TSTP Solution File: KLE128+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE128+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 02:22:21 EDT 2022
% Result : Theorem 8.30s 8.58s
% Output : Refutation 8.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE128+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 13:16:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.70/0.99 ============================== Prover9 ===============================
% 0.70/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.70/0.99 Process 1934 was started by sandbox2 on n025.cluster.edu,
% 0.70/0.99 Thu Jun 16 13:16:42 2022
% 0.70/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1745_n025.cluster.edu".
% 0.70/0.99 ============================== end of head ===========================
% 0.70/0.99
% 0.70/0.99 ============================== INPUT =================================
% 0.70/0.99
% 0.70/0.99 % Reading from file /tmp/Prover9_1745_n025.cluster.edu
% 0.70/0.99
% 0.70/0.99 set(prolog_style_variables).
% 0.70/0.99 set(auto2).
% 0.70/0.99 % set(auto2) -> set(auto).
% 0.70/0.99 % set(auto) -> set(auto_inference).
% 0.70/0.99 % set(auto) -> set(auto_setup).
% 0.70/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.70/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/0.99 % set(auto) -> set(auto_limits).
% 0.70/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/0.99 % set(auto) -> set(auto_denials).
% 0.70/0.99 % set(auto) -> set(auto_process).
% 0.70/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.70/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.70/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.70/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.70/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.70/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.70/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.70/0.99 % set(auto2) -> assign(stats, some).
% 0.70/0.99 % set(auto2) -> clear(echo_input).
% 0.70/0.99 % set(auto2) -> set(quiet).
% 0.70/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.70/0.99 % set(auto2) -> clear(print_given).
% 0.70/0.99 assign(lrs_ticks,-1).
% 0.70/0.99 assign(sos_limit,10000).
% 0.70/0.99 assign(order,kbo).
% 0.70/0.99 set(lex_order_vars).
% 0.70/0.99 clear(print_given).
% 0.70/0.99
% 0.70/0.99 % formulas(sos). % not echoed (29 formulas)
% 0.70/0.99
% 0.70/0.99 ============================== end of input ==========================
% 0.70/0.99
% 0.70/0.99 % From the command line: assign(max_seconds, 300).
% 0.70/0.99
% 0.70/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/0.99
% 0.70/0.99 % Formulas that are not ordinary clauses:
% 0.70/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 2.03/2.32 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 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].
% 2.03/2.32 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 27 (all X0 forward_diamond(X0,divergence(X0)) = divergence(X0)) # label(divergence1) # label(axiom) # label(non_clause). [assumption].
% 2.03/2.32 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].
% 2.03/2.32 29 -(all X0 (divergence(X0) = zero -> (all X1 (addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1)) -> domain(X1) = zero)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.03/2.32
% 2.03/2.32 ============================== end of process non-clausal formulas ===
% 2.03/2.32
% 2.03/2.32 ============================== PROCESS INITIAL CLAUSES ===============
% 2.03/2.32
% 2.03/2.32 ============================== PREDICATE ELIMINATION =================
% 2.03/2.32 30 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.03/2.32 31 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.03/2.32
% 2.03/2.32 ============================== end predicate elimination =============
% 2.03/2.32
% 2.03/2.32 Auto_denials:
% 2.03/2.32 % copying label goals to answer in negative clause
% 2.03/2.32
% 2.03/2.32 Term ordering decisions:
% 2.03/2.32 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. forward_diamond=1. backward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. domain=1. antidomain=1. coantidomain=1. c=1. divergence=1. codomain=1. star=1.
% 2.03/2.32
% 2.03/2.32 ============================== end of process initial clauses ========
% 2.03/2.32
% 2.03/2.32 ============================== CLAUSES FOR SEARCH ====================
% 2.03/2.32
% 2.03/2.32 ============================== end of clauses for search =============
% 2.03/2.32
% 2.03/2.32 ============================== SEARCH ================================
% 2.03/2.32
% 2.03/2.32 % Starting search at 0.01 seconds.
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=98.000, iters=3441
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=94.000, iters=3404
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=78.000, iters=3474
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=72.000, iters=3465
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=58.000, iters=3538
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=54.000, iters=3526
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=50.000, iters=3511
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=46.000, iters=3489
% 2.03/2.32
% 2.03/2.32 Low Water (keep): wt=38.000, iters=3349
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=35.000, iters=3389
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=33.000, iters=3347
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=32.000, iters=3338
% 8.30/8.58
% 8.30/8.58 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 69 (0.00 of 1.44 sec).
