TSTP Solution File: KLE035+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 02:21:54 EDT 2022
% Result : Theorem 2.33s 2.60s
% Output : Refutation 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.37 % Computer : n004.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 10:33:24 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.52/1.07 ============================== Prover9 ===============================
% 0.52/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.52/1.07 Process 25784 was started by sandbox2 on n004.cluster.edu,
% 0.52/1.07 Thu Jun 16 10:33:24 2022
% 0.52/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25630_n004.cluster.edu".
% 0.52/1.07 ============================== end of head ===========================
% 0.52/1.07
% 0.52/1.07 ============================== INPUT =================================
% 0.52/1.07
% 0.52/1.07 % Reading from file /tmp/Prover9_25630_n004.cluster.edu
% 0.52/1.07
% 0.52/1.07 set(prolog_style_variables).
% 0.52/1.07 set(auto2).
% 0.52/1.07 % set(auto2) -> set(auto).
% 0.52/1.07 % set(auto) -> set(auto_inference).
% 0.52/1.07 % set(auto) -> set(auto_setup).
% 0.52/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.52/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.52/1.07 % set(auto) -> set(auto_limits).
% 0.52/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.52/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.52/1.07 % set(auto) -> set(auto_denials).
% 0.52/1.07 % set(auto) -> set(auto_process).
% 0.52/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.52/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.52/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.52/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.52/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.52/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.52/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.52/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.52/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.52/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.52/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.52/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.52/1.07 % set(auto2) -> assign(stats, some).
% 0.52/1.07 % set(auto2) -> clear(echo_input).
% 0.52/1.07 % set(auto2) -> set(quiet).
% 0.52/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.52/1.07 % set(auto2) -> clear(print_given).
% 0.52/1.07 assign(lrs_ticks,-1).
% 0.52/1.07 assign(sos_limit,10000).
% 0.52/1.07 assign(order,kbo).
% 0.52/1.07 set(lex_order_vars).
% 0.52/1.07 clear(print_given).
% 0.52/1.07
% 0.52/1.07 % formulas(sos). % not echoed (19 formulas)
% 0.52/1.07
% 0.52/1.07 ============================== end of input ==========================
% 0.52/1.07
% 0.52/1.07 % From the command line: assign(max_seconds, 300).
% 0.52/1.07
% 0.52/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.52/1.07
% 0.52/1.07 % Formulas that are not ordinary clauses:
% 0.52/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 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].
% 0.52/1.07 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 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].
% 0.52/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 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].
% 0.52/1.07 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].
% 0.52/1.07 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.52/1.07 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].
% 1.96/2.24 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 17 (all X0 all X1 (test(X0) & test(X1) -> c(addition(X0,X1)) = multiplication(c(X0),c(X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 18 (all X0 all X1 (test(X0) & test(X1) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.24 19 -(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].
% 1.96/2.24
% 1.96/2.24 ============================== end of process non-clausal formulas ===
% 1.96/2.24
% 1.96/2.24 ============================== PROCESS INITIAL CLAUSES ===============
% 1.96/2.24
% 1.96/2.24 ============================== PREDICATE ELIMINATION =================
% 1.96/2.24 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 1.96/2.24 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 1.96/2.24 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 1.96/2.24 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 1.96/2.24 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 1.96/2.24 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 1.96/2.24 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 1.96/2.24 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 1.96/2.24 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 1.96/2.24 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 1.96/2.24 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 1.96/2.24 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 1.96/2.24 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 1.96/2.24 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 1.96/2.24 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 1.96/2.24 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 1.96/2.24 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 1.96/2.24 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 1.96/2.24
% 1.96/2.24 ============================== end predicate elimination =============
% 1.96/2.24
% 1.96/2.24 Auto_denials: (non-Horn, no changes).
% 1.96/2.24
% 1.96/2.24 Term ordering decisions:
% 1.96/2.24 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. multiplication=1. addition=1. c=1. f1=1.
% 1.96/2.24
% 1.96/2.24 ============================== end of process initial clauses ========
% 1.96/2.24
% 1.96/2.24 ============================== CLAUSES FOR SEARCH ====================
% 1.96/2.24
% 1.96/2.24 ============================== end of clauses for search =============
% 1.96/2.24
% 1.96/2.24 ============================== SEARCH ================================
% 1.96/2.24
% 1.96/2.24 % Starting search at 0.02 seconds.
% 1.96/2.24
% 1.96/2.24 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 55 (0.00 of 0.85 sec).
