TSTP Solution File: KLE090+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE090+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 02:22:11 EDT 2022
% Result : Theorem 12.89s 13.24s
% Output : Refutation 12.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KLE090+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.08/0.28 % Computer : n005.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Thu Jun 16 14:50:23 EDT 2022
% 0.13/0.28 % CPUTime :
% 0.63/0.93 ============================== Prover9 ===============================
% 0.63/0.93 Prover9 (32) version 2009-11A, November 2009.
% 0.63/0.93 Process 4288 was started by sandbox on n005.cluster.edu,
% 0.63/0.93 Thu Jun 16 14:50:24 2022
% 0.63/0.93 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4135_n005.cluster.edu".
% 0.63/0.93 ============================== end of head ===========================
% 0.63/0.93
% 0.63/0.93 ============================== INPUT =================================
% 0.63/0.93
% 0.63/0.93 % Reading from file /tmp/Prover9_4135_n005.cluster.edu
% 0.63/0.93
% 0.63/0.93 set(prolog_style_variables).
% 0.63/0.93 set(auto2).
% 0.63/0.93 % set(auto2) -> set(auto).
% 0.63/0.93 % set(auto) -> set(auto_inference).
% 0.63/0.93 % set(auto) -> set(auto_setup).
% 0.63/0.93 % set(auto_setup) -> set(predicate_elim).
% 0.63/0.93 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.63/0.93 % set(auto) -> set(auto_limits).
% 0.63/0.93 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.63/0.93 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.63/0.93 % set(auto) -> set(auto_denials).
% 0.63/0.93 % set(auto) -> set(auto_process).
% 0.63/0.93 % set(auto2) -> assign(new_constants, 1).
% 0.63/0.93 % set(auto2) -> assign(fold_denial_max, 3).
% 0.63/0.93 % set(auto2) -> assign(max_weight, "200.000").
% 0.63/0.93 % set(auto2) -> assign(max_hours, 1).
% 0.63/0.93 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.63/0.93 % set(auto2) -> assign(max_seconds, 0).
% 0.63/0.93 % set(auto2) -> assign(max_minutes, 5).
% 0.63/0.93 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.63/0.93 % set(auto2) -> set(sort_initial_sos).
% 0.63/0.93 % set(auto2) -> assign(sos_limit, -1).
% 0.63/0.93 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.63/0.93 % set(auto2) -> assign(max_megs, 400).
% 0.63/0.93 % set(auto2) -> assign(stats, some).
% 0.63/0.93 % set(auto2) -> clear(echo_input).
% 0.63/0.93 % set(auto2) -> set(quiet).
% 0.63/0.93 % set(auto2) -> clear(print_initial_clauses).
% 0.63/0.93 % set(auto2) -> clear(print_given).
% 0.63/0.93 assign(lrs_ticks,-1).
% 0.63/0.93 assign(sos_limit,10000).
% 0.63/0.93 assign(order,kbo).
% 0.63/0.93 set(lex_order_vars).
% 0.63/0.93 clear(print_given).
% 0.63/0.93
% 0.63/0.93 % formulas(sos). % not echoed (21 formulas)
% 0.63/0.93
% 0.63/0.93 ============================== end of input ==========================
% 0.63/0.93
% 0.63/0.93 % From the command line: assign(max_seconds, 300).
% 0.63/0.93
% 0.63/0.93 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.63/0.93
% 0.63/0.93 % Formulas that are not ordinary clauses:
% 0.63/0.93 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 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].
% 0.63/0.93 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 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].
% 0.63/0.93 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 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].
% 0.63/0.93 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].
% 0.63/0.93 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.63/0.93 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].
% 12.89/13.24 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 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].
