TSTP Solution File: KLE104-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE104-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 02:22:14 EDT 2022
% Result : Unsatisfiable 12.09s 12.36s
% Output : Refutation 12.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE104-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n014.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 15:17:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.91/4.20 ============================== Prover9 ===============================
% 3.91/4.20 Prover9 (32) version 2009-11A, November 2009.
% 3.91/4.20 Process 7151 was started by sandbox2 on n014.cluster.edu,
% 3.91/4.20 Thu Jun 16 15:17:06 2022
% 3.91/4.20 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6998_n014.cluster.edu".
% 3.91/4.20 ============================== end of head ===========================
% 3.91/4.20
% 3.91/4.20 ============================== INPUT =================================
% 3.91/4.20
% 3.91/4.20 % Reading from file /tmp/Prover9_6998_n014.cluster.edu
% 3.91/4.20
% 3.91/4.20 set(prolog_style_variables).
% 3.91/4.20 set(auto2).
% 3.91/4.20 % set(auto2) -> set(auto).
% 3.91/4.20 % set(auto) -> set(auto_inference).
% 3.91/4.20 % set(auto) -> set(auto_setup).
% 3.91/4.20 % set(auto_setup) -> set(predicate_elim).
% 3.91/4.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.91/4.20 % set(auto) -> set(auto_limits).
% 3.91/4.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.91/4.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.91/4.20 % set(auto) -> set(auto_denials).
% 3.91/4.20 % set(auto) -> set(auto_process).
% 3.91/4.20 % set(auto2) -> assign(new_constants, 1).
% 3.91/4.20 % set(auto2) -> assign(fold_denial_max, 3).
% 3.91/4.20 % set(auto2) -> assign(max_weight, "200.000").
% 3.91/4.20 % set(auto2) -> assign(max_hours, 1).
% 3.91/4.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.91/4.20 % set(auto2) -> assign(max_seconds, 0).
% 3.91/4.20 % set(auto2) -> assign(max_minutes, 5).
% 3.91/4.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.91/4.20 % set(auto2) -> set(sort_initial_sos).
% 3.91/4.20 % set(auto2) -> assign(sos_limit, -1).
% 3.91/4.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.91/4.20 % set(auto2) -> assign(max_megs, 400).
% 3.91/4.20 % set(auto2) -> assign(stats, some).
% 3.91/4.20 % set(auto2) -> clear(echo_input).
% 3.91/4.20 % set(auto2) -> set(quiet).
% 3.91/4.20 % set(auto2) -> clear(print_initial_clauses).
% 3.91/4.20 % set(auto2) -> clear(print_given).
% 3.91/4.20 assign(lrs_ticks,-1).
% 3.91/4.20 assign(sos_limit,10000).
% 3.91/4.20 assign(order,kbo).
% 3.91/4.20 set(lex_order_vars).
% 3.91/4.20 clear(print_given).
% 3.91/4.20
% 3.91/4.20 % formulas(sos). % not echoed (31 formulas)
% 3.91/4.20
% 3.91/4.20 ============================== end of input ==========================
% 3.91/4.20
% 3.91/4.20 % From the command line: assign(max_seconds, 300).
% 3.91/4.20
% 3.91/4.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.91/4.20
% 3.91/4.20 % Formulas that are not ordinary clauses:
% 3.91/4.20
% 3.91/4.20 ============================== end of process non-clausal formulas ===
% 3.91/4.20
% 3.91/4.20 ============================== PROCESS INITIAL CLAUSES ===============
% 3.91/4.20
% 3.91/4.20 ============================== PREDICATE ELIMINATION =================
% 3.91/4.20
% 3.91/4.20 ============================== end predicate elimination =============
% 3.91/4.20
% 3.91/4.20 Auto_denials:
% 3.91/4.20 % copying label goals_1 to answer in negative clause
% 3.91/4.20
% 3.91/4.20 Term ordering decisions:
% 3.91/4.20 Function symbol KB weights: zero=1. one=1. true=1. sK1_goals_X2=1. sK2_goals_X1=1. sK3_goals_X0=1. multiplication=1. addition=1. backward_box=1. backward_diamond=1. forward_diamond=1. leq=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1. ifeq=1. ifeq2=1.
