TSTP Solution File: KLE118+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE118+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 02:22:19 EDT 2022
% Result : Theorem 181.65s 181.91s
% Output : Refutation 181.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE118+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 07:50:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.40/1.00 ============================== Prover9 ===============================
% 0.40/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.40/1.00 Process 6030 was started by sandbox2 on n011.cluster.edu,
% 0.40/1.00 Thu Jun 16 07:50:36 2022
% 0.40/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5877_n011.cluster.edu".
% 0.40/1.00 ============================== end of head ===========================
% 0.40/1.00
% 0.40/1.00 ============================== INPUT =================================
% 0.40/1.00
% 0.40/1.00 % Reading from file /tmp/Prover9_5877_n011.cluster.edu
% 0.40/1.00
% 0.40/1.00 set(prolog_style_variables).
% 0.40/1.00 set(auto2).
% 0.40/1.00 % set(auto2) -> set(auto).
% 0.40/1.00 % set(auto) -> set(auto_inference).
% 0.40/1.00 % set(auto) -> set(auto_setup).
% 0.40/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.40/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/1.00 % set(auto) -> set(auto_limits).
% 0.40/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/1.00 % set(auto) -> set(auto_denials).
% 0.40/1.00 % set(auto) -> set(auto_process).
% 0.40/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.40/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.40/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.40/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.40/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.40/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.40/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.40/1.00 % set(auto2) -> assign(stats, some).
% 0.40/1.00 % set(auto2) -> clear(echo_input).
% 0.40/1.00 % set(auto2) -> set(quiet).
% 0.40/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.40/1.00 % set(auto2) -> clear(print_given).
% 0.40/1.00 assign(lrs_ticks,-1).
% 0.40/1.00 assign(sos_limit,10000).
% 0.40/1.00 assign(order,kbo).
% 0.40/1.00 set(lex_order_vars).
% 0.40/1.00 clear(print_given).
% 0.40/1.00
% 0.40/1.00 % formulas(sos). % not echoed (27 formulas)
% 0.40/1.00
% 0.40/1.00 ============================== end of input ==========================
% 0.40/1.00
% 0.40/1.00 % From the command line: assign(max_seconds, 300).
% 0.40/1.00
% 0.40/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/1.00
% 0.40/1.00 % Formulas that are not ordinary clauses:
% 0.40/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 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].
% 0.40/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 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].
% 0.40/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 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].
% 0.40/1.00 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].
% 0.40/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.00 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].
% 4.36/4.63 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 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].
% 4.36/4.63 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 4.36/4.63 27 -(all X0 all X1 (addition(X0,X1) = X1 -> (all X2 addition(forward_box(X0,domain(X2)),forward_box(X1,domain(X2))) = forward_box(X0,domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.36/4.63
% 4.36/4.63 ============================== end of process non-clausal formulas ===
% 4.36/4.63
% 4.36/4.63 ============================== PROCESS INITIAL CLAUSES ===============
% 4.36/4.63
% 4.36/4.63 ============================== PREDICATE ELIMINATION =================
% 4.36/4.63 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 4.36/4.63 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 4.36/4.63
% 4.36/4.63 ============================== end predicate elimination =============
% 4.36/4.63
% 4.36/4.63 Auto_denials:
% 4.36/4.63 % copying label goals to answer in negative clause
% 4.36/4.63
% 4.36/4.63 Term ordering decisions:
% 4.36/4.63 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=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.
% 4.36/4.63
% 4.36/4.63 ============================== end of process initial clauses ========
% 4.36/4.63
% 4.36/4.63 ============================== CLAUSES FOR SEARCH ====================
% 4.36/4.63
% 4.36/4.63 ============================== end of clauses for search =============
% 4.36/4.63
% 4.36/4.63 ============================== SEARCH ================================
% 4.36/4.63
% 4.36/4.63 % Starting search at 0.02 seconds.
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=44.000, iters=3474
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=40.000, iters=3481
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=35.000, iters=3368
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=34.000, iters=3343
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=31.000, iters=3350
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=30.000, iters=3356
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=29.000, iters=3355
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=28.000, iters=3357
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=27.000, iters=3360
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=26.000, iters=3351
% 4.36/4.63
% 4.36/4.63 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 1.47 sec).
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=25.000, iters=3358
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=24.000, iters=3405
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=23.000, iters=3425
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=22.000, iters=3386
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=21.000, iters=3345
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=20.000, iters=3343
% 4.36/4.63
% 4.36/4.63 Low Water (keep): wt=19.000, iters=5038
% 4.36/4.63
% 4.36/4.63 Low Water (displace): id=6591, wt=49.000
% 4.36/4.63
% 4.36/4.63 Low Water (displace): id=3698, wt=48.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=7159, wt=47.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=8574, wt=46.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=8164, wt=45.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=6264, wt=44.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=8517, wt=43.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=8589, wt=42.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=14786, wt=16.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=14792, wt=15.000
% 181.65/181.91
% 181.65/181.91 Low Water (keep): wt=18.000, iters=3335
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=17254, wt=14.000
% 181.65/181.91
% 181.65/181.91 Low Water (displace): id=17629, wt=12.000
% 181.65/181.91
% 181.65/181.91 Low Water (keep): wt=17.000, iters=3333
% 181.65/181.91
% 181.65/181.91 Low Water (keep): wt=16.000, iters=3336
% 181.65/181.91
% 181.65/181.91 Low Water (keep): wt=15.000, iters=3346
% 181.65/181.91
% 181.65/181.91 Low Water (keep): wt=14.000, iters=3338
% 181.65/181.91
% 181.65/181.91 ============================== PROOF =================================
% 181.65/181.91 % SZS status Theorem
% 181.65/181.91 % SZS output start Refutation
% 181.65/181.91
% 181.65/181.91 % Proof 1 at 174.48 (+ 6.44) seconds: goals.