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=31.000, iters=3426
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=30.000, iters=3369
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=29.000, iters=3351
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=28.000, iters=3395
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=27.000, iters=3343
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=25.000, iters=3364
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=24.000, iters=3341
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=23.000, iters=3359
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=22.000, iters=3348
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=21.000, iters=3335
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=20.000, iters=3425
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=19.000, iters=3378
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=6317, wt=146.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=4345, wt=126.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=4460, wt=122.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=4344, wt=118.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=6776, wt=114.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=6783, wt=110.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=16057, wt=17.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=16064, wt=15.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=16065, wt=13.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=16077, wt=12.000
% 8.30/8.58
% 8.30/8.58 Low Water (displace): id=16123, wt=11.000
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=18.000, iters=3340
% 8.30/8.58
% 8.30/8.58 Low Water (keep): wt=17.000, iters=3341
% 8.30/8.58
% 8.30/8.58 ============================== PROOF =================================
% 8.30/8.58 % SZS status Theorem
% 8.30/8.58 % SZS output start Refutation
% 8.30/8.58
% 8.30/8.58 % Proof 1 at 7.35 (+ 0.25) seconds: goals.
% 8.30/8.58 % Length of proof is 74.
% 8.30/8.58 % Level of proof is 12.
% 8.30/8.58 % Maximum clause weight is 62.000.
% 8.30/8.58 % Given clauses 1601.
% 8.30/8.58
% 8.30/8.58 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 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].
% 8.30/8.58 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 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].
% 8.30/8.58 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].
% 8.30/8.58 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 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].
% 8.30/8.58 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 8.30/8.58 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].
% 8.30/8.58 29 -(all X0 (divergence(X0) = zero -> (all X1 (addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1)) -> domain(X1) = zero)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.30/8.58 32 divergence(c1) = zero # label(goals) # label(negated_conjecture). [clausify(29)].
% 8.30/8.58 33 zero = divergence(c1). [copy(32),flip(a)].
% 8.30/8.58 34 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 8.30/8.58 35 addition(A,divergence(c1)) = A. [copy(34),rewrite([33(1)])].
% 8.30/8.58 36 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 8.30/8.58 37 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 8.30/8.58 38 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 8.30/8.58 39 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 8.30/8.58 40 multiplication(A,divergence(c1)) = divergence(c1). [copy(39),rewrite([33(1),33(4)])].
% 8.30/8.58 43 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 8.30/8.58 44 multiplication(antidomain(A),A) = divergence(c1). [copy(43),rewrite([33(3)])].
% 8.30/8.58 45 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 8.30/8.58 51 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 8.30/8.58 54 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 8.30/8.58 55 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(54),rewrite([51(4)])].
% 8.30/8.58 60 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 8.30/8.58 61 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(60),rewrite([45(2),45(5)])].
% 8.30/8.58 68 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 8.30/8.58 69 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(68),rewrite([51(2)]),flip(a)].
% 8.30/8.58 71 forward_diamond(c1,domain(c2)) = addition(domain(c2),forward_diamond(c1,domain(c2))) # label(goals) # label(negated_conjecture). [clausify(29)].
% 8.30/8.58 72 addition(antidomain(antidomain(c2)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))). [copy(71),rewrite([45(3),61(5),45(11),45(15),61(17)]),flip(a)].
% 8.30/8.58 73 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 8.30/8.58 74 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(73),flip(a)].
% 8.30/8.58 75 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 8.30/8.58 76 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(75),flip(a)].
% 8.30/8.58 77 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 8.30/8.58 78 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(77),flip(a)].
% 8.30/8.58 81 domain(c2) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(29)].
% 8.30/8.58 82 antidomain(antidomain(c2)) != divergence(c1) # answer(goals). [copy(81),rewrite([45(2),33(4)])].
% 8.30/8.58 83 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)].
% 8.30/8.58 84 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(83),rewrite([45(1),61(3),45(8),51(10),45(11),45(13),61(15),45(20),51(22),45(27),61(29),45(35),45(39),61(41)]),flip(a),flip(b)].
% 8.30/8.58 86 antidomain(antidomain(c2)) = c_0. [new_symbol(82)].
% 8.30/8.58 87 divergence(c1) != c_0 # answer(goals). [back_rewrite(82),rewrite([86(3)]),flip(a)].
% 8.30/8.58 88 addition(c_0,antidomain(antidomain(multiplication(c1,antidomain(antidomain(c_0)))))) = antidomain(antidomain(multiplication(c1,antidomain(antidomain(c_0))))). [back_rewrite(72),rewrite([86(3),86(5),86(13)])].
% 8.30/8.58 89 divergence(c1) = antidomain(one). [para(44(a,1),37(a,1))].
% 8.30/8.58 90 antidomain(one) != c_0 # answer(goals). [back_rewrite(87),rewrite([89(2)])].
% 8.30/8.58 92 multiplication(antidomain(A),A) = antidomain(one). [back_rewrite(44),rewrite([89(4)])].
% 8.30/8.58 94 multiplication(A,antidomain(one)) = antidomain(one). [back_rewrite(40),rewrite([89(2),89(5)])].
% 8.30/8.58 95 addition(A,antidomain(one)) = A. [back_rewrite(35),rewrite([89(2)])].
% 8.30/8.58 97 addition(A,addition(A,B)) = addition(A,B). [para(69(a,1),36(a,1)),rewrite([51(1),51(2),69(2,R),36(1),51(3)])].