% 3.91/4.20
% 3.91/4.20 ============================== end of process initial clauses ========
% 3.91/4.20
% 3.91/4.20 ============================== CLAUSES FOR SEARCH ====================
% 3.91/4.20
% 3.91/4.20 ============================== end of clauses for search =============
% 3.91/4.20
% 3.91/4.20 ============================== SEARCH ================================
% 3.91/4.20
% 3.91/4.20 % Starting search at 0.02 seconds.
% 3.91/4.20
% 3.91/4.20 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 1.03 sec).
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=46.000, iters=3402
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=43.000, iters=3456
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=41.000, iters=3427
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=37.000, iters=3356
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=36.000, iters=3346
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=35.000, iters=3441
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=33.000, iters=3337
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=32.000, iters=3367
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=31.000, iters=3380
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=30.000, iters=3376
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=29.000, iters=3345
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=28.000, iters=3342
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=27.000, iters=3349
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=26.000, iters=3342
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=25.000, iters=3420
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=24.000, iters=3432
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=23.000, iters=3341
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=22.000, iters=3334
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=21.000, iters=3336
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=20.000, iters=3335
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=19.000, iters=3338
% 3.91/4.20
% 12.09/12.36 Low Water (keep): wt=18.000, iters=3348
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9074, wt=69.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9060, wt=67.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9047, wt=62.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9043, wt=61.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9058, wt=59.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9034, wt=58.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9036, wt=57.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9051, wt=56.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9035, wt=55.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9024, wt=54.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9063, wt=53.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9048, wt=52.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9045, wt=51.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9026, wt=50.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=9078, wt=49.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=15599, wt=15.000
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=15970, wt=14.000
% 12.09/12.36
% 12.09/12.36 Low Water (keep): wt=17.000, iters=3343
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=18897, wt=13.000
% 12.09/12.36
% 12.09/12.36 Low Water (keep): wt=16.000, iters=3334
% 12.09/12.36
% 12.09/12.36 Low Water (displace): id=20762, wt=12.000
% 12.09/12.36
% 12.09/12.36 ============================== PROOF =================================
% 12.09/12.36 % SZS status Unsatisfiable
% 12.09/12.36 % SZS output start Refutation
% 12.09/12.36
% 12.09/12.36 % Proof 1 at 10.93 (+ 0.43) seconds: goals_1.
% 12.09/12.36 % Length of proof is 129.
% 12.09/12.36 % Level of proof is 29.
% 12.09/12.36 % Maximum clause weight is 39.000.
% 12.09/12.36 % Given clauses 1561.
% 12.09/12.36
% 12.09/12.36 1 addition(A,zero) = A # label(additive_identity) # label(axiom). [assumption].
% 12.09/12.36 2 addition(A,A) = A # label(additive_idempotence) # label(axiom). [assumption].
% 12.09/12.36 3 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [assumption].
% 12.09/12.36 4 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [assumption].
% 12.09/12.36 5 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [assumption].
% 12.09/12.36 6 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [assumption].
% 12.09/12.36 7 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [assumption].
% 12.09/12.36 8 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [assumption].
% 12.09/12.36 9 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [assumption].
% 12.09/12.36 10 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [assumption].
% 12.09/12.36 11 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [assumption].
% 12.09/12.36 12 c(A) = antidomain(antidomain(antidomain(A))). [copy(11),rewrite([8(2)])].
% 12.09/12.36 13 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 12.09/12.36 14 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 12.09/12.36 15 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [assumption].
% 12.09/12.36 16 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [assumption].
% 12.09/12.36 17 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(16),rewrite([15(4)])].
% 12.09/12.36 18 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [assumption].
% 12.09/12.36 19 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(18),rewrite([15(4)])].
% 12.09/12.36 22 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [assumption].
% 12.09/12.36 23 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(22),rewrite([8(2),8(5)])].
% 12.09/12.36 24 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [assumption].
% 12.09/12.36 25 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(24),rewrite([10(2),10(5)])].
% 12.09/12.36 26 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom). [assumption].
% 12.09/12.36 27 forward_box(A,B) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(antidomain(antidomain(antidomain(B))))))))))). [copy(26),rewrite([12(2),23(5),12(10)])].
% 12.09/12.36 28 backward_box(A,B) = c(backward_diamond(A,c(B))) # label(backward_box) # label(axiom). [assumption].
