TSTP Solution File: HEN010-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN010-3 : 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 13:00:57 EDT 2022
% Result : Unsatisfiable 0.82s 1.14s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN010-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n019.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 : Fri Jul 1 13:07:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.82/1.14 ============================== Prover9 ===============================
% 0.82/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.14 Process 25226 was started by sandbox on n019.cluster.edu,
% 0.82/1.14 Fri Jul 1 13:07:54 2022
% 0.82/1.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25073_n019.cluster.edu".
% 0.82/1.14 ============================== end of head ===========================
% 0.82/1.14
% 0.82/1.14 ============================== INPUT =================================
% 0.82/1.14
% 0.82/1.14 % Reading from file /tmp/Prover9_25073_n019.cluster.edu
% 0.82/1.14
% 0.82/1.14 set(prolog_style_variables).
% 0.82/1.14 set(auto2).
% 0.82/1.14 % set(auto2) -> set(auto).
% 0.82/1.14 % set(auto) -> set(auto_inference).
% 0.82/1.14 % set(auto) -> set(auto_setup).
% 0.82/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.14 % set(auto) -> set(auto_limits).
% 0.82/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.14 % set(auto) -> set(auto_denials).
% 0.82/1.14 % set(auto) -> set(auto_process).
% 0.82/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.14 % set(auto2) -> assign(stats, some).
% 0.82/1.14 % set(auto2) -> clear(echo_input).
% 0.82/1.14 % set(auto2) -> set(quiet).
% 0.82/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.14 % set(auto2) -> clear(print_given).
% 0.82/1.14 assign(lrs_ticks,-1).
% 0.82/1.14 assign(sos_limit,10000).
% 0.82/1.14 assign(order,kbo).
% 0.82/1.14 set(lex_order_vars).
% 0.82/1.14 clear(print_given).
% 0.82/1.14
% 0.82/1.14 % formulas(sos). % not echoed (8 formulas)
% 0.82/1.14
% 0.82/1.14 ============================== end of input ==========================
% 0.82/1.14
% 0.82/1.14 % From the command line: assign(max_seconds, 300).
% 0.82/1.14
% 0.82/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.14
% 0.82/1.14 % Formulas that are not ordinary clauses:
% 0.82/1.14
% 0.82/1.14 ============================== end of process non-clausal formulas ===
% 0.82/1.14
% 0.82/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.14
% 0.82/1.14 ============================== PREDICATE ELIMINATION =================
% 0.82/1.14
% 0.82/1.14 ============================== end predicate elimination =============
% 0.82/1.14
% 0.82/1.14 Auto_denials:
% 0.82/1.14 % copying label prove_property_of_inversion to answer in negative clause
% 0.82/1.14
% 0.82/1.14 Term ordering decisions:
% 0.82/1.14 Function symbol KB weights: zero=1. identity=1. a=1. divide=1.
% 0.82/1.14
% 0.82/1.14 ============================== end of process initial clauses ========
% 0.82/1.14
% 0.82/1.14 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.14
% 0.82/1.14 ============================== end of clauses for search =============
% 0.82/1.14
% 0.82/1.14 ============================== SEARCH ================================
% 0.82/1.14
% 0.82/1.14 % Starting search at 0.01 seconds.
% 0.82/1.14
% 0.82/1.14 ============================== PROOF =================================
% 0.82/1.14 % SZS status Unsatisfiable
% 0.82/1.14 % SZS output start Refutation
% 0.82/1.14
% 0.82/1.14 % Proof 1 at 0.14 (+ 0.01) seconds: prove_property_of_inversion.
% 0.82/1.14 % Length of proof is 43.
% 0.82/1.14 % Level of proof is 18.
% 0.82/1.14 % Maximum clause weight is 19.000.
% 0.82/1.14 % Given clauses 86.
% 0.82/1.14
% 0.82/1.14 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 0.82/1.14 2 less_equal(A,identity) # label(identity_is_largest) # label(axiom). [assumption].
% 0.82/1.14 3 less_equal(divide(A,B),A) # label(quotient_smaller_than_numerator) # label(axiom). [assumption].
% 0.82/1.14 4 less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) # label(quotient_property) # label(axiom). [assumption].