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=75.000, iters=3393
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=65.000, iters=3373
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=61.000, iters=3469
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=53.000, iters=3385
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=47.000, iters=3533
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=41.000, iters=3381
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=40.000, iters=3412
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=39.000, iters=3380
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=37.000, iters=3393
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=35.000, iters=3365
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=34.000, iters=3361
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=32.000, iters=3435
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=31.000, iters=3384
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=30.000, iters=3360
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=29.000, iters=3410
% 1.96/2.24
% 1.96/2.24 Low Water (keep): wt=28.000, iters=3341
% 2.33/2.60
% 2.33/2.60 Low Water (keep): wt=27.000, iters=3387
% 2.33/2.60
% 2.33/2.60 Low Water (keep): wt=26.000, iters=3333
% 2.33/2.60
% 2.33/2.60 Low Water (keep): wt=25.000, iters=3340
% 2.33/2.60
% 2.33/2.60 ============================== PROOF =================================
% 2.33/2.60 % SZS status Theorem
% 2.33/2.60 % SZS output start Refutation
% 2.33/2.60
% 2.33/2.60 % Proof 1 at 1.52 (+ 0.03) seconds.
% 2.33/2.60 % Length of proof is 31.
% 2.33/2.60 % Level of proof is 7.
% 2.33/2.60 % Maximum clause weight is 15.000.
% 2.33/2.60 % Given clauses 757.
% 2.33/2.60
% 2.33/2.60 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.60 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.60 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].
% 2.33/2.60 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].
% 2.33/2.60 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].
% 2.33/2.60 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.60 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.60 19 -(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].
% 2.33/2.60 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.33/2.60 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.33/2.60 37 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.33/2.60 38 leq(multiplication(multiplication(c3,c1),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.33/2.60 39 leq(multiplication(multiplication(c3,c2),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.33/2.60 42 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.33/2.60 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.33/2.60 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)].
% 2.33/2.60 45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.33/2.60 46 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(45),flip(a)].
% 2.33/2.60 47 -leq(multiplication(multiplication(c3,addition(c1,c2)),c(c4)),zero) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.33/2.60 48 -leq(multiplication(c3,multiplication(addition(c1,c2),c(c4))),zero). [copy(47),rewrite([42(8)])].
% 2.33/2.60 49 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.33/2.60 50 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.33/2.60 66 leq(multiplication(c3,multiplication(c2,c(c4))),zero). [back_rewrite(39),rewrite([42(6)])].
% 2.33/2.60 67 leq(multiplication(c3,multiplication(c1,c(c4))),zero). [back_rewrite(38),rewrite([42(6)])].
% 2.33/2.60 73 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),44(a,2,2)),rewrite([34(3),37(3)])].
% 2.33/2.60 79 multiplication(c3,multiplication(addition(c1,c2),c(c4))) != zero. [ur(50,a,48,a),rewrite([37(10),73(10)])].
% 2.33/2.60 131 multiplication(c3,multiplication(c2,c(c4))) = zero. [resolve(66,a,49,a),rewrite([37(8),73(8)])].
% 2.33/2.60 132 multiplication(c3,multiplication(c1,c(c4))) = zero. [resolve(67,a,49,a),rewrite([37(8),73(8)])].
% 2.33/2.60 530 multiplication(c3,addition(A,multiplication(c2,c(c4)))) = multiplication(c3,A). [para(131(a,1),44(a,1,1)),rewrite([73(4),37(8)]),flip(a)].
% 2.33/2.60 10776 multiplication(c3,multiplication(addition(A,c2),c(c4))) = multiplication(c3,multiplication(A,c(c4))). [para(46(a,1),530(a,1,2))].
% 2.33/2.60 10805 $F. [back_rewrite(79),rewrite([10776(8),132(6)]),xx(a)].
% 2.33/2.60
% 2.33/2.60 % SZS output end Refutation
% 2.33/2.60 ============================== end of proof ==========================
% 2.33/2.60
% 2.33/2.60 ============================== STATISTICS ============================
% 2.33/2.60
% 2.33/2.60 Given=757. Generated=55956. Kept=10770. proofs=1.
% 2.33/2.60 Usable=587. Sos=8106. Demods=2221. Limbo=29, Disabled=2087. Hints=0.
% 2.33/2.60 Megabytes=11.56.
% 2.33/2.60 User_CPU=1.52, System_CPU=0.03, Wall_clock=2.
% 2.33/2.60
% 2.33/2.60 ============================== end of statistics =====================
% 2.33/2.60
% 2.33/2.60 ============================== end of search =========================
% 2.33/2.60
% 2.33/2.60 THEOREM PROVED
% 2.33/2.60 % SZS status Theorem
% 2.33/2.60
% 2.33/2.60 Exiting with 1 proof.
% 2.33/2.60
% 2.33/2.60 Process 25784 exit (max_proofs) Thu Jun 16 10:33:26 2022
% 2.33/2.60 Prover9 interrupted
%------------------------------------------------------------------------------