% 181.65/181.91 % Length of proof is 83.
% 181.65/181.91 % Level of proof is 14.
% 181.65/181.91 % Maximum clause weight is 47.000.
% 181.65/181.91 % Given clauses 6099.
% 181.65/181.91
% 181.65/181.91 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 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].
% 181.65/181.91 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 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].
% 181.65/181.91 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 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].
% 181.65/181.91 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].
% 181.65/181.91 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 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].
% 181.65/181.91 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 181.65/181.91 27 -(all X0 all X1 (addition(X0,X1) = X1 -> (all X2 addition(forward_box(X0,domain(X2)),forward_box(X1,domain(X2))) = forward_box(X0,domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 181.65/181.91 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 181.65/181.91 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 181.65/181.91 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 181.65/181.91 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 181.65/181.91 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 181.65/181.91 36 addition(c1,c2) = c2 # label(goals) # label(negated_conjecture). [clausify(27)].
% 181.65/181.91 37 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 181.65/181.91 38 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 181.65/181.91 41 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)].
% 181.65/181.91 42 c(A) = antidomain(antidomain(antidomain(A))). [copy(41),rewrite([38(2)])].
% 181.65/181.91 43 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 181.65/181.91 44 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 181.65/181.91 45 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(44),rewrite([43(4)])].
% 181.65/181.91 50 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 181.65/181.91 51 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(50),rewrite([38(2),38(5)])].
% 181.65/181.91 54 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom). [clausify(25)].
% 181.65/181.91 55 forward_box(A,B) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(antidomain(antidomain(antidomain(B))))))))))). [copy(54),rewrite([42(2),51(5),42(10)])].
% 181.65/181.91 58 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 181.65/181.91 59 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(58),rewrite([43(2)]),flip(a)].
% 181.65/181.91 60 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 181.65/181.91 61 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 181.65/181.91 62 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(61),flip(a)].
% 181.65/181.91 63 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 181.65/181.91 64 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(63),flip(a)].
% 181.65/181.91 65 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 181.65/181.91 66 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(65),flip(a)].
% 181.65/181.91 69 forward_box(c1,domain(c3)) != addition(forward_box(c1,domain(c3)),forward_box(c2,domain(c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 181.65/181.91 70 addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))))))))),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c2,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3)))))))))))))) != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c3))))))))))))) # answer(goals). [copy(69),rewrite([38(3),55(5),38(18),55(20),38(33),55(35)]),flip(a)].
% 181.65/181.91 71 antidomain(one) = zero. [para(37(a,1),32(a,1)),flip(a)].
% 181.65/181.91 73 addition(A,addition(A,B)) = addition(A,B). [para(59(a,1),31(a,1)),rewrite([43(1),43(2),59(2,R),31(1),43(3)])].
% 181.65/181.91 77 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),62(a,2,2)),rewrite([34(3),43(3)])].
% 181.65/181.91 78 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),62(a,1,1)),rewrite([43(4)]),flip(a)].
% 181.65/181.91 79 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(37(a,1),62(a,1,1)),rewrite([77(4)]),flip(a)].
% 181.65/181.91 81 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),64(a,1,1)),rewrite([43(4)]),flip(a)].
% 181.65/181.91 82 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(37(a,1),64(a,1,1)),rewrite([77(3),43(3)]),flip(a)].
% 181.65/181.91 87 addition(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(33(a,1),66(a,1,1,1)),rewrite([33(5),33(9)])].
% 181.65/181.91 89 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))). [para(37(a,1),66(a,1,1,1))].
% 181.65/181.91 100 addition(zero,antidomain(zero)) = one. [para(71(a,1),45(a,1,1)),rewrite([71(3)])].
% 181.65/181.91 104 multiplication(A,antidomain(zero)) = A. [para(100(a,1),62(a,2,2)),rewrite([34(2),77(5),32(5)])].
% 181.65/181.91 110 addition(one,antidomain(A)) = one. [para(45(a,1),73(a,1,2)),rewrite([43(3),45(7)])].
% 181.65/181.91 112 antidomain(zero) = one. [para(104(a,1),33(a,1)),flip(a)].
% 181.65/181.91 114 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one. [back_rewrite(89),rewrite([112(2),110(7)]),flip(a)].
% 181.65/181.91 123 addition(A,multiplication(A,antidomain(B))) = A. [para(110(a,1),62(a,2,2)),rewrite([32(2),32(5)])].