% 12.89/13.24 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 21 -(all X0 all X1 (addition(X0,X1) = X1 -> addition(antidomain(X1),antidomain(X0)) = antidomain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 12.89/13.24
% 12.89/13.24 ============================== end of process non-clausal formulas ===
% 12.89/13.24
% 12.89/13.24 ============================== PROCESS INITIAL CLAUSES ===============
% 12.89/13.24
% 12.89/13.24 ============================== PREDICATE ELIMINATION =================
% 12.89/13.24 22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 12.89/13.24 23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 12.89/13.24
% 12.89/13.24 ============================== end predicate elimination =============
% 12.89/13.24
% 12.89/13.24 Auto_denials:
% 12.89/13.24 % copying label goals to answer in negative clause
% 12.89/13.24
% 12.89/13.24 Term ordering decisions:
% 12.89/13.24 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. antidomain=1. coantidomain=1. codomain=1. domain=1.
% 12.89/13.24
% 12.89/13.24 ============================== end of process initial clauses ========
% 12.89/13.24
% 12.89/13.24 ============================== CLAUSES FOR SEARCH ====================
% 12.89/13.24
% 12.89/13.24 ============================== end of clauses for search =============
% 12.89/13.24
% 12.89/13.24 ============================== SEARCH ================================
% 12.89/13.24
% 12.89/13.24 % Starting search at 0.01 seconds.
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=44.000, iters=3470
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=39.000, iters=3470
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=35.000, iters=3383
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=31.000, iters=3351
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=30.000, iters=3361
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=29.000, iters=3351
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=28.000, iters=3333
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=27.000, iters=3370
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=26.000, iters=3349
% 12.89/13.24
% 12.89/13.24 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 2.40 sec).
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=25.000, iters=3355
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=24.000, iters=3402
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=23.000, iters=3428
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=22.000, iters=3386
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=21.000, iters=3344
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=20.000, iters=3335
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=19.000, iters=3341
% 12.89/13.24
% 12.89/13.24 Low Water (displace): id=6549, wt=49.000
% 12.89/13.24
% 12.89/13.24 Low Water (displace): id=3668, wt=48.000
% 12.89/13.24
% 12.89/13.24 Low Water (displace): id=14711, wt=17.000
% 12.89/13.24
% 12.89/13.24 Low Water (displace): id=14761, wt=16.000
% 12.89/13.24
% 12.89/13.24 Low Water (displace): id=14762, wt=15.000
% 12.89/13.24
% 12.89/13.24 Low Water (keep): wt=18.000, iters=3335
% 12.89/13.24
% 12.89/13.24 Low Water (displace): id=17235, wt=14.000
% 12.89/13.24
% 12.89/13.24 Low Water (displace): id=17617, wt=13.000
% 12.89/13.24
% 12.89/13.24 ============================== PROOF =================================
% 12.89/13.24 % SZS status Theorem
% 12.89/13.24 % SZS output start Refutation
% 12.89/13.24
% 12.89/13.24 % Proof 1 at 11.86 (+ 0.42) seconds: goals.
% 12.89/13.24 % Length of proof is 118.
% 12.89/13.24 % Level of proof is 19.
% 12.89/13.24 % Maximum clause weight is 19.000.
% 12.89/13.24 % Given clauses 1109.
% 12.89/13.24
% 12.89/13.24 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 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].
% 12.89/13.24 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 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].
% 12.89/13.24 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 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].
% 12.89/13.24 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].
% 12.89/13.24 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 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].
% 12.89/13.24 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 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].
% 12.89/13.24 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 12.89/13.24 21 -(all X0 all X1 (addition(X0,X1) = X1 -> addition(antidomain(X1),antidomain(X0)) = antidomain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 12.89/13.24 24 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 12.89/13.24 25 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 12.89/13.24 26 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 12.89/13.24 27 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 12.89/13.24 28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 12.89/13.24 29 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 12.89/13.24 30 addition(c1,c2) = c2 # label(goals) # label(negated_conjecture). [clausify(21)].
% 12.89/13.24 31 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 12.89/13.24 33 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 12.89/13.24 35 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 12.89/13.24 36 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 12.89/13.24 37 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(36),rewrite([35(4)])].
% 12.89/13.24 38 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 12.89/13.24 39 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(38),rewrite([35(4)])].
