TSTP Solution File: KLE120+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE120+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 02:22:19 EDT 2022
% Result : Theorem 2.15s 2.47s
% Output : Refutation 2.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE120+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 : n025.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 15:12:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/1.02 ============================== Prover9 ===============================
% 0.45/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.02 Process 2450 was started by sandbox on n025.cluster.edu,
% 0.45/1.02 Thu Jun 16 15:12:42 2022
% 0.45/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2297_n025.cluster.edu".
% 0.45/1.02 ============================== end of head ===========================
% 0.45/1.02
% 0.45/1.02 ============================== INPUT =================================
% 0.45/1.02
% 0.45/1.02 % Reading from file /tmp/Prover9_2297_n025.cluster.edu
% 0.45/1.02
% 0.45/1.02 set(prolog_style_variables).
% 0.45/1.02 set(auto2).
% 0.45/1.02 % set(auto2) -> set(auto).
% 0.45/1.02 % set(auto) -> set(auto_inference).
% 0.45/1.02 % set(auto) -> set(auto_setup).
% 0.45/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.02 % set(auto) -> set(auto_limits).
% 0.45/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.02 % set(auto) -> set(auto_denials).
% 0.45/1.02 % set(auto) -> set(auto_process).
% 0.45/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.02 % set(auto2) -> assign(stats, some).
% 0.45/1.02 % set(auto2) -> clear(echo_input).
% 0.45/1.02 % set(auto2) -> set(quiet).
% 0.45/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.02 % set(auto2) -> clear(print_given).
% 0.45/1.02 assign(lrs_ticks,-1).
% 0.45/1.02 assign(sos_limit,10000).
% 0.45/1.02 assign(order,kbo).
% 0.45/1.02 set(lex_order_vars).
% 0.45/1.02 clear(print_given).
% 0.45/1.02
% 0.45/1.02 % formulas(sos). % not echoed (27 formulas)
% 0.45/1.02
% 0.45/1.02 ============================== end of input ==========================
% 0.45/1.02
% 0.45/1.02 % From the command line: assign(max_seconds, 300).
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.02
% 0.45/1.02 % Formulas that are not ordinary clauses:
% 0.45/1.02 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 2.15/2.47 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 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].
% 2.15/2.47 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 27 -(all X0 addition(backward_diamond(one,domain(X0)),domain(X0)) = domain(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.15/2.47
% 2.15/2.47 ============================== end of process non-clausal formulas ===
% 2.15/2.47
% 2.15/2.47 ============================== PROCESS INITIAL CLAUSES ===============
% 2.15/2.47
% 2.15/2.47 ============================== PREDICATE ELIMINATION =================
% 2.15/2.47 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.15/2.47 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.15/2.47
% 2.15/2.47 ============================== end predicate elimination =============
% 2.15/2.47
% 2.15/2.47 Auto_denials:
% 2.15/2.47 % copying label goals to answer in negative clause
% 2.15/2.47
% 2.15/2.47 Term ordering decisions:
% 2.15/2.47 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. c=1. domain=1. codomain=1.
% 2.15/2.47
% 2.15/2.47 ============================== end of process initial clauses ========
% 2.15/2.47
% 2.15/2.47 ============================== CLAUSES FOR SEARCH ====================
% 2.15/2.47
% 2.15/2.47 ============================== end of clauses for search =============
% 2.15/2.47
% 2.15/2.47 ============================== SEARCH ================================
% 2.15/2.47
% 2.15/2.47 % Starting search at 0.02 seconds.
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=36.000, iters=3371
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=33.000, iters=3334
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=32.000, iters=3363
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=31.000, iters=3361
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=30.000, iters=3341
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=29.000, iters=3400
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=28.000, iters=3336
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=27.000, iters=3356
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=26.000, iters=3342
% 2.15/2.47
% 2.15/2.47 Low Water (keep): wt=25.000, iters=3336
% 2.15/2.47
% 2.15/2.47 ============================== PROOF =================================
% 2.15/2.47 % SZS status Theorem
% 2.15/2.47 % SZS output start Refutation
% 2.15/2.47
% 2.15/2.47 % Proof 1 at 1.42 (+ 0.05) seconds: goals.
% 2.15/2.47 % Length of proof is 102.
% 2.15/2.47 % Level of proof is 18.
% 2.15/2.47 % Maximum clause weight is 18.000.
% 2.15/2.47 % Given clauses 427.
