TSTP Solution File: KLE080+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE080+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 02:22:07 EDT 2022
% Result : Theorem 2.77s 3.06s
% Output : Refutation 2.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE080+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Thu Jun 16 10:19:20 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.47/1.04 ============================== Prover9 ===============================
% 0.47/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.04 Process 28427 was started by sandbox on n023.cluster.edu,
% 0.47/1.04 Thu Jun 16 10:19:20 2022
% 0.47/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28274_n023.cluster.edu".
% 0.47/1.04 ============================== end of head ===========================
% 0.47/1.04
% 0.47/1.04 ============================== INPUT =================================
% 0.47/1.04
% 0.47/1.04 % Reading from file /tmp/Prover9_28274_n023.cluster.edu
% 0.47/1.04
% 0.47/1.04 set(prolog_style_variables).
% 0.47/1.04 set(auto2).
% 0.47/1.04 % set(auto2) -> set(auto).
% 0.47/1.04 % set(auto) -> set(auto_inference).
% 0.47/1.04 % set(auto) -> set(auto_setup).
% 0.47/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.04 % set(auto) -> set(auto_limits).
% 0.47/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.04 % set(auto) -> set(auto_denials).
% 0.47/1.04 % set(auto) -> set(auto_process).
% 0.47/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.04 % set(auto2) -> assign(stats, some).
% 0.47/1.04 % set(auto2) -> clear(echo_input).
% 0.47/1.04 % set(auto2) -> set(quiet).
% 0.47/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.04 % set(auto2) -> clear(print_given).
% 0.47/1.04 assign(lrs_ticks,-1).
% 0.47/1.04 assign(sos_limit,10000).
% 0.47/1.04 assign(order,kbo).
% 0.47/1.04 set(lex_order_vars).
% 0.47/1.04 clear(print_given).
% 0.47/1.04
% 0.47/1.04 % formulas(sos). % not echoed (18 formulas)
% 0.47/1.04
% 0.47/1.04 ============================== end of input ==========================
% 0.47/1.04
% 0.47/1.04 % From the command line: assign(max_seconds, 300).
% 0.47/1.04
% 0.47/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.04
% 0.47/1.04 % Formulas that are not ordinary clauses:
% 0.47/1.04 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 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].
% 0.47/1.04 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 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].
% 0.47/1.04 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 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].
% 0.47/1.04 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].
% 0.47/1.04 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 17 -(all X0 ((all X1 (addition(domain(X1),antidomain(X1)) = one & multiplication(domain(X1),antidomain(X1)) = zero)) -> antidomain(antidomain(X0)) = domain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.77/3.06
% 2.77/3.06 ============================== end of process non-clausal formulas ===
% 2.77/3.06
% 2.77/3.06 ============================== PROCESS INITIAL CLAUSES ===============
% 2.77/3.06
% 2.77/3.06 ============================== PREDICATE ELIMINATION =================
% 2.77/3.06 18 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.77/3.06 19 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.77/3.06
% 2.77/3.06 ============================== end predicate elimination =============
% 2.77/3.06
% 2.77/3.06 Auto_denials:
% 2.77/3.06 % copying label goals to answer in negative clause
% 2.77/3.06
% 2.77/3.06 Term ordering decisions:
% 2.77/3.06 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. domain=1. antidomain=1.
% 2.77/3.06
% 2.77/3.06 ============================== end of process initial clauses ========
% 2.77/3.06
% 2.77/3.06 ============================== CLAUSES FOR SEARCH ====================
% 2.77/3.06
% 2.77/3.06 ============================== end of clauses for search =============
% 2.77/3.06
% 2.77/3.06 ============================== SEARCH ================================
% 2.77/3.06
% 2.77/3.06 % Starting search at 0.01 seconds.
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=35.000, iters=3333
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=34.000, iters=3361
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=33.000, iters=3340
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=32.000, iters=3390
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=31.000, iters=3401
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=30.000, iters=3370
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=29.000, iters=3337
% 2.77/3.06
% 2.77/3.06 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.93 sec).
% 2.77/3.06
% 2.77/3.06 Low Water (keep): wt=28.000, iters=3406
% 2.77/3.06
% 2.77/3.06 ============================== PROOF =================================
% 2.77/3.06 % SZS status Theorem
% 2.77/3.06 % SZS output start Refutation
% 2.77/3.06
% 2.77/3.06 % Proof 1 at 1.95 (+ 0.09) seconds: goals.
% 2.77/3.06 % Length of proof is 85.
% 2.77/3.06 % Level of proof is 18.
% 2.77/3.06 % Maximum clause weight is 24.000.
% 2.77/3.06 % Given clauses 502.
% 2.77/3.06
% 2.77/3.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 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].
% 2.77/3.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 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].
% 2.77/3.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 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].
% 2.77/3.06 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].
% 2.77/3.06 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 2.77/3.06 17 -(all X0 ((all X1 (addition(domain(X1),antidomain(X1)) = one & multiplication(domain(X1),antidomain(X1)) = zero)) -> antidomain(antidomain(X0)) = domain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.77/3.06 20 domain(zero) = zero # label(domain4) # label(axiom). [assumption].
