TSTP Solution File: KLE133+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE133+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 02:22:22 EDT 2022
% Result : Theorem 0.73s 1.04s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE133+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 10:37:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 14534 was started by sandbox on n018.cluster.edu,
% 0.43/1.00 Thu Jun 16 10:37:31 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14308_n018.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_14308_n018.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (29 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 27 (all X0 forward_diamond(X0,divergence(X0)) = divergence(X0)) # label(divergence1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 28 (all X0 all X1 all X2 (addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2)) -> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))))) # label(divergence2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 29 -(all X0 ((all X1 addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) & (all X2 forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))) -> (all X3 addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.00
% 0.43/1.00 ============================== PREDICATE ELIMINATION =================
% 0.43/1.00 30 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.43/1.00 31 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.43/1.00
% 0.43/1.00 ============================== end predicate elimination =============
% 0.43/1.00
% 0.43/1.00 Auto_denials:
% 0.43/1.00 % copying label goals to answer in negative clause
% 0.43/1.00
% 0.43/1.00 Term ordering decisions:
% 0.43/1.00 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. forward_diamond=1. domain_difference=1. backward_diamond=1. backward_box=1. forward_box=1. domain=1. antidomain=1. coantidomain=1. c=1. divergence=1. star=1. codomain=1.
% 0.43/1.00
% 0.43/1.00 ============================== end of process initial clauses ========
% 0.43/1.00
% 0.43/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.00
% 0.43/1.00 ============================== end of clauses for search =============
% 0.43/1.00
% 0.43/1.00 ============================== SEARCH ================================
% 0.73/1.04
% 0.73/1.04 % Starting search at 0.01 seconds.
% 0.73/1.04
% 0.73/1.04 ============================== PROOF =================================
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04 % SZS output start Refutation
% 0.73/1.04
% 0.73/1.04 % Proof 1 at 0.05 (+ 0.00) seconds: goals.
% 0.73/1.04 % Length of proof is 61.
% 0.73/1.04 % Level of proof is 9.
% 0.73/1.04 % Maximum clause weight is 57.000.
% 0.73/1.04 % Given clauses 52.
% 0.73/1.04
% 0.73/1.04 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 27 (all X0 forward_diamond(X0,divergence(X0)) = divergence(X0)) # label(divergence1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 29 -(all X0 ((all X1 addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) & (all X2 forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))) -> (all X3 addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.04 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.73/1.04 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.73/1.04 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.73/1.04 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.73/1.04 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.73/1.04 37 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 0.73/1.04 38 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 0.73/1.04 39 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 0.73/1.04 44 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.73/1.04 45 divergence(A) = forward_diamond(A,divergence(A)) # label(divergence1) # label(axiom). [clausify(27)].
% 0.73/1.04 46 forward_diamond(A,divergence(A)) = divergence(A). [copy(45),flip(a)].
% 0.73/1.04 47 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 0.73/1.04 48 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(47),rewrite([44(4)])].
% 0.73/1.04 51 domain_difference(A,B) = multiplication(domain(A),antidomain(B)) # label(domain_difference) # label(axiom). [clausify(22)].
% 0.73/1.04 52 domain_difference(A,B) = multiplication(antidomain(antidomain(A)),antidomain(B)). [copy(51),rewrite([39(2)])].
% 0.73/1.04 53 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 0.73/1.04 54 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(53),rewrite([39(2),39(5)])].
% 0.73/1.04 61 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.73/1.04 62 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(61),rewrite([44(2)]),flip(a)].
% 0.73/1.04 64 forward_diamond(c1,forward_diamond(c1,domain(A))) = forward_diamond(c1,domain(A)) # label(goals) # label(negated_conjecture). [clausify(29)].
% 0.73/1.04 65 antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A)))))))))))) = antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A))))))). [copy(64),rewrite([39(3),54(5),54(10),39(16),54(18)])].
% 0.73/1.04 66 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.73/1.04 67 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(66),flip(a)].
% 0.73/1.04 74 forward_diamond(star(c1),domain_difference(domain(A),forward_diamond(c1,domain(A)))) = addition(domain(A),forward_diamond(star(c1),domain_difference(domain(A),forward_diamond(c1,domain(A))))) # label(goals) # label(negated_conjecture). [clausify(29)].
% 0.73/1.04 75 addition(antidomain(antidomain(A)),antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A))))))))))))))) = antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(A)))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A)))))))))))))). [copy(74),rewrite([39(3),39(6),54(8),52(13),54(17),39(22),39(26),39(29),54(31),52(36),54(40)]),flip(a)].