% 181.65/181.91 124 addition(A,multiplication(antidomain(B),A)) = A. [para(110(a,1),64(a,2,1)),rewrite([33(2),33(5)])].
% 181.65/181.91 145 addition(zero,antidomain(A)) = antidomain(A). [para(37(a,1),78(a,2,2)),rewrite([79(4),32(3),43(4)]),flip(a)].
% 181.65/181.91 168 multiplication(antidomain(A),antidomain(antidomain(A))) = zero. [para(114(a,1),37(a,1,1)),rewrite([33(6)])].
% 181.65/181.91 179 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(124(a,1),79(a,1,2)),rewrite([37(2)]),flip(a)].
% 181.65/181.91 183 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))). [para(168(a,1),64(a,1,1)),rewrite([77(5),43(5)]),flip(a)].
% 181.65/181.91 217 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(79(a,1),179(a,1,2))].
% 181.65/181.91 257 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(45(a,1),82(a,1,1)),rewrite([33(3)]),flip(a)].
% 181.65/181.91 258 addition(multiplication(A,B),multiplication(addition(A,antidomain(B)),C)) = multiplication(addition(A,antidomain(B)),addition(B,C)). [para(82(a,1),62(a,1,1))].
% 181.65/181.91 261 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero. [para(66(a,1),82(a,1,1)),rewrite([37(8)]),flip(a)].
% 181.65/181.91 287 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(257(a,1),60(a,1,1)),flip(a)].
% 181.65/181.91 289 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(257(a,1),64(a,1,1)),rewrite([81(4,R),43(6)]),flip(a)].
% 181.65/181.91 901 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(43(a,1),217(a,1,1,1))].
% 181.65/181.91 1832 multiplication(antidomain(addition(A,B)),A) = zero. [para(73(a,1),901(a,1,1,1)),rewrite([287(6)])].
% 181.65/181.91 1875 multiplication(antidomain(multiplication(addition(A,B),C)),multiplication(A,C)) = zero. [para(64(a,1),1832(a,1,1,1))].
% 181.65/181.91 3998 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(45(a,1),183(a,1,1)),rewrite([33(5)]),flip(a)].
% 181.65/181.91 8470 addition(multiplication(A,antidomain(B)),multiplication(addition(A,one),antidomain(antidomain(B)))) = addition(A,antidomain(antidomain(B))). [para(45(a,1),258(a,2,2)),rewrite([289(8),32(13)])].
% 181.65/181.91 10463 multiplication(antidomain(multiplication(c2,A)),multiplication(c1,A)) = zero. [para(36(a,1),1875(a,1,1,1,1))].
% 181.65/181.91 10569 multiplication(antidomain(multiplication(c2,A)),antidomain(antidomain(multiplication(c1,A)))) = zero. [para(10463(a,1),261(a,1,1,1)),rewrite([112(2),33(10)])].
% 181.65/181.91 13224 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(3998(a,1),123(a,1,2)),rewrite([87(5)])].
% 181.65/181.91 13262 addition(antidomain(multiplication(c1,antidomain(c3))),antidomain(multiplication(c2,antidomain(c3)))) != antidomain(multiplication(c1,antidomain(c3))) # answer(goals). [back_rewrite(70),rewrite([13224(5),13224(5),13224(5),13224(7),13224(7),13224(10),13224(10),13224(10),13224(12),13224(12),13224(16),13224(16),13224(16),13224(18),13224(18)])].
% 181.65/181.91 41447 addition(antidomain(multiplication(c1,A)),antidomain(multiplication(c2,A))) = antidomain(multiplication(c1,A)). [para(10569(a,1),8470(a,1,1)),rewrite([43(6),110(6),13224(7),33(6),145(5),13224(11),43(10)]),flip(a)].
% 181.65/181.91 41448 $F # answer(goals). [resolve(41447,a,13262,a)].
% 181.65/181.91
% 181.65/181.91 % SZS output end Refutation
% 181.65/181.91 ============================== end of proof ==========================
% 181.65/181.91
% 181.65/181.91 ============================== STATISTICS ============================
% 181.65/181.91
% 181.65/181.91 Given=6099. Generated=11843157. Kept=41404. proofs=1.
% 181.65/181.91 Usable=4671. Sos=8802. Demods=13328. Limbo=0, Disabled=27959. Hints=0.
% 181.65/181.91 Megabytes=30.17.
% 181.65/181.91 User_CPU=174.49, System_CPU=6.44, Wall_clock=181.
% 181.65/181.91
% 181.65/181.91 ============================== end of statistics =====================
% 181.65/181.91
% 181.65/181.91 ============================== end of search =========================
% 181.65/181.91
% 181.65/181.91 THEOREM PROVED
% 181.65/181.91 % SZS status Theorem
% 181.65/181.91
% 181.65/181.91 Exiting with 1 proof.
% 181.65/181.91
% 181.65/181.91 Process 6030 exit (max_proofs) Thu Jun 16 07:53:37 2022
% 181.65/181.91 Prover9 interrupted
%------------------------------------------------------------------------------