TSTP Solution File: KLE132+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE132+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 02:22:22 EDT 2022
% Result : Theorem 1.29s 1.58s
% Output : Refutation 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : KLE132+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 600
% 0.11/0.29 % DateTime : Thu Jun 16 13:03:30 EDT 2022
% 0.11/0.29 % CPUTime :
% 0.50/0.78 ============================== Prover9 ===============================
% 0.50/0.78 Prover9 (32) version 2009-11A, November 2009.
% 0.50/0.78 Process 12485 was started by sandbox on n032.cluster.edu,
% 0.50/0.78 Thu Jun 16 13:03:30 2022
% 0.50/0.78 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12331_n032.cluster.edu".
% 0.50/0.78 ============================== end of head ===========================
% 0.50/0.78
% 0.50/0.78 ============================== INPUT =================================
% 0.50/0.78
% 0.50/0.78 % Reading from file /tmp/Prover9_12331_n032.cluster.edu
% 0.50/0.78
% 0.50/0.78 set(prolog_style_variables).
% 0.50/0.78 set(auto2).
% 0.50/0.78 % set(auto2) -> set(auto).
% 0.50/0.78 % set(auto) -> set(auto_inference).
% 0.50/0.78 % set(auto) -> set(auto_setup).
% 0.50/0.78 % set(auto_setup) -> set(predicate_elim).
% 0.50/0.78 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.50/0.78 % set(auto) -> set(auto_limits).
% 0.50/0.78 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.50/0.78 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.50/0.78 % set(auto) -> set(auto_denials).
% 0.50/0.78 % set(auto) -> set(auto_process).
% 0.50/0.78 % set(auto2) -> assign(new_constants, 1).
% 0.50/0.78 % set(auto2) -> assign(fold_denial_max, 3).
% 0.50/0.78 % set(auto2) -> assign(max_weight, "200.000").
% 0.50/0.78 % set(auto2) -> assign(max_hours, 1).
% 0.50/0.78 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.50/0.78 % set(auto2) -> assign(max_seconds, 0).
% 0.50/0.78 % set(auto2) -> assign(max_minutes, 5).
% 0.50/0.78 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.50/0.78 % set(auto2) -> set(sort_initial_sos).
% 0.50/0.78 % set(auto2) -> assign(sos_limit, -1).
% 0.50/0.78 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.50/0.78 % set(auto2) -> assign(max_megs, 400).
% 0.50/0.78 % set(auto2) -> assign(stats, some).
% 0.50/0.78 % set(auto2) -> clear(echo_input).
% 0.50/0.78 % set(auto2) -> set(quiet).
% 0.50/0.78 % set(auto2) -> clear(print_initial_clauses).
% 0.50/0.78 % set(auto2) -> clear(print_given).
% 0.50/0.78 assign(lrs_ticks,-1).
% 0.50/0.78 assign(sos_limit,10000).
% 0.50/0.78 assign(order,kbo).
% 0.50/0.78 set(lex_order_vars).
% 0.50/0.78 clear(print_given).
% 0.50/0.78
% 0.50/0.78 % formulas(sos). % not echoed (29 formulas)
% 0.50/0.78
% 0.50/0.78 ============================== end of input ==========================
% 0.50/0.78
% 0.50/0.78 % From the command line: assign(max_seconds, 300).
% 0.50/0.78
% 0.50/0.78 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.50/0.78
% 0.50/0.78 % Formulas that are not ordinary clauses:
% 0.50/0.78 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 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].
% 0.50/0.78 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 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].
% 0.50/0.78 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 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].
% 0.50/0.78 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].
% 0.50/0.78 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.78 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].
% 1.29/1.58 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 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].
