TSTP Solution File: KLE090-10 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 02:22:11 EDT 2022
% Result : Unsatisfiable 2.65s 2.95s
% Output : Refutation 2.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n021.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 13:56:30 EDT 2022
% 0.12/0.35 % CPUTime :
% 2.65/2.95 ============================== Prover9 ===============================
% 2.65/2.95 Prover9 (32) version 2009-11A, November 2009.
% 2.65/2.95 Process 22237 was started by sandbox2 on n021.cluster.edu,
% 2.65/2.95 Thu Jun 16 13:56:30 2022
% 2.65/2.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22082_n021.cluster.edu".
% 2.65/2.95 ============================== end of head ===========================
% 2.65/2.95
% 2.65/2.95 ============================== INPUT =================================
% 2.65/2.95
% 2.65/2.95 % Reading from file /tmp/Prover9_22082_n021.cluster.edu
% 2.65/2.95
% 2.65/2.95 set(prolog_style_variables).
% 2.65/2.95 set(auto2).
% 2.65/2.95 % set(auto2) -> set(auto).
% 2.65/2.95 % set(auto) -> set(auto_inference).
% 2.65/2.95 % set(auto) -> set(auto_setup).
% 2.65/2.95 % set(auto_setup) -> set(predicate_elim).
% 2.65/2.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.65/2.95 % set(auto) -> set(auto_limits).
% 2.65/2.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.65/2.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.65/2.95 % set(auto) -> set(auto_denials).
% 2.65/2.95 % set(auto) -> set(auto_process).
% 2.65/2.95 % set(auto2) -> assign(new_constants, 1).
% 2.65/2.95 % set(auto2) -> assign(fold_denial_max, 3).
% 2.65/2.95 % set(auto2) -> assign(max_weight, "200.000").
% 2.65/2.95 % set(auto2) -> assign(max_hours, 1).
% 2.65/2.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.65/2.95 % set(auto2) -> assign(max_seconds, 0).
% 2.65/2.95 % set(auto2) -> assign(max_minutes, 5).
% 2.65/2.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.65/2.95 % set(auto2) -> set(sort_initial_sos).
% 2.65/2.95 % set(auto2) -> assign(sos_limit, -1).
% 2.65/2.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.65/2.95 % set(auto2) -> assign(max_megs, 400).
% 2.65/2.95 % set(auto2) -> assign(stats, some).
% 2.65/2.95 % set(auto2) -> clear(echo_input).
% 2.65/2.95 % set(auto2) -> set(quiet).
% 2.65/2.95 % set(auto2) -> clear(print_initial_clauses).
% 2.65/2.95 % set(auto2) -> clear(print_given).
% 2.65/2.95 assign(lrs_ticks,-1).
% 2.65/2.95 assign(sos_limit,10000).
% 2.65/2.95 assign(order,kbo).
% 2.65/2.95 set(lex_order_vars).
% 2.65/2.95 clear(print_given).
% 2.65/2.95
% 2.65/2.95 % formulas(sos). % not echoed (25 formulas)
% 2.65/2.95
% 2.65/2.95 ============================== end of input ==========================
% 2.65/2.95
% 2.65/2.95 % From the command line: assign(max_seconds, 300).
% 2.65/2.95
% 2.65/2.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.65/2.95
% 2.65/2.95 % Formulas that are not ordinary clauses:
% 2.65/2.95
% 2.65/2.95 ============================== end of process non-clausal formulas ===
% 2.65/2.95
% 2.65/2.95 ============================== PROCESS INITIAL CLAUSES ===============
% 2.65/2.95
% 2.65/2.95 ============================== PREDICATE ELIMINATION =================
% 2.65/2.95
% 2.65/2.95 ============================== end predicate elimination =============
% 2.65/2.95
% 2.65/2.95 Auto_denials:
% 2.65/2.95 % copying label goals_1 to answer in negative clause
% 2.65/2.95
% 2.65/2.95 Term ordering decisions:
% 2.65/2.95 Function symbol KB weights: zero=1. one=1. true=1. sK1_goals_X1=1. sK2_goals_X0=1. multiplication=1. addition=1. leq=1. antidomain=1. coantidomain=1. codomain=1. domain=1. ifeq=1. ifeq2=1.
