TSTP Solution File: KLE025+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE025+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 02:21:49 EDT 2022
% Result : Theorem 3.93s 4.21s
% Output : Refutation 3.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE025+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n014.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 14:49:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 16441 was started by sandbox on n014.cluster.edu,
% 0.43/0.99 Thu Jun 16 14:49:51 2022
% 0.43/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16288_n014.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_16288_n014.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (17 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 2.95/3.20 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.95/3.20 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.95/3.20 17 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (multiplication(multiplication(X1,X0),c(X2)) = zero -> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.95/3.20
% 2.95/3.20 ============================== end of process non-clausal formulas ===
% 2.95/3.20
% 2.95/3.20 ============================== PROCESS INITIAL CLAUSES ===============
% 2.95/3.20
% 2.95/3.20 ============================== PREDICATE ELIMINATION =================
% 2.95/3.20 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.95/3.20 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.95/3.20 20 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.95/3.20 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.95/3.20 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.95/3.20 Derived: complement(f1(c2),c2). [resolve(18,a,19,a)].
% 2.95/3.20 Derived: complement(f1(c3),c3). [resolve(18,a,20,a)].
% 2.95/3.20 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 2.95/3.20 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 2.95/3.20 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.95/3.20 Derived: c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 2.95/3.20 Derived: c(c3) != A | complement(c3,A). [resolve(23,a,20,a)].
% 2.95/3.20 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 2.95/3.20 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 2.95/3.20 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.95/3.20 Derived: c(c2) = A | -complement(c2,A). [resolve(24,a,19,a)].
% 2.95/3.20 Derived: c(c3) = A | -complement(c3,A). [resolve(24,a,20,a)].
% 2.95/3.20 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.95/3.20 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.95/3.20 25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.95/3.20 26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.95/3.20
% 2.95/3.20 ============================== end predicate elimination =============
% 2.95/3.20
% 2.95/3.20 Auto_denials: (non-Horn, no changes).
% 2.95/3.20
% 2.95/3.20 Term ordering decisions:
% 2.95/3.20 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. c=1. f1=1.
% 2.95/3.20
% 2.95/3.20 ============================== end of process initial clauses ========
% 2.95/3.20
% 2.95/3.20 ============================== CLAUSES FOR SEARCH ====================
% 2.95/3.20
% 2.95/3.20 ============================== end of clauses for search =============
% 2.95/3.20
% 2.95/3.20 ============================== SEARCH ================================
% 2.95/3.20
% 2.95/3.20 % Starting search at 0.01 seconds.
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=60.000, iters=3355
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=56.000, iters=3434
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=48.000, iters=3346
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=46.000, iters=3381
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=45.000, iters=3385
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=44.000, iters=3382
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=42.000, iters=3391
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=40.000, iters=3344
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=39.000, iters=3409
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=38.000, iters=3387
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=37.000, iters=3358
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=35.000, iters=3361
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=34.000, iters=3378
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=33.000, iters=3350
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=32.000, iters=3368
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=31.000, iters=3346
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=30.000, iters=3343
% 2.95/3.20
% 2.95/3.20 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 104 (0.00 of 1.63 sec).
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=29.000, iters=3389
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=27.000, iters=3351
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=26.000, iters=3350
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=25.000, iters=3391
% 2.95/3.20
% 2.95/3.20 Low Water (keep): wt=24.000, iters=3388
% 2.95/3.20
% 2.95/3.20 Low Water (displace): id=6306, wt=107.000
% 2.95/3.20
% 2.95/3.20 Low Water (displace): id=6324, wt=88.000
% 2.95/3.20
% 2.95/3.20 Low Water (displace): id=5944, wt=85.000
% 2.95/3.20
% 2.95/3.20 Low Water (displace): id=6325, wt=82.000
% 2.95/3.20
% 2.95/3.20 Low Water (displace): id=5472, wt=81.000
% 2.95/3.20
% 2.95/3.20 Low Water (displace): id=6319, wt=80.000
% 2.95/3.20
% 2.95/3.20 Low Water (displace): id=5474, wt=79.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=5896, wt=75.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=6021, wt=74.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=6323, wt=72.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=5902, wt=69.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=6326, wt=68.000
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=23.000, iters=3377
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=5892, wt=67.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=6041, wt=66.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=6322, wt=64.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=11707, wt=18.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=11825, wt=17.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=11842, wt=16.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=12947, wt=15.000
% 3.93/4.21
% 3.93/4.21 Low Water (displace): id=13081, wt=13.000
% 3.93/4.21
% 3.93/4.21 Low Water (keep): wt=22.000, iters=3341
% 3.93/4.21
% 3.93/4.21 ============================== PROOF =================================
% 3.93/4.21 % SZS status Theorem
% 3.93/4.21 % SZS output start Refutation
% 3.93/4.21
% 3.93/4.21 % Proof 1 at 3.16 (+ 0.08) seconds.