% 12.89/13.24 40 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 12.89/13.24 41 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(40),rewrite([35(2)]),flip(a)].
% 12.89/13.24 42 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 12.89/13.24 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 12.89/13.24 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)].
% 12.89/13.24 45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 12.89/13.24 46 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(45),flip(a)].
% 12.89/13.24 47 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 12.89/13.24 48 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(47),flip(a)].
% 12.89/13.24 49 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 12.89/13.24 50 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(49),flip(a)].
% 12.89/13.24 51 antidomain(c1) != addition(antidomain(c2),antidomain(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(21)].
% 12.89/13.24 52 addition(antidomain(c1),antidomain(c2)) != antidomain(c1) # answer(goals). [copy(51),rewrite([35(7)]),flip(a)].
% 12.89/13.24 53 antidomain(one) = zero. [para(31(a,1),26(a,1)),flip(a)].
% 12.89/13.24 54 coantidomain(one) = zero. [para(33(a,1),27(a,1)),flip(a)].
% 12.89/13.24 55 addition(A,addition(A,B)) = addition(A,B). [para(41(a,1),25(a,1)),rewrite([35(1),35(2),41(2,R),25(1),35(3)])].
% 12.89/13.24 56 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(31(a,1),42(a,1,1)),rewrite([29(2)]),flip(a)].
% 12.89/13.24 57 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(42(a,1),33(a,1))].
% 12.89/13.24 59 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(24(a,1),44(a,2,2)),rewrite([28(3),35(3)])].
% 12.89/13.24 60 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(26(a,1),44(a,1,1)),rewrite([35(4)]),flip(a)].
% 12.89/13.24 61 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(31(a,1),44(a,1,1)),rewrite([59(4)]),flip(a)].
% 12.89/13.24 62 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(33(a,1),44(a,1,1)),rewrite([59(3),35(3)]),flip(a)].
% 12.89/13.24 63 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(27(a,1),46(a,1,1)),rewrite([35(4)]),flip(a)].
% 12.89/13.24 64 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(31(a,1),46(a,1,1)),rewrite([59(3),35(3)]),flip(a)].
% 12.89/13.24 65 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(33(a,1),46(a,1,1)),rewrite([59(4),35(3)]),flip(a)].
% 12.89/13.24 69 addition(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(27(a,1),48(a,1,1,1)),rewrite([27(5),27(9)])].
% 12.89/13.24 71 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))). [para(31(a,1),48(a,1,1,1))].
% 12.89/13.24 73 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(33(a,1),48(a,1,1,1))].
% 12.89/13.24 82 addition(zero,antidomain(zero)) = one. [para(53(a,1),37(a,1,1)),rewrite([53(3)])].
% 12.89/13.24 83 addition(zero,coantidomain(zero)) = one. [para(54(a,1),39(a,1,1)),rewrite([54(3)])].
% 12.89/13.24 86 multiplication(A,antidomain(zero)) = A. [para(82(a,1),44(a,2,2)),rewrite([28(2),59(5),26(5)])].
% 12.89/13.24 90 multiplication(A,coantidomain(zero)) = A. [para(83(a,1),44(a,2,2)),rewrite([28(2),59(5),26(5)])].
% 12.89/13.24 92 addition(one,antidomain(A)) = one. [para(37(a,1),55(a,1,2)),rewrite([35(3),37(7)])].
% 12.89/13.24 93 addition(one,coantidomain(A)) = one. [para(39(a,1),55(a,1,2)),rewrite([35(3),39(7)])].
% 12.89/13.24 94 antidomain(zero) = one. [para(86(a,1),27(a,1)),flip(a)].
% 12.89/13.24 95 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(73),rewrite([94(2),92(7)]),flip(a)].
% 12.89/13.24 96 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one. [back_rewrite(71),rewrite([94(2),92(7)]),flip(a)].
% 12.89/13.24 97 coantidomain(zero) = one. [para(90(a,1),27(a,1)),flip(a)].
% 12.89/13.24 103 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(56(a,1),48(a,1,1,1)),rewrite([94(2),92(8)]),flip(a)].