% 1.29/1.58 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 27 (all X0 forward_diamond(X0,divergence(X0)) = divergence(X0)) # label(divergence1) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 28 (all X0 all X1 all X2 (addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2)) -> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))))) # label(divergence2) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 29 -(all X0 ((all X1 addition(forward_diamond(X0,domain(X1)),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) -> (all X2 (addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) -> domain(X2) = zero)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.29/1.58
% 1.29/1.58 ============================== end of process non-clausal formulas ===
% 1.29/1.58
% 1.29/1.58 ============================== PROCESS INITIAL CLAUSES ===============
% 1.29/1.58
% 1.29/1.58 ============================== PREDICATE ELIMINATION =================
% 1.29/1.58 30 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 1.29/1.58 31 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 1.29/1.58
% 1.29/1.58 ============================== end predicate elimination =============
% 1.29/1.58
% 1.29/1.58 Auto_denials:
% 1.29/1.58 % copying label goals to answer in negative clause
% 1.29/1.58
% 1.29/1.58 Term ordering decisions:
% 1.29/1.58 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. forward_diamond=1. domain_difference=1. backward_diamond=1. backward_box=1. forward_box=1. domain=1. antidomain=1. coantidomain=1. c=1. divergence=1. star=1. codomain=1.
% 1.29/1.58
% 1.29/1.58 ============================== end of process initial clauses ========
% 1.29/1.58
% 1.29/1.58 ============================== CLAUSES FOR SEARCH ====================
% 1.29/1.58
% 1.29/1.58 ============================== end of clauses for search =============
% 1.29/1.58
% 1.29/1.58 ============================== SEARCH ================================
% 1.29/1.58
% 1.29/1.58 % Starting search at 0.01 seconds.
% 1.29/1.58
% 1.29/1.58 ============================== PROOF =================================
% 1.29/1.58 % SZS status Theorem
% 1.29/1.58 % SZS output start Refutation
% 1.29/1.58
% 1.29/1.58 % Proof 1 at 0.77 (+ 0.03) seconds: goals.
% 1.29/1.58 % Length of proof is 71.
% 1.29/1.58 % Level of proof is 11.
% 1.29/1.58 % Maximum clause weight is 62.000.
% 1.29/1.58 % Given clauses 356.
% 1.29/1.58
% 1.29/1.58 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 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].
% 1.29/1.58 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 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].
% 1.29/1.58 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 27 (all X0 forward_diamond(X0,divergence(X0)) = divergence(X0)) # label(divergence1) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 28 (all X0 all X1 all X2 (addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2)) -> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))))) # label(divergence2) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.58 29 -(all X0 ((all X1 addition(forward_diamond(X0,domain(X1)),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) -> (all X2 (addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) -> domain(X2) = zero)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.29/1.58 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 1.29/1.58 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 1.29/1.58 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 1.29/1.58 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 1.29/1.58 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 1.29/1.58 37 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 1.29/1.58 38 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 1.29/1.58 39 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 1.29/1.58 44 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 1.29/1.58 45 divergence(A) = forward_diamond(A,divergence(A)) # label(divergence1) # label(axiom). [clausify(27)].
% 1.29/1.58 46 forward_diamond(A,divergence(A)) = divergence(A). [copy(45),flip(a)].
% 1.29/1.58 47 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 1.29/1.58 48 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(47),rewrite([44(4)])].
% 1.29/1.58 51 domain_difference(A,B) = multiplication(domain(A),antidomain(B)) # label(domain_difference) # label(axiom). [clausify(22)].
% 1.29/1.58 52 domain_difference(A,B) = multiplication(antidomain(antidomain(A)),antidomain(B)). [copy(51),rewrite([39(2)])].
% 1.29/1.58 53 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 1.29/1.58 54 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(53),rewrite([39(2),39(5)])].
% 1.29/1.58 61 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 1.29/1.58 62 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(61),rewrite([44(2)]),flip(a)].
% 1.29/1.58 64 forward_diamond(c1,domain(c2)) = addition(domain(c2),forward_diamond(c1,domain(c2))) # label(goals) # label(negated_conjecture). [clausify(29)].
% 1.29/1.58 65 addition(antidomain(antidomain(c2)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))). [copy(64),rewrite([39(3),54(5),39(11),39(15),54(17)]),flip(a)].
% 1.29/1.58 66 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 1.29/1.58 67 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(66),flip(a)].