% 3.93/4.21 % Length of proof is 33.
% 3.93/4.21 % Level of proof is 6.
% 3.93/4.21 % Maximum clause weight is 14.000.
% 3.93/4.21 % Given clauses 843.
% 3.93/4.21
% 3.93/4.21 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 3.93/4.21 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 3.93/4.21 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].
% 3.93/4.21 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 3.93/4.21 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 3.93/4.21 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].
% 3.93/4.21 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 3.93/4.21 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].
% 3.93/4.21 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 3.93/4.21 17 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (multiplication(multiplication(X1,X0),c(X2)) = zero -> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.93/4.21 20 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.93/4.21 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 3.93/4.21 27 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 3.93/4.21 29 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 3.93/4.21 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 3.93/4.21 31 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 3.93/4.21 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 3.93/4.21 34 multiplication(multiplication(c2,c1),c(c3)) = zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.93/4.21 37 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 3.93/4.21 38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 3.93/4.21 39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(38),flip(a)].
% 3.93/4.21 42 multiplication(multiplication(c2,c1),c3) != multiplication(c2,c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 3.93/4.21 43 multiplication(c2,multiplication(c1,c3)) != multiplication(c2,c1). [copy(42),rewrite([37(5)])].
% 3.93/4.21 46 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 3.93/4.21 47 -complement(A,B) | addition(A,B) = one. [copy(46),rewrite([33(2)])].
% 3.93/4.21 55 c(c3) != A | complement(c3,A). [resolve(23,a,20,a)].
% 3.93/4.21 62 multiplication(c2,multiplication(c1,c(c3))) = zero. [back_rewrite(34),rewrite([37(6)])].
% 3.93/4.21 67 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(27(a,1),39(a,2,2)),rewrite([31(3),33(3)])].
% 3.93/4.21 89 complement(c3,c(c3)). [resolve(55,a,30,a(flip)),rewrite([30(5)])].
% 3.93/4.21 101 multiplication(c2,addition(A,multiplication(c1,c(c3)))) = multiplication(c2,A). [para(62(a,1),39(a,1,1)),rewrite([67(4),33(8)]),flip(a)].
% 3.93/4.21 118 addition(c3,c(c3)) = one. [resolve(89,a,47,a)].
% 3.93/4.21 435 multiplication(c2,multiplication(c1,addition(A,c(c3)))) = multiplication(c2,multiplication(c1,A)). [para(39(a,1),101(a,1,2))].
% 3.93/4.21 14429 $F. [para(118(a,1),435(a,1,2,2)),rewrite([29(4)]),flip(a),unit_del(a,43)].
% 3.93/4.21
% 3.93/4.21 % SZS output end Refutation
% 3.93/4.21 ============================== end of proof ==========================
% 3.93/4.21
% 3.93/4.21 ============================== STATISTICS ============================
% 3.93/4.21
% 3.93/4.21 Given=843. Generated=111019. Kept=14396. proofs=1.
% 3.93/4.21 Usable=701. Sos=9999. Demods=2910. Limbo=1, Disabled=3733. Hints=0.
% 3.93/4.21 Megabytes=15.40.
% 3.93/4.21 User_CPU=3.16, System_CPU=0.08, Wall_clock=3.
% 3.93/4.21
% 3.93/4.21 ============================== end of statistics =====================
% 3.93/4.21
% 3.93/4.21 ============================== end of search =========================
% 3.93/4.21
% 3.93/4.21 THEOREM PROVED
% 3.93/4.21 % SZS status Theorem
% 3.93/4.21
% 3.93/4.21 Exiting with 1 proof.
% 3.93/4.21
% 3.93/4.21 Process 16441 exit (max_proofs) Thu Jun 16 14:49:54 2022
% 3.93/4.21 Prover9 interrupted
%------------------------------------------------------------------------------