TSTP Solution File: KLE107+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE107+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 02:22:15 EDT 2022
% Result : Theorem 10.21s 10.49s
% Output : Refutation 10.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE107+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n006.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 09:14:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 30879 was started by sandbox2 on n006.cluster.edu,
% 0.44/1.01 Thu Jun 16 09:14:42 2022
% 0.44/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30725_n006.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_30725_n006.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (27 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 4.89/5.19 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 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].
% 4.89/5.19 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 4.89/5.19 27 -(all X0 all X1 all X2 (addition(backward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) -> addition(domain(X1),forward_box(X0,domain(X2))) = forward_box(X0,domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.89/5.19
% 4.89/5.19 ============================== end of process non-clausal formulas ===
% 4.89/5.19
% 4.89/5.19 ============================== PROCESS INITIAL CLAUSES ===============
% 4.89/5.19
% 4.89/5.19 ============================== PREDICATE ELIMINATION =================
% 4.89/5.19 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 4.89/5.19 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 4.89/5.19
% 4.89/5.19 ============================== end predicate elimination =============
% 4.89/5.19
% 4.89/5.19 Auto_denials:
% 4.89/5.19 % copying label goals to answer in negative clause
% 4.89/5.19
% 4.89/5.19 Term ordering decisions:
% 4.89/5.19 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. domain=1. c=1. codomain=1.
% 4.89/5.19
% 4.89/5.19 ============================== end of process initial clauses ========
% 4.89/5.19
% 4.89/5.19 ============================== CLAUSES FOR SEARCH ====================
% 4.89/5.19
% 4.89/5.19 ============================== end of clauses for search =============
% 4.89/5.19
% 4.89/5.19 ============================== SEARCH ================================
% 4.89/5.19
% 4.89/5.19 % Starting search at 0.01 seconds.
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=36.000, iters=3376
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=33.000, iters=3339
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=32.000, iters=3368
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=31.000, iters=3366
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=30.000, iters=3346
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=29.000, iters=3405
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=28.000, iters=3341
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=27.000, iters=3361
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=26.000, iters=3347
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=25.000, iters=3341
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=23.000, iters=4389
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=22.000, iters=3945
% 4.89/5.19
% 4.89/5.19 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.80 sec).
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=21.000, iters=3333
% 4.89/5.19
% 4.89/5.19 Low Water (keep): wt=20.000, iters=3335
% 4.89/5.19
% 4.89/5.19 Low Water (displace): id=6286, wt=49.000
% 4.89/5.19
% 4.89/5.19 Low Water (displace): id=3708, wt=48.000
% 4.89/5.19
% 4.89/5.19 Low Water (displace): id=6934, wt=47.000
% 4.89/5.19
% 4.89/5.19 Low Water (displace): id=4670, wt=46.000
% 4.89/5.19
% 4.89/5.19 Low Water (displace): id=6935, wt=45.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=5896, wt=44.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=4338, wt=43.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=15567, wt=19.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=15574, wt=18.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=15575, wt=17.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=15606, wt=16.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=15610, wt=15.000
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=16150, wt=14.000
% 10.21/10.49
% 10.21/10.49 Low Water (keep): wt=19.000, iters=3333
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=18544, wt=13.000
% 10.21/10.49
% 10.21/10.49 Low Water (keep): wt=18.000, iters=3388
% 10.21/10.49
% 10.21/10.49 Low Water (displace): id=22553, wt=12.000
% 10.21/10.49
% 10.21/10.49 ============================== PROOF =================================
% 10.21/10.49 % SZS status Theorem
% 10.21/10.49 % SZS output start Refutation
% 10.21/10.49
% 10.21/10.49 % Proof 1 at 9.14 (+ 0.36) seconds: goals.
% 10.21/10.49 % Length of proof is 139.
% 10.21/10.49 % Level of proof is 26.
% 10.21/10.49 % Maximum clause weight is 35.000.
% 10.21/10.49 % Given clauses 1147.
% 10.21/10.49
% 10.21/10.49 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 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].
% 10.21/10.49 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 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].
% 10.21/10.49 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 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].
% 10.21/10.49 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].
% 10.21/10.49 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 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].
% 10.21/10.49 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 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].