% 1.29/1.58 74 forward_diamond(star(c1),domain_difference(domain(A),forward_diamond(c1,domain(A)))) = addition(forward_diamond(c1,domain(A)),forward_diamond(star(c1),domain_difference(domain(A),forward_diamond(c1,domain(A))))) # label(goals) # label(negated_conjecture). [clausify(29)].
% 1.29/1.58 75 addition(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A))))))),antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A)))))))))))))). [copy(74),rewrite([39(3),39(6),54(8),52(13),54(17),39(23),54(25),39(32),39(35),54(37),52(42),54(46)]),flip(a)].
% 1.29/1.58 76 domain(c2) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(29)].
% 1.29/1.58 77 antidomain(antidomain(c2)) != zero # answer(goals). [copy(76),rewrite([39(2)])].
% 1.29/1.58 78 addition(forward_diamond(A,domain(B)),domain(C)) != addition(domain(B),addition(forward_diamond(A,domain(B)),domain(C))) | addition(divergence(A),forward_diamond(star(A),domain(C))) = addition(domain(B),addition(divergence(A),forward_diamond(star(A),domain(C)))) # label(divergence2) # label(axiom). [clausify(28)].
% 1.29/1.58 79 addition(antidomain(antidomain(A)),addition(antidomain(antidomain(B)),antidomain(antidomain(multiplication(C,antidomain(antidomain(antidomain(antidomain(A))))))))) != addition(antidomain(antidomain(B)),antidomain(antidomain(multiplication(C,antidomain(antidomain(antidomain(antidomain(A)))))))) | addition(antidomain(antidomain(A)),addition(divergence(C),antidomain(antidomain(multiplication(star(C),antidomain(antidomain(antidomain(antidomain(B))))))))) = addition(divergence(C),antidomain(antidomain(multiplication(star(C),antidomain(antidomain(antidomain(antidomain(B)))))))). [copy(78),rewrite([39(1),54(3),39(8),44(10),39(11),39(13),54(15),39(20),44(22),39(27),54(29),39(35),39(39),54(41)]),flip(a),flip(b)].
% 1.29/1.58 80 antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = divergence(A). [back_rewrite(46),rewrite([54(2)])].
% 1.29/1.58 81 antidomain(one) = zero. [para(38(a,1),34(a,1)),flip(a)].
% 1.29/1.58 83 addition(A,addition(A,B)) = addition(A,B). [para(62(a,1),33(a,1)),rewrite([44(1),44(2),62(2,R),33(1),44(3)])].
% 1.29/1.58 87 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),67(a,2,2)),rewrite([36(3),44(3)])].
% 1.29/1.58 88 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(34(a,1),67(a,1,1)),rewrite([44(4)]),flip(a)].
% 1.29/1.58 89 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(38(a,1),67(a,1,1)),rewrite([87(4)]),flip(a)].
% 1.29/1.58 118 antidomain(antidomain(zero)) = divergence(zero). [para(37(a,1),80(a,1,1,1))].
% 1.29/1.58 126 addition(antidomain(antidomain(multiplication(c1,antidomain(antidomain(divergence(A)))))),antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(divergence(A)))))))))))))) = antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(A))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(divergence(A))))))))))))). [para(80(a,1),75(a,1,1,1,1,2,1,1)),rewrite([80(15),80(19),80(35),80(39)])].
% 1.29/1.58 134 addition(zero,antidomain(zero)) = one. [para(81(a,1),48(a,1,1)),rewrite([81(3)])].
% 1.29/1.58 139 multiplication(divergence(zero),antidomain(zero)) = zero. [para(118(a,1),38(a,1,1))].
% 1.29/1.58 143 addition(divergence(zero),addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A))))))))) != addition(divergence(zero),antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A)))))))) | addition(antidomain(antidomain(A)),addition(divergence(B),antidomain(antidomain(multiplication(star(B),antidomain(antidomain(divergence(zero)))))))) = addition(divergence(B),antidomain(antidomain(multiplication(star(B),antidomain(antidomain(divergence(zero))))))). [para(118(a,1),79(a,1,2,1)),rewrite([62(13,R),44(12),118(16),118(31),118(42)])].