% 12.09/12.36 29 backward_box(A,B) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(B))))),A)))))). [copy(28),rewrite([12(2),25(5),12(10)])].
% 12.09/12.36 30 addition(domain(sK2_goals_X1),backward_box(sK3_goals_X0,domain(sK1_goals_X2))) = one # label(goals) # label(negated_conjecture). [assumption].
% 12.09/12.36 31 one = addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0))))))). [copy(30),rewrite([8(2),8(6),29(8)]),flip(a)].
% 12.09/12.36 32 addition(A,addition(B,C)) = addition(addition(A,B),C) # label(additive_associativity) # label(axiom). [assumption].
% 12.09/12.36 33 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(32),rewrite([15(4)])].
% 12.09/12.36 34 multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) # label(multiplicative_associativity) # label(axiom). [assumption].
% 12.09/12.36 35 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)). [copy(34),flip(a)].
% 12.09/12.36 36 ifeq(leq(A,B),true,addition(A,B),B) = B # label(order_1) # label(axiom). [assumption].
% 12.09/12.36 37 ifeq2(addition(A,B),B,leq(A,B),true) = true # label(order) # label(axiom). [assumption].
% 12.09/12.36 38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [assumption].
% 12.09/12.36 39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(38),flip(a)].
% 12.09/12.36 40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [assumption].
% 12.09/12.36 41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(40),flip(a)].
% 12.09/12.36 42 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))) # label(domain2) # label(axiom). [assumption].
% 12.09/12.36 43 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)) # label(codomain2) # label(axiom). [assumption].
% 12.09/12.36 44 addition(forward_box(sK3_goals_X0,domain(sK2_goals_X1)),domain(sK1_goals_X2)) != one # label(goals_1) # label(negated_conjecture) # answer(goals_1). [assumption].
% 12.09/12.36 45 addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0))))))) != addition(antidomain(antidomain(sK1_goals_X2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2_goals_X1)))))))))))))) # answer(goals_1). [copy(44),rewrite([8(3),27(5),8(17),15(19),31(20)]),flip(a)].
% 12.09/12.36 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0))))))). [back_rewrite(19),rewrite([31(5)])].
% 12.09/12.36 47 addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0))))))) = addition(antidomain(A),antidomain(antidomain(A))). [back_rewrite(17),rewrite([31(5)]),flip(a)].
% 12.09/12.36 48 multiplication(addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0))))))),A) = A. [back_rewrite(4),rewrite([31(1)])].
% 12.09/12.36 49 multiplication(A,addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)))))))) = A. [back_rewrite(3),rewrite([31(1)])].
% 12.09/12.36 50 addition(A,addition(A,B)) = addition(A,B). [para(33(a,1),2(a,1)),rewrite([15(1),15(2),33(2,R),2(1),15(3)])].
% 12.09/12.36 53 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(9(a,1),35(a,1,1)),rewrite([6(2)]),flip(a)].
% 12.09/12.36 58 ifeq2(addition(A,B),A,leq(B,A),true) = true. [para(15(a,1),37(a,1,1))].
% 12.09/12.36 61 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(1(a,1),39(a,2,2)),rewrite([5(3),15(3)])].
% 12.09/12.36 62 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(7(a,1),39(a,1,1)),rewrite([61(4)]),flip(a)].
% 12.09/12.36 63 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(9(a,1),39(a,1,1)),rewrite([61(3),15(3)]),flip(a)].
% 12.09/12.36 64 ifeq(leq(multiplication(A,B),multiplication(A,C)),true,multiplication(A,addition(B,C)),multiplication(A,C)) = multiplication(A,C). [para(39(a,1),36(a,1,3))].
% 12.09/12.36 66 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(7(a,1),41(a,1,1)),rewrite([61(3),15(3)]),flip(a)].
% 12.09/12.36 67 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(9(a,1),41(a,1,1)),rewrite([61(4),15(3)]),flip(a)].
% 12.09/12.36 75 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(9(a,1),42(a,1,1,1))].
% 12.09/12.36 80 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(7(a,1),43(a,1,1,1))].
% 12.09/12.36 91 multiplication(A,addition(coantidomain(B),coantidomain(coantidomain(B)))) = A. [para(46(a,1),39(a,2,2)),rewrite([39(6),49(25)])].