% 8.30/8.58 99 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(38(a,1),76(a,1,1)),rewrite([51(4)]),flip(a)].
% 8.30/8.58 103 addition(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(38(a,1),78(a,1,1,1)),rewrite([38(5),38(9)])].
% 8.30/8.58 123 addition(c_0,antidomain(c2)) = one. [para(86(a,1),55(a,1,2)),rewrite([51(4)])].
% 8.30/8.58 127 addition(c_0,addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(B,antidomain(antidomain(c_0))))))) != addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(B,antidomain(antidomain(c_0)))))) | addition(c_0,addition(divergence(B),antidomain(antidomain(multiplication(star(B),antidomain(antidomain(antidomain(antidomain(A))))))))) = addition(divergence(B),antidomain(antidomain(multiplication(star(B),antidomain(antidomain(antidomain(antidomain(A)))))))). [para(86(a,1),84(a,1,1)),rewrite([86(6),86(16),86(24)])].
% 8.30/8.58 131 addition(antidomain(one),multiplication(A,B)) = multiplication(A,B). [para(95(a,1),74(a,2,2)),rewrite([94(4),51(4)])].
% 8.30/8.58 143 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(92(a,1),74(a,1,1)),rewrite([131(5)]),flip(a)].
% 8.30/8.58 159 addition(one,antidomain(A)) = one. [para(55(a,1),97(a,1,2)),rewrite([51(3),55(7)])].
% 8.30/8.58 164 addition(A,multiplication(A,antidomain(B))) = A. [para(159(a,1),74(a,2,2)),rewrite([37(2),37(5)])].
% 8.30/8.58 239 addition(antidomain(one),antidomain(antidomain(A))) = antidomain(antidomain(A)). [para(92(a,1),164(a,1,2)),rewrite([51(5)])].
% 8.30/8.58 297 addition(antidomain(c2),antidomain(c_0)) = antidomain(c_0). [para(86(a,1),103(a,1,2,1)),rewrite([86(8)])].
% 8.30/8.58 813 antidomain(antidomain(one)) = one. [para(239(a,1),55(a,1))].
% 8.30/8.58 1107 addition(c_0,antidomain(antidomain(multiplication(A,antidomain(antidomain(c_0)))))) != antidomain(antidomain(multiplication(A,antidomain(antidomain(c_0))))) | addition(c_0,divergence(A)) = divergence(A). [para(813(a,1),127(a,1,2,1,1)),rewrite([239(10),813(11),239(17),813(21),813(21),94(21),813(20),95(20),813(23),813(23),94(23),813(22),95(22)])].
% 8.30/8.58 1305 multiplication(antidomain(c_0),antidomain(c2)) = antidomain(c_0). [para(123(a,1),143(a,1,2)),rewrite([37(4)]),flip(a)].
% 8.30/8.58 1326 antidomain(c_0) = antidomain(c2). [para(1305(a,1),99(a,2,2)),rewrite([51(4),159(4),38(4),297(7)]),flip(a)].
% 8.30/8.58 1383 addition(c_0,antidomain(antidomain(multiplication(A,c_0)))) != antidomain(antidomain(multiplication(A,c_0))) | addition(c_0,divergence(A)) = divergence(A). [back_rewrite(1107),rewrite([1326(3),86(4),1326(8),86(9)])].
% 8.30/8.58 1433 addition(c_0,antidomain(antidomain(multiplication(c1,c_0)))) = antidomain(antidomain(multiplication(c1,c_0))). [back_rewrite(88),rewrite([1326(4),86(5),1326(10),86(11)])].
% 8.30/8.58 25572 antidomain(one) = c_0. [hyper(1383,a,1433,a),rewrite([89(3),95(4),89(3)]),flip(a)].
% 8.30/8.58 25573 $F # answer(goals). [resolve(25572,a,90,a)].
% 8.30/8.58
% 8.30/8.58 % SZS output end Refutation
% 8.30/8.58 ============================== end of proof ==========================
% 8.30/8.58
% 8.30/8.58 ============================== STATISTICS ============================
% 8.30/8.58
% 8.30/8.58 Given=1601. Generated=418960. Kept=25518. proofs=1.
% 8.30/8.58 Usable=832. Sos=8267. Demods=8520. Limbo=0, Disabled=16450. Hints=0.
% 8.30/8.58 Megabytes=23.03.
% 8.30/8.58 User_CPU=7.35, System_CPU=0.25, Wall_clock=7.
% 8.30/8.58
% 8.30/8.58 ============================== end of statistics =====================
% 8.30/8.58
% 8.30/8.58 ============================== end of search =========================
% 8.30/8.58
% 8.30/8.58 THEOREM PROVED
% 8.30/8.58 % SZS status Theorem
% 8.30/8.58
% 8.30/8.58 Exiting with 1 proof.
% 8.30/8.58
% 8.30/8.58 Process 1934 exit (max_proofs) Thu Jun 16 13:16:49 2022
% 8.30/8.58 Prover9 interrupted
%------------------------------------------------------------------------------