,coantidomain(A)) = one. [para(46(a,1),74(a,1,2)),rewrite([42(3),46(7)])].
% 46.89/47.13 113 antidomain(zero) = one. [para(105(a,1),33(a,1)),flip(a)].
% 46.89/47.13 114 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(92),rewrite([113(2),111(7)]),flip(a)].
% 46.89/47.13 116 coantidomain(zero) = one. [para(109(a,1),33(a,1)),flip(a)].
% 46.89/47.13 118 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(97),rewrite([116(2),112(7)]),flip(a)].
% 46.89/47.13 119 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(61(a,1),75(a,1,2))].
% 46.89/47.13 122 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(75(a,1),67(a,1,1,1)),rewrite([113(2),111(8)]),flip(a)].
% 46.89/47.13 125 addition(A,multiplication(antidomain(B),A)) = A. [para(111(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 46.89/47.13 126 addition(A,multiplication(A,coantidomain(B))) = A. [para(112(a,1),63(a,2,2)),rewrite([32(2),32(5)])].
% 46.89/47.13 127 addition(A,multiplication(coantidomain(B),A)) = A. [para(112(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 46.89/47.13 161 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(114(a,1),36(a,1,1)),rewrite([33(6)])].
% 46.89/47.13 166 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(161(a,1),63(a,1,1)),rewrite([78(3),42(5)]),flip(a)].
% 46.89/47.13 172 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),80(a,1,2)),rewrite([32(4)]),flip(a)].
% 46.89/47.13 177 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(65(a,1),80(a,1,2))].
% 46.89/47.13 181 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(125(a,1),80(a,1,2)),rewrite([36(2)]),flip(a)].
% 46.89/47.13 194 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),81(a,1,2)),rewrite([32(3)]),flip(a)].
% 46.89/47.13 203 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(194(a,1),63(a,1,1)),rewrite([79(4,R),42(7)]),flip(a)].
% 46.89/47.13 208 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(118(a,1),38(a,1,2)),rewrite([32(6)])].
% 46.89/47.13 212 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(208(a,1),65(a,1,1)),rewrite([78(3),42(5)]),flip(a)].
% 46.89/47.13 216 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(181(a,1),65(a,1,1)),rewrite([78(5),42(5)]),flip(a)].
% 46.89/47.13 219 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(80(a,1),181(a,1,2))].
% 46.89/47.13 242 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(81(a,1),82(a,2,2)),rewrite([42(9),60(9),42(8),60(9,R),42(8)])].
% 46.89/47.13 259 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(44(a,1),83(a,1,1)),rewrite([33(3)]),flip(a)].
% 46.89/47.13 267 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),84(a,1,1))].
% 46.89/47.13 268 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),84(a,1,1)),rewrite([33(5)]),flip(a)].
% 46.89/47.13 269 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),84(a,1,1)),rewrite([33(5)]),flip(a)].
% 46.89/47.13 282 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(259(a,1),61(a,1,1)),flip(a)].
% 46.89/47.13 521 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(122(a,1),36(a,1,1)),rewrite([33(7)])].
% 46.89/47.13 529 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(521(a,1),63(a,1,1)),rewrite([78(4),42(7)]),flip(a)].
% 46.89/47.13 585 multiplication(coantidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero. [para(100(a,1),81(a,1,2)),rewrite([38(10),61(9)]),flip(a)].
% 46.89/47.13 660 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(172(a,1),125(a,1,2)),rewrite([42(5)])].
% 46.89/47.13 758 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(42(a,1),219(a,1,1,1))].
% 46.89/47.13 857 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),267(a,1,1)),rewrite([33(4)]),flip(a)].
% 46.89/47.13 1190 multiplication(antidomain(addition(A,B)),A) = zero. [para(74(a,1),758(a,1,1,1)),rewrite([282(6)])].
% 46.89/47.13 1210 multiplication(antidomain(addition(A,B)),multiplication(A,C)) = zero. [para(1190(a,1),61(a,1,1)),rewrite([35(2)]),flip(a)].
% 46.89/47.13 1448 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(857(a,1),126(a,1,2))].