% 1.29/1.58 146 multiplication(A,antidomain(zero)) = A. [para(134(a,1),67(a,2,2)),rewrite([36(2),87(5),34(5)])].
% 1.29/1.58 150 divergence(zero) = zero. [back_rewrite(139),rewrite([146(5)])].
% 1.29/1.58 151 addition(zero,addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A))))))))) != addition(zero,antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A)))))))) | addition(zero,addition(divergence(B),antidomain(antidomain(A)))) = addition(zero,divergence(B)). [back_rewrite(143),rewrite([150(2),150(14),150(28),118(29),150(28),36(28),118(28),150(27),44(27),62(28,R),150(32),118(33),150(32),36(32),118(32),150(31),44(31)])].
% 1.29/1.58 160 addition(one,antidomain(A)) = one. [para(48(a,1),83(a,1,2)),rewrite([44(3),48(7)])].
% 1.29/1.58 165 antidomain(zero) = one. [para(146(a,1),35(a,1)),flip(a)].
% 1.29/1.58 176 addition(A,multiplication(A,antidomain(B))) = A. [para(160(a,1),67(a,2,2)),rewrite([34(2),34(5)])].
% 1.29/1.58 197 addition(zero,antidomain(antidomain(A))) = antidomain(antidomain(A)). [para(38(a,1),176(a,1,2)),rewrite([44(4)])].
% 1.29/1.58 201 addition(zero,addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A))))))))) != antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A))))))) | addition(zero,addition(divergence(B),antidomain(antidomain(A)))) = addition(zero,divergence(B)). [back_rewrite(151),rewrite([197(21)])].
% 1.29/1.58 208 addition(zero,antidomain(A)) = antidomain(A). [para(38(a,1),88(a,2,2)),rewrite([89(4),34(3),44(4)]),flip(a)].
% 1.29/1.58 223 addition(zero,divergence(A)) = divergence(A). [para(80(a,1),208(a,1,2)),rewrite([80(9)])].
% 1.29/1.58 224 addition(zero,addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A))))))))) != antidomain(antidomain(multiplication(B,antidomain(antidomain(antidomain(antidomain(A))))))) | addition(zero,addition(divergence(B),antidomain(antidomain(A)))) = divergence(B). [back_rewrite(201),rewrite([223(29)])].
% 1.29/1.58 1257 divergence(c1) = zero. [para(80(a,1),126(a,1,1)),rewrite([80(16),38(12),165(6),81(6),36(6),165(4),81(4),44(4),223(4),80(16),38(12),165(6),81(6),36(6),165(4),81(4)])].
% 1.29/1.58 4407 antidomain(antidomain(c2)) = zero. [para(65(a,1),224(a,1,2)),rewrite([208(11),1257(22),208(25),208(24),1257(24)]),xx(a)].
% 1.29/1.58 4408 $F # answer(goals). [resolve(4407,a,77,a)].
% 1.29/1.58
% 1.29/1.58 % SZS output end Refutation
% 1.29/1.58 ============================== end of proof ==========================
% 1.29/1.58
% 1.29/1.58 ============================== STATISTICS ============================
% 1.29/1.58
% 1.29/1.58 Given=356. Generated=36039. Kept=4358. proofs=1.
% 1.29/1.58 Usable=292. Sos=3404. Demods=3232. Limbo=3, Disabled=690. Hints=0.
% 1.29/1.58 Megabytes=6.27.
% 1.29/1.58 User_CPU=0.77, System_CPU=0.03, Wall_clock=1.
% 1.29/1.58
% 1.29/1.58 ============================== end of statistics =====================
% 1.29/1.58
% 1.29/1.58 ============================== end of search =========================
% 1.29/1.58
% 1.29/1.58 THEOREM PROVED
% 1.29/1.58 % SZS status Theorem
% 1.29/1.58
% 1.29/1.58 Exiting with 1 proof.
% 1.29/1.58
% 1.29/1.58 Process 12485 exit (max_proofs) Thu Jun 16 13:03:31 2022
% 1.29/1.58 Prover9 interrupted
%------------------------------------------------------------------------------