TSTP Solution File: KLE111+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE111+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 02:22:17 EDT 2022
% Result : Theorem 8.73s 9.00s
% Output : Refutation 8.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE111+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 08:38:05 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.48/1.05 ============================== Prover9 ===============================
% 0.48/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.05 Process 17004 was started by sandbox on n027.cluster.edu,
% 0.48/1.05 Thu Jun 16 08:38:06 2022
% 0.48/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16851_n027.cluster.edu".
% 0.48/1.05 ============================== end of head ===========================
% 0.48/1.05
% 0.48/1.05 ============================== INPUT =================================
% 0.48/1.05
% 0.48/1.05 % Reading from file /tmp/Prover9_16851_n027.cluster.edu
% 0.48/1.05
% 0.48/1.05 set(prolog_style_variables).
% 0.48/1.05 set(auto2).
% 0.48/1.05 % set(auto2) -> set(auto).
% 0.48/1.05 % set(auto) -> set(auto_inference).
% 0.48/1.05 % set(auto) -> set(auto_setup).
% 0.48/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.05 % set(auto) -> set(auto_limits).
% 0.48/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.05 % set(auto) -> set(auto_denials).
% 0.48/1.05 % set(auto) -> set(auto_process).
% 0.48/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.05 % set(auto2) -> assign(stats, some).
% 0.48/1.05 % set(auto2) -> clear(echo_input).
% 0.48/1.05 % set(auto2) -> set(quiet).
% 0.48/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.05 % set(auto2) -> clear(print_given).
% 0.48/1.05 assign(lrs_ticks,-1).
% 0.48/1.05 assign(sos_limit,10000).
% 0.48/1.05 assign(order,kbo).
% 0.48/1.05 set(lex_order_vars).
% 0.48/1.05 clear(print_given).
% 0.48/1.05
% 0.48/1.05 % formulas(sos). % not echoed (27 formulas)
% 0.48/1.05
% 0.48/1.05 ============================== end of input ==========================
% 0.48/1.05
% 0.48/1.05 % From the command line: assign(max_seconds, 300).
% 0.48/1.05
% 0.48/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.05
% 0.48/1.05 % Formulas that are not ordinary clauses:
% 0.48/1.05 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 5.08/5.41 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 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].
% 5.08/5.41 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.41 27 -(all X0 all X1 addition(backward_diamond(X0,forward_box(X0,domain(X1))),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.08/5.41
% 5.08/5.41 ============================== end of process non-clausal formulas ===
% 5.08/5.41
% 5.08/5.41 ============================== PROCESS INITIAL CLAUSES ===============
% 5.08/5.41
% 5.08/5.41 ============================== PREDICATE ELIMINATION =================
% 5.08/5.41 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 5.08/5.41 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 5.08/5.41
% 5.08/5.41 ============================== end predicate elimination =============
% 5.08/5.41
% 5.08/5.41 Auto_denials:
% 5.08/5.41 % copying label goals to answer in negative clause
% 5.08/5.41
% 5.08/5.41 Term ordering decisions:
% 5.08/5.41 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. c=1. domain=1. codomain=1.
% 5.08/5.41
% 5.08/5.41 ============================== end of process initial clauses ========
% 5.08/5.41
% 5.08/5.41 ============================== CLAUSES FOR SEARCH ====================
% 5.08/5.41
% 5.08/5.41 ============================== end of clauses for search =============
% 5.08/5.41
% 5.08/5.41 ============================== SEARCH ================================
% 5.08/5.41
% 5.08/5.41 % Starting search at 0.01 seconds.
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=36.000, iters=3371
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=33.000, iters=3334
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=32.000, iters=3363
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=31.000, iters=3361
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=30.000, iters=3341
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=29.000, iters=3400
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=28.000, iters=3336
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=27.000, iters=3356
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=26.000, iters=3342
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=25.000, iters=3336
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=21.000, iters=4360
% 5.08/5.41
% 5.08/5.41 Low Water (keep): wt=20.000, iters=3982
% 5.08/5.41
% 5.08/5.41 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 1.87 sec).
