TSTP Solution File: KLE035+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE035+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 02:21:53 EDT 2022
% Result : Theorem 2.39s 2.67s
% Output : Refutation 2.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE035+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 12:35:57 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.02 ============================== Prover9 ===============================
% 0.46/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.02 Process 19252 was started by sandbox2 on n029.cluster.edu,
% 0.46/1.02 Thu Jun 16 12:35:58 2022
% 0.46/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19099_n029.cluster.edu".
% 0.46/1.02 ============================== end of head ===========================
% 0.46/1.02
% 0.46/1.02 ============================== INPUT =================================
% 0.46/1.02
% 0.46/1.02 % Reading from file /tmp/Prover9_19099_n029.cluster.edu
% 0.46/1.02
% 0.46/1.02 set(prolog_style_variables).
% 0.46/1.02 set(auto2).
% 0.46/1.02 % set(auto2) -> set(auto).
% 0.46/1.02 % set(auto) -> set(auto_inference).
% 0.46/1.02 % set(auto) -> set(auto_setup).
% 0.46/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.02 % set(auto) -> set(auto_limits).
% 0.46/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.02 % set(auto) -> set(auto_denials).
% 0.46/1.02 % set(auto) -> set(auto_process).
% 0.46/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.02 % set(auto2) -> assign(stats, some).
% 0.46/1.02 % set(auto2) -> clear(echo_input).
% 0.46/1.02 % set(auto2) -> set(quiet).
% 0.46/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.02 % set(auto2) -> clear(print_given).
% 0.46/1.02 assign(lrs_ticks,-1).
% 0.46/1.02 assign(sos_limit,10000).
% 0.46/1.02 assign(order,kbo).
% 0.46/1.02 set(lex_order_vars).
% 0.46/1.02 clear(print_given).
% 0.46/1.02
% 0.46/1.02 % formulas(sos). % not echoed (17 formulas)
% 0.46/1.02
% 0.46/1.02 ============================== end of input ==========================
% 0.46/1.02
% 0.46/1.02 % From the command line: assign(max_seconds, 300).
% 0.46/1.02
% 0.46/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.02
% 0.46/1.02 % Formulas that are not ordinary clauses:
% 0.46/1.02 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 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].
% 0.46/1.02 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 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].
% 0.46/1.02 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 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].
% 0.46/1.02 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].
% 0.46/1.02 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 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].
% 2.39/2.67 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 17 -(all X0 all X1 all X2 all X3 (test(X3) & test(X2) & leq(multiplication(multiplication(X2,X0),c(X3)),zero) & leq(multiplication(multiplication(X2,X1),c(X3)),zero) -> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.39/2.67
% 2.39/2.67 ============================== end of process non-clausal formulas ===
% 2.39/2.67
% 2.39/2.67 ============================== PROCESS INITIAL CLAUSES ===============
% 2.39/2.67
% 2.39/2.67 ============================== PREDICATE ELIMINATION =================
% 2.39/2.67 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.39/2.67 19 test(c4) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.39/2.67 20 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.39/2.67 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.39/2.67 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.39/2.67 Derived: complement(f1(c4),c4). [resolve(18,a,19,a)].
% 2.39/2.67 Derived: complement(f1(c3),c3). [resolve(18,a,20,a)].
% 2.39/2.67 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 2.39/2.67 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 2.39/2.67 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.39/2.67 Derived: c(c4) != A | complement(c4,A). [resolve(23,a,19,a)].
% 2.39/2.67 Derived: c(c3) != A | complement(c3,A). [resolve(23,a,20,a)].
% 2.39/2.67 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 2.39/2.67 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 2.39/2.67 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.39/2.67 Derived: c(c4) = A | -complement(c4,A). [resolve(24,a,19,a)].
% 2.39/2.67 Derived: c(c3) = A | -complement(c3,A). [resolve(24,a,20,a)].
% 2.39/2.67 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.39/2.67 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.39/2.67
% 2.39/2.67 ============================== end predicate elimination =============
% 2.39/2.67
% 2.39/2.67 Auto_denials: (non-Horn, no changes).
% 2.39/2.67
% 2.39/2.67 Term ordering decisions:
% 2.39/2.67 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. multiplication=1. addition=1. c=1. f1=1.
% 2.39/2.67
% 2.39/2.67 ============================== end of process initial clauses ========
% 2.39/2.67
% 2.39/2.67 ============================== CLAUSES FOR SEARCH ====================
% 2.39/2.67
% 2.39/2.67 ============================== end of clauses for search =============
% 2.39/2.67
% 2.39/2.67 ============================== SEARCH ================================
% 2.39/2.67
% 2.39/2.67 % Starting search at 0.01 seconds.
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=62.000, iters=3408
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=54.000, iters=3334
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=50.000, iters=3363
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=48.000, iters=3339
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=46.000, iters=3342
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=45.000, iters=3453
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=42.000, iters=3400
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=40.000, iters=3333
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=38.000, iters=3360
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=37.000, iters=3351
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=36.000, iters=3343
% 2.39/2.67
% 2.39/2.67 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 1.18 sec).
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=34.000, iters=3385
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=33.000, iters=3335
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=32.000, iters=3369
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=31.000, iters=3478
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=30.000, iters=3336
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=29.000, iters=3368
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=28.000, iters=3358
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=27.000, iters=3398
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=26.000, iters=3390
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=25.000, iters=3337
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=24.000, iters=3341
% 2.39/2.67
% 2.39/2.67 Low Water (keep): wt=23.000, iters=3350
% 2.39/2.67
% 2.39/2.67 ============================== PROOF =================================
% 2.39/2.67 % SZS status Theorem
% 2.39/2.67 % SZS output start Refutation
% 2.39/2.67
% 2.39/2.67 % Proof 1 at 1.63 (+ 0.03) seconds.
% 2.39/2.67 % Length of proof is 53.
% 2.39/2.67 % Level of proof is 8.
% 2.39/2.67 % Maximum clause weight is 18.000.
% 2.39/2.67 % Given clauses 630.
% 2.39/2.67
% 2.39/2.67 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 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].
% 2.39/2.67 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 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].
% 2.39/2.67 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].
% 2.39/2.67 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 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].
% 2.39/2.67 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.39/2.67 17 -(all X0 all X1 all X2 all X3 (test(X3) & test(X2) & leq(multiplication(multiplication(X2,X0),c(X3)),zero) & leq(multiplication(multiplication(X2,X1),c(X3)),zero) -> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.39/2.67 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.39/2.67 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.39/2.67 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.39/2.67 25 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.39/2.67 27 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.39/2.67 29 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.39/2.67 31 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.39/2.67 32 leq(multiplication(multiplication(c3,c1),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.39/2.67 33 leq(multiplication(multiplication(c3,c2),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.39/2.67 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.39/2.67 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.39/2.67 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 2.39/2.67 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.39/2.67 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 2.39/2.67 41 -leq(multiplication(multiplication(c3,addition(c1,c2)),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.39/2.67 42 -leq(multiplication(c3,multiplication(addition(c1,c2),c(c4))),zero). [copy(41),rewrite([36(8)])].
% 2.39/2.67 43 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.39/2.67 44 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.39/2.67 47 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.39/2.67 48 -complement(A,B) | addition(A,B) = one. [copy(47),rewrite([31(2)])].
% 2.39/2.67 49 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.39/2.67 50 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(A,B) != one. [copy(49),rewrite([31(8)])].
% 2.39/2.67 61 c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.39/2.67 62 c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.39/2.67 63 leq(multiplication(c3,multiplication(c2,c(c4))),zero). [back_rewrite(33),rewrite([36(6)])].
% 2.39/2.67 64 leq(multiplication(c3,multiplication(c1,c(c4))),zero). [back_rewrite(32),rewrite([36(6)])].
% 2.39/2.67 66 c(A) = zero | -complement(A,zero). [factor(61,a,c)].
% 2.39/2.67 69 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(25(a,1),38(a,2,2)),rewrite([29(3),31(3)])].
% 2.39/2.67 75 multiplication(c3,multiplication(addition(c1,c2),c(c4))) != zero. [ur(44,a,42,a),rewrite([31(10),69(10)])].
% 2.39/2.67 80 complement(one,zero). [resolve(50,d,25,a),rewrite([27(6),29(9)]),xx(b),xx(c)].
% 2.39/2.67 107 multiplication(c3,multiplication(c2,c(c4))) = zero. [resolve(63,a,43,a),rewrite([31(8),69(8)])].
% 2.39/2.67 108 multiplication(c3,multiplication(c1,c(c4))) = zero. [resolve(64,a,43,a),rewrite([31(8),69(8)])].
% 2.39/2.67 114 c(one) = zero. [resolve(80,a,66,b)].
% 2.39/2.67 118 addition(zero,one) = one. [resolve(80,a,48,a),rewrite([31(3)])].
% 2.39/2.67 137 complement(zero,one). [resolve(118,a,50,d),rewrite([29(6),27(9)]),xx(b),xx(c)].
% 2.39/2.67 155 zero = A | -complement(one,A). [resolve(137,a,62,c),rewrite([114(2)])].
% 2.39/2.67 345 -complement(one,multiplication(c3,multiplication(addition(c1,c2),c(c4)))). [ur(155,a,75,a(flip))].
% 2.39/2.67 436 multiplication(c3,addition(A,multiplication(c2,c(c4)))) = multiplication(c3,A). [para(107(a,1),38(a,1,1)),rewrite([69(4),31(8)]),flip(a)].
% 2.39/2.67 10527 multiplication(c3,multiplication(addition(A,c2),c(c4))) = multiplication(c3,multiplication(A,c(c4))). [para(40(a,1),436(a,1,2))].
% 2.39/2.67 10564 $F. [back_rewrite(345),rewrite([10527(9),108(7)]),unit_del(a,80)].
% 2.39/2.67
% 2.39/2.67 % SZS output end Refutation
% 2.39/2.67 ============================== end of proof ==========================
% 2.39/2.67
% 2.39/2.67 ============================== STATISTICS ============================
% 2.39/2.67
% 2.39/2.67 Given=630. Generated=53034. Kept=10533. proofs=1.
% 2.39/2.67 Usable=571. Sos=9376. Demods=1512. Limbo=37, Disabled=588. Hints=0.
% 2.39/2.67 Megabytes=12.38.
% 2.39/2.67 User_CPU=1.63, System_CPU=0.03, Wall_clock=1.
% 2.39/2.67
% 2.39/2.67 ============================== end of statistics =====================
% 2.39/2.67
% 2.39/2.67 ============================== end of search =========================
% 2.39/2.67
% 2.39/2.67 THEOREM PROVED
% 2.39/2.67 % SZS status Theorem
% 2.39/2.67
% 2.39/2.67 Exiting with 1 proof.
% 2.39/2.67
% 2.39/2.67 Process 19252 exit (max_proofs) Thu Jun 16 12:35:59 2022
% 2.39/2.67 Prover9 interrupted
%------------------------------------------------------------------------------