TSTP Solution File: KLE119+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 0.45s 1.00s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.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 12:49:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/0.99 ============================== Prover9 ===============================
% 0.45/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.99 Process 22930 was started by sandbox2 on n009.cluster.edu,
% 0.45/0.99 Thu Jun 16 12:49:38 2022
% 0.45/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22777_n009.cluster.edu".
% 0.45/0.99 ============================== end of head ===========================
% 0.45/0.99
% 0.45/0.99 ============================== INPUT =================================
% 0.45/0.99
% 0.45/0.99 % Reading from file /tmp/Prover9_22777_n009.cluster.edu
% 0.45/0.99
% 0.45/0.99 set(prolog_style_variables).
% 0.45/0.99 set(auto2).
% 0.45/0.99 % set(auto2) -> set(auto).
% 0.45/0.99 % set(auto) -> set(auto_inference).
% 0.45/0.99 % set(auto) -> set(auto_setup).
% 0.45/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.99 % set(auto) -> set(auto_limits).
% 0.45/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.99 % set(auto) -> set(auto_denials).
% 0.45/0.99 % set(auto) -> set(auto_process).
% 0.45/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.99 % set(auto2) -> assign(stats, some).
% 0.45/0.99 % set(auto2) -> clear(echo_input).
% 0.45/0.99 % set(auto2) -> set(quiet).
% 0.45/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.99 % set(auto2) -> clear(print_given).
% 0.45/0.99 assign(lrs_ticks,-1).
% 0.45/0.99 assign(sos_limit,10000).
% 0.45/0.99 assign(order,kbo).
% 0.45/0.99 set(lex_order_vars).
% 0.45/0.99 clear(print_given).
% 0.45/0.99
% 0.45/0.99 % formulas(sos). % not echoed (27 formulas)
% 0.45/0.99
% 0.45/0.99 ============================== end of input ==========================
% 0.45/0.99
% 0.45/0.99 % From the command line: assign(max_seconds, 300).
% 0.45/0.99
% 0.45/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.99
% 0.45/0.99 % Formulas that are not ordinary clauses:
% 0.45/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 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].
% 0.45/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 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].
% 0.45/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 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].
% 0.45/0.99 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].
% 0.45/0.99 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 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].
% 0.45/1.00 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 0.45/1.00 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 27 -(all X0 all X1 addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.00
% 0.45/1.00 ============================== end of process non-clausal formulas ===
% 0.45/1.00
% 0.45/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.00
% 0.45/1.00 ============================== PREDICATE ELIMINATION =================
% 0.45/1.00 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.45/1.00 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.45/1.00
% 0.45/1.00 ============================== end predicate elimination =============
% 0.45/1.00
% 0.45/1.00 Auto_denials:
% 0.45/1.00 % copying label goals to answer in negative clause
% 0.45/1.00
% 0.45/1.00 Term ordering decisions:
% 0.45/1.00 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.
% 0.45/1.00
% 0.45/1.00 ============================== end of process initial clauses ========
% 0.45/1.00
% 0.45/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.00
% 0.45/1.00 ============================== end of clauses for search =============
% 0.45/1.00
% 0.45/1.00 ============================== SEARCH ================================
% 0.45/1.00
% 0.45/1.00 % Starting search at 0.01 seconds.
% 0.45/1.00
% 0.45/1.00 ============================== PROOF =================================
% 0.45/1.00 % SZS status Theorem
% 0.45/1.00 % SZS output start Refutation
% 0.45/1.00
% 0.45/1.00 % Proof 1 at 0.02 (+ 0.01) seconds: goals.
% 0.45/1.00 % Length of proof is 49.
% 0.45/1.00 % Level of proof is 7.
% 0.45/1.00 % Maximum clause weight is 13.000.
% 0.45/1.00 % Given clauses 42.
% 0.45/1.00
% 0.45/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 0.45/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 27 -(all X0 all X1 addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.01 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.45/1.01 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.45/1.01 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.45/1.01 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.45/1.01 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.45/1.01 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 0.45/1.01 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 0.45/1.01 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 0.45/1.01 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 0.45/1.01 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.45/1.01 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 0.45/1.01 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 0.45/1.01 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 0.45/1.01 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 0.45/1.01 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 0.45/1.01 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 0.45/1.01 57 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.45/1.01 58 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(57),rewrite([42(2)]),flip(a)].
% 0.45/1.01 60 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.45/1.01 61 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(60),flip(a)].
% 0.45/1.01 68 domain(c2) != addition(backward_diamond(zero,domain(c1)),domain(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 0.45/1.01 69 addition(antidomain(antidomain(c2)),coantidomain(coantidomain(zero))) != antidomain(antidomain(c2)) # answer(goals). [copy(68),rewrite([37(2),37(6),52(8),34(10),37(8),42(10)]),flip(a)].
% 0.45/1.01 71 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 0.45/1.01 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)])].
% 0.45/1.01 76 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),61(a,2,2)),rewrite([34(3),42(3)])].
% 0.45/1.01 100 addition(zero,coantidomain(zero)) = one. [para(71(a,1),46(a,1,1)),rewrite([71(3)])].
% 0.45/1.01 107 multiplication(A,coantidomain(zero)) = A. [para(100(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 0.45/1.01 109 addition(one,antidomain(A)) = one. [para(44(a,1),72(a,1,2)),rewrite([42(3),44(7)])].
% 0.45/1.01 114 coantidomain(zero) = one. [para(107(a,1),33(a,1)),flip(a)].
% 0.45/1.01 117 addition(zero,antidomain(antidomain(c2))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(69),rewrite([114(5),71(5),42(5)])].
% 0.45/1.01 123 addition(A,multiplication(A,antidomain(B))) = A. [para(109(a,1),61(a,2,2)),rewrite([32(2),32(5)])].
% 0.45/1.01 132 addition(zero,antidomain(antidomain(A))) = antidomain(antidomain(A)). [para(36(a,1),123(a,1,2)),rewrite([42(4)])].
% 0.45/1.01 133 $F # answer(goals). [resolve(132,a,117,a)].
% 0.45/1.01
% 0.45/1.01 % SZS output end Refutation
% 0.45/1.01 ============================== end of proof ==========================
% 0.45/1.01
% 0.45/1.01 ============================== STATISTICS ============================
% 0.45/1.01
% 0.45/1.01 Given=42. Generated=474. Kept=89. proofs=1.
% 0.45/1.01 Usable=37. Sos=31. Demods=67. Limbo=0, Disabled=48. Hints=0.
% 0.45/1.01 Megabytes=0.14.
% 0.45/1.01 User_CPU=0.02, System_CPU=0.01, Wall_clock=0.
% 0.45/1.01
% 0.45/1.01 ============================== end of statistics =====================
% 0.45/1.01
% 0.45/1.01 ============================== end of search =========================
% 0.45/1.01
% 0.45/1.01 THEOREM PROVED
% 0.45/1.01 % SZS status Theorem
% 0.45/1.01
% 0.45/1.01 Exiting with 1 proof.
% 0.45/1.01
% 0.45/1.01 Process 22930 exit (max_proofs) Thu Jun 16 12:49:38 2022
% 0.45/1.01 Prover9 interrupted
%------------------------------------------------------------------------------