TSTP Solution File: KLE124+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE124+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 02:22:20 EDT 2022
% Result : Theorem 275.57s 275.93s
% Output : Refutation 275.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE124+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n024.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 14:13:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/0.97 ============================== Prover9 ===============================
% 0.70/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.70/0.97 Process 31352 was started by sandbox on n024.cluster.edu,
% 0.70/0.97 Thu Jun 16 14:13:48 2022
% 0.70/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31199_n024.cluster.edu".
% 0.70/0.97 ============================== end of head ===========================
% 0.70/0.97
% 0.70/0.97 ============================== INPUT =================================
% 0.70/0.97
% 0.70/0.97 % Reading from file /tmp/Prover9_31199_n024.cluster.edu
% 0.70/0.97
% 0.70/0.97 set(prolog_style_variables).
% 0.70/0.97 set(auto2).
% 0.70/0.97 % set(auto2) -> set(auto).
% 0.70/0.97 % set(auto) -> set(auto_inference).
% 0.70/0.97 % set(auto) -> set(auto_setup).
% 0.70/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.70/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/0.97 % set(auto) -> set(auto_limits).
% 0.70/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/0.97 % set(auto) -> set(auto_denials).
% 0.70/0.97 % set(auto) -> set(auto_process).
% 0.70/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.70/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.70/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.70/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.70/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.70/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.70/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.70/0.97 % set(auto2) -> assign(stats, some).
% 0.70/0.97 % set(auto2) -> clear(echo_input).
% 0.70/0.97 % set(auto2) -> set(quiet).
% 0.70/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.70/0.97 % set(auto2) -> clear(print_given).
% 0.70/0.97 assign(lrs_ticks,-1).
% 0.70/0.97 assign(sos_limit,10000).
% 0.70/0.97 assign(order,kbo).
% 0.70/0.97 set(lex_order_vars).
% 0.70/0.97 clear(print_given).
% 0.70/0.97
% 0.70/0.97 % formulas(sos). % not echoed (27 formulas)
% 0.70/0.97
% 0.70/0.97 ============================== end of input ==========================
% 0.70/0.97
% 0.70/0.97 % From the command line: assign(max_seconds, 300).
% 0.70/0.97
% 0.70/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/0.97
% 0.70/0.97 % Formulas that are not ordinary clauses:
% 0.70/0.97 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 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].
% 0.70/0.97 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 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].
% 0.70/0.97 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 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].
% 0.70/0.97 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].
% 0.70/0.97 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.97 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].
% 3.04/3.36 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 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].
% 3.04/3.36 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 3.04/3.36 27 -(all X0 all X1 all X2 all X3 all X4 (addition(domain(X2),domain(X1)) = domain(X1) & addition(backward_diamond(X0,domain(X1)),domain(X3)) = domain(X3) & addition(domain(X3),domain(X4)) = domain(X4) -> addition(backward_diamond(X0,domain(X2)),domain(X4)) = domain(X4))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.04/3.36
% 3.04/3.36 ============================== end of process non-clausal formulas ===
% 3.04/3.36
% 3.04/3.36 ============================== PROCESS INITIAL CLAUSES ===============
% 3.04/3.36
% 3.04/3.36 ============================== PREDICATE ELIMINATION =================
% 3.04/3.36 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 3.04/3.36 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 3.04/3.36
% 3.04/3.36 ============================== end predicate elimination =============
% 3.04/3.36
% 3.04/3.36 Auto_denials:
% 3.04/3.36 % copying label goals to answer in negative clause
% 3.04/3.36
% 3.04/3.36 Term ordering decisions:
% 3.04/3.36 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. domain=1. coantidomain=1. c=1. codomain=1.
% 3.04/3.36
% 3.04/3.36 ============================== end of process initial clauses ========
% 3.04/3.36
% 3.04/3.36 ============================== CLAUSES FOR SEARCH ====================
% 3.04/3.36
% 3.04/3.36 ============================== end of clauses for search =============
% 3.04/3.36
% 3.04/3.36 ============================== SEARCH ================================
% 3.04/3.36
% 3.04/3.36 % Starting search at 0.01 seconds.
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=37.000, iters=3352
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=34.000, iters=3369
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=33.000, iters=3362
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=32.000, iters=3352
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=31.000, iters=3462
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=30.000, iters=3363
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=29.000, iters=3337
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=27.000, iters=3335
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=26.000, iters=3343
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=25.000, iters=3353
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=24.000, iters=3336
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=23.000, iters=3347
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=22.000, iters=3340
% 3.04/3.36
% 3.04/3.36 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 1.61 sec).