% 2.77/3.06 21 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.77/3.06 22 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.77/3.06 23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.77/3.06 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.77/3.06 25 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.77/3.06 26 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.77/3.06 27 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(15)].
% 2.77/3.06 28 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.77/3.06 29 addition(domain(A),antidomain(A)) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.77/3.06 30 multiplication(domain(A),antidomain(A)) = zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.77/3.06 31 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(14)].
% 2.77/3.06 32 domain(addition(A,B)) = addition(domain(A),domain(B)) # label(domain5) # label(axiom). [clausify(16)].
% 2.77/3.06 33 addition(domain(A),domain(B)) = domain(addition(A,B)). [copy(32),flip(a)].
% 2.77/3.06 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.77/3.06 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([28(2)]),flip(a)].
% 2.77/3.06 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.77/3.06 37 multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)) # label(domain1) # label(axiom). [clausify(13)].
% 2.77/3.06 38 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A). [copy(37),flip(a)].
% 2.77/3.06 39 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.77/3.06 40 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(39),flip(a)].
% 2.77/3.06 41 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.77/3.06 42 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(41),flip(a)].
% 2.77/3.06 43 antidomain(antidomain(c1)) != domain(c1) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 2.77/3.06 44 addition(one,domain(A)) = one. [back_rewrite(27),rewrite([28(3)])].
% 2.77/3.06 46 domain(domain(A)) = domain(A). [para(24(a,1),31(a,1,1)),rewrite([24(4)])].
% 2.77/3.06 51 domain(addition(A,antidomain(A))) = domain(one). [para(29(a,1),33(a,2,1)),rewrite([46(2),33(4)])].
% 2.77/3.06 53 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),22(a,1)),rewrite([28(1),28(2),35(2,R),22(1),28(3)])].
% 2.77/3.06 55 domain(one) = one. [para(23(a,1),38(a,1,2)),rewrite([44(4),23(5)]),flip(a)].
% 2.77/3.06 56 addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))). [para(31(a,1),38(a,1,2,1)),rewrite([31(11)])].
% 2.77/3.06 58 domain(addition(A,antidomain(A))) = one. [back_rewrite(51),rewrite([55(5)])].
% 2.77/3.06 59 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(21(a,1),40(a,2,2)),rewrite([25(3),28(3)])].
% 2.77/3.06 62 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(24(a,1),42(a,1,1)),rewrite([28(4)]),flip(a)].
% 2.77/3.06 63 multiplication(addition(A,domain(B)),antidomain(B)) = multiplication(A,antidomain(B)). [para(30(a,1),42(a,1,1)),rewrite([59(4),28(4)]),flip(a)].
% 2.77/3.06 67 multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)). [back_rewrite(56),rewrite([62(8,R),28(4),44(4),24(4)]),flip(a)].
% 2.77/3.06 69 addition(A,multiplication(A,domain(B))) = A. [para(44(a,1),40(a,2,2)),rewrite([23(2),23(5)])].
% 2.77/3.06 70 addition(A,multiplication(domain(B),A)) = A. [para(44(a,1),42(a,2,1)),rewrite([24(2),24(5)])].
% 2.77/3.06 71 multiplication(domain(A),A) = A. [back_rewrite(38),rewrite([70(3)]),flip(a)].
% 2.77/3.06 81 addition(domain(A),antidomain(domain(A))) = one. [para(46(a,1),29(a,1,1))].
% 2.77/3.06 83 domain(addition(A,domain(B))) = domain(addition(B,A)). [para(46(a,1),33(a,1,1)),rewrite([33(3),28(4)]),flip(a)].
% 2.77/3.06 84 addition(A,multiplication(domain(A),B)) = multiplication(domain(A),addition(A,B)). [para(71(a,1),40(a,1,1))].
% 2.77/3.06 85 multiplication(addition(A,domain(B)),B) = addition(B,multiplication(A,B)). [para(71(a,1),42(a,1,1)),rewrite([28(4)]),flip(a)].
% 2.77/3.06 98 domain(addition(A,addition(B,antidomain(B)))) = one. [para(58(a,1),33(a,1,1)),rewrite([44(3),28(4)]),flip(a)].
% 2.77/3.06 106 domain(addition(A,multiplication(A,B))) = domain(A). [para(69(a,1),33(a,2,1)),rewrite([31(4),33(4)])].
% 2.77/3.06 108 addition(zero,antidomain(A)) = antidomain(A). [para(30(a,1),70(a,1,2)),rewrite([28(3)])].
% 2.77/3.06 169 domain(addition(A,addition(B,antidomain(A)))) = one. [para(28(a,1),98(a,1,1)),rewrite([28(3),35(3,R),28(2)])].
% 2.77/3.06 176 addition(domain(A),antidomain(addition(A,multiplication(A,B)))) = one. [para(106(a,1),29(a,1,1))].
% 2.77/3.06 507 multiplication(domain(A),domain(antidomain(A))) = zero. [para(30(a,1),67(a,1,1,1)),rewrite([20(2),26(6)]),flip(a)].