% 2.65/2.95
% 2.65/2.95 ============================== end of process initial clauses ========
% 2.65/2.95
% 2.65/2.95 ============================== CLAUSES FOR SEARCH ====================
% 2.65/2.95
% 2.65/2.95 ============================== end of clauses for search =============
% 2.65/2.95
% 2.65/2.95 ============================== SEARCH ================================
% 2.65/2.95
% 2.65/2.95 % Starting search at 0.01 seconds.
% 2.65/2.95
% 2.65/2.95 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 0.83 sec).
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=41.000, iters=3408
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=37.000, iters=3353
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=35.000, iters=3442
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=33.000, iters=3336
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=31.000, iters=3335
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=29.000, iters=3378
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=27.000, iters=3358
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=25.000, iters=3360
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=24.000, iters=3338
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=23.000, iters=3359
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=22.000, iters=3341
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=21.000, iters=3339
% 2.65/2.95
% 2.65/2.95 Low Water (keep): wt=20.000, iters=3365
% 2.65/2.95
% 2.65/2.95 ============================== PROOF =================================
% 2.65/2.95 % SZS status Unsatisfiable
% 2.65/2.95 % SZS output start Refutation
% 2.65/2.95
% 2.65/2.95 % Proof 1 at 1.88 (+ 0.06) seconds: goals_1.
% 2.65/2.95 % Length of proof is 48.
% 2.65/2.95 % Level of proof is 12.
% 2.65/2.95 % Maximum clause weight is 24.000.
% 2.65/2.95 % Given clauses 753.
% 2.65/2.95
% 2.65/2.95 1 addition(A,zero) = A # label(additive_identity) # label(axiom). [assumption].
% 2.65/2.95 2 addition(A,A) = A # label(additive_idempotence) # label(axiom). [assumption].
% 2.65/2.95 3 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [assumption].
% 2.65/2.95 4 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [assumption].
% 2.65/2.95 5 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [assumption].
% 2.65/2.95 7 addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1 # label(goals) # label(negated_conjecture). [assumption].
% 2.65/2.95 8 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [assumption].
% 2.65/2.95 12 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 2.65/2.95 13 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 2.65/2.95 14 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [assumption].
% 2.65/2.95 15 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [assumption].
% 2.65/2.95 16 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(15),rewrite([14(4)])].
% 2.65/2.95 19 addition(A,addition(B,C)) = addition(addition(A,B),C) # label(additive_associativity) # label(axiom). [assumption].
% 2.65/2.95 20 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(19),rewrite([14(4)])].
% 2.65/2.95 23 ifeq(leq(A,B),true,addition(A,B),B) = B # label(order_1) # label(axiom). [assumption].
% 2.65/2.95 24 ifeq2(addition(A,B),B,leq(A,B),true) = true # label(order) # label(axiom). [assumption].
% 2.65/2.95 25 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [assumption].
% 2.65/2.95 26 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(25),flip(a)].
% 2.65/2.95 27 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [assumption].
% 2.65/2.95 28 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(27),flip(a)].
% 2.65/2.95 29 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))) # label(domain2) # label(axiom). [assumption].
% 2.65/2.95 31 addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0) # label(goals_1) # label(negated_conjecture) # answer(goals_1). [assumption].
% 2.65/2.95 32 addition(sK1_goals_X1,sK2_goals_X0) = sK1_goals_X1. [back_rewrite(7),rewrite([14(3)])].
% 2.65/2.95 33 antidomain(one) = zero. [para(8(a,1),3(a,1)),flip(a)].
% 2.65/2.95 35 addition(A,addition(A,B)) = addition(A,B). [para(20(a,1),2(a,1)),rewrite([14(1),14(2),20(2,R),2(1),14(3)])].
% 2.65/2.95 50 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(1(a,1),26(a,2,2)),rewrite([5(3),14(3)])].
% 2.65/2.95 52 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(8(a,1),26(a,1,1)),rewrite([50(4)]),flip(a)].
% 2.65/2.95 54 ifeq(leq(multiplication(A,B),multiplication(A,C)),true,multiplication(A,addition(B,C)),multiplication(A,C)) = multiplication(A,C). [para(26(a,1),23(a,1,3))].