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=21.000, iters=3338
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=20.000, iters=3334
% 3.04/3.36
% 3.04/3.36 Low Water (keep): wt=19.000, iters=4523
% 275.57/275.93
% 275.57/275.93 Low Water (keep): wt=18.000, iters=3661
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=6137, wt=49.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=3922, wt=48.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=6868, wt=47.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=4640, wt=46.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=6869, wt=45.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=16610, wt=17.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=16640, wt=16.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=16678, wt=15.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=16688, wt=14.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=18177, wt=13.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=18178, wt=12.000
% 275.57/275.93
% 275.57/275.93 Low Water (keep): wt=17.000, iters=3340
% 275.57/275.93
% 275.57/275.93 Low Water (keep): wt=16.000, iters=3356
% 275.57/275.93
% 275.57/275.93 Low Water (keep): wt=15.000, iters=3333
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=31234, wt=11.000
% 275.57/275.93
% 275.57/275.93 Low Water (displace): id=31242, wt=10.000
% 275.57/275.93
% 275.57/275.93 Low Water (keep): wt=14.000, iters=3352
% 275.57/275.93
% 275.57/275.93 ============================== PROOF =================================
% 275.57/275.93 % SZS status Theorem
% 275.57/275.93 % SZS output start Refutation
% 275.57/275.93
% 275.57/275.93 % Proof 1 at 264.75 (+ 10.18) seconds: goals.
% 275.57/275.93 % Length of proof is 249.
% 275.57/275.93 % Level of proof is 32.
% 275.57/275.93 % Maximum clause weight is 24.000.
% 275.57/275.93 % Given clauses 8332.
% 275.57/275.93
% 275.57/275.93 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 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].
% 275.57/275.93 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 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].
% 275.57/275.93 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 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].
% 275.57/275.93 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].
% 275.57/275.93 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 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].
% 275.57/275.93 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 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].
% 275.57/275.93 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 275.57/275.93 27 -(all X0 all X1 all X2 all X3 all X4 (addition(domain(X2),domain(X1)) = domain(X1) & addition(backward_diamond(X0,domain(X1)),domain(X3)) = domain(X3) & addition(domain(X3),domain(X4)) = domain(X4) -> addition(backward_diamond(X0,domain(X2)),domain(X4)) = domain(X4))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 275.57/275.93 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 275.57/275.93 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 275.57/275.93 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 275.57/275.93 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 275.57/275.93 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 275.57/275.93 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 275.57/275.93 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 275.57/275.93 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 275.57/275.93 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 275.57/275.93 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 275.57/275.93 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 275.57/275.93 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 275.57/275.93 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 275.57/275.93 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 275.57/275.93 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 275.57/275.93 47 domain(c2) = addition(domain(c3),domain(c2)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 275.57/275.93 48 addition(antidomain(antidomain(c2)),antidomain(antidomain(c3))) = antidomain(antidomain(c2)). [copy(47),rewrite([37(2),37(5),37(8),42(10)]),flip(a)].
% 275.57/275.93 49 domain(c5) = addition(domain(c4),domain(c5)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 275.57/275.93 50 addition(antidomain(antidomain(c4)),antidomain(antidomain(c5))) = antidomain(antidomain(c5)). [copy(49),rewrite([37(2),37(5),37(8)]),flip(a)].
% 275.57/275.93 53 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 275.57/275.93 54 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(53),rewrite([37(2),37(5)])].
% 275.57/275.93 55 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 275.57/275.93 56 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(55),rewrite([39(2),39(5)])].
% 275.57/275.93 61 domain(c4) = addition(backward_diamond(c1,domain(c2)),domain(c4)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 275.57/275.93 62 addition(antidomain(antidomain(c4)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c2)))),c1)))) = antidomain(antidomain(c4)). [copy(61),rewrite([37(2),37(6),56(8),37(14),42(16)]),flip(a)].
% 275.57/275.93 63 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 275.57/275.93 64 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(63),rewrite([42(2)]),flip(a)].
% 275.57/275.93 65 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 275.57/275.93 66 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 275.57/275.93 67 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(66),flip(a)].
% 275.57/275.93 68 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 275.57/275.93 69 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(68),flip(a)].
% 275.57/275.93 70 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 275.57/275.93 71 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(70),flip(a)].
% 275.57/275.93 72 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 275.57/275.93 73 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(72),flip(a)].
% 275.57/275.93 74 domain(c5) != addition(backward_diamond(c1,domain(c3)),domain(c5)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 275.57/275.93 75 addition(antidomain(antidomain(c5)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) != antidomain(antidomain(c5)) # answer(goals). [copy(74),rewrite([37(2),37(6),56(8),37(14),42(16)]),flip(a)].
% 275.57/275.93 76 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 275.57/275.93 77 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 275.57/275.93 78 addition(A,addition(A,B)) = addition(A,B). [para(64(a,1),31(a,1)),rewrite([42(1),42(2),64(2,R),31(1),42(3)])].
% 275.57/275.93 79 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),65(a,1,1)),rewrite([35(2)]),flip(a)].
% 275.57/275.93 80 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(65(a,1),38(a,1))].
% 275.57/275.93 81 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(38(a,1),65(a,1,1)),rewrite([35(2)]),flip(a)].
% 275.57/275.93 82 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),67(a,2,2)),rewrite([34(3),42(3)])].
% 275.57/275.93 83 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),67(a,1,1)),rewrite([42(4)]),flip(a)].
% 275.57/275.93 84 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),67(a,1,1)),rewrite([82(4)]),flip(a)].
% 275.57/275.93 85 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),67(a,1,1)),rewrite([82(3),42(3)]),flip(a)].
% 275.57/275.93 86 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),69(a,1,1)),rewrite([42(4)]),flip(a)].
% 275.57/275.93 87 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(36(a,1),69(a,1,1)),rewrite([82(3),42(3)]),flip(a)].
% 275.57/275.93 88 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),69(a,1,1)),rewrite([82(4),42(3)]),flip(a)].