% 2.77/3.06 523 multiplication(domain(A),multiplication(domain(antidomain(A)),B)) = zero. [para(507(a,1),36(a,1,1)),rewrite([26(2)]),flip(a)].
% 2.77/3.06 645 multiplication(domain(addition(A,B)),B) = B. [para(33(a,1),85(a,1,1)),rewrite([70(6)])].
% 2.77/3.06 674 multiplication(domain(A),multiplication(domain(B),A)) = multiplication(domain(B),A). [para(70(a,1),645(a,1,1,1))].
% 2.77/3.06 2755 multiplication(domain(antidomain(A)),A) = zero. [para(674(a,1),523(a,1))].
% 2.77/3.06 2789 multiplication(domain(antidomain(A)),addition(A,B)) = multiplication(domain(antidomain(A)),B). [para(2755(a,1),40(a,1,1)),rewrite([59(5)]),flip(a)].
% 2.77/3.06 2790 multiplication(addition(A,domain(antidomain(B))),B) = multiplication(A,B). [para(2755(a,1),42(a,1,1)),rewrite([59(3),28(4)]),flip(a)].
% 2.77/3.06 2797 multiplication(domain(antidomain(A)),domain(A)) = zero. [para(2755(a,1),67(a,1,1,1)),rewrite([20(2),26(6)]),flip(a)].
% 2.77/3.06 2847 domain(antidomain(A)) = antidomain(A). [para(2797(a,1),84(a,1,2)),rewrite([28(3),108(3),28(6),29(6),23(5)]),flip(a)].
% 2.77/3.06 2850 addition(antidomain(A),antidomain(antidomain(A))) = one. [para(2797(a,1),176(a,1,2,1,2)),rewrite([2847(2),2847(2),2847(3),28(4),108(4)])].
% 2.77/3.06 2922 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [back_rewrite(2790),rewrite([2847(2)])].
% 2.77/3.06 2923 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [back_rewrite(2789),rewrite([2847(2),2847(5)])].
% 2.77/3.06 2927 domain(addition(A,antidomain(B))) = addition(antidomain(B),domain(A)). [para(2847(a,1),33(a,1,1)),rewrite([28(5)]),flip(a)].
% 2.77/3.06 3776 multiplication(addition(antidomain(A),domain(addition(B,A))),A) = A. [para(645(a,1),2922(a,2)),rewrite([28(4)])].
% 2.77/3.06 5339 multiplication(antidomain(domain(A)),antidomain(A)) = antidomain(domain(A)). [para(29(a,1),2923(a,1,2)),rewrite([23(4)]),flip(a)].
% 2.77/3.06 5391 antidomain(domain(A)) = antidomain(A). [para(5339(a,1),63(a,2)),rewrite([28(4),81(4),24(3)]),flip(a)].
% 2.77/3.06 6350 addition(domain(A),addition(antidomain(B),domain(C))) = domain(addition(A,addition(C,antidomain(B)))). [para(2927(a,1),33(a,1,2))].
% 2.77/3.06 6997 addition(antidomain(A),domain(addition(A,B))) = one. [para(3776(a,1),69(a,1,2)),rewrite([5391(2),83(4),28(6),6350(6),28(3),35(3),28(2),35(3,R),28(2),53(4),169(4),5391(3),83(5)]),flip(a)].
% 2.77/3.06 7066 multiplication(antidomain(antidomain(A)),domain(addition(A,B))) = antidomain(antidomain(A)). [para(6997(a,1),2923(a,1,2)),rewrite([23(4)]),flip(a)].
% 2.77/3.06 11669 multiplication(antidomain(antidomain(A)),domain(A)) = antidomain(antidomain(A)). [para(21(a,1),7066(a,1,2,1))].
% 2.77/3.06 11723 antidomain(antidomain(A)) = domain(A). [para(11669(a,1),2922(a,2)),rewrite([5391(4),28(4),2850(4),24(3)]),flip(a)].
% 2.77/3.06 11724 $F # answer(goals). [resolve(11723,a,43,a)].
% 2.77/3.06
% 2.77/3.06 % SZS output end Refutation
% 2.77/3.06 ============================== end of proof ==========================
% 2.77/3.06
% 2.77/3.06 ============================== STATISTICS ============================
% 2.77/3.06
% 2.77/3.06 Given=502. Generated=124245. Kept=11699. proofs=1.
% 2.77/3.06 Usable=361. Sos=6202. Demods=6330. Limbo=16, Disabled=5140. Hints=0.
% 2.77/3.06 Megabytes=12.13.
% 2.77/3.06 User_CPU=1.95, System_CPU=0.09, Wall_clock=2.
% 2.77/3.06
% 2.77/3.06 ============================== end of statistics =====================
% 2.77/3.06
% 2.77/3.06 ============================== end of search =========================
% 2.77/3.06
% 2.77/3.06 THEOREM PROVED
% 2.77/3.06 % SZS status Theorem
% 2.77/3.06
% 2.77/3.06 Exiting with 1 proof.
% 2.77/3.06
% 2.77/3.06 Process 28427 exit (max_proofs) Thu Jun 16 10:19:22 2022
% 2.77/3.06 Prover9 interrupted
%------------------------------------------------------------------------------