% 10.21/10.49 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 10.21/10.49 27 -(all X0 all X1 all X2 (addition(backward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) -> addition(domain(X1),forward_box(X0,domain(X2))) = forward_box(X0,domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 10.21/10.49 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 10.21/10.49 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 10.21/10.49 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 10.21/10.49 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 10.21/10.49 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 10.21/10.49 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 10.21/10.49 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 10.21/10.49 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 10.21/10.49 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 10.21/10.49 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 10.21/10.49 40 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)].
% 10.21/10.49 41 c(A) = antidomain(antidomain(antidomain(A))). [copy(40),rewrite([37(2)])].
% 10.21/10.49 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 10.21/10.49 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 10.21/10.49 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 10.21/10.49 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 10.21/10.49 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 10.21/10.49 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 10.21/10.49 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 10.21/10.49 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 10.21/10.49 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 10.21/10.49 53 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom). [clausify(25)].
% 10.21/10.49 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)])].
% 10.21/10.49 57 domain(c3) = addition(backward_diamond(c1,domain(c2)),domain(c3)) # label(goals) # label(negated_conjecture). [clausify(27)].
% 10.21/10.49 58 addition(antidomain(antidomain(c3)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c2)))),c1)))) = antidomain(antidomain(c3)). [copy(57),rewrite([37(2),37(6),52(8),37(14),42(16)]),flip(a)].
% 10.21/10.49 59 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 10.21/10.49 60 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(59),rewrite([42(2)]),flip(a)].
% 10.21/10.49 61 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 10.21/10.49 62 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 10.21/10.49 63 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(62),flip(a)].
% 10.21/10.49 64 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 10.21/10.49 65 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(64),flip(a)].
% 10.21/10.49 66 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 10.21/10.49 67 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(66),flip(a)].
% 10.21/10.49 68 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 10.21/10.49 69 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(68),flip(a)].
% 10.21/10.49 70 forward_box(c1,domain(c3)) != addition(domain(c2),forward_box(c1,domain(c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 10.21/10.49 71 addition(antidomain(antidomain(c2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(c1,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(70),rewrite([37(3),54(5),37(17),37(21),54(23)]),flip(a)].
% 10.21/10.49 72 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 10.21/10.49 73 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 10.21/10.49 74 addition(A,addition(A,B)) = addition(A,B). [para(60(a,1),31(a,1)),rewrite([42(1),42(2),60(2,R),31(1),42(3)])].
% 10.21/10.49 75 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),61(a,1,1)),rewrite([35(2)]),flip(a)].
% 10.21/10.49 78 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),63(a,2,2)),rewrite([34(3),42(3)])].
% 10.21/10.49 79 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),63(a,1,1)),rewrite([42(4)]),flip(a)].
% 10.21/10.49 80 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),63(a,1,1)),rewrite([78(4)]),flip(a)].
% 10.21/10.49 81 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),63(a,1,1)),rewrite([78(3),42(3)]),flip(a)].
% 10.21/10.49 84 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),65(a,1,1)),rewrite([78(4),42(3)]),flip(a)].
% 10.21/10.49 92 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),67(a,1,1,1))].
% 10.21/10.49 97 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),69(a,1,1,1))].
% 10.21/10.49 101 addition(zero,antidomain(zero)) = one. [para(72(a,1),44(a,1,1)),rewrite([72(3)])].
% 10.21/10.49 102 addition(zero,coantidomain(zero)) = one. [para(73(a,1),46(a,1,1)),rewrite([73(3)])].
% 10.21/10.49 105 multiplication(A,antidomain(zero)) = A. [para(101(a,1),63(a,2,2)),rewrite([34(2),78(5),32(5)])].
% 10.21/10.49 109 multiplication(A,coantidomain(zero)) = A. [para(102(a,1),63(a,2,2)),rewrite([34(2),78(5),32(5)])].
% 10.21/10.49 111 addition(one,antidomain(A)) = one. [para(44(a,1),74(a,1,2)),rewrite([42(3),44(7)])].
% 10.21/10.49 112 addition(one,coantidomain(A)) = one. [para(46(a,1),74(a,1,2)),rewrite([42(3),46(7)])].
% 10.21/10.49 113 antidomain(zero) = one. [para(105(a,1),33(a,1)),flip(a)].
% 10.21/10.49 114 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(92),rewrite([113(2),111(7)]),flip(a)].
% 10.21/10.49 116 coantidomain(zero) = one. [para(109(a,1),33(a,1)),flip(a)].