% 275.57/275.93 89 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(65(a,1),69(a,1,1)),rewrite([42(6)])].
% 275.57/275.93 94 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))). [para(36(a,1),71(a,1,1,1))].
% 275.57/275.93 96 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),71(a,1,1,1))].
% 275.57/275.93 101 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),73(a,1,1,1))].
% 275.57/275.93 102 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(A)))) = coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(A))). [para(38(a,1),73(a,1,1,1))].
% 275.57/275.93 104 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(65(a,1),73(a,1,1,1))].
% 275.57/275.93 105 addition(zero,antidomain(zero)) = one. [para(76(a,1),44(a,1,1)),rewrite([76(3)])].
% 275.57/275.93 106 addition(zero,coantidomain(zero)) = one. [para(77(a,1),46(a,1,1)),rewrite([77(3)])].
% 275.57/275.93 109 multiplication(A,antidomain(zero)) = A. [para(105(a,1),67(a,2,2)),rewrite([34(2),82(5),32(5)])].
% 275.57/275.93 113 multiplication(A,coantidomain(zero)) = A. [para(106(a,1),67(a,2,2)),rewrite([34(2),82(5),32(5)])].
% 275.57/275.93 115 addition(one,antidomain(A)) = one. [para(44(a,1),78(a,1,2)),rewrite([42(3),44(7)])].
% 275.57/275.93 116 addition(one,coantidomain(A)) = one. [para(46(a,1),78(a,1,2)),rewrite([42(3),46(7)])].
% 275.57/275.93 117 antidomain(zero) = one. [para(109(a,1),33(a,1)),flip(a)].
% 275.57/275.93 118 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(96),rewrite([117(2),115(7)]),flip(a)].
% 275.57/275.93 119 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one. [back_rewrite(94),rewrite([117(2),115(7)]),flip(a)].
% 275.57/275.93 120 coantidomain(zero) = one. [para(113(a,1),33(a,1)),flip(a)].
% 275.57/275.93 121 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(A))) = one. [back_rewrite(102),rewrite([120(2),116(7)]),flip(a)].
% 275.57/275.93 122 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(101),rewrite([120(2),116(7)]),flip(a)].
% 275.57/275.93 123 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(65(a,1),79(a,1,2))].
% 275.57/275.93 126 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(79(a,1),71(a,1,1,1)),rewrite([117(2),115(8)]),flip(a)].
% 275.57/275.93 128 addition(A,multiplication(A,antidomain(B))) = A. [para(115(a,1),67(a,2,2)),rewrite([32(2),32(5)])].
% 275.57/275.93 129 addition(A,multiplication(antidomain(B),A)) = A. [para(115(a,1),69(a,2,1)),rewrite([33(2),33(5)])].
% 275.57/275.93 130 addition(A,multiplication(A,coantidomain(B))) = A. [para(116(a,1),67(a,2,2)),rewrite([32(2),32(5)])].
% 275.57/275.93 131 addition(A,multiplication(coantidomain(B),A)) = A. [para(116(a,1),69(a,2,1)),rewrite([33(2),33(5)])].
% 275.57/275.93 133 multiplication(A,addition(B,multiplication(coantidomain(A),C))) = multiplication(A,B). [para(81(a,1),67(a,1,1)),rewrite([82(3),42(4)]),flip(a)].
% 275.57/275.93 141 multiplication(addition(A,B),multiplication(C,coantidomain(multiplication(B,C)))) = multiplication(A,multiplication(C,coantidomain(multiplication(B,C)))). [para(80(a,1),69(a,1,1)),rewrite([82(6),42(5)]),flip(a)].
% 275.57/275.93 150 addition(zero,antidomain(A)) = antidomain(A). [para(36(a,1),83(a,2,2)),rewrite([84(4),32(3),42(4)]),flip(a)].
% 275.57/275.93 165 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(118(a,1),36(a,1,1)),rewrite([33(6)])].
% 275.57/275.93 170 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(165(a,1),67(a,1,1)),rewrite([82(3),42(5)]),flip(a)].
% 275.57/275.93 173 multiplication(antidomain(A),antidomain(antidomain(A))) = zero. [para(119(a,1),36(a,1,1)),rewrite([33(6)])].
% 275.57/275.93 176 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),84(a,1,2)),rewrite([32(4)]),flip(a)].
% 275.57/275.93 181 addition(multiplication(antidomain(A),B),multiplication(C,addition(A,B))) = multiplication(addition(C,antidomain(A)),addition(A,B)). [para(84(a,1),69(a,1,1)),rewrite([42(7)])].
% 275.57/275.93 182 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(69(a,1),84(a,1,2))].
% 275.57/275.93 185 addition(addition(A,B),multiplication(antidomain(A),B)) = addition(A,B). [para(84(a,1),129(a,1,2))].
% 275.57/275.93 186 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(129(a,1),84(a,1,2)),rewrite([36(2)]),flip(a)].
% 275.57/275.93 190 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))). [para(173(a,1),69(a,1,1)),rewrite([82(5),42(5)]),flip(a)].
% 275.57/275.93 192 multiplication(coantidomain(coantidomain(A)),coantidomain(A)) = zero. [para(121(a,1),38(a,1,2)),rewrite([32(6)])].
