TSTP Solution File: KLE084-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE084-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 02:22:09 EDT 2022
% Result : Unsatisfiable 3.77s 4.05s
% Output : Refutation 3.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE084-10 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 10:04:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.77/4.05 ============================== Prover9 ===============================
% 3.77/4.05 Prover9 (32) version 2009-11A, November 2009.
% 3.77/4.05 Process 7533 was started by sandbox on n009.cluster.edu,
% 3.77/4.05 Thu Jun 16 10:04:23 2022
% 3.77/4.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7380_n009.cluster.edu".
% 3.77/4.05 ============================== end of head ===========================
% 3.77/4.05
% 3.77/4.05 ============================== INPUT =================================
% 3.77/4.05
% 3.77/4.05 % Reading from file /tmp/Prover9_7380_n009.cluster.edu
% 3.77/4.05
% 3.77/4.05 set(prolog_style_variables).
% 3.77/4.05 set(auto2).
% 3.77/4.05 % set(auto2) -> set(auto).
% 3.77/4.05 % set(auto) -> set(auto_inference).
% 3.77/4.05 % set(auto) -> set(auto_setup).
% 3.77/4.05 % set(auto_setup) -> set(predicate_elim).
% 3.77/4.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.77/4.05 % set(auto) -> set(auto_limits).
% 3.77/4.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.77/4.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.77/4.05 % set(auto) -> set(auto_denials).
% 3.77/4.05 % set(auto) -> set(auto_process).
% 3.77/4.05 % set(auto2) -> assign(new_constants, 1).
% 3.77/4.05 % set(auto2) -> assign(fold_denial_max, 3).
% 3.77/4.05 % set(auto2) -> assign(max_weight, "200.000").
% 3.77/4.05 % set(auto2) -> assign(max_hours, 1).
% 3.77/4.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.77/4.05 % set(auto2) -> assign(max_seconds, 0).
% 3.77/4.05 % set(auto2) -> assign(max_minutes, 5).
% 3.77/4.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.77/4.05 % set(auto2) -> set(sort_initial_sos).
% 3.77/4.05 % set(auto2) -> assign(sos_limit, -1).
% 3.77/4.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.77/4.05 % set(auto2) -> assign(max_megs, 400).
% 3.77/4.05 % set(auto2) -> assign(stats, some).
% 3.77/4.05 % set(auto2) -> clear(echo_input).
% 3.77/4.05 % set(auto2) -> set(quiet).
% 3.77/4.05 % set(auto2) -> clear(print_initial_clauses).
% 3.77/4.05 % set(auto2) -> clear(print_given).
% 3.77/4.05 assign(lrs_ticks,-1).
% 3.77/4.05 assign(sos_limit,10000).
% 3.77/4.05 assign(order,kbo).
% 3.77/4.05 set(lex_order_vars).
% 3.77/4.05 clear(print_given).
% 3.77/4.05
% 3.77/4.05 % formulas(sos). % not echoed (24 formulas)
% 3.77/4.05
% 3.77/4.05 ============================== end of input ==========================
% 3.77/4.05
% 3.77/4.05 % From the command line: assign(max_seconds, 300).
% 3.77/4.05
% 3.77/4.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.77/4.05
% 3.77/4.05 % Formulas that are not ordinary clauses:
% 3.77/4.05
% 3.77/4.05 ============================== end of process non-clausal formulas ===
% 3.77/4.05
% 3.77/4.05 ============================== PROCESS INITIAL CLAUSES ===============
% 3.77/4.05
% 3.77/4.05 ============================== PREDICATE ELIMINATION =================
% 3.77/4.05
% 3.77/4.05 ============================== end predicate elimination =============
% 3.77/4.05
% 3.77/4.05 Auto_denials:
% 3.77/4.05 % copying label goals to answer in negative clause
% 3.77/4.05
% 3.77/4.05 Term ordering decisions:
% 3.77/4.05 Function symbol KB weights: zero=1. one=1. true=1. sK1_goals_X1=1. sK2_goals_X0=1. multiplication=1. addition=1. leq=1. antidomain=1. coantidomain=1. codomain=1. domain=1. ifeq=1. ifeq2=1.