% 10.21/10.49 118 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(97),rewrite([116(2),112(7)]),flip(a)].
% 10.21/10.49 122 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(75(a,1),67(a,1,1,1)),rewrite([113(2),111(8)]),flip(a)].
% 10.21/10.49 125 addition(A,multiplication(antidomain(B),A)) = A. [para(111(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 10.21/10.49 126 addition(A,multiplication(A,coantidomain(B))) = A. [para(112(a,1),63(a,2,2)),rewrite([32(2),32(5)])].
% 10.21/10.49 127 addition(A,multiplication(coantidomain(B),A)) = A. [para(112(a,1),65(a,2,1)),rewrite([33(2),33(5)])].
% 10.21/10.49 161 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(114(a,1),36(a,1,1)),rewrite([33(6)])].
% 10.21/10.49 166 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(161(a,1),63(a,1,1)),rewrite([78(3),42(5)]),flip(a)].
% 10.21/10.49 172 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),80(a,1,2)),rewrite([32(4)]),flip(a)].
% 10.21/10.49 177 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(65(a,1),80(a,1,2))].
% 10.21/10.49 181 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(125(a,1),80(a,1,2)),rewrite([36(2)]),flip(a)].
% 10.21/10.49 194 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),81(a,1,2)),rewrite([32(3)]),flip(a)].
% 10.21/10.49 203 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(194(a,1),63(a,1,1)),rewrite([79(4,R),42(7)]),flip(a)].
% 10.21/10.49 208 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(118(a,1),38(a,1,2)),rewrite([32(6)])].
% 10.21/10.49 212 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(208(a,1),65(a,1,1)),rewrite([78(3),42(5)]),flip(a)].
% 10.21/10.49 216 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(181(a,1),65(a,1,1)),rewrite([78(5),42(5)]),flip(a)].
% 10.21/10.49 267 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),84(a,1,1))].
% 10.21/10.49 268 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),84(a,1,1)),rewrite([33(5)]),flip(a)].
% 10.21/10.49 269 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),84(a,1,1)),rewrite([33(5)]),flip(a)].
% 10.21/10.49 520 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(122(a,1),36(a,1,1)),rewrite([33(7)])].
% 10.21/10.49 528 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(520(a,1),63(a,1,1)),rewrite([78(4),42(7)]),flip(a)].
% 10.21/10.49 659 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(172(a,1),125(a,1,2)),rewrite([42(5)])].
% 10.21/10.49 856 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),267(a,1,1)),rewrite([33(4)]),flip(a)].
% 10.21/10.49 857 multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c2)))),c1))),coantidomain(antidomain(antidomain(c3)))) = zero. [para(58(a,1),267(a,1,1)),rewrite([38(8)]),flip(a)].
% 10.21/10.49 2397 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),166(a,1,2)),rewrite([32(2)]),flip(a)].
% 10.21/10.49 2419 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2397(a,1),61(a,1,1)),flip(a)].
% 10.21/10.49 2420 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2397(a,1),61(a,1)),flip(a)].
% 10.21/10.49 2427 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2397(a,1),127(a,1,2)),rewrite([42(5)])].
% 10.21/10.49 2526 multiplication(A,coantidomain(coantidomain(A))) = A. [para(172(a,1),2419(a,1,2)),rewrite([2397(3)]),flip(a)].
% 10.21/10.49 2559 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(269),rewrite([2526(5)]),flip(a)].
% 10.21/10.49 2588 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2559(a,1),659(a,1,2)),rewrite([42(5),2427(5),2559(6)])].
% 10.21/10.49 2690 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2588(a,1),44(a,1,1)),rewrite([2588(4)])].
% 10.21/10.49 2696 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2588(a,1),856(a,1,1,1)),rewrite([2588(5),172(5),2588(5)]),flip(a)].
% 10.21/10.49 2698 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2588(a,1),856(a,2,1)),rewrite([2696(2),2696(6),856(9),2696(6)])].
% 10.21/10.49 2705 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2559(a,1),2588(a,1,1,1)),rewrite([2696(2),2696(5)]),flip(a)].
% 10.21/10.49 2706 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2559(a,1),2588(a,2)),rewrite([2696(2),2705(3),2698(4)])].
% 10.21/10.49 2986 multiplication(antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c2)))),c1))),coantidomain(antidomain(antidomain(c3)))) = zero. [back_rewrite(857),rewrite([2696(5),2696(9)])].