% 275.57/275.93 198 addition(zero,coantidomain(A)) = coantidomain(A). [para(192(a,1),131(a,1,2)),rewrite([42(3)])].
% 275.57/275.93 199 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),85(a,1,2)),rewrite([32(3)]),flip(a)].
% 275.57/275.93 208 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(199(a,1),67(a,1,1)),rewrite([83(4,R),42(7)]),flip(a)].
% 275.57/275.93 213 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(122(a,1),38(a,1,2)),rewrite([32(6)])].
% 275.57/275.93 217 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(213(a,1),69(a,1,1)),rewrite([82(3),42(5)]),flip(a)].
% 275.57/275.93 221 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(186(a,1),69(a,1,1)),rewrite([82(5),42(5)]),flip(a)].
% 275.57/275.93 244 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)). [para(86(a,2),83(a,2)),flip(a)].
% 275.57/275.93 247 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(85(a,1),86(a,2,2)),rewrite([42(9),64(9),42(8),64(9,R),42(8)])].
% 275.57/275.93 264 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(44(a,1),87(a,1,1)),rewrite([33(3)]),flip(a)].
% 275.57/275.93 265 multiplication(antidomain(antidomain(c4)),antidomain(c5)) = zero. [para(50(a,1),87(a,1,1)),rewrite([36(6)]),flip(a)].
% 275.57/275.93 272 multiplication(addition(A,antidomain(B)),addition(B,one)) = addition(A,addition(antidomain(B),multiplication(A,B))). [para(87(a,1),83(a,2,2)),rewrite([42(9),64(9),42(8),64(9,R),42(8)])].
% 275.57/275.93 273 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),88(a,1,1))].
% 275.57/275.93 274 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),88(a,1,1)),rewrite([33(5)]),flip(a)].
% 275.57/275.93 275 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),88(a,1,1)),rewrite([33(5)]),flip(a)].
% 275.57/275.93 279 addition(multiplication(A,coantidomain(B)),multiplication(addition(A,B),C)) = multiplication(addition(A,B),addition(C,coantidomain(B))). [para(88(a,1),67(a,1,1)),rewrite([42(8)])].
% 275.57/275.93 285 multiplication(A,coantidomain(addition(A,B))) = zero. [para(78(a,1),88(a,1,1)),rewrite([38(4)]),flip(a)].
% 275.57/275.93 290 multiplication(antidomain(A),addition(B,antidomain(A))) = multiplication(antidomain(A),addition(B,one)). [para(264(a,1),67(a,1,1)),rewrite([83(4,R),42(7)]),flip(a)].
% 275.57/275.93 291 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(264(a,1),69(a,1,1)),rewrite([86(4,R),42(6)]),flip(a)].
% 275.57/275.93 293 addition(antidomain(antidomain(antidomain(A))),antidomain(multiplication(antidomain(antidomain(A)),A))) = antidomain(antidomain(antidomain(A))). [para(264(a,1),71(a,1,2,1)),rewrite([42(8),264(13)])].
% 275.57/275.93 297 multiplication(addition(A,antidomain(antidomain(c4))),antidomain(c5)) = multiplication(A,antidomain(c5)). [para(265(a,1),69(a,1,1)),rewrite([82(5),42(7)]),flip(a)].
% 275.57/275.93 300 coantidomain(addition(A,one)) = zero. [para(285(a,1),33(a,1)),rewrite([42(3)]),flip(a)].
% 275.57/275.93 305 multiplication(A,multiplication(B,coantidomain(multiplication(A,addition(B,C))))) = zero. [para(67(a,1),285(a,1,2,1)),rewrite([65(5)])].
% 275.57/275.93 310 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B)))) = one. [para(285(a,1),73(a,1,1,1)),rewrite([120(2),116(8)]),flip(a)].
% 275.57/275.93 312 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = zero. [para(83(a,2),285(a,1,2,1))].
% 275.57/275.93 318 addition(coantidomain(A),coantidomain(multiplication(addition(B,one),A))) = coantidomain(A). [para(300(a,1),73(a,1,2,1,1,1)),rewrite([120(6),33(6),42(6),300(9),120(8),33(8)])].
% 275.57/275.93 371 multiplication(addition(A,multiplication(B,antidomain(C))),antidomain(C)) = multiplication(addition(B,A),antidomain(C)). [para(264(a,1),89(a,1,1,2)),rewrite([69(5)]),flip(a)].
% 275.57/275.93 374 multiplication(addition(antidomain(antidomain(c4)),multiplication(A,B)),antidomain(c5)) = multiplication(A,multiplication(B,antidomain(c5))). [para(265(a,1),89(a,1,2)),rewrite([42(6),82(6)]),flip(a)].
% 275.57/275.93 482 multiplication(A,multiplication(B,coantidomain(multiplication(A,multiplication(B,addition(C,one)))))) = zero. [para(312(a,1),65(a,1)),rewrite([65(5)]),flip(a)].
% 275.57/275.93 577 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(126(a,1),36(a,1,1)),rewrite([33(7)])].
% 275.57/275.93 585 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(38(a,1),104(a,1,1,1,2)),rewrite([34(2),120(2),116(8)]),flip(a)].
