TSTP Solution File: HEN006-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 : Sat Jul 16 13:00:50 EDT 2022
% Result : Unsatisfiable 0.68s 1.00s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n019.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 : Fri Jul 1 14:55:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.68/0.99 ============================== Prover9 ===============================
% 0.68/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.99 Process 23651 was started by sandbox on n019.cluster.edu,
% 0.68/0.99 Fri Jul 1 14:55:39 2022
% 0.68/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23498_n019.cluster.edu".
% 0.68/0.99 ============================== end of head ===========================
% 0.68/0.99
% 0.68/0.99 ============================== INPUT =================================
% 0.68/0.99
% 0.68/0.99 % Reading from file /tmp/Prover9_23498_n019.cluster.edu
% 0.68/0.99
% 0.68/0.99 set(prolog_style_variables).
% 0.68/0.99 set(auto2).
% 0.68/0.99 % set(auto2) -> set(auto).
% 0.68/0.99 % set(auto) -> set(auto_inference).
% 0.68/0.99 % set(auto) -> set(auto_setup).
% 0.68/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.99 % set(auto) -> set(auto_limits).
% 0.68/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.99 % set(auto) -> set(auto_denials).
% 0.68/0.99 % set(auto) -> set(auto_process).
% 0.68/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.68/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.68/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.68/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.68/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.68/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.68/1.00 % set(auto2) -> assign(stats, some).
% 0.68/1.00 % set(auto2) -> clear(echo_input).
% 0.68/1.00 % set(auto2) -> set(quiet).
% 0.68/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.68/1.00 % set(auto2) -> clear(print_given).
% 0.68/1.00 assign(lrs_ticks,-1).
% 0.68/1.00 assign(sos_limit,10000).
% 0.68/1.00 assign(order,kbo).
% 0.68/1.00 set(lex_order_vars).
% 0.68/1.00 clear(print_given).
% 0.68/1.00
% 0.68/1.00 % formulas(sos). % not echoed (12 formulas)
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% 0.68/1.00 ============================== end of input ==========================
% 0.68/1.00
% 0.68/1.00 % From the command line: assign(max_seconds, 300).
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% 0.68/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/1.00
% 0.68/1.00 % Formulas that are not ordinary clauses:
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% 0.68/1.00 ============================== end of process non-clausal formulas ===
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% 0.68/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.68/1.00 ============================== PREDICATE ELIMINATION =================
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% 0.68/1.00 ============================== end predicate elimination =============
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% 0.68/1.00 Auto_denials:
% 0.68/1.00 % copying label prove_a_divide_d_LE_b to answer in negative clause
% 0.68/1.00
% 0.68/1.00 Term ordering decisions:
% 0.68/1.00 Function symbol KB weights: zero=1. identity=1. a=1. b=1. d=1. divide=1.
% 0.68/1.00
% 0.68/1.00 ============================== end of process initial clauses ========
% 0.68/1.00
% 0.68/1.00 ============================== CLAUSES FOR SEARCH ====================
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% 0.68/1.00 ============================== end of clauses for search =============
% 0.68/1.00
% 0.68/1.00 ============================== SEARCH ================================
% 0.68/1.00
% 0.68/1.00 % Starting search at 0.01 seconds.
% 0.68/1.00
% 0.68/1.00 ============================== PROOF =================================
% 0.68/1.00 % SZS status Unsatisfiable
% 0.68/1.00 % SZS output start Refutation
% 0.68/1.00
% 0.68/1.00 % Proof 1 at 0.02 (+ 0.00) seconds: prove_a_divide_d_LE_b.
% 0.68/1.00 % Length of proof is 27.
% 0.68/1.00 % Level of proof is 10.
% 0.68/1.00 % Maximum clause weight is 13.000.
% 0.68/1.00 % Given clauses 53.
% 0.68/1.00
% 0.68/1.00 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 0.68/1.00 3 less_equal(divide(A,B),A) # label(quotient_smaller_than_numerator) # label(axiom). [assumption].
% 0.68/1.00 5 divide(zero,A) = zero # label(zero_divide_anything_is_zero) # label(axiom). [assumption].