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=6268, wt=49.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=3690, wt=48.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=6916, wt=47.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=4652, wt=46.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=6917, wt=45.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=5878, wt=44.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=4320, wt=43.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=15504, wt=19.000
% 5.08/5.41
% 5.08/5.41 Low Water (displace): id=15512, wt=18.000
% 8.73/9.00
% 8.73/9.00 Low Water (displace): id=15513, wt=17.000
% 8.73/9.00
% 8.73/9.00 Low Water (displace): id=15538, wt=15.000
% 8.73/9.00
% 8.73/9.00 Low Water (displace): id=15970, wt=14.000
% 8.73/9.00
% 8.73/9.00 Low Water (keep): wt=19.000, iters=3338
% 8.73/9.00
% 8.73/9.00 Low Water (displace): id=16591, wt=13.000
% 8.73/9.00
% 8.73/9.00 Low Water (keep): wt=18.000, iters=3338
% 8.73/9.00
% 8.73/9.00 ============================== PROOF =================================
% 8.73/9.00 % SZS status Theorem
% 8.73/9.00 % SZS output start Refutation
% 8.73/9.00
% 8.73/9.00 % Proof 1 at 7.69 (+ 0.28) seconds: goals.
% 8.73/9.00 % Length of proof is 139.
% 8.73/9.00 % Level of proof is 26.
% 8.73/9.00 % Maximum clause weight is 29.000.
% 8.73/9.00 % Given clauses 1013.
% 8.73/9.00
% 8.73/9.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.00 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].
% 8.73/9.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 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].
% 8.73/9.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 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].
% 8.73/9.01 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].
% 8.73/9.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 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].
% 8.73/9.01 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 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].
% 8.73/9.01 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 8.73/9.01 27 -(all X0 all X1 addition(backward_diamond(X0,forward_box(X0,domain(X1))),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 8.73/9.01 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 8.73/9.01 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 8.73/9.01 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 8.73/9.01 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 8.73/9.01 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 8.73/9.01 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 8.73/9.01 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 8.73/9.01 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 8.73/9.01 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 8.73/9.01 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 8.73/9.01 40 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)].
% 8.73/9.01 41 c(A) = antidomain(antidomain(antidomain(A))). [copy(40),rewrite([37(2)])].
% 8.73/9.01 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 8.73/9.01 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 8.73/9.01 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 8.73/9.01 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 8.73/9.01 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 8.73/9.01 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 8.73/9.01 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 8.73/9.01 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 8.73/9.01 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 8.73/9.01 53 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom). [clausify(25)].
% 8.73/9.01 54 forward_box(A,B) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(antidomain(antidomain(antidomain(B))))))))))). [copy(53),rewrite([41(2),50(5),41(10)])].
% 8.73/9.01 57 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 8.73/9.01 58 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(57),rewrite([42(2)]),flip(a)].
% 8.73/9.01 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 8.73/9.01 60 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 8.73/9.01 61 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(60),flip(a)].
% 8.73/9.01 62 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 8.73/9.01 63 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(62),flip(a)].
% 8.73/9.01 64 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 8.73/9.01 65 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(64),flip(a)].
% 8.73/9.01 66 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 8.73/9.01 67 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(66),flip(a)].
% 8.73/9.01 68 domain(c2) != addition(backward_diamond(c1,forward_box(c1,domain(c2))),domain(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 8.73/9.01 69 addition(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))))))))))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [copy(68),rewrite([37(2),37(7),54(9),52(20),37(26),42(28)]),flip(a)].
% 8.73/9.01 70 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 8.73/9.01 71 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 8.73/9.01 72 addition(A,addition(A,B)) = addition(A,B). [para(58(a,1),31(a,1)),rewrite([42(1),42(2),58(2,R),31(1),42(3)])].
% 8.73/9.01 73 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),59(a,1,1)),rewrite([35(2)]),flip(a)].
% 8.73/9.01 76 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),61(a,2,2)),rewrite([34(3),42(3)])].
% 8.73/9.01 77 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),61(a,1,1)),rewrite([42(4)]),flip(a)].
% 8.73/9.01 78 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),61(a,1,1)),rewrite([76(4)]),flip(a)].
% 8.73/9.01 79 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),61(a,1,1)),rewrite([76(3),42(3)]),flip(a)].
% 8.73/9.01 82 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),63(a,1,1)),rewrite([76(4),42(3)]),flip(a)].
% 8.73/9.01 90 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),65(a,1,1,1))].
% 8.73/9.01 95 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),67(a,1,1,1))].
% 8.73/9.01 98 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(59(a,1),67(a,1,1,1))].