% 46.89/47.13 1461 multiplication(antidomain(addition(A,antidomain(antidomain(B)))),coantidomain(antidomain(B))) = zero. [para(857(a,1),1210(a,1,2)),rewrite([42(3)])].
% 46.89/47.13 2397 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),166(a,1,2)),rewrite([32(2)]),flip(a)].
% 46.89/47.13 2419 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2397(a,1),61(a,1,1)),flip(a)].
% 46.89/47.13 2420 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2397(a,1),61(a,1)),flip(a)].
% 46.89/47.13 2427 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2397(a,1),127(a,1,2)),rewrite([42(5)])].
% 46.89/47.13 2526 multiplication(A,coantidomain(coantidomain(A))) = A. [para(172(a,1),2419(a,1,2)),rewrite([2397(3)]),flip(a)].
% 46.89/47.13 2559 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(269),rewrite([2526(5)]),flip(a)].
% 46.89/47.13 2588 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2559(a,1),660(a,1,2)),rewrite([42(5),2427(5),2559(6)])].
% 46.89/47.13 2603 addition(antidomain(antidomain(c2)),antidomain(antidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1))))) != antidomain(antidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1)))) # answer(goals). [back_rewrite(71),rewrite([2588(16),2588(30)])].
% 46.89/47.13 2690 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2588(a,1),44(a,1,1)),rewrite([2588(4)])].
% 46.89/47.13 2696 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2588(a,1),857(a,1,1,1)),rewrite([2588(5),172(5),2588(5)]),flip(a)].
% 46.89/47.13 2698 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2588(a,1),857(a,2,1)),rewrite([2696(2),2696(6),857(9),2696(6)])].
% 46.89/47.13 2705 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2559(a,1),2588(a,1,1,1)),rewrite([2696(2),2696(5)]),flip(a)].
% 46.89/47.13 2706 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2559(a,1),2588(a,2)),rewrite([2696(2),2705(3),2698(4)])].
% 46.89/47.13 2719 addition(antidomain(antidomain(c2)),coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1))) != coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))),c1)) # answer(goals). [back_rewrite(2603),rewrite([2696(11),2706(16),2696(23),2706(28)])].
% 46.89/47.13 3032 multiplication(antidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero. [back_rewrite(585),rewrite([2696(3)])].
% 46.89/47.13 3057 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(212),rewrite([2696(3)])].
% 46.89/47.13 3507 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),177(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 46.89/47.13 3960 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(268(a,1),126(a,1,2))].
% 46.89/47.13 5024 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1448(a,1),203(a,1,2)),rewrite([42(11),111(11),32(9)])].
% 46.89/47.13 5029 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3960(a,1),203(a,1,2)),rewrite([42(11),111(11),32(10)])].
% 46.89/47.13 5364 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),216(a,1,1)),rewrite([33(5)]),flip(a)].
% 46.89/47.13 6338 multiplication(antidomain(antidomain(antidomain(c3))),coantidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = zero. [para(58(a,1),1461(a,1,1,1))].
% 46.89/47.13 7712 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(5024(a,1),242(a,2,2,2)),rewrite([42(4),112(4),2696(6),33(8),2696(11),42(14),2690(14),42(10),111(10)])].
% 46.89/47.13 9046 multiplication(coantidomain(antidomain(A)),A) = A. [para(2690(a,1),3057(a,1,1)),rewrite([33(2)]),flip(a)].
% 46.89/47.13 9056 multiplication(antidomain(antidomain(A)),A) = A. [para(7712(a,1),3057(a,1,1)),rewrite([33(2)]),flip(a)].
% 46.89/47.13 9060 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(5029),rewrite([9046(5)]),flip(a)].
% 46.89/47.13 9074 addition(antidomain(antidomain(c2)),coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))),c1))) != coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))),c1)) # answer(goals). [back_rewrite(2719),rewrite([9060(10),9060(20)])].
% 46.89/47.13 9144 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9056(a,1),119(a,1,2,2))].
% 46.89/47.13 9176 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9060(a,1),2696(a,1,1)),rewrite([9060(5)])].
% 46.89/47.13 9177 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9060(a,1),2696(a,2,1)),rewrite([9176(3),9176(4)])].