% 2.15/2.47
% 2.15/2.47 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 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].
% 2.15/2.47 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 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].
% 2.15/2.47 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 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].
% 2.15/2.47 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].
% 2.15/2.47 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 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].
% 2.15/2.47 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 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].
% 2.15/2.47 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 2.15/2.47 27 -(all X0 addition(backward_diamond(one,domain(X0)),domain(X0)) = domain(X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.15/2.47 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.15/2.47 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.15/2.47 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.15/2.47 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.15/2.47 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.15/2.47 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 2.15/2.47 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 2.15/2.47 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 2.15/2.47 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 2.15/2.47 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.15/2.47 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 2.15/2.47 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 2.15/2.47 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 2.15/2.47 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 2.15/2.47 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 2.15/2.47 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 2.15/2.47 57 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.15/2.47 58 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(57),rewrite([42(2)]),flip(a)].
% 2.15/2.47 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.15/2.47 60 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.15/2.47 61 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(60),flip(a)].
% 2.15/2.47 62 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.15/2.47 63 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(62),flip(a)].
% 2.15/2.47 64 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 2.15/2.47 65 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(64),flip(a)].
% 2.15/2.47 66 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 2.15/2.47 67 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(66),flip(a)].
% 2.15/2.47 68 domain(c1) != addition(backward_diamond(one,domain(c1)),domain(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 2.15/2.47 69 addition(antidomain(antidomain(c1)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(c1))))))) != antidomain(antidomain(c1)) # answer(goals). [copy(68),rewrite([37(2),37(6),52(8),32(10),37(12),42(14)]),flip(a)].
% 2.15/2.47 70 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 2.15/2.47 71 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 2.15/2.47 72 addition(A,addition(A,B)) = addition(A,B). [para(58(a,1),31(a,1)),rewrite([42(1),42(2),58(2,R),31(1),42(3)])].
% 2.15/2.47 76 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),61(a,2,2)),rewrite([34(3),42(3)])].
% 2.15/2.47 77 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),61(a,1,1)),rewrite([42(4)]),flip(a)].
% 2.15/2.47 78 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),61(a,1,1)),rewrite([76(4)]),flip(a)].
% 2.15/2.47 79 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),61(a,1,1)),rewrite([76(3),42(3)]),flip(a)].
% 2.15/2.47 82 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),63(a,1,1)),rewrite([76(4),42(3)]),flip(a)].
% 2.15/2.47 90 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),65(a,1,1,1))].
% 2.15/2.47 95 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),67(a,1,1,1))].
% 2.15/2.47 99 addition(zero,antidomain(zero)) = one. [para(70(a,1),44(a,1,1)),rewrite([70(3)])].
% 2.15/2.47 100 addition(zero,coantidomain(zero)) = one. [para(71(a,1),46(a,1,1)),rewrite([71(3)])].
% 2.15/2.47 103 multiplication(A,antidomain(zero)) = A. [para(99(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 2.15/2.47 107 multiplication(A,coantidomain(zero)) = A. [para(100(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 2.15/2.47 109 addition(one,antidomain(A)) = one. [para(44(a,1),72(a,1,2)),rewrite([42(3),44(7)])].
% 2.15/2.47 110 addition(one,coantidomain(A)) = one. [para(46(a,1),72(a,1,2)),rewrite([42(3),46(7)])].
% 2.15/2.47 111 antidomain(zero) = one. [para(103(a,1),33(a,1)),flip(a)].
% 2.15/2.47 112 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(90),rewrite([111(2),109(7)]),flip(a)].
% 2.15/2.47 114 coantidomain(zero) = one. [para(107(a,1),33(a,1)),flip(a)].
% 2.15/2.47 116 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(95),rewrite([114(2),110(7)]),flip(a)].
% 2.15/2.47 123 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 2.15/2.47 124 addition(A,multiplication(A,coantidomain(B))) = A. [para(110(a,1),61(a,2,2)),rewrite([32(2),32(5)])].
% 2.15/2.47 125 addition(A,multiplication(coantidomain(B),A)) = A. [para(110(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 2.15/2.47 159 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(112(a,1),36(a,1,1)),rewrite([33(6)])].
% 2.15/2.47 164 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(159(a,1),61(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 2.15/2.47 170 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),78(a,1,2)),rewrite([32(4)]),flip(a)].
% 2.15/2.47 191 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),79(a,1,2)),rewrite([32(3)]),flip(a)].