% 12.09/12.36 92 multiplication(addition(coantidomain(A),coantidomain(coantidomain(A))),B) = B. [para(46(a,1),41(a,2,1)),rewrite([41(6),48(25)])].
% 12.09/12.36 93 addition(coantidomain(A),coantidomain(coantidomain(A))) != addition(antidomain(antidomain(sK1_goals_X2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2_goals_X1)))))))))))))) # answer(goals_1). [para(46(a,2),45(a,1))].
% 12.09/12.36 94 addition(coantidomain(A),coantidomain(coantidomain(A))) = addition(coantidomain(B),coantidomain(coantidomain(B))). [para(46(a,2),46(a,2))].
% 12.09/12.36 95 addition(coantidomain(A),coantidomain(coantidomain(A))) = c_0. [new_symbol(94)].
% 12.09/12.36 96 addition(antidomain(antidomain(sK1_goals_X2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2_goals_X1)))))))))))))) != c_0 # answer(goals_1). [back_rewrite(93),rewrite([95(4)]),flip(a)].
% 12.09/12.36 97 multiplication(c_0,A) = A. [back_rewrite(92),rewrite([95(4)])].
% 12.09/12.36 98 multiplication(A,c_0) = A. [back_rewrite(91),rewrite([95(4)])].
% 12.09/12.36 102 addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0))))))) = c_0. [back_rewrite(46),rewrite([95(4)]),flip(a)].
% 12.09/12.36 105 addition(antidomain(A),antidomain(antidomain(A))) = c_0. [back_rewrite(47),rewrite([102(19)]),flip(a)].
% 12.09/12.36 109 coantidomain(c_0) = zero. [para(97(a,1),9(a,1))].
% 12.09/12.36 110 multiplication(addition(A,c_0),B) = addition(B,multiplication(A,B)). [para(97(a,1),41(a,1,1)),rewrite([15(4)]),flip(a)].
% 12.09/12.36 119 antidomain(c_0) = zero. [para(98(a,1),7(a,1))].
% 12.09/12.36 137 addition(c_0,coantidomain(A)) = c_0. [para(95(a,1),50(a,1,2)),rewrite([15(3),95(7)])].
% 12.09/12.36 138 addition(zero,coantidomain(zero)) = c_0. [para(109(a,1),95(a,1,1)),rewrite([109(3)])].
% 12.09/12.36 142 addition(A,multiplication(A,coantidomain(B))) = A. [para(137(a,1),39(a,2,2)),rewrite([98(2),98(5)])].
% 12.09/12.36 143 addition(A,multiplication(coantidomain(B),A)) = A. [para(137(a,1),41(a,2,1)),rewrite([97(2),97(5)])].
% 12.09/12.36 150 multiplication(A,coantidomain(zero)) = A. [para(138(a,1),39(a,2,2)),rewrite([5(2),61(5),98(5)])].
% 12.09/12.36 153 coantidomain(zero) = c_0. [para(150(a,1),97(a,1)),flip(a)].
% 12.09/12.36 158 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = c_0. [back_rewrite(80),rewrite([153(2),137(7)]),flip(a)].
% 12.09/12.36 161 addition(c_0,antidomain(A)) = c_0. [para(105(a,1),50(a,1,2)),rewrite([15(3),105(7)])].
% 12.09/12.36 162 addition(zero,antidomain(zero)) = c_0. [para(119(a,1),105(a,1,1)),rewrite([119(3)])].
% 12.09/12.36 166 addition(A,multiplication(A,antidomain(B))) = A. [para(161(a,1),39(a,2,2)),rewrite([98(2),98(5)])].
% 12.09/12.36 167 addition(A,multiplication(antidomain(B),A)) = A. [para(161(a,1),41(a,2,1)),rewrite([97(2),97(5)])].
% 12.09/12.36 169 ifeq(leq(zero,antidomain(zero)),true,c_0,antidomain(zero)) = antidomain(zero). [para(162(a,1),36(a,1,3))].
% 12.09/12.36 173 leq(zero,A) = true. [para(1(a,1),58(a,1,1)),rewrite([13(4)])].
% 12.09/12.36 184 antidomain(zero) = c_0. [back_rewrite(169),rewrite([173(4),14(6)]),flip(a)].