% 46.89/47.13 9178 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9060(a,1),2706(a,2)),rewrite([9176(3),9177(4)])].
% 46.89/47.13 9248 multiplication(antidomain(c3),antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2)))))) = zero. [back_rewrite(6338),rewrite([9178(4),9178(7),9176(9)])].
% 46.89/47.13 9329 addition(antidomain(antidomain(c2)),coantidomain(multiplication(antidomain(c3),c1))) != coantidomain(multiplication(antidomain(c3),c1)) # answer(goals). [back_rewrite(9074),rewrite([9178(7),9178(7),9178(13),9178(13)])].
% 46.89/47.13 11881 multiplication(antidomain(c3),multiplication(c1,antidomain(antidomain(c2)))) = zero. [para(9248(a,1),9144(a,1,1,1)),rewrite([113(2),33(10)])].
% 46.89/47.13 11882 multiplication(antidomain(c3),multiplication(c1,multiplication(antidomain(antidomain(c2)),A))) = zero. [para(11881(a,1),61(a,1,1)),rewrite([35(2),61(9)]),flip(a)].
% 46.89/47.13 12287 multiplication(antidomain(c3),multiplication(c1,c2)) = zero. [para(9056(a,1),11882(a,1,2,2))].
% 46.89/47.13 17307 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(44(a,1),529(a,1,2)),rewrite([32(3)]),flip(a)].
% 46.89/47.13 17474 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17307(a,1),125(a,1,2)),rewrite([42(4)])].
% 46.89/47.13 17502 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17307(a,1),2420(a,1,2,2,1,1)),rewrite([9176(5),9178(6),5364(6),17307(8)])].
% 46.89/47.13 17683 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17502(a,1),61(a,1,1)),flip(a)].
% 46.89/47.13 17715 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3507),rewrite([17683(7)]),flip(a)].
% 46.89/47.13 18295 addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(A,B)))) = antidomain(antidomain(A)). [para(17502(a,1),17474(a,1,2,1)),rewrite([42(6),17502(10)])].
% 46.89/47.13 34238 multiplication(antidomain(coantidomain(multiplication(antidomain(c3),c1))),c2) = zero. [para(12287(a,1),3032(a,1,2,2,1)),rewrite([116(9),32(9)])].
% 46.89/47.13 34262 multiplication(coantidomain(multiplication(antidomain(c3),c1)),c2) = c2. [para(34238(a,1),17715(a,1,1,1)),rewrite([113(2),33(3),2706(8)]),flip(a)].
% 46.89/47.13 34294 addition(antidomain(antidomain(c2)),coantidomain(multiplication(antidomain(c3),c1))) = coantidomain(multiplication(antidomain(c3),c1)). [para(34262(a,1),18295(a,1,2,1,1)),rewrite([2706(7),42(9),2706(16)])].
% 46.89/47.13 34295 $F # answer(goals). [resolve(34294,a,9329,a)].
% 46.89/47.13
% 46.89/47.13 % SZS output end Refutation
% 46.89/47.13 ============================== end of proof ==========================
% 46.89/47.13
% 46.89/47.13 ============================== STATISTICS ============================
% 46.89/47.13
% 46.89/47.13 Given=2769. Generated=3149914. Kept=34250. proofs=1.
% 46.89/47.13 Usable=1781. Sos=8674. Demods=10279. Limbo=30, Disabled=23793. Hints=0.
% 46.89/47.13 Megabytes=25.75.
% 46.89/47.13 User_CPU=44.36, System_CPU=1.71, Wall_clock=47.
% 46.89/47.13
% 46.89/47.13 ============================== end of statistics =====================
% 46.89/47.13
% 46.89/47.13 ============================== end of search =========================
% 46.89/47.13
% 46.89/47.13 THEOREM PROVED
% 46.89/47.13 % SZS status Theorem
% 46.89/47.13
% 46.89/47.13 Exiting with 1 proof.
% 46.89/47.13
% 46.89/47.13 Process 18966 exit (max_proofs) Thu Jun 16 08:09:23 2022
% 46.89/47.13 Prover9 interrupted
%------------------------------------------------------------------------------