% 0.82/1.14 5 divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))) # label(prove_property_of_inversion) # label(negated_conjecture) # answer(prove_property_of_inversion). [assumption].
% 0.82/1.14 6 divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a) # answer(prove_property_of_inversion). [copy(5),flip(a)].
% 0.82/1.14 7 -less_equal(A,B) | divide(A,B) = zero # label(quotient_less_equal1) # label(axiom). [assumption].
% 0.82/1.14 8 divide(A,B) != zero | less_equal(A,B) # label(quotient_less_equal2) # label(axiom). [assumption].
% 0.82/1.14 9 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.82/1.14 10 divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero. [hyper(7,a,4,a)].
% 0.82/1.14 11 divide(divide(A,B),A) = zero. [hyper(7,a,3,a)].
% 0.82/1.14 12 divide(A,identity) = zero. [hyper(7,a,2,a)].
% 0.82/1.14 13 divide(zero,A) = zero. [hyper(7,a,1,a)].
% 0.82/1.14 14 -less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) # answer(prove_property_of_inversion). [ur(9,b,3,a,c,6,a(flip))].
% 0.82/1.14 25 less_equal(divide(divide(A,B),divide(identity,B)),zero). [para(12(a,1),4(a,2,1)),rewrite([13(6)])].
% 0.82/1.14 27 less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)). [para(13(a,1),4(a,1,2))].
% 0.82/1.14 29 less_equal(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)). [para(11(a,1),4(a,1,2))].
% 0.82/1.14 31 less_equal(divide(divide(A,A),divide(B,A)),zero). [para(11(a,1),4(a,2))].
% 0.82/1.14 33 divide(divide(divide(divide(A,B),C),divide(A,C)),zero) = zero. [para(11(a,1),10(a,1,2,1)),rewrite([13(6)])].
% 0.82/1.14 35 divide(divide(A,B),divide(identity,B)) = zero. [hyper(9,a,1,a,b,25,a),flip(a)].
% 0.82/1.14 51 less_equal(divide(divide(A,A),zero),zero). [para(13(a,1),31(a,1,2))].
% 0.82/1.14 52 divide(divide(A,A),zero) = zero. [hyper(9,a,1,a,b,51,a),flip(a)].
% 0.82/1.14 53 less_equal(divide(A,A),zero). [hyper(8,a,52,a)].
% 0.82/1.14 60 divide(A,A) = zero. [hyper(9,a,1,a,b,53,a),flip(a)].
% 0.82/1.14 79 less_equal(divide(A,B),divide(identity,B)). [hyper(8,a,35,a)].
% 0.82/1.14 105 less_equal(divide(divide(A,divide(A,zero)),zero),zero). [para(60(a,1),27(a,2))].
% 0.82/1.14 107 divide(divide(A,divide(A,zero)),zero) = zero. [hyper(9,a,1,a,b,105,a),flip(a)].
% 0.82/1.14 109 less_equal(divide(A,divide(A,zero)),zero). [hyper(8,a,107,a)].
% 0.82/1.14 141 divide(A,divide(A,zero)) = zero. [hyper(9,a,1,a,b,109,a),flip(a)].
% 0.82/1.14 142 less_equal(A,divide(A,zero)). [hyper(8,a,141,a)].
% 0.82/1.14 148 divide(divide(divide(A,divide(divide(A,B),zero)),divide(B,divide(divide(A,B),zero))),zero) = zero. [para(141(a,1),10(a,1,2))].
% 0.82/1.14 158 divide(A,zero) = A. [hyper(9,a,3,a,b,142,a)].
% 0.82/1.14 163 divide(divide(A,divide(A,B)),divide(B,divide(A,B))) = zero. [back_rewrite(148),rewrite([158(3),158(5),158(7)])].
% 0.82/1.14 197 divide(divide(divide(A,B),C),divide(A,C)) = zero. [back_rewrite(33),rewrite([158(6)])].
% 0.82/1.14 199 less_equal(divide(A,B),divide(divide(A,divide(B,C)),B)). [back_rewrite(29),rewrite([158(3)])].
% 0.82/1.14 237 less_equal(divide(divