TSTP Solution File: KLE027+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE027+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 02:21:50 EDT 2022
% Result : Theorem 0.82s 1.09s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE027+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 16 09:17:38 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.42/0.96 ============================== Prover9 ===============================
% 0.42/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.96 Process 21416 was started by sandbox on n005.cluster.edu,
% 0.42/0.96 Thu Jun 16 09:17:39 2022
% 0.42/0.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21263_n005.cluster.edu".
% 0.42/0.96 ============================== end of head ===========================
% 0.42/0.96
% 0.42/0.96 ============================== INPUT =================================
% 0.42/0.96
% 0.42/0.96 % Reading from file /tmp/Prover9_21263_n005.cluster.edu
% 0.42/0.96
% 0.42/0.96 set(prolog_style_variables).
% 0.42/0.96 set(auto2).
% 0.42/0.96 % set(auto2) -> set(auto).
% 0.42/0.96 % set(auto) -> set(auto_inference).
% 0.42/0.96 % set(auto) -> set(auto_setup).
% 0.42/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.96 % set(auto) -> set(auto_limits).
% 0.42/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.96 % set(auto) -> set(auto_denials).
% 0.42/0.96 % set(auto) -> set(auto_process).
% 0.42/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.96 % set(auto2) -> assign(stats, some).
% 0.42/0.96 % set(auto2) -> clear(echo_input).
% 0.42/0.96 % set(auto2) -> set(quiet).
% 0.42/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.96 % set(auto2) -> clear(print_given).
% 0.42/0.96 assign(lrs_ticks,-1).
% 0.42/0.96 assign(sos_limit,10000).
% 0.42/0.96 assign(order,kbo).
% 0.42/0.96 set(lex_order_vars).
% 0.42/0.96 clear(print_given).
% 0.42/0.96
% 0.42/0.96 % formulas(sos). % not echoed (17 formulas)
% 0.42/0.96
% 0.42/0.96 ============================== end of input ==========================
% 0.42/0.96
% 0.42/0.96 % From the command line: assign(max_seconds, 300).
% 0.42/0.96
% 0.42/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.96
% 0.42/0.96 % Formulas that are not ordinary clauses:
% 0.42/0.96 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 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].
% 0.42/0.96 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 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].
% 0.42/0.96 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 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].
% 0.42/0.96 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].
% 0.42/0.96 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 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].
% 0.82/1.09 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 17 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) & leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09
% 0.82/1.09 ============================== end of process non-clausal formulas ===
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.09
% 0.82/1.09 ============================== PREDICATE ELIMINATION =================
% 0.82/1.09 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.82/1.09 19 test(c4) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.82/1.09 20 test(c5) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.82/1.09 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 0.82/1.09 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.82/1.09 Derived: complement(f1(c4),c4). [resolve(18,a,19,a)].
% 0.82/1.09 Derived: complement(f1(c5),c5). [resolve(18,a,20,a)].
% 0.82/1.09 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 0.82/1.09 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 0.82/1.09 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.82/1.09 Derived: c(c4) != A | complement(c4,A). [resolve(23,a,19,a)].
% 0.82/1.09 Derived: c(c5) != A | complement(c5,A). [resolve(23,a,20,a)].
% 0.82/1.09 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 0.82/1.09 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 0.82/1.09 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.82/1.09 Derived: c(c4) = A | -complement(c4,A). [resolve(24,a,19,a)].
% 0.82/1.09 Derived: c(c5) = A | -complement(c5,A). [resolve(24,a,20,a)].
% 0.82/1.09 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 0.82/1.09 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 0.82/1.09
% 0.82/1.09 ============================== end predicate elimination =============
% 0.82/1.09
% 0.82/1.09 Auto_denials: (non-Horn, no changes).
% 0.82/1.09
% 0.82/1.09 Term ordering decisions:
% 0.82/1.09 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. c=1. f1=1.
% 0.82/1.09
% 0.82/1.09 ============================== end of process initial clauses ========
% 0.82/1.09
% 0.82/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.09
% 0.82/1.09 ============================== end of clauses for search =============
% 0.82/1.09
% 0.82/1.09 ============================== SEARCH ================================
% 0.82/1.09
% 0.82/1.09 % Starting search at 0.01 seconds.
% 0.82/1.09
% 0.82/1.09 ============================== PROOF =================================
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09 % SZS output start Refutation
% 0.82/1.09
% 0.82/1.09 % Proof 1 at 0.13 (+ 0.00) seconds.
% 0.82/1.09 % Length of proof is 44.
% 0.82/1.09 % Level of proof is 8.
% 0.82/1.09 % Maximum clause weight is 48.000.
% 0.82/1.09 % Given clauses 222.
% 0.82/1.09
% 0.82/1.09 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 17 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) & leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09 19 test(c4) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.82/1.09 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.82/1.09 25 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.82/1.09 26 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.82/1.09 27 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.82/1.09 28 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.82/1.09 29 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.82/1.09 30 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 0.82/1.09 31 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.82/1.09 34 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.82/1.09 35 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.82/1.09 36 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(35),flip(a)].
% 0.82/1.09 39 -leq(addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3)),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3))) # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.82/1.09 40 -leq(addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2)))),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))))). [copy(39),rewrite([31(15),31(47)])].
% 0.82/1.09 42 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.82/1.09 44 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 46 -complement(A,B) | addition(A,B) = one. [copy(45),rewrite([31(2)])].
% 0.82/1.09 53 c(c4) != A | complement(c4,A). [resolve(23,a,19,a)].
% 0.82/1.09 65 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(25(a,1),36(a,2,2)),rewrite([29(3),31(3)])].
% 0.82/1.09 70 leq(A,A). [resolve(42,b,26,a)].
% 0.82/1.09 89 complement(c4,c(c4)). [resolve(53,a,28,a(flip)),rewrite([28(5)])].
% 0.82/1.09 112 addition(c4,c(c4)) = one. [resolve(89,a,46,a)].
% 0.82/1.09 113 multiplication(c4,c(c4)) = zero. [resolve(89,a,44,a)].
% 0.82/1.09 277 multiplication(c4,multiplication(c(c4),A)) = zero. [para(113(a,1),34(a,1,1)),rewrite([30(2)]),flip(a)].
% 0.82/1.09 278 multiplication(c4,addition(A,c(c4))) = multiplication(c4,A). [para(113(a,1),36(a,1,1)),rewrite([65(4),31(6)]),flip(a)].
% 0.82/1.09 470 multiplication(c4,addition(A,multiplication(c(c4),B))) = multiplication(c4,A). [para(277(a,1),36(a,1,1)),rewrite([65(4),31(7)]),flip(a)].
% 0.82/1.09 474 -leq(addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1))),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1)))). [back_rewrite(40),rewrite([470(14),470(41)])].
% 0.82/1.09 1257 multiplication(c4,c4) = c4. [para(112(a,1),278(a,1,2)),rewrite([27(3)]),flip(a)].
% 0.82/1.09 1272 multiplication(c4,multiplication(c4,A)) = multiplication(c4,A). [para(1257(a,1),34(a,1,1)),flip(a)].
% 0.82/1.09 1281 $F. [back_rewrite(474),rewrite([1272(9),31(8),1272(34),31(33)]),merge(b),unit_del(a,70)].
% 0.82/1.09
% 0.82/1.09 % SZS output end Refutation
% 0.82/1.09 ============================== end of proof ==========================
% 0.82/1.09
% 0.82/1.09 ============================== STATISTICS ============================
% 0.82/1.09
% 0.82/1.09 Given=222. Generated=4805. Kept=1250. proofs=1.
% 0.82/1.09 Usable=195. Sos=929. Demods=221. Limbo=9, Disabled=154. Hints=0.
% 0.82/1.09 Megabytes=1.46.
% 0.82/1.09 User_CPU=0.13, System_CPU=0.00, Wall_clock=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of statistics =====================
% 0.82/1.09
% 0.82/1.09 ============================== end of search =========================
% 0.82/1.09
% 0.82/1.09 THEOREM PROVED
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09
% 0.82/1.09 Exiting with 1 proof.
% 0.82/1.09
% 0.82/1.09 Process 21416 exit (max_proofs) Thu Jun 16 09:17:39 2022
% 0.82/1.09 Prover9 interrupted
%------------------------------------------------------------------------------