% 3.77/4.05
% 3.77/4.05 ============================== end of process initial clauses ========
% 3.77/4.05
% 3.77/4.05 ============================== CLAUSES FOR SEARCH ====================
% 3.77/4.05
% 3.77/4.05 ============================== end of clauses for search =============
% 3.77/4.05
% 3.77/4.05 ============================== SEARCH ================================
% 3.77/4.05
% 3.77/4.05 % Starting search at 0.01 seconds.
% 3.77/4.05
% 3.77/4.05 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 1.00 sec).
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=43.000, iters=3397
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=42.000, iters=3387
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=40.000, iters=3361
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=39.000, iters=3334
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=36.000, iters=3376
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=35.000, iters=3368
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=33.000, iters=3343
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=32.000, iters=3365
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=31.000, iters=3382
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=30.000, iters=3363
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=29.000, iters=3338
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=27.000, iters=3356
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=25.000, iters=3336
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=24.000, iters=3358
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=23.000, iters=3344
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=22.000, iters=3337
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=21.000, iters=3335
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=20.000, iters=3341
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=19.000, iters=3333
% 3.77/4.05
% 3.77/4.05 Low Water (keep): wt=18.000, iters=3341
% 3.77/4.05
% 3.77/4.05 ============================== PROOF =================================
% 3.77/4.05 % SZS status Unsatisfiable
% 3.77/4.05 % SZS output start Refutation
% 3.77/4.05
% 3.77/4.05 % Proof 1 at 2.96 (+ 0.12) seconds: goals.
% 3.77/4.05 % Length of proof is 109.
% 3.77/4.05 % Level of proof is 19.
% 3.77/4.05 % Maximum clause weight is 26.000.
% 3.77/4.05 % Given clauses 868.
% 3.77/4.05
% 3.77/4.05 1 addition(A,zero) = A # label(additive_identity) # label(axiom). [assumption].
% 3.77/4.05 2 addition(A,A) = A # label(additive_idempotence) # label(axiom). [assumption].
% 3.77/4.05 3 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [assumption].
% 3.77/4.05 4 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [assumption].
% 3.77/4.05 5 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [assumption].
% 3.77/4.05 6 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [assumption].
% 3.77/4.05 7 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [assumption].
% 3.77/4.05 8 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [assumption].
% 3.77/4.05 9 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [assumption].
% 3.77/4.05 11 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 3.77/4.05 12 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 3.77/4.05 13 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [assumption].
% 3.77/4.05 14 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [assumption].
% 3.77/4.05 15 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(14),rewrite([13(4)])].
% 3.77/4.05 16 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [assumption].
% 3.77/4.05 17 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(16),rewrite([13(4)])].
% 3.77/4.05 18 addition(A,addition(B,C)) = addition(addition(A,B),C) # label(additive_associativity) # label(axiom). [assumption].
% 3.77/4.05 19 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(18),rewrite([13(4)])].
% 3.77/4.05 20 multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) # label(multiplicative_associativity) # label(axiom). [assumption].
% 3.77/4.05 21 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)). [copy(20),flip(a)].
% 3.77/4.05 22 ifeq(leq(A,B),true,addition(A,B),B) = B # label(order_1) # label(axiom). [assumption].
% 3.77/4.05 23 ifeq2(addition(A,B),B,leq(A,B),true) = true # label(order) # label(axiom). [assumption].
% 3.77/4.05 24 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [assumption].
% 3.77/4.05 25 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(24),flip(a)].
% 3.77/4.05 26 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [assumption].
% 3.77/4.05 27 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(26),flip(a)].
% 3.77/4.05 28 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))) # label(domain2) # label(axiom). [assumption].
% 3.77/4.05 29 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)) # label(codomain2) # label(axiom). [assumption].