% 10.21/10.49 3062 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(212),rewrite([2696(3)])].
% 10.21/10.49 3482 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),177(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 10.21/10.49 3976 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(268(a,1),126(a,1,2))].
% 10.21/10.49 4954 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3976(a,1),203(a,1,2)),rewrite([42(11),111(11),32(10)])].
% 10.21/10.49 5168 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),216(a,1,1)),rewrite([33(5)]),flip(a)].
% 10.21/10.49 9162 multiplication(coantidomain(antidomain(A)),A) = A. [para(2690(a,1),3062(a,1,1)),rewrite([33(2)]),flip(a)].
% 10.21/10.49 9176 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4954),rewrite([9162(5)]),flip(a)].
% 10.21/10.49 9189 multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(c2)),c1))),antidomain(c3)) = zero. [back_rewrite(2986),rewrite([9176(4),9176(11)])].
% 10.21/10.49 9317 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9176(a,1),2696(a,1,1)),rewrite([9176(5)])].
% 10.21/10.49 9318 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9176(a,1),2696(a,2,1)),rewrite([9317(3),9317(4)])].
% 10.21/10.49 9319 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9176(a,1),2706(a,2)),rewrite([9317(3),9318(4)])].
% 10.21/10.49 9507 addition(antidomain(antidomain(c2)),antidomain(multiplication(c1,antidomain(c3)))) != antidomain(multiplication(c1,antidomain(c3))) # answer(goals). [back_rewrite(71),rewrite([9319(8),9319(8),9319(8),9319(10),9319(10),9319(14),9319(14),9319(14),9319(16),9319(16)])].
% 10.21/10.49 11824 multiplication(antidomain(antidomain(c2)),multiplication(c1,antidomain(c3))) = zero. [para(9189(a,1),2419(a,1,2)),rewrite([34(7),61(9)]),flip(a)].
% 10.21/10.49 17322 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(44(a,1),528(a,1,2)),rewrite([32(3)]),flip(a)].
% 10.21/10.49 17454 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17322(a,1),125(a,1,2)),rewrite([42(4)])].
% 10.21/10.49 17479 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17322(a,1),2420(a,1,2,2,1,1)),rewrite([9317(5),9319(6),5168(6),17322(8)])].
% 10.21/10.49 17652 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17479(a,1),61(a,1,1)),flip(a)].
% 10.21/10.49 17684 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3482),rewrite([17652(7)]),flip(a)].
% 10.21/10.49 18741 multiplication(antidomain(c2),multiplication(c1,antidomain(c3))) = multiplication(c1,antidomain(c3)). [para(11824(a,1),17684(a,1,1,1)),rewrite([113(2),33(6),9319(8)]),flip(a)].
% 10.21/10.49 22726 addition(antidomain(antidomain(c2)),antidomain(multiplication(c1,antidomain(c3)))) = antidomain(multiplication(c1,antidomain(c3))). [para(18741(a,1),17454(a,1,2,1)),rewrite([18741(16)])].
% 10.21/10.49 22727 $F # answer(goals). [resolve(22726,a,9507,a)].
% 10.21/10.49
% 10.21/10.49 % SZS output end Refutation
% 10.21/10.49 ============================== end of proof ==========================
% 10.21/10.49
% 10.21/10.49 ============================== STATISTICS ============================
% 10.21/10.49
% 10.21/10.49 Given=1147. Generated=654521. Kept=22682. proofs=1.
% 10.21/10.49 Usable=775. Sos=9999. Demods=10368. Limbo=23, Disabled=11913. Hints=0.
% 10.21/10.49 Megabytes=20.18.
% 10.21/10.49 User_CPU=9.14, System_CPU=0.36, Wall_clock=9.
% 10.21/10.49
% 10.21/10.49 ============================== end of statistics =====================
% 10.21/10.49
% 10.21/10.49 ============================== end of search =========================
% 10.21/10.49
% 10.21/10.49 THEOREM PROVED
% 10.21/10.49 % SZS status Theorem
% 10.21/10.49
% 10.21/10.49 Exiting with 1 proof.
% 10.21/10.49
% 10.21/10.49 Process 30879 exit (max_proofs) Thu Jun 16 09:14:51 2022
% 10.21/10.49 Prover9 interrupted
%------------------------------------------------------------------------------