% 12.09/12.36 188 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = c_0. [back_rewrite(75),rewrite([184(2),161(7)]),flip(a)].
% 12.09/12.36 199 leq(multiplication(coantidomain(A),B),B) = true. [para(143(a,1),58(a,1,1)),rewrite([13(5)])].
% 12.09/12.36 223 ifeq(leq(A,multiplication(antidomain(B),A)),true,A,multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(167(a,1),36(a,1,3))].
% 12.09/12.36 263 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(95(a,1),62(a,1,2)),rewrite([98(4)]),flip(a)].
% 12.09/12.36 268 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(158(a,1),9(a,1,2)),rewrite([98(6)])].
% 12.09/12.36 272 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(268(a,1),41(a,1,1)),rewrite([61(3),15(5)]),flip(a)].
% 12.09/12.36 274 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(188(a,1),7(a,1,1)),rewrite([97(6)])].
% 12.09/12.36 279 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(274(a,1),39(a,1,1)),rewrite([61(3),15(5)]),flip(a)].
% 12.09/12.36 313 ifeq(leq(multiplication(A,antidomain(B)),multiplication(A,antidomain(antidomain(B)))),true,A,multiplication(A,antidomain(antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [para(105(a,1),64(a,1,3,2)),rewrite([98(9)])].
% 12.09/12.36 337 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero. [para(42(a,1),66(a,1,1)),rewrite([7(8)]),flip(a)].
% 12.09/12.36 387 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(15(a,1),67(a,1,1))].
% 12.09/12.36 398 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(95(a,1),67(a,1,1)),rewrite([97(5)]),flip(a)].
% 12.09/12.36 399 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(105(a,1),67(a,1,1)),rewrite([97(5)]),flip(a)].
% 12.09/12.36 848 multiplication(addition(A,c_0),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(63(a,1),110(a,2,2)),rewrite([15(9),33(9),15(8),33(9,R),15(8)])].
% 12.09/12.36 1356 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(263(a,1),167(a,1,2)),rewrite([15(5)])].
% 12.09/12.36 1634 multiplication(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)))))),coantidomain(antidomain(antidomain(sK2_goals_X1)))) = coantidomain(antidomain(antidomain(sK2_goals_X1))). [para(102(a,1),387(a,1,1)),rewrite([97(6)]),flip(a)].
% 12.09/12.36 3841 multiplication(coantidomain(antidomain(A)),A) = A. [para(95(a,1),272(a,1,1)),rewrite([97(2)]),flip(a)].
% 12.09/12.36 3884 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(3841(a,1),166(a,1,2)),rewrite([15(5)])].
% 12.09/12.36 4551 ifeq(leq(coantidomain(coantidomain(A)),antidomain(coantidomain(A))),true,coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(263(a,1),223(a,1,1,2)),rewrite([263(13),263(16)])].
% 12.09/12.36 4577 multiplication(A,antidomain(coantidomain(A))) = A. [para(105(a,1),279(a,1,2)),rewrite([98(2)]),flip(a)].
% 12.09/12.36 4622 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(4577(a,1),35(a,1,1)),flip(a)].
% 12.09/12.36 4629 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(4577(a,1),143(a,1,2)),rewrite([15(5)])].
% 12.09/12.36 4631 leq(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = true. [para(4577(a,1),199(a,1,1))].
% 12.09/12.36 4740 multiplication(A,coantidomain(coantidomain(A))) = A. [para(263(a,1),4622(a,1,2)),rewrite([4577(3)]),flip(a)].
% 12.09/12.36 4807 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(398),rewrite([4740(5)]),flip(a)].
% 12.09/12.36 4914 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(4807(a,1),1356(a,1,2)),rewrite([15(5),4629(5),4807(6)])].
% 12.09/12.36 4919 leq(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = true. [para(4807(a,1),4631(a,1,2,1))].
% 12.09/12.36 4949 multiplication(antidomain(antidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)))),coantidomain(antidomain(antidomain(sK2_goals_X1)))) = coantidomain(antidomain(antidomain(sK2_goals_X1))). [back_rewrite(1634),rewrite([4914(13)])].
% 12.09/12.36 4966 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [back_rewrite(4551),rewrite([4919(5),14(7)])].