% 12.89/13.24 105 addition(A,multiplication(A,antidomain(B))) = A. [para(92(a,1),44(a,2,2)),rewrite([26(2),26(5)])].
% 12.89/13.24 106 addition(A,multiplication(antidomain(B),A)) = A. [para(92(a,1),46(a,2,1)),rewrite([27(2),27(5)])].
% 12.89/13.24 107 addition(A,multiplication(A,coantidomain(B))) = A. [para(93(a,1),44(a,2,2)),rewrite([26(2),26(5)])].
% 12.89/13.24 108 addition(A,multiplication(coantidomain(B),A)) = A. [para(93(a,1),46(a,2,1)),rewrite([27(2),27(5)])].
% 12.89/13.24 118 multiplication(addition(A,B),multiplication(C,coantidomain(multiplication(B,C)))) = multiplication(A,multiplication(C,coantidomain(multiplication(B,C)))). [para(57(a,1),46(a,1,1)),rewrite([59(6),35(5)]),flip(a)].
% 12.89/13.24 142 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(95(a,1),31(a,1,1)),rewrite([27(6)])].
% 12.89/13.25 147 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(142(a,1),44(a,1,1)),rewrite([59(3),35(5)]),flip(a)].
% 12.89/13.25 150 multiplication(antidomain(A),antidomain(antidomain(A))) = zero. [para(96(a,1),31(a,1,1)),rewrite([27(6)])].
% 12.89/13.25 153 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(39(a,1),61(a,1,2)),rewrite([26(4)]),flip(a)].
% 12.89/13.25 161 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(106(a,1),61(a,1,2)),rewrite([31(2)]),flip(a)].
% 12.89/13.25 165 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))). [para(150(a,1),46(a,1,1)),rewrite([59(5),35(5)]),flip(a)].
% 12.89/13.25 174 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(39(a,1),62(a,1,2)),rewrite([26(3)]),flip(a)].
% 12.89/13.25 183 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(174(a,1),44(a,1,1)),rewrite([60(4,R),35(7)]),flip(a)].
% 12.89/13.25 199 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(61(a,1),161(a,1,2))].
% 12.89/13.25 222 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(62(a,1),63(a,2,2)),rewrite([35(9),41(9),35(8),41(9,R),35(8)])].
% 12.89/13.25 239 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(37(a,1),64(a,1,1)),rewrite([27(3)]),flip(a)].
% 12.89/13.25 248 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(35(a,1),65(a,1,1))].
% 12.89/13.25 250 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(39(a,1),65(a,1,1)),rewrite([27(5)]),flip(a)].
% 12.89/13.25 269 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(239(a,1),42(a,1,1)),flip(a)].
% 12.89/13.25 656 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(103(a,1),31(a,1,1)),rewrite([27(7)])].
% 12.89/13.25 663 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(656(a,1),44(a,1,1)),rewrite([59(4),35(7)]),flip(a)].
% 12.89/13.25 769 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(153(a,1),106(a,1,2)),rewrite([35(5)])].
% 12.89/13.25 880 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(35(a,1),199(a,1,1,1))].
% 12.89/13.25 1002 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(37(a,1),248(a,1,1)),rewrite([27(4)]),flip(a)].
% 12.89/13.25 1794 multiplication(antidomain(c2),c1) = zero. [para(30(a,1),880(a,1,1,1)),rewrite([269(7)])].
% 12.89/13.25 1835 coantidomain(multiplication(coantidomain(coantidomain(antidomain(c2))),c1)) = one. [para(1794(a,1),50(a,1,1,1)),rewrite([97(2),93(9)]),flip(a)].
% 12.89/13.25 2024 multiplication(coantidomain(coantidomain(antidomain(c2))),c1) = zero. [para(1835(a,1),33(a,1,2)),rewrite([26(8)])].
% 12.89/13.25 2028 multiplication(addition(A,coantidomain(coantidomain(antidomain(c2)))),c1) = multiplication(A,c1). [para(1835(a,1),118(a,1,2,2)),rewrite([26(8),2024(14),97(10),26(10)])].