% 0.73/1.04 76 forward_diamond(star(c1),domain_difference(domain(c2),forward_diamond(c1,domain(c2)))) != addition(forward_diamond(c1,domain(c2)),forward_diamond(star(c1),domain_difference(domain(c2),forward_diamond(c1,domain(c2))))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(29)].
% 0.73/1.04 77 addition(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(c2)))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))))))))))) != antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(c2)))),antidomain(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))))))))) # answer(goals). [copy(76),rewrite([39(4),39(8),54(10),52(15),54(19),39(26),54(28),39(36),39(40),54(42),52(47),54(51)]),flip(a)].
% 0.73/1.04 80 antidomain(antidomain(multiplication(A,antidomain(antidomain(divergence(A)))))) = divergence(A). [back_rewrite(46),rewrite([54(2)])].
% 0.73/1.04 81 antidomain(one) = zero. [para(38(a,1),34(a,1)),flip(a)].
% 0.73/1.04 83 addition(A,addition(A,B)) = addition(A,B). [para(62(a,1),33(a,1)),rewrite([44(1),44(2),62(2,R),33(1),44(3)])].
% 0.73/1.04 89 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),67(a,2,2)),rewrite([36(3),44(3)])].
% 0.73/1.04 114 addition(antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(zero))))),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A)))))))) = antidomain(antidomain(multiplication(star(c1),antidomain(antidomain(zero))))). [para(65(a,1),75(a,1,1)),rewrite([65(24),65(35),65(34),38(30),44(17),65(33),65(44),65(43),38(39)])].
% 0.73/1.04 123 antidomain(antidomain(zero)) = divergence(zero). [para(37(a,1),80(a,1,1,1))].
% 0.73/1.04 140 addition(antidomain(antidomain(multiplication(star(c1),divergence(zero)))),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A)))))))) = antidomain(antidomain(multiplication(star(c1),divergence(zero)))). [back_rewrite(114),rewrite([123(5),123(21)])].
% 0.73/1.04 142 addition(zero,antidomain(zero)) = one. [para(81(a,1),48(a,1,1)),rewrite([81(3)])].
% 0.73/1.04 148 multiplication(divergence(zero),antidomain(zero)) = zero. [para(123(a,1),38(a,1,1))].
% 0.73/1.04 155 multiplication(A,antidomain(zero)) = A. [para(142(a,1),67(a,2,2)),rewrite([36(2),89(5),34(5)])].
% 0.73/1.04 159 divergence(zero) = zero. [back_rewrite(148),rewrite([155(5)])].
% 0.73/1.04 166 addition(zero,antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A)))))))) = zero. [back_rewrite(140),rewrite([159(4),36(4),123(3),159(2),159(14),36(14),123(13),159(12)])].
% 0.73/1.04 171 addition(one,antidomain(A)) = one. [para(48(a,1),83(a,1,2)),rewrite([44(3),48(7)])].
% 0.73/1.04 176 antidomain(zero) = one. [para(155(a,1),35(a,1)),flip(a)].
% 0.73/1.04 189 addition(A,multiplication(A,antidomain(B))) = A. [para(171(a,1),67(a,2,2)),rewrite([34(2),34(5)])].
% 0.73/1.04 216 addition(zero,antidomain(antidomain(A))) = antidomain(antidomain(A)). [para(38(a,1),189(a,1,2)),rewrite([44(4)])].
% 0.73/1.04 220 antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(A))))))) = zero. [back_rewrite(166),rewrite([216(10)])].
% 0.73/1.04 225 $F # answer(goals). [back_rewrite(77),rewrite([220(9),220(17),176(10),34(10),216(14),220(28),176(21),34(21)]),xx(a)].
% 0.73/1.04
% 0.73/1.04 % SZS output end Refutation
% 0.73/1.04 ============================== end of proof ==========================
% 0.73/1.04
% 0.73/1.04 ============================== STATISTICS ============================
% 0.73/1.04
% 0.73/1.04 Given=52. Generated=877. Kept=175. proofs=1.
% 0.73/1.04 Usable=44. Sos=66. Demods=101. Limbo=5, Disabled=92. Hints=0.
% 0.73/1.04 Megabytes=0.36.
% 0.73/1.04 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.73/1.04
% 0.73/1.04 ============================== end of statistics =====================
% 0.73/1.04
% 0.73/1.04 ============================== end of search =========================
% 0.73/1.04
% 0.73/1.04 THEOREM PROVED
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04
% 0.73/1.04 Exiting with 1 proof.
% 0.73/1.04
% 0.73/1.04 Process 14534 exit (max_proofs) Thu Jun 16 10:37:31 2022
% 0.73/1.04 Prover9 interrupted
%------------------------------------------------------------------------------