% 3.77/4.05 30 domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 3.77/4.05 31 antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))) != antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) # answer(goals). [copy(30),rewrite([8(4),8(8),8(11)]),flip(a)].
% 3.77/4.05 32 antidomain(one) = zero. [para(7(a,1),3(a,1)),flip(a)].
% 3.77/4.05 33 coantidomain(one) = zero. [para(9(a,1),4(a,1)),flip(a)].
% 3.77/4.05 34 addition(A,addition(A,B)) = addition(A,B). [para(19(a,1),2(a,1)),rewrite([13(1),13(2),19(2,R),2(1),13(3)])].
% 3.77/4.05 35 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(7(a,1),21(a,1,1)),rewrite([6(2)]),flip(a)].
% 3.77/4.05 36 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(21(a,1),9(a,1))].
% 3.77/4.05 44 ifeq2(addition(A,B),A,leq(B,A),true) = true. [para(13(a,1),23(a,1,1))].
% 3.77/4.05 49 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(1(a,1),25(a,2,2)),rewrite([5(3),13(3)])].
% 3.77/4.05 50 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(3(a,1),25(a,1,1)),rewrite([13(4)]),flip(a)].
% 3.77/4.05 51 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(7(a,1),25(a,1,1)),rewrite([49(4)]),flip(a)].
% 3.77/4.05 52 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(9(a,1),25(a,1,1)),rewrite([49(3),13(3)]),flip(a)].
% 3.77/4.05 53 ifeq(leq(multiplication(A,B),multiplication(A,C)),true,multiplication(A,addition(B,C)),multiplication(A,C)) = multiplication(A,C). [para(25(a,1),22(a,1,3))].
% 3.77/4.05 55 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(4(a,1),27(a,1,1)),rewrite([13(4)]),flip(a)].
% 3.77/4.05 56 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(7(a,1),27(a,1,1)),rewrite([49(3),13(3)]),flip(a)].
% 3.77/4.05 57 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(9(a,1),27(a,1,1)),rewrite([49(4),13(3)]),flip(a)].
% 3.77/4.05 63 addition(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(4(a,1),28(a,1,1,1)),rewrite([4(5),4(9)])].
% 3.77/4.05 65 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))). [para(7(a,1),28(a,1,1,1))].
% 3.77/4.05 67 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(9(a,1),28(a,1,1,1))].
% 3.77/4.05 74 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(7(a,1),29(a,1,1,1))].
% 3.77/4.05 80 addition(zero,antidomain(zero)) = one. [para(32(a,1),15(a,1,1)),rewrite([32(3)])].
% 3.77/4.05 81 addition(zero,coantidomain(zero)) = one. [para(33(a,1),17(a,1,1)),rewrite([33(3)])].
% 3.77/4.05 86 multiplication(A,antidomain(zero)) = A. [para(80(a,1),25(a,2,2)),rewrite([5(2),49(5),3(5)])].
% 3.77/4.05 91 addition(one,antidomain(A)) = one. [para(15(a,1),34(a,1,2)),rewrite([13(3),15(7)])].
% 3.77/4.05 92 addition(one,coantidomain(A)) = one. [para(17(a,1),34(a,1,2)),rewrite([13(3),17(7)])].
% 3.77/4.05 98 multiplication(A,coantidomain(zero)) = A. [para(81(a,1),25(a,2,2)),rewrite([5(2),49(5),3(5)])].
% 3.77/4.05 100 antidomain(zero) = one. [para(86(a,1),4(a,1)),flip(a)].
% 3.77/4.05 101 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(67),rewrite([100(2),91(7)]),flip(a)].
% 3.77/4.05 102 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one. [back_rewrite(65),rewrite([100(2),91(7)]),flip(a)].
% 3.77/4.05 103 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(21(a,1),35(a,1,2))].
% 3.77/4.05 110 addition(A,multiplication(A,antidomain(B))) = A. [para(91(a,1),25(a,2,2)),rewrite([3(2),3(5)])].