% 275.57/275.93 597 multiplication(coantidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero. [para(104(a,1),85(a,1,2)),rewrite([38(10),65(9)]),flip(a)].
% 275.57/275.93 636 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(577(a,1),67(a,1,1)),rewrite([82(4),42(7)]),flip(a)].
% 275.57/275.93 676 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),multiplication(B,C))) = one. [para(123(a,1),104(a,1,1,1)),rewrite([120(2),116(10)]),flip(a)].
% 275.57/275.93 726 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(176(a,1),129(a,1,2)),rewrite([42(5)])].
% 275.57/275.93 856 multiplication(A,addition(B,addition(C,multiplication(coantidomain(A),D)))) = multiplication(A,addition(B,C)). [para(133(a,1),67(a,1,1)),rewrite([67(3),42(6),64(6,R),42(5)]),flip(a)].
% 275.57/275.93 876 addition(multiplication(addition(A,one),B),multiplication(A,addition(A,one))) = multiplication(addition(A,one),addition(A,B)). [para(244(a,1),67(a,1,2)),rewrite([42(10)])].
% 275.57/275.93 929 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),273(a,1,1)),rewrite([33(4)]),flip(a)].
% 275.57/275.93 930 multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c2)))),c1))),coantidomain(antidomain(antidomain(c4)))) = zero. [para(62(a,1),273(a,1,1)),rewrite([38(8)]),flip(a)].
% 275.57/275.93 932 addition(multiplication(A,coantidomain(B)),multiplication(addition(B,A),C)) = multiplication(addition(B,A),addition(C,coantidomain(B))). [para(273(a,1),67(a,1,2)),rewrite([42(5)])].
% 275.57/275.93 936 multiplication(A,multiplication(antidomain(B),coantidomain(A))) = zero. [para(128(a,1),273(a,1,1)),rewrite([38(2),65(5)]),flip(a)].
% 275.57/275.93 981 multiplication(A,addition(B,multiplication(antidomain(C),coantidomain(A)))) = multiplication(A,B). [para(936(a,1),67(a,1,1)),rewrite([82(3),42(5)]),flip(a)].
% 275.57/275.93 1174 multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [para(310(a,1),38(a,1,2)),rewrite([32(7)])].
% 275.57/275.93 1188 multiplication(antidomain(A),multiplication(B,coantidomain(multiplication(antidomain(antidomain(A)),B)))) = multiplication(B,coantidomain(multiplication(antidomain(antidomain(A)),B))). [para(44(a,1),141(a,1,1)),rewrite([33(7)]),flip(a)].
% 275.57/275.93 1272 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [para(585(a,1),38(a,1,2)),rewrite([32(7)])].
% 275.57/275.93 1281 multiplication(addition(A,coantidomain(coantidomain(multiplication(B,C)))),coantidomain(C)) = multiplication(A,coantidomain(C)). [para(585(a,1),141(a,1,2,2)),rewrite([32(7),1272(12),120(9),32(9)])].
% 275.57/275.93 1569 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(929(a,1),130(a,1,2))].
% 275.57/275.93 2627 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),170(a,1,2)),rewrite([32(2)]),flip(a)].
% 275.57/275.93 2762 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2627(a,1),65(a,1,1)),flip(a)].
% 275.57/275.93 2770 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2627(a,1),131(a,1,2)),rewrite([42(5)])].
% 275.57/275.93 2819 multiplication(A,coantidomain(coantidomain(A))) = A. [para(176(a,1),2762(a,1,2)),rewrite([2627(3)]),flip(a)].
% 275.57/275.93 2853 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(275),rewrite([2819(5)]),flip(a)].
% 275.57/275.93 2940 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2853(a,1),726(a,1,2)),rewrite([42(5),2770(5),2853(6)])].
% 275.57/275.93 2959 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2940(a,1),44(a,1,1)),rewrite([2940(4)])].
% 275.57/275.93 2965 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2940(a,1),929(a,1,1,1)),rewrite([2940(5),176(5),2940(5)]),flip(a)].
% 275.57/275.93 2967 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2940(a,1),929(a,2,1)),rewrite([2965(2),2965(6),929(9),2965(6)])].
% 275.57/275.93 2974 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2853(a,1),2940(a,1,1,1)),rewrite([2965(2),2965(5)]),flip(a)].
% 275.57/275.93 2975 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2853(a,1),2940(a,2)),rewrite([2965(2),2974(3),2967(4)])].
% 275.57/275.93 3270 multiplication(addition(A,antidomain(coantidomain(multiplication(B,C)))),coantidomain(C)) = multiplication(A,coantidomain(C)). [back_rewrite(1281),rewrite([2965(3)])].
% 275.57/275.93 3311 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [back_rewrite(1174),rewrite([2965(2)])].
% 275.57/275.93 3337 multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c2)))),c1))),coantidomain(antidomain(antidomain(c4)))) = zero. [back_rewrite(930),rewrite([2965(5),2965(9)])].
% 275.57/275.93 3362 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),multiplication(B,C))) = one. [back_rewrite(676),rewrite([2965(5)])].
% 275.57/275.93 3395 multiplication(antidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero. [back_rewrite(597),rewrite([2965(3)])].
% 275.57/275.93 3420 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(217),rewrite([2965(3)])].
