TSTP Solution File: KLE022+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 02:21:47 EDT 2022
% Result : Theorem 0.49s 1.07s
% Output : Refutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.37 % Computer : n021.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Thu Jun 16 13:40:45 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.49/1.06 ============================== Prover9 ===============================
% 0.49/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.06 Process 6347 was started by sandbox2 on n021.cluster.edu,
% 0.49/1.06 Thu Jun 16 13:40:45 2022
% 0.49/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6193_n021.cluster.edu".
% 0.49/1.06 ============================== end of head ===========================
% 0.49/1.06
% 0.49/1.06 ============================== INPUT =================================
% 0.49/1.06
% 0.49/1.06 % Reading from file /tmp/Prover9_6193_n021.cluster.edu
% 0.49/1.06
% 0.49/1.06 set(prolog_style_variables).
% 0.49/1.06 set(auto2).
% 0.49/1.06 % set(auto2) -> set(auto).
% 0.49/1.06 % set(auto) -> set(auto_inference).
% 0.49/1.06 % set(auto) -> set(auto_setup).
% 0.49/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.06 % set(auto) -> set(auto_limits).
% 0.49/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.06 % set(auto) -> set(auto_denials).
% 0.49/1.06 % set(auto) -> set(auto_process).
% 0.49/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.06 % set(auto2) -> assign(stats, some).
% 0.49/1.06 % set(auto2) -> clear(echo_input).
% 0.49/1.06 % set(auto2) -> set(quiet).
% 0.49/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.06 % set(auto2) -> clear(print_given).
% 0.49/1.06 assign(lrs_ticks,-1).
% 0.49/1.06 assign(sos_limit,10000).
% 0.49/1.06 assign(order,kbo).
% 0.49/1.06 set(lex_order_vars).
% 0.49/1.06 clear(print_given).
% 0.49/1.06
% 0.49/1.06 % formulas(sos). % not echoed (17 formulas)
% 0.49/1.06
% 0.49/1.06 ============================== end of input ==========================
% 0.49/1.06
% 0.49/1.06 % From the command line: assign(max_seconds, 300).
% 0.49/1.06
% 0.49/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.06
% 0.49/1.06 % Formulas that are not ordinary clauses:
% 0.49/1.06 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 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].
% 0.49/1.06 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].
% 0.49/1.06 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.06 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 17 -(all X0 all X1 (test(X1) -> leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) & leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.49/1.07
% 0.49/1.07 ============================== end of process non-clausal formulas ===
% 0.49/1.07
% 0.49/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.49/1.07
% 0.49/1.07 ============================== PREDICATE ELIMINATION =================
% 0.49/1.07 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.49/1.07 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.49/1.07 20 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 0.49/1.07 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.49/1.07 Derived: complement(f1(c2),c2). [resolve(18,a,19,a)].
% 0.49/1.07 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,20,a)].
% 0.49/1.07 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,21,a)].
% 0.49/1.07 22 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.49/1.07 Derived: c(c2) != A | complement(c2,A). [resolve(22,a,19,a)].
% 0.49/1.07 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(22,a,20,a)].
% 0.49/1.07 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(22,a,21,a)].
% 0.49/1.07 23 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.49/1.07 Derived: c(c2) = A | -complement(c2,A). [resolve(23,a,19,a)].
% 0.49/1.07 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(23,a,20,a)].
% 0.49/1.07 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(23,a,21,a)].
% 0.49/1.07
% 0.49/1.07 ============================== end predicate elimination =============
% 0.49/1.07
% 0.49/1.07 Auto_denials: (non-Horn, no changes).
% 0.49/1.07
% 0.49/1.07 Term ordering decisions:
% 0.49/1.07 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 0.49/1.07
% 0.49/1.07 ============================== end of process initial clauses ========
% 0.49/1.07
% 0.49/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.49/1.07
% 0.49/1.07 ============================== end of clauses for search =============
% 0.49/1.07
% 0.49/1.07 ============================== SEARCH ================================
% 0.49/1.07
% 0.49/1.07 % Starting search at 0.01 seconds.
% 0.49/1.07
% 0.49/1.07 ============================== PROOF =================================
% 0.49/1.07 % SZS status Theorem
% 0.49/1.07 % SZS output start Refutation
% 0.49/1.07
% 0.49/1.07 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.49/1.07 % Length of proof is 27.
% 0.49/1.07 % Level of proof is 5.
% 0.49/1.07 % Maximum clause weight is 16.000.
% 0.49/1.07 % Given clauses 34.
% 0.49/1.07
% 0.49/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 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].
% 0.49/1.07 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.07 17 -(all X0 all X1 (test(X1) -> leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) & leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.49/1.07 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.49/1.07 22 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.49/1.07 25 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.49/1.07 26 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.49/1.07 27 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.49/1.07 30 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.49/1.07 34 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.49/1.07 35 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(34),flip(a)].
% 0.49/1.07 38 -leq(c1,addition(multiplication(c1,c2),multiplication(c1,c(c2)))) | -leq(addition(multiplication(c1,c2),multiplication(c1,c(c2))),c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.49/1.07 39 -leq(c1,multiplication(c1,addition(c2,c(c2)))) | -leq(multiplication(c1,addition(c2,c(c2))),c1). [copy(38),rewrite([35(9),35(16)])].
% 0.49/1.07 41 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.49/1.07 44 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.49/1.07 45 -complement(A,B) | addition(A,B) = one. [copy(44),rewrite([30(2)])].
% 0.49/1.07 51 c(c2) != A | complement(c2,A). [resolve(22,a,19,a)].
% 0.49/1.07 66 leq(A,A). [resolve(41,b,25,a)].
% 0.49/1.07 82 complement(c2,c(c2)). [resolve(51,a,27,a(flip)),rewrite([27(5)])].
% 0.49/1.07 101 addition(c2,c(c2)) = one. [resolve(82,a,45,a)].
% 0.49/1.07 104 $F. [back_rewrite(39),rewrite([101(6),26(4),101(8),26(6)]),merge(b),unit_del(a,66)].
% 0.49/1.07
% 0.49/1.07 % SZS output end Refutation
% 0.49/1.07 ============================== end of proof ==========================
% 0.49/1.07
% 0.49/1.07 ============================== STATISTICS ============================
% 0.49/1.07
% 0.49/1.07 Given=34. Generated=251. Kept=74. proofs=1.
% 0.49/1.07 Usable=33. Sos=37. Demods=25. Limbo=3, Disabled=34. Hints=0.
% 0.49/1.07 Megabytes=0.12.
% 0.49/1.07 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.49/1.07
% 0.49/1.07 ============================== end of statistics =====================
% 0.49/1.07
% 0.49/1.07 ============================== end of search =========================
% 0.49/1.07
% 0.49/1.07 THEOREM PROVED
% 0.49/1.07 % SZS status Theorem
% 0.49/1.07
% 0.49/1.07 Exiting with 1 proof.
% 0.49/1.07
% 0.49/1.07 Process 6347 exit (max_proofs) Thu Jun 16 13:40:45 2022
% 0.49/1.07 Prover9 interrupted
%------------------------------------------------------------------------------