% 3.77/4.05 111 addition(A,multiplication(antidomain(B),A)) = A. [para(91(a,1),27(a,2,1)),rewrite([4(2),4(5)])].
% 3.77/4.05 114 addition(A,multiplication(A,coantidomain(B))) = A. [para(92(a,1),25(a,2,2)),rewrite([3(2),3(5)])].
% 3.77/4.05 115 addition(A,multiplication(coantidomain(B),A)) = A. [para(92(a,1),27(a,2,1)),rewrite([4(2),4(5)])].
% 3.77/4.05 116 coantidomain(zero) = one. [para(98(a,1),4(a,1)),flip(a)].
% 3.77/4.05 119 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(74),rewrite([116(2),92(7)]),flip(a)].
% 3.77/4.05 124 antidomain(multiplication(A,antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))) = one. [para(36(a,1),28(a,1,1,1)),rewrite([100(2),91(9)]),flip(a)].
% 3.77/4.05 140 ifeq(leq(A,multiplication(antidomain(B),A)),true,A,multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(111(a,1),22(a,1,3))].
% 3.77/4.05 151 leq(zero,multiplication(A,B)) = true. [para(49(a,1),23(a,1,1)),rewrite([11(7)])].
% 3.77/4.05 152 leq(zero,A) = true. [para(3(a,1),151(a,1,2))].
% 3.77/4.05 153 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(101(a,1),7(a,1,1)),rewrite([4(6)])].
% 3.77/4.05 158 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(153(a,1),25(a,1,1)),rewrite([49(3),13(5)]),flip(a)].
% 3.77/4.05 161 multiplication(antidomain(A),antidomain(antidomain(A))) = zero. [para(102(a,1),7(a,1,1)),rewrite([4(6)])].
% 3.77/4.05 165 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))). [para(161(a,1),27(a,1,1)),rewrite([49(5),13(5)]),flip(a)].
% 3.77/4.05 180 leq(multiplication(coantidomain(A),B),B) = true. [para(115(a,1),44(a,1,1)),rewrite([11(5)])].
% 3.77/4.05 190 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(119(a,1),9(a,1,2)),rewrite([3(6)])].
% 3.77/4.05 194 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(190(a,1),27(a,1,1)),rewrite([49(3),13(5)]),flip(a)].
% 3.77/4.05 196 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(17(a,1),52(a,1,2)),rewrite([3(3)]),flip(a)].
% 3.77/4.05 207 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(196(a,1),25(a,1,1)),rewrite([50(4,R),13(7)]),flip(a)].
% 3.77/4.05 252 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(15(a,1),56(a,1,1)),rewrite([4(3)]),flip(a)].
% 3.77/4.05 255 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [para(56(a,1),28(a,1,2,1)),rewrite([13(11),56(18)])].
% 3.77/4.05 263 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(252(a,1),27(a,1,1)),rewrite([55(4,R),13(6)]),flip(a)].
% 3.77/4.05 312 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(17(a,1),51(a,1,2)),rewrite([3(4)]),flip(a)].
% 3.77/4.05 356 ifeq(leq(multiplication(A,antidomain(B)),multiplication(A,antidomain(antidomain(B)))),true,A,multiplication(A,antidomain(antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [para(15(a,1),53(a,1,3,2)),rewrite([3(9)])].
% 3.77/4.05 513 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(13(a,1),57(a,1,1))].
% 3.77/4.05 515 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(17(a,1),57(a,1,1)),rewrite([4(5)]),flip(a)].
% 3.77/4.05 1683 multiplication(A,antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B)))))) = zero. [para(124(a,1),7(a,1,1)),rewrite([4(8)])].
% 3.77/4.05 1940 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(15(a,1),513(a,1,1)),rewrite([4(4)]),flip(a)].
% 3.77/4.05 2100 ifeq(leq(coantidomain(coantidomain(A)),antidomain(coantidomain(A))),true,coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(312(a,1),140(a,1,1,2)),rewrite([312(13),312(16)])].