% 0.68/1.00 6 divide(A,A) = zero # label(x_divide_x_is_zero) # label(axiom). [assumption].
% 0.68/1.00 7 less_equal(divide(a,b),d) # label(a_divide_b_LE_d) # label(hypothesis). [assumption].
% 0.68/1.00 8 less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) # label(quotient_property) # label(axiom). [assumption].
% 0.68/1.00 9 -less_equal(divide(a,d),b) # label(prove_a_divide_d_LE_b) # label(negated_conjecture) # answer(prove_a_divide_d_LE_b). [assumption].
% 0.68/1.00 10 -less_equal(A,B) | divide(A,B) = zero # label(quotient_less_equal1) # label(axiom). [assumption].
% 0.68/1.00 11 divide(A,B) != zero | less_equal(A,B) # label(quotient_less_equal2) # label(axiom). [assumption].
% 0.68/1.00 12 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.68/1.00 14 less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)). [para(5(a,1),8(a,1,2))].
% 0.68/1.00 18 divide(divide(a,b),d) = zero. [hyper(10,a,7,a)].
% 0.68/1.00 19 divide(divide(A,B),A) = zero. [hyper(10,a,3,a)].
% 0.68/1.00 21 divide(divide(a,d),b) != zero # answer(prove_a_divide_d_LE_b). [ur(11,b,9,a)].
% 0.68/1.00 23 -less_equal(divide(divide(a,d),b),zero) # answer(prove_a_divide_d_LE_b). [ur(12,b,1,a,c,21,a)].
% 0.68/1.00 29 less_equal(divide(divide(a,d),divide(b,d)),zero). [para(18(a,1),8(a,2))].
% 0.68/1.00 30 less_equal(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)). [para(19(a,1),8(a,1,2))].
% 0.68/1.00 37 less_equal(divide(divide(A,divide(A,zero)),zero),zero). [para(6(a,1),14(a,2))].
% 0.68/1.00 43 divide(divide(a,d),divide(b,d)) = zero. [hyper(12,a,1,a,b,29,a),flip(a)].
% 0.68/1.00 44 divide(divide(A,divide(A,zero)),zero) = zero. [hyper(12,a,1,a,b,37,a),flip(a)].
% 0.68/1.00 55 less_equal(divide(A,divide(A,zero)),zero). [hyper(11,a,44,a)].
% 0.68/1.00 58 divide(A,divide(A,zero)) = zero. [hyper(12,a,1,a,b,55,a),flip(a)].
% 0.68/1.00 64 less_equal(A,divide(A,zero)). [hyper(11,a,58,a)].
% 0.68/1.00 71 divide(A,zero) = A. [hyper(12,a,3,a,b,64,a)].
% 0.68/1.00 76 less_equal(divide(A,B),divide(divide(A,divide(B,C)),B)). [back_rewrite(30),rewrite([71(3)])].
% 0.68/1.00 104 less_equal(divide(divide(a,d),b),zero). [para(43(a,1),76(a,2,1)),rewrite([5(8)])].
% 0.68/1.00 105 $F # answer(prove_a_divide_d_LE_b). [resolve(104,a,23,a)].
% 0.68/1.00
% 0.68/1.00 % SZS output end Refutation
% 0.68/1.00 ============================== end of proof ==========================
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% 0.68/1.00 ============================== STATISTICS ============================
% 0.68/1.00
% 0.68/1.00 Given=53. Generated=555. Kept=104. proofs=1.
% 0.68/1.00 Usable=27. Sos=22. Demods=27. Limbo=2, Disabled=64. Hints=0.
% 0.68/1.00 Megabytes=0.11.
% 0.68/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.68/1.00
% 0.68/1.00 ============================== end of statistics =====================
% 0.68/1.00
% 0.68/1.00 ============================== end of search =========================
% 0.68/1.00
% 0.68/1.00 THEOREM PROVED
% 0.68/1.00 % SZS status Unsatisfiable
% 0.68/1.00
% 0.68/1.00 Exiting with 1 proof.
% 0.68/1.00
% 0.68/1.00 Process 23651 exit (max_proofs) Fri Jul 1 14:55:39 2022
% 0.68/1.00 Prover9 interrupted
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