% 12.89/13.25 2559 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(1002(a,1),107(a,1,2))].
% 12.89/13.25 2791 multiplication(A,antidomain(coantidomain(A))) = A. [para(37(a,1),147(a,1,2)),rewrite([26(2)]),flip(a)].
% 12.89/13.25 2814 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2791(a,1),42(a,1,1)),flip(a)].
% 12.89/13.25 2822 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2791(a,1),108(a,1,2)),rewrite([35(5)])].
% 12.89/13.25 3968 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(37(a,1),165(a,1,1)),rewrite([27(5)]),flip(a)].
% 12.89/13.25 4867 multiplication(A,coantidomain(coantidomain(A))) = A. [para(153(a,1),2814(a,1,2)),rewrite([2791(3)]),flip(a)].
% 12.89/13.25 4910 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(250),rewrite([4867(5)]),flip(a)].
% 12.89/13.25 5082 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(4910(a,1),769(a,1,2)),rewrite([35(5),2822(5),4910(6)])].
% 12.89/13.25 5091 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(5082(a,1),37(a,1,1)),rewrite([5082(4)])].
% 12.89/13.25 5097 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(5082(a,1),1002(a,1,1,1)),rewrite([5082(5),153(5),5082(5)]),flip(a)].
% 12.89/13.25 5603 multiplication(addition(A,antidomain(coantidomain(antidomain(c2)))),c1) = multiplication(A,c1). [back_rewrite(2028),rewrite([5097(4)])].
% 12.89/13.25 5867 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(2559(a,1),183(a,1,2)),rewrite([35(11),92(11),26(9)])].
% 12.89/13.25 7826 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(5867(a,1),222(a,2,2,2)),rewrite([35(4),93(4),5097(6),27(8),5097(11),35(14),5091(14),35(10),92(10)])].
% 12.89/13.25 13191 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(3968(a,1),105(a,1,2)),rewrite([69(5)])].
% 12.89/13.25 14211 multiplication(antidomain(antidomain(c2)),c1) = c1. [para(7826(a,1),5603(a,1,1)),rewrite([27(3)]),flip(a)].
% 12.89/13.25 19080 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(37(a,1),663(a,1,2)),rewrite([26(3)]),flip(a)].
% 12.89/13.25 19318 multiplication(antidomain(c2),antidomain(c1)) = antidomain(c2). [para(14211(a,1),19080(a,1,2,1)),rewrite([13191(4),13191(9)])].
% 12.89/13.25 19346 addition(antidomain(c1),antidomain(c2)) = antidomain(c1). [para(19318(a,1),106(a,1,2))].
% 12.89/13.25 19347 $F # answer(goals). [resolve(19346,a,52,a)].
% 12.89/13.25
% 12.89/13.25 % SZS output end Refutation
% 12.89/13.25 ============================== end of proof ==========================
% 12.89/13.25
% 12.89/13.25 ============================== STATISTICS ============================
% 12.89/13.25
% 12.89/13.25 Given=1109. Generated=444632. Kept=19315. proofs=1.
% 12.89/13.25 Usable=775. Sos=9174. Demods=9408. Limbo=3, Disabled=9385. Hints=0.
% 12.89/13.25 Megabytes=18.27.
% 12.89/13.25 User_CPU=11.86, System_CPU=0.42, Wall_clock=12.
% 12.89/13.25
% 12.89/13.25 ============================== end of statistics =====================
% 12.89/13.25
% 12.89/13.25 ============================== end of search =========================
% 12.89/13.25
% 12.89/13.25 THEOREM PROVED
% 12.89/13.25 % SZS status Theorem
% 12.89/13.25
% 12.89/13.25 Exiting with 1 proof.
% 12.89/13.25
% 12.89/13.25 Process 4288 exit (max_proofs) Thu Jun 16 14:50:36 2022
% 12.89/13.25 Prover9 interrupted
%------------------------------------------------------------------------------