% 275.57/275.93 3427 addition(antidomain(antidomain(c5)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) != antidomain(antidomain(c5)) # answer(goals). [back_rewrite(75),rewrite([2965(8),2965(12)])].
% 275.57/275.93 3645 multiplication(A,multiplication(addition(coantidomain(A),antidomain(B)),addition(B,C))) = multiplication(A,multiplication(antidomain(B),C)). [para(181(a,1),133(a,1,2))].
% 275.57/275.93 3698 addition(multiplication(antidomain(coantidomain(A)),B),multiplication(coantidomain(A),addition(B,one))) = addition(B,coantidomain(A)). [para(2959(a,1),181(a,2,1)),rewrite([42(6),208(7),42(11),33(12)])].
% 275.57/275.93 3715 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),182(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 275.57/275.93 3811 multiplication(antidomain(multiplication(coantidomain(A),B)),multiplication(antidomain(coantidomain(A)),B)) = multiplication(antidomain(multiplication(coantidomain(A),B)),B). [para(2959(a,1),182(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 275.57/275.93 4099 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(44(a,1),190(a,1,1)),rewrite([33(5)]),flip(a)].
% 275.57/275.93 4437 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(274(a,1),130(a,1,2))].
% 275.57/275.93 5064 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1569(a,1),208(a,1,2)),rewrite([42(11),115(11),32(9)])].
% 275.57/275.93 5070 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(4437(a,1),208(a,1,2)),rewrite([42(11),115(11),32(10)])].
% 275.57/275.93 5073 multiplication(coantidomain(multiplication(addition(A,one),B)),coantidomain(B)) = coantidomain(multiplication(addition(A,one),B)). [para(318(a,1),208(a,1,2)),rewrite([42(13),116(13),32(12)])].
% 275.57/275.93 5351 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),221(a,1,1)),rewrite([33(5)]),flip(a)].
% 275.57/275.93 5384 multiplication(coantidomain(A),multiplication(antidomain(B),coantidomain(A))) = multiplication(antidomain(B),coantidomain(A)). [para(2959(a,1),221(a,1,1)),rewrite([33(5)]),flip(a)].
% 275.57/275.93 7548 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(5064(a,1),247(a,2,2,2)),rewrite([42(4),116(4),2965(6),33(8),2965(11),42(14),2959(14),42(10),115(10)])].
% 275.57/275.93 9329 multiplication(antidomain(antidomain(c3)),antidomain(antidomain(c2))) = antidomain(antidomain(c3)). [para(48(a,1),290(a,1,2)),rewrite([42(15),115(15),32(12)])].
% 275.57/275.94 9355 addition(antidomain(c3),antidomain(antidomain(c2))) = one. [para(9329(a,1),185(a,1,2)),rewrite([42(10),64(10),42(9),44(9),42(5),115(5)]),flip(a)].
% 275.57/275.94 9366 multiplication(antidomain(c3),antidomain(c2)) = antidomain(c2). [para(9355(a,1),87(a,1,1)),rewrite([33(4)]),flip(a)].
% 275.57/275.94 9397 multiplication(antidomain(antidomain(c3)),antidomain(c2)) = zero. [para(9366(a,1),79(a,1,2))].
% 275.57/275.94 9443 multiplication(addition(A,antidomain(B)),addition(antidomain(B),coantidomain(antidomain(B)))) = addition(multiplication(A,coantidomain(antidomain(B))),multiplication(addition(A,one),antidomain(B))). [para(291(a,1),279(a,1,2)),flip(a)].
% 275.57/275.94 9464 multiplication(antidomain(antidomain(c3)),multiplication(antidomain(c2),A)) = zero. [para(9397(a,1),65(a,1,1)),rewrite([35(2)]),flip(a)].
% 275.57/275.94 9527 multiplication(antidomain(multiplication(antidomain(antidomain(A)),A)),antidomain(antidomain(antidomain(A)))) = antidomain(multiplication(antidomain(antidomain(A)),A)). [para(293(a,1),290(a,1,2)),rewrite([42(17),115(17),32(14)])].
% 275.57/275.94 9655 multiplication(antidomain(c4),antidomain(c5)) = antidomain(c5). [para(44(a,1),297(a,1,1)),rewrite([33(4)]),flip(a)].
% 275.57/275.94 12142 multiplication(coantidomain(antidomain(A)),A) = A. [para(2959(a,1),3420(a,1,1)),rewrite([33(2)]),flip(a)].
% 275.57/275.94 12149 multiplication(antidomain(antidomain(A)),A) = A. [para(7548(a,1),3420(a,1,1)),rewrite([33(2)]),flip(a)].
% 275.57/275.94 12155 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(5070),rewrite([12142(5)]),flip(a)].
% 275.57/275.94 12156 antidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(9527),rewrite([12149(3),4099(5),12149(6)])].
% 275.57/275.94 12180 addition(antidomain(antidomain(c5)),antidomain(coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) != antidomain(antidomain(c5)) # answer(goals). [back_rewrite(3427),rewrite([12155(7)])].
% 275.57/275.94 12181 multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(c2)),c1))),antidomain(c4)) = zero. [back_rewrite(3337),rewrite([12155(4),12155(11)])].
% 275.57/275.94 12212 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(12142(a,1),54(a,2,1,1)),rewrite([12156(3),54(3),5064(5),2975(4),12156(5)])].