% 3.77/4.05 2622 multiplication(A,antidomain(coantidomain(A))) = A. [para(15(a,1),158(a,1,2)),rewrite([3(2)]),flip(a)].
% 3.77/4.05 2663 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2622(a,1),21(a,1,1)),flip(a)].
% 3.77/4.05 2673 leq(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = true. [para(2622(a,1),180(a,1,1))].
% 3.77/4.05 2879 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(15(a,1),165(a,1,1)),rewrite([4(5)]),flip(a)].
% 3.77/4.05 2918 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(1940(a,1),114(a,1,2))].
% 3.77/4.05 3267 multiplication(A,coantidomain(coantidomain(A))) = A. [para(312(a,1),2663(a,1,2)),rewrite([2622(3)]),flip(a)].
% 3.77/4.05 3312 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(515),rewrite([3267(5)]),flip(a)].
% 3.77/4.05 3407 leq(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = true. [para(3312(a,1),2673(a,1,2,1))].
% 3.77/4.05 3424 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [back_rewrite(2100),rewrite([3407(5),12(7)])].
% 3.77/4.05 3777 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(194),rewrite([3424(3)])].
% 3.77/4.05 3786 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [back_rewrite(17),rewrite([3424(3)])].
% 3.77/4.05 4614 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(2918(a,1),207(a,1,2)),rewrite([13(11),91(11),3(9)])].
% 3.77/4.05 8558 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B))) = antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B)). [para(255(a,1),263(a,1,1)),rewrite([13(17),91(17),4(19)])].
% 3.77/4.05 9205 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(2879(a,1),110(a,1,2)),rewrite([63(5)])].
% 3.77/4.05 9248 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [back_rewrite(8558),rewrite([9205(7),56(7),9205(10),56(10)])].
% 3.77/4.05 11324 multiplication(coantidomain(antidomain(A)),A) = A. [para(3786(a,1),3777(a,1,1)),rewrite([4(2)]),flip(a)].
% 3.77/4.05 11329 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(4614(a,1),3777(a,2)),rewrite([9205(5),3786(6),4(4)]),flip(a)].
% 3.77/4.05 11330 multiplication(antidomain(antidomain(A)),A) = A. [back_rewrite(11324),rewrite([11329(2)])].
% 3.77/4.05 11433 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(11330(a,1),103(a,1,2,2))].
% 3.77/4.05 13672 multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A. [para(1683(a,1),356(a,1,1,1)),rewrite([9205(7),152(7),9205(8),12(8),9205(6)]),flip(a)].
% 3.77/4.05 15607 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [para(11433(a,1),13672(a,1,2,1,2,1)),rewrite([116(7),3(7),9248(7)]),flip(a)].
% 3.77/4.05 15628 $F # answer(goals). [back_rewrite(31),rewrite([15607(6)]),xx(a)].
% 3.77/4.05
% 3.77/4.05 % SZS output end Refutation
% 3.77/4.05 ============================== end of proof ==========================
% 3.77/4.05
% 3.77/4.05 ============================== STATISTICS ============================
% 3.77/4.05
% 3.77/4.05 Given=868. Generated=201351. Kept=15620. proofs=1.
% 3.77/4.05 Usable=653. Sos=9291. Demods=9821. Limbo=21, Disabled=5679. Hints=0.
% 3.77/4.05 Megabytes=16.08.
% 3.77/4.05 User_CPU=2.96, System_CPU=0.12, Wall_clock=3.
% 3.77/4.05
% 3.77/4.05 ============================== end of statistics =====================
% 3.77/4.05
% 3.77/4.05 ============================== end of search =========================
% 3.77/4.05
% 3.77/4.05 THEOREM PROVED
% 3.77/4.05 % SZS status Unsatisfiable
% 3.77/4.05
% 3.77/4.05 Exiting with 1 proof.
% 3.77/4.05
% 3.77/4.05 Process 7533 exit (max_proofs) Thu Jun 16 10:04:26 2022
% 3.77/4.05 Prover9 interrupted
%------------------------------------------------------------------------------