TSTP Solution File: KLE048+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 02:21:59 EDT 2022
% Result : Theorem 0.69s 1.03s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 12:04:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.69/0.99 ============================== Prover9 ===============================
% 0.69/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.69/0.99 Process 20517 was started by sandbox2 on n007.cluster.edu,
% 0.69/0.99 Thu Jun 16 12:04:12 2022
% 0.69/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20363_n007.cluster.edu".
% 0.69/0.99 ============================== end of head ===========================
% 0.69/0.99
% 0.69/0.99 ============================== INPUT =================================
% 0.69/0.99
% 0.69/0.99 % Reading from file /tmp/Prover9_20363_n007.cluster.edu
% 0.69/0.99
% 0.69/0.99 set(prolog_style_variables).
% 0.69/0.99 set(auto2).
% 0.69/0.99 % set(auto2) -> set(auto).
% 0.69/0.99 % set(auto) -> set(auto_inference).
% 0.69/0.99 % set(auto) -> set(auto_setup).
% 0.69/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.69/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/0.99 % set(auto) -> set(auto_limits).
% 0.69/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/0.99 % set(auto) -> set(auto_denials).
% 0.69/0.99 % set(auto) -> set(auto_process).
% 0.69/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.69/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.69/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.69/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.69/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.69/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.69/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.69/0.99 % set(auto2) -> assign(stats, some).
% 0.69/0.99 % set(auto2) -> clear(echo_input).
% 0.69/0.99 % set(auto2) -> set(quiet).
% 0.69/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.69/0.99 % set(auto2) -> clear(print_given).
% 0.69/0.99 assign(lrs_ticks,-1).
% 0.69/0.99 assign(sos_limit,10000).
% 0.69/0.99 assign(order,kbo).
% 0.69/0.99 set(lex_order_vars).
% 0.69/0.99 clear(print_given).
% 0.69/0.99
% 0.69/0.99 % formulas(sos). % not echoed (21 formulas)
% 0.69/0.99
% 0.69/0.99 ============================== end of input ==========================
% 0.69/0.99
% 0.69/0.99 % From the command line: assign(max_seconds, 300).
% 0.69/0.99
% 0.69/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/0.99
% 0.69/0.99 % Formulas that are not ordinary clauses:
% 0.69/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 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].
% 0.69/0.99 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 13 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 15 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 17 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 18 (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].
% 0.69/1.03 19 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 20 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 21 -(all X0 (test(X0) -> star(X0) = one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.69/1.03
% 0.69/1.03 ============================== end of process non-clausal formulas ===
% 0.69/1.03
% 0.69/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.69/1.03
% 0.69/1.03 ============================== PREDICATE ELIMINATION =================
% 0.69/1.03 22 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(17)].
% 0.69/1.03 23 test(c1) # label(goals) # label(negated_conjecture). [clausify(21)].
% 0.69/1.03 24 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(20)].
% 0.69/1.03 25 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(17)].
% 0.69/1.03 Derived: complement(f1(c1),c1). [resolve(22,a,23,a)].
% 0.69/1.03 Derived: complement(f1(A),A) | c(A) = zero. [resolve(22,a,24,a)].
% 0.69/1.03 Derived: complement(f1(A),A) | -complement(B,A). [resolve(22,a,25,a)].
% 0.69/1.03 26 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(19)].
% 0.69/1.03 Derived: c(c1) != A | complement(c1,A). [resolve(26,a,23,a)].
% 0.69/1.03 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(26,a,24,a)].
% 0.69/1.03 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(26,a,25,a)].
% 0.69/1.03 27 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(19)].
% 0.69/1.03 Derived: c(c1) = A | -complement(c1,A). [resolve(27,a,23,a)].
% 0.69/1.03 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(27,a,24,a)].
% 0.69/1.03 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(27,a,25,a)].
% 0.69/1.03
% 0.69/1.03 ============================== end predicate elimination =============
% 0.69/1.03
% 0.69/1.03 Auto_denials: (non-Horn, no changes).
% 0.69/1.03
% 0.69/1.03 Term ordering decisions:
% 0.69/1.03 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. c=1. star=1. f1=1.
% 0.69/1.03
% 0.69/1.03 ============================== end of process initial clauses ========
% 0.69/1.03
% 0.69/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.69/1.03
% 0.69/1.03 ============================== end of clauses for search =============
% 0.69/1.03
% 0.69/1.03 ============================== SEARCH ================================
% 0.69/1.03
% 0.69/1.03 % Starting search at 0.01 seconds.