% 275.57/275.94 12220 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(12142(a,1),123(a,1,2,2)),rewrite([12212(2)])].
% 275.57/275.94 12291 addition(multiplication(A,antidomain(antidomain(B))),multiplication(addition(A,one),antidomain(B))) = addition(A,antidomain(B)). [back_rewrite(9443),rewrite([12212(5),44(6),32(4),12212(4)]),flip(a)].
% 275.57/275.94 12967 multiplication(addition(antidomain(A),antidomain(B)),antidomain(A)) = antidomain(A). [para(129(a,1),371(a,1,1)),rewrite([264(3),42(4)]),flip(a)].
% 275.57/275.94 15756 multiplication(antidomain(antidomain(c2)),multiplication(c1,antidomain(c4))) = zero. [para(12181(a,1),2762(a,1,2)),rewrite([34(7),65(9)]),flip(a)].
% 275.57/275.94 16857 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(44(a,1),636(a,1,2)),rewrite([32(3)]),flip(a)].
% 275.57/275.94 17036 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(16857(a,1),129(a,1,2)),rewrite([42(4)])].
% 275.57/275.94 17037 multiplication(antidomain(antidomain(multiplication(A,B))),antidomain(A)) = zero. [para(16857(a,1),186(a,1,2))].
% 275.57/275.94 17051 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(16857(a,1),247(a,2,2,2)),rewrite([42(3),115(3),12212(5),42(6),33(7),12212(9),42(11),44(11),42(9),115(9)])].
% 275.57/275.94 17205 multiplication(antidomain(antidomain(multiplication(antidomain(A),B))),A) = zero. [para(17037(a,1),12220(a,1,1,1)),rewrite([117(2),33(7)])].
% 275.57/275.94 17223 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17051(a,1),273(a,1,1)),rewrite([12212(4),12156(4),33(3),12212(6),12156(6)]),flip(a)].
% 275.57/275.94 17331 multiplication(antidomain(antidomain(multiplication(antidomain(addition(A,B)),C))),A) = zero. [para(17205(a,1),305(a,1,2,2,1)),rewrite([120(7),32(7)])].
% 275.57/275.94 17448 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17223(a,1),65(a,1,1)),flip(a)].
% 275.57/275.94 17479 multiplication(antidomain(multiplication(coantidomain(A),B)),B) = multiplication(antidomain(coantidomain(A)),B). [back_rewrite(3811),rewrite([17448(7)]),flip(a)].
% 275.57/275.94 17480 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3715),rewrite([17448(7)]),flip(a)].
% 275.57/275.94 19425 multiplication(A,addition(coantidomain(A),antidomain(B))) = multiplication(A,antidomain(B)). [para(272(a,2),856(a,1,2)),rewrite([3645(7),32(3)]),flip(a)].
% 275.57/275.94 20767 addition(antidomain(A),multiplication(antidomain(B),antidomain(antidomain(A)))) = addition(antidomain(B),antidomain(A)). [para(12967(a,1),932(a,1,2)),rewrite([12212(3),42(6),42(9),12212(12),44(13),32(11)])].
% 275.57/275.94 21774 multiplication(antidomain(A),addition(antidomain(A),antidomain(B))) = antidomain(A). [para(264(a,1),981(a,2)),rewrite([12212(5),20767(7),42(4)])].
% 275.57/275.94 21793 multiplication(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,B)). [para(71(a,1),21774(a,1,2))].
% 275.57/275.94 23252 multiplication(antidomain(c2),multiplication(c1,antidomain(c4))) = multiplication(c1,antidomain(c4)). [para(15756(a,1),1188(a,1,2,2,1)),rewrite([120(8),32(8),15756(19),120(13),32(13)])].
% 275.57/275.94 23306 multiplication(antidomain(multiplication(antidomain(addition(A,B)),C)),A) = A. [para(17331(a,1),1188(a,1,2,2,1)),rewrite([120(6),32(6),17331(11),120(7),32(7)])].
% 275.57/275.94 23462 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(32(a,1),23306(a,1,1,1))].
% 275.57/275.94 23518 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(42(a,1),23462(a,1,1,1,1))].
% 275.57/275.94 23592 addition(antidomain(A),antidomain(antidomain(addition(B,A)))) = one. [para(23518(a,1),17051(a,1,2,1)),rewrite([12156(4),42(5)])].
% 275.57/275.94 23597 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(23518(a,1),17036(a,1,2,1)),rewrite([12156(4),42(4),23518(8)])].
% 275.57/275.94 23860 addition(antidomain(A),antidomain(multiplication(coantidomain(B),A))) = antidomain(multiplication(coantidomain(B),A)). [para(131(a,1),23597(a,1,2,1)),rewrite([42(5)])].
% 275.57/275.94 25673 multiplication(antidomain(antidomain(c3)),multiplication(c1,antidomain(c4))) = zero. [para(23252(a,1),9464(a,1,2))].
% 275.57/275.94 25885 multiplication(antidomain(antidomain(c3)),multiplication(c1,antidomain(c5))) = zero. [para(25673(a,1),374(a,1,1,2)),rewrite([42(5),150(5),265(6),65(11),9655(10)]),flip(a)].