% 8.73/9.01 99 addition(zero,antidomain(zero)) = one. [para(70(a,1),44(a,1,1)),rewrite([70(3)])].
% 8.73/9.01 100 addition(zero,coantidomain(zero)) = one. [para(71(a,1),46(a,1,1)),rewrite([71(3)])].
% 8.73/9.01 103 multiplication(A,antidomain(zero)) = A. [para(99(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 8.73/9.01 107 multiplication(A,coantidomain(zero)) = A. [para(100(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 8.73/9.01 109 addition(one,antidomain(A)) = one. [para(44(a,1),72(a,1,2)),rewrite([42(3),44(7)])].
% 8.73/9.01 110 addition(one,coantidomain(A)) = one. [para(46(a,1),72(a,1,2)),rewrite([42(3),46(7)])].
% 8.73/9.01 111 antidomain(zero) = one. [para(103(a,1),33(a,1)),flip(a)].
% 8.73/9.01 112 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(90),rewrite([111(2),109(7)]),flip(a)].
% 8.73/9.01 114 coantidomain(zero) = one. [para(107(a,1),33(a,1)),flip(a)].
% 8.73/9.01 116 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(95),rewrite([114(2),110(7)]),flip(a)].
% 8.73/9.01 120 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(73(a,1),65(a,1,1,1)),rewrite([111(2),109(8)]),flip(a)].
% 8.73/9.01 123 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 8.73/9.01 124 addition(A,multiplication(A,coantidomain(B))) = A. [para(110(a,1),61(a,2,2)),rewrite([32(2),32(5)])].
% 8.73/9.01 125 addition(A,multiplication(coantidomain(B),A)) = A. [para(110(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 8.73/9.01 159 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(112(a,1),36(a,1,1)),rewrite([33(6)])].
% 8.73/9.01 164 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(159(a,1),61(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 8.73/9.01 170 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),78(a,1,2)),rewrite([32(4)]),flip(a)].
% 8.73/9.01 174 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(63(a,1),78(a,1,2))].
% 8.73/9.01 178 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(123(a,1),78(a,1,2)),rewrite([36(2)]),flip(a)].
% 8.73/9.01 191 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),79(a,1,2)),rewrite([32(3)]),flip(a)].
% 8.73/9.01 200 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(191(a,1),61(a,1,1)),rewrite([77(4,R),42(7)]),flip(a)].
% 8.73/9.01 205 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(116(a,1),38(a,1,2)),rewrite([32(6)])].
% 8.73/9.01 209 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(205(a,1),63(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 8.73/9.01 213 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(178(a,1),63(a,1,1)),rewrite([76(5),42(5)]),flip(a)].
% 8.73/9.01 264 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),82(a,1,1))].
% 8.73/9.01 265 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 8.73/9.01 266 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 8.73/9.01 517 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(120(a,1),36(a,1,1)),rewrite([33(7)])].
% 8.73/9.01 525 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(517(a,1),61(a,1,1)),rewrite([76(4),42(7)]),flip(a)].
% 8.73/9.01 568 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(36(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 8.73/9.01 656 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(170(a,1),123(a,1,2)),rewrite([42(5)])].
% 8.73/9.01 853 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),264(a,1,1)),rewrite([33(4)]),flip(a)].
% 8.73/9.01 2387 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),164(a,1,2)),rewrite([32(2)]),flip(a)].
% 8.73/9.01 2409 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2387(a,1),59(a,1,1)),flip(a)].
% 8.73/9.01 2410 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2387(a,1),59(a,1)),flip(a)].
% 8.73/9.01 2417 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2387(a,1),125(a,1,2)),rewrite([42(5)])].
% 8.73/9.01 2516 multiplication(A,coantidomain(coantidomain(A))) = A. [para(170(a,1),2409(a,1,2)),rewrite([2387(3)]),flip(a)].
% 8.73/9.01 2549 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(266),rewrite([2516(5)]),flip(a)].
% 8.73/9.01 2578 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2549(a,1),656(a,1,2)),rewrite([42(5),2417(5),2549(6)])].
% 8.73/9.01 2679 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2578(a,1),44(a,1,1)),rewrite([2578(4)])].
% 8.73/9.01 2685 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2578(a,1),853(a,1,1,1)),rewrite([2578(5),170(5),2578(5)]),flip(a)].