% 2.65/2.95 66 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))). [para(8(a,1),29(a,1,1,1))].
% 2.65/2.95 83 addition(zero,antidomain(zero)) = one. [para(33(a,1),16(a,1,1)),rewrite([33(3)])].
% 2.65/2.95 89 multiplication(A,antidomain(zero)) = A. [para(83(a,1),26(a,2,2)),rewrite([5(2),50(5),3(5)])].
% 2.65/2.95 94 addition(one,antidomain(A)) = one. [para(16(a,1),35(a,1,2)),rewrite([14(3),16(7)])].
% 2.65/2.95 103 antidomain(zero) = one. [para(89(a,1),4(a,1)),flip(a)].
% 2.65/2.95 105 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one. [back_rewrite(66),rewrite([103(2),94(7)]),flip(a)].
% 2.65/2.95 114 addition(A,multiplication(antidomain(B),A)) = A. [para(94(a,1),28(a,2,1)),rewrite([4(2),4(5)])].
% 2.65/2.95 154 leq(zero,multiplication(A,B)) = true. [para(50(a,1),24(a,1,1)),rewrite([12(7)])].
% 2.65/2.95 155 leq(zero,A) = true. [para(3(a,1),154(a,1,2))].
% 2.65/2.95 180 multiplication(antidomain(A),antidomain(antidomain(A))) = zero. [para(105(a,1),8(a,1,1)),rewrite([4(6)])].
% 2.65/2.95 184 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))). [para(180(a,1),28(a,1,1)),rewrite([50(5),14(5)]),flip(a)].
% 2.65/2.95 304 multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero. [para(32(a,1),52(a,1,2)),rewrite([8(4)]),flip(a)].
% 2.65/2.95 311 antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = one. [para(304(a,1),29(a,1,1,1)),rewrite([103(2),94(9)]),flip(a)].
% 2.65/2.95 326 ifeq(leq(multiplication(A,antidomain(B)),multiplication(A,antidomain(antidomain(B)))),true,A,multiplication(A,antidomain(antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [para(16(a,1),54(a,1,3,2)),rewrite([3(9)])].
% 2.65/2.95 359 multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))) = zero. [para(311(a,1),8(a,1,1)),rewrite([4(8)])].
% 2.65/2.95 3321 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(16(a,1),184(a,1,1)),rewrite([4(5)]),flip(a)].
% 2.65/2.95 12510 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(180(a,1),326(a,1,1,1)),rewrite([3321(6),155(5),3321(8),13(7),3321(6)]),flip(a)].
% 2.65/2.95 12511 multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1). [para(359(a,1),326(a,1,1,1)),rewrite([12510(7),155(7),12510(10),13(10),12510(8)]),flip(a)].
% 2.65/2.95 12595 addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK2_goals_X0). [para(12511(a,1),114(a,1,2)),rewrite([14(5)])].
% 2.65/2.95 12596 $F # answer(goals_1). [resolve(12595,a,31,a)].
% 2.65/2.95
% 2.65/2.95 % SZS output end Refutation
% 2.65/2.95 ============================== end of proof ==========================
% 2.65/2.95
% 2.65/2.95 ============================== STATISTICS ============================
% 2.65/2.95
% 2.65/2.95 Given=753. Generated=125216. Kept=12589. proofs=1.
% 2.65/2.95 Usable=587. Sos=8558. Demods=8932. Limbo=3, Disabled=3465. Hints=0.
% 2.65/2.95 Megabytes=14.42.
% 2.65/2.95 User_CPU=1.88, System_CPU=0.06, Wall_clock=2.
% 2.65/2.95
% 2.65/2.95 ============================== end of statistics =====================
% 2.65/2.95
% 2.65/2.95 ============================== end of search =========================
% 2.65/2.95
% 2.65/2.95 THEOREM PROVED
% 2.65/2.95 % SZS status Unsatisfiable
% 2.65/2.95
% 2.65/2.95 Exiting with 1 proof.
% 2.65/2.95
% 2.65/2.95 Process 22237 exit (max_proofs) Thu Jun 16 13:56:32 2022
% 2.65/2.95 Prover9 interrupted
%------------------------------------------------------------------------------