% 275.57/275.94 33122 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(2959(a,1),3270(a,1,1)),rewrite([33(3)]),flip(a)].
% 275.57/275.94 33123 coantidomain(multiplication(addition(A,one),B)) = coantidomain(B). [back_rewrite(5073),rewrite([33122(6)]),flip(a)].
% 275.57/275.94 33801 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(3362(a,1),482(a,1,2,2)),rewrite([32(7)])].
% 275.57/275.94 33894 multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(c3)),c1))),antidomain(c5)) = zero. [para(25885(a,1),3395(a,1,2,2,1)),rewrite([120(11),32(11)])].
% 275.57/275.94 34745 addition(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(A). [para(3311(a,1),3698(a,1,1)),rewrite([42(6),116(6),32(4),198(3),42(5)]),flip(a)].
% 275.57/275.94 34762 addition(coantidomain(A),coantidomain(addition(B,A))) = coantidomain(A). [para(876(a,1),34745(a,1,2,1)),rewrite([33123(4),33123(6),33123(8)])].
% 275.57/275.94 34792 addition(coantidomain(A),antidomain(coantidomain(addition(B,A)))) = one. [para(34762(a,1),23592(a,1,2,1,1)),rewrite([2975(6),42(5)])].
% 275.57/275.94 34893 addition(antidomain(coantidomain(A)),coantidomain(multiplication(A,antidomain(B)))) = one. [para(128(a,1),34792(a,1,2,1,1)),rewrite([42(6)])].
% 275.57/275.94 34941 addition(coantidomain(A),coantidomain(multiplication(coantidomain(A),antidomain(B)))) = one. [para(2965(a,1),34893(a,1,1,1)),rewrite([2975(3)])].
% 275.57/275.94 34942 addition(antidomain(A),coantidomain(multiplication(antidomain(A),antidomain(B)))) = one. [para(12212(a,1),34893(a,1,1,1)),rewrite([12156(3)])].
% 275.57/275.94 34976 multiplication(coantidomain(A),antidomain(B)) = multiplication(antidomain(B),coantidomain(A)). [para(34941(a,1),85(a,1,2)),rewrite([32(5),65(8),5384(8)])].
% 275.57/275.94 35014 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(34942(a,1),85(a,1,2)),rewrite([32(5),65(8),5351(8)])].
% 275.57/275.94 35061 multiplication(antidomain(c5),antidomain(coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) = zero. [back_rewrite(33894),rewrite([35014(10)])].
% 275.57/275.94 37112 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(33801(a,1),17480(a,1,1,1)),rewrite([117(2),33(2),2975(6)]),flip(a)].
% 275.57/275.94 37151 addition(antidomain(A),coantidomain(multiplication(antidomain(multiplication(B,A)),B))) = one. [para(37112(a,1),17051(a,1,2,1)),rewrite([2975(6),42(6)])].
% 275.57/275.94 37252 addition(coantidomain(A),antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = one. [para(80(a,1),37151(a,1,2,1,1,1)),rewrite([117(6),33(6),42(6)])].
% 275.57/275.94 37696 multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A. [para(37252(a,1),19425(a,1,2)),rewrite([32(2)]),flip(a)].
% 275.57/275.94 37726 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [para(12220(a,1),37696(a,1,2,1,2,1)),rewrite([120(7),32(7),35014(7),21793(7)]),flip(a)].
% 275.57/275.94 37782 multiplication(antidomain(c5),coantidomain(multiplication(antidomain(antidomain(c3)),c1))) = antidomain(c5). [para(35061(a,1),37696(a,1,2,1,2,1)),rewrite([120(11),32(11),2975(10)])].
% 275.57/275.94 40960 addition(antidomain(A),antidomain(coantidomain(B))) = antidomain(multiplication(coantidomain(B),A)). [para(17479(a,1),12291(a,1,1)),rewrite([37726(10),42(10),115(10),33(8),42(7),20767(7),42(4),37726(9),42(9),23860(9)])].
% 275.57/275.94 40969 $F # answer(goals). [back_rewrite(12180),rewrite([40960(11),34976(9),37782(9)]),xx(a)].
% 275.57/275.94
% 275.57/275.94 % SZS output end Refutation
% 275.57/275.94 ============================== end of proof ==========================
% 275.57/275.94
% 275.57/275.94 ============================== STATISTICS ============================
% 275.57/275.94
% 275.57/275.94 Given=8332. Generated=19216622. Kept=40922. proofs=1.
% 275.57/275.94 Usable=6510. Sos=7755. Demods=14145. Limbo=9, Disabled=26679. Hints=0.
% 275.57/275.94 Megabytes=29.69.
% 275.57/275.94 User_CPU=264.75, System_CPU=10.18, Wall_clock=275.
% 275.57/275.94
% 275.57/275.94 ============================== end of statistics =====================
% 275.57/275.94
% 275.57/275.94 ============================== end of search =========================
% 275.57/275.94
% 275.57/275.94 THEOREM PROVED
% 275.57/275.94 % SZS status Theorem
% 275.57/275.94
% 275.57/275.94 Exiting with 1 proof.
% 275.57/275.94
% 275.57/275.94 Process 31352 exit (max_proofs) Thu Jun 16 14:18:23 2022
% 275.57/275.94 Prover9 interrupted
%------------------------------------------------------------------------------