% 8.73/9.01 2687 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2578(a,1),853(a,2,1)),rewrite([2685(2),2685(6),853(9),2685(6)])].
% 8.73/9.01 2694 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2549(a,1),2578(a,1,1,1)),rewrite([2685(2),2685(5)]),flip(a)].
% 8.73/9.01 2695 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2549(a,1),2578(a,2)),rewrite([2685(2),2694(3),2687(4)])].
% 8.73/9.01 3025 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(568),rewrite([2685(5)])].
% 8.73/9.01 3044 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(209),rewrite([2685(3)])].
% 8.73/9.01 3051 addition(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))))))))))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(69),rewrite([2685(20),2685(24)])].
% 8.73/9.01 3464 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),174(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 8.73/9.01 3958 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(265(a,1),124(a,1,2))].
% 8.73/9.01 4936 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3958(a,1),200(a,1,2)),rewrite([42(11),109(11),32(10)])].
% 8.73/9.01 5150 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),213(a,1,1)),rewrite([33(5)]),flip(a)].
% 8.73/9.01 9144 multiplication(coantidomain(antidomain(A)),A) = A. [para(2679(a,1),3044(a,1,1)),rewrite([33(2)]),flip(a)].
% 8.73/9.01 9158 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4936),rewrite([9144(5)]),flip(a)].
% 8.73/9.01 9170 addition(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))))))))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(3051),rewrite([9158(19)])].
% 8.73/9.01 9250 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9158(a,1),2685(a,1,1)),rewrite([9158(5)])].
% 8.73/9.01 9251 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9158(a,1),2685(a,2,1)),rewrite([9250(3),9250(4)])].
% 8.73/9.01 9252 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9158(a,1),2695(a,2)),rewrite([9250(3),9251(4)])].
% 8.73/9.01 9407 addition(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(multiplication(c1,antidomain(c2))),c1)))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(9170),rewrite([9252(8),9252(8),9252(8),9252(10),9252(10)])].
% 8.73/9.01 13345 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(3025(a,1),38(a,1,2)),rewrite([32(8)])].
% 8.73/9.01 17171 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(44(a,1),525(a,1,2)),rewrite([32(3)]),flip(a)].
% 8.73/9.01 17299 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17171(a,1),123(a,1,2)),rewrite([42(4)])].
% 8.73/9.01 17324 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17171(a,1),2410(a,1,2,2,1,1)),rewrite([9250(5),9252(6),5150(6),17171(8)])].
% 8.73/9.01 17498 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17324(a,1),59(a,1,1)),flip(a)].
% 8.73/9.01 17530 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3464),rewrite([17498(7)]),flip(a)].
% 8.73/9.01 18565 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(13345(a,1),17530(a,1,1,1)),rewrite([111(2),33(2),2695(6)]),flip(a)].
% 8.73/9.01 19820 addition(antidomain(A),antidomain(coantidomain(multiplication(antidomain(multiplication(B,A)),B)))) = antidomain(A). [para(18565(a,1),17299(a,1,2,1)),rewrite([42(7),18565(12)])].
% 8.73/9.01 19821 $F # answer(goals). [resolve(19820,a,9407,a)].
% 8.73/9.01
% 8.73/9.01 % SZS output end Refutation
% 8.73/9.01 ============================== end of proof ==========================
% 8.73/9.01
% 8.73/9.01 ============================== STATISTICS ============================
% 8.73/9.01
% 8.73/9.01 Given=1013. Generated=522739. Kept=19777. proofs=1.
% 8.73/9.01 Usable=678. Sos=9531. Demods=9818. Limbo=62, Disabled=9533. Hints=0.
% 8.73/9.01 Megabytes=18.53.
% 8.73/9.01 User_CPU=7.69, System_CPU=0.28, Wall_clock=8.
% 8.73/9.01
% 8.73/9.01 ============================== end of statistics =====================
% 8.73/9.01
% 8.73/9.01 ============================== end of search =========================
% 8.73/9.01
% 8.73/9.01 THEOREM PROVED
% 8.73/9.01 % SZS status Theorem
% 8.73/9.01
% 8.73/9.01 Exiting with 1 proof.
% 8.73/9.01
% 8.73/9.01 Process 17004 exit (max_proofs) Thu Jun 16 08:38:14 2022
% 8.73/9.01 Prover9 interrupted
%------------------------------------------------------------------------------