% 0.69/1.03
% 0.69/1.03 ============================== PROOF =================================
% 0.69/1.03 % SZS status Theorem
% 0.69/1.03 % SZS output start Refutation
% 0.69/1.03
% 0.69/1.03 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.69/1.03 % Length of proof is 42.
% 0.69/1.03 % Level of proof is 8.
% 0.69/1.03 % Maximum clause weight is 13.000.
% 0.69/1.03 % Given clauses 100.
% 0.69/1.03
% 0.69/1.03 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 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].
% 0.69/1.03 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 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].
% 0.69/1.03 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 16 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 17 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.03 18 (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].
% 0.69/1.03 21 -(all X0 (test(X0) -> star(X0) = one)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.69/1.03 22 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(17)].
% 0.69/1.03 23 test(c1) # label(goals) # label(negated_conjecture). [clausify(21)].
% 0.69/1.03 29 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.69/1.03 30 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.69/1.03 31 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.69/1.03 34 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.69/1.03 36 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom). [clausify(14)].
% 0.69/1.03 37 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.69/1.03 38 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(37),rewrite([34(2)]),flip(a)].
% 0.69/1.03 40 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.69/1.03 41 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(40),flip(a)].
% 0.69/1.03 44 star(c1) != one # label(goals) # label(negated_conjecture). [clausify(21)].
% 0.69/1.03 45 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.69/1.03 46 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.69/1.03 49 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(18)].
% 0.69/1.03 50 -complement(A,B) | addition(A,B) = one. [copy(49),rewrite([34(2)])].
% 0.69/1.03 53 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom). [clausify(16)].
% 0.69/1.03 54 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B). [copy(53),rewrite([34(2)])].
% 0.69/1.03 57 complement(f1(c1),c1). [resolve(22,a,23,a)].
% 0.69/1.03 71 addition(A,addition(A,B)) = addition(A,B). [para(38(a,1),29(a,1)),rewrite([34(1),34(2),38(2,R),29(1),34(3)])].
% 0.69/1.03 74 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(30(a,1),41(a,1,1)),rewrite([34(4)]),flip(a)].
% 0.69/1.03 78 addition(one,multiplication(star(A),addition(A,one))) = star(A). [resolve(45,a,36,a),rewrite([34(6),38(6,R),34(5),74(5,R)])].
% 0.69/1.03 80 leq(A,A). [resolve(46,b,29,a)].
% 0.69/1.03 106 addition(c1,f1(c1)) = one. [resolve(57,a,50,a),rewrite([34(4)])].
% 0.69/1.03 183 addition(one,c1) = one. [para(106(a,1),71(a,1,2)),rewrite([34(3),106(7)])].
% 0.69/1.03 215 addition(A,multiplication(A,c1)) = A. [para(183(a,1),41(a,2,2)),rewrite([30(2),30(5)])].
% 0.69/1.03 287 addition(one,star(A)) = star(A). [para(78(a,1),71(a,1,2)),rewrite([78(9)])].
% 0.69/1.03 327 leq(multiplication(A,star(c1)),A). [para(215(a,1),54(a,1)),unit_del(a,80)].
% 0.69/1.03 339 leq(star(c1),one). [para(31(a,1),327(a,1))].
% 0.69/1.03 341 $F. [resolve(339,a,45,a),rewrite([34(4),287(4)]),unit_del(a,44)].
% 0.69/1.03
% 0.69/1.03 % SZS output end Refutation
% 0.69/1.03 ============================== end of proof ==========================
% 0.69/1.03
% 0.69/1.03 ============================== STATISTICS ============================
% 0.69/1.03
% 0.69/1.03 Given=100. Generated=1071. Kept=306. proofs=1.
% 0.69/1.03 Usable=85. Sos=176. Demods=74. Limbo=0, Disabled=82. Hints=0.
% 0.69/1.03 Megabytes=0.34.
% 0.69/1.03 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.69/1.03
% 0.69/1.03 ============================== end of statistics =====================
% 0.69/1.03
% 0.69/1.03 ============================== end of search =========================
% 0.69/1.03
% 0.69/1.03 THEOREM PROVED
% 0.69/1.03 % SZS status Theorem
% 0.69/1.03
% 0.69/1.03 Exiting with 1 proof.
% 0.69/1.03
% 0.69/1.03 Process 20517 exit (max_proofs) Thu Jun 16 12:04:12 2022
% 0.69/1.03 Prover9 interrupted
%------------------------------------------------------------------------------