% 12.09/12.36 4987 multiplication(antidomain(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)))),coantidomain(antidomain(antidomain(sK2_goals_X1)))) = coantidomain(antidomain(antidomain(sK2_goals_X1))). [back_rewrite(4949),rewrite([4966(8)])].
% 12.09/12.36 5006 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(4914),rewrite([4966(2)])].
% 12.09/12.36 5439 multiplication(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)),coantidomain(antidomain(antidomain(sK2_goals_X1)))) = coantidomain(antidomain(antidomain(sK2_goals_X1))). [back_rewrite(4987),rewrite([5006(13)])].
% 12.09/12.36 6020 coantidomain(antidomain(antidomain(A))) = antidomain(A). [para(399(a,1),142(a,1,2)),rewrite([3884(5)])].
% 12.09/12.36 6033 multiplication(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))),sK3_goals_X0)),antidomain(sK2_goals_X1)) = antidomain(sK2_goals_X1). [back_rewrite(5439),rewrite([6020(7),6020(13),6020(16)])].
% 12.09/12.36 6058 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(6020(a,1),4966(a,1,1)),rewrite([6020(5)])].
% 12.09/12.36 6059 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(6020(a,1),4966(a,2,1)),rewrite([6058(3),6058(4)])].
% 12.09/12.36 6060 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(6020(a,1),5006(a,2)),rewrite([6058(3),6059(4)])].
% 12.09/12.36 6187 multiplication(coantidomain(multiplication(antidomain(sK1_goals_X2),sK3_goals_X0)),antidomain(sK2_goals_X1)) = antidomain(sK2_goals_X1). [back_rewrite(6033),rewrite([6060(4),6060(4)])].
% 12.09/12.36 6199 addition(antidomain(antidomain(sK1_goals_X2)),antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))) != c_0 # answer(goals_1). [back_rewrite(96),rewrite([6060(8),6060(8),6060(8),6060(10),6060(10)])].
% 12.09/12.36 6252 multiplication(antidomain(sK1_goals_X2),multiplication(sK3_goals_X0,antidomain(sK2_goals_X1))) = zero. [para(6187(a,1),53(a,1,2)),rewrite([35(7)])].
% 12.09/12.36 6292 multiplication(antidomain(sK1_goals_X2),antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1))))) = zero. [para(6252(a,1),337(a,1,1,1)),rewrite([184(2),97(11)])].
% 12.09/12.36 9505 multiplication(antidomain(sK1_goals_X2),antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))) = antidomain(sK1_goals_X2). [para(6292(a,1),313(a,1,1,1)),rewrite([6060(10),173(10),6060(13),14(13),6060(11)]),flip(a)].
% 12.09/12.36 22943 addition(antidomain(antidomain(sK1_goals_X2)),antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))) = c_0. [para(9505(a,1),848(a,2,2,2)),rewrite([15(4),161(4),6058(9),15(10),97(11),6058(17),15(20),105(20),15(16),161(16)])].
% 12.09/12.36 22944 $F # answer(goals_1). [resolve(22943,a,6199,a)].
% 12.09/12.36
% 12.09/12.36 % SZS output end Refutation
% 12.09/12.36 ============================== end of proof ==========================
% 12.09/12.36
% 12.09/12.36 ============================== STATISTICS ============================
% 12.09/12.36
% 12.09/12.36 Given=1561. Generated=821027. Kept=22929. proofs=1.
% 12.09/12.36 Usable=1270. Sos=9999. Demods=11211. Limbo=5, Disabled=11685. Hints=0.
% 12.09/12.36 Megabytes=20.07.
% 12.09/12.36 User_CPU=10.93, System_CPU=0.43, Wall_clock=11.
% 12.09/12.36
% 12.09/12.36 ============================== end of statistics =====================
% 12.09/12.36
% 12.09/12.36 ============================== end of search =========================
% 12.09/12.36
% 12.09/12.36 THEOREM PROVED
% 12.09/12.36 % SZS status Unsatisfiable
% 12.09/12.36
% 12.09/12.36 Exiting with 1 proof.
% 12.09/12.36
% 12.09/12.36 Process 7151 exit (max_proofs) Thu Jun 16 15:17:17 2022
% 12.09/12.36 Prover9 interrupted
%------------------------------------------------------------------------------