% 2.15/2.47 200 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(191(a,1),61(a,1,1)),rewrite([77(4,R),42(7)]),flip(a)].
% 2.15/2.47 205 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(116(a,1),38(a,1,2)),rewrite([32(6)])].
% 2.15/2.47 209 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(205(a,1),63(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 2.15/2.47 264 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),82(a,1,1))].
% 2.15/2.47 265 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 2.15/2.47 266 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 2.15/2.47 656 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(170(a,1),123(a,1,2)),rewrite([42(5)])].
% 2.15/2.47 853 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),264(a,1,1)),rewrite([33(4)]),flip(a)].
% 2.15/2.47 2387 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),164(a,1,2)),rewrite([32(2)]),flip(a)].
% 2.15/2.47 2409 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2387(a,1),59(a,1,1)),flip(a)].
% 2.15/2.47 2417 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2387(a,1),125(a,1,2)),rewrite([42(5)])].
% 2.15/2.47 2516 multiplication(A,coantidomain(coantidomain(A))) = A. [para(170(a,1),2409(a,1,2)),rewrite([2387(3)]),flip(a)].
% 2.15/2.47 2549 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(266),rewrite([2516(5)]),flip(a)].
% 2.15/2.47 2552 addition(antidomain(antidomain(c1)),coantidomain(coantidomain(antidomain(antidomain(c1))))) != antidomain(antidomain(c1)) # answer(goals). [back_rewrite(69),rewrite([2549(9)])].
% 2.15/2.47 2558 addition(antidomain(A),coantidomain(coantidomain(antidomain(A)))) = coantidomain(coantidomain(antidomain(A))). [para(2516(a,1),123(a,1,2)),rewrite([42(5)])].
% 2.15/2.47 2572 coantidomain(coantidomain(antidomain(antidomain(c1)))) != antidomain(antidomain(c1)) # answer(goals). [back_rewrite(2552),rewrite([2558(9)])].
% 2.15/2.47 2580 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2549(a,1),656(a,1,2)),rewrite([42(5),2417(5),2549(6)])].
% 2.15/2.47 2681 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2580(a,1),44(a,1,1)),rewrite([2580(4)])].
% 2.15/2.47 2687 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2580(a,1),853(a,1,1,1)),rewrite([2580(5),170(5),2580(5)]),flip(a)].
% 2.15/2.47 2714 antidomain(coantidomain(antidomain(antidomain(c1)))) != antidomain(antidomain(c1)) # answer(goals). [back_rewrite(2572),rewrite([2687(5)])].
% 2.15/2.47 3047 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(209),rewrite([2687(3)])].
% 2.15/2.47 3960 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(265(a,1),124(a,1,2))].
% 2.15/2.47 4938 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3960(a,1),200(a,1,2)),rewrite([42(11),109(11),32(10)])].
% 2.15/2.47 9146 multiplication(coantidomain(antidomain(A)),A) = A. [para(2681(a,1),3047(a,1,1)),rewrite([33(2)]),flip(a)].
% 2.15/2.47 9160 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4938),rewrite([9146(5)]),flip(a)].
% 2.15/2.47 9172 $F # answer(goals). [back_rewrite(2714),rewrite([9160(4)]),xx(a)].
% 2.15/2.47
% 2.15/2.47 % SZS output end Refutation
% 2.15/2.47 ============================== end of proof ==========================
% 2.15/2.47
% 2.15/2.47 ============================== STATISTICS ============================
% 2.15/2.47
% 2.15/2.47 Given=427. Generated=77258. Kept=9128. proofs=1.
% 2.15/2.47 Usable=323. Sos=6480. Demods=6340. Limbo=12, Disabled=2341. Hints=0.
% 2.15/2.47 Megabytes=10.50.
% 2.15/2.47 User_CPU=1.42, System_CPU=0.05, Wall_clock=1.
% 2.15/2.47
% 2.15/2.47 ============================== end of statistics =====================
% 2.15/2.47
% 2.15/2.47 ============================== end of search =========================
% 2.15/2.47
% 2.15/2.47 THEOREM PROVED
% 2.15/2.47 % SZS status Theorem
% 2.15/2.47
% 2.15/2.47 Exiting with 1 proof.
% 2.15/2.47
% 2.15/2.47 Process 2450 exit (max_proofs) Thu Jun 16 15:12:43 2022
% 2.15/2.47 Prover9 interrupted
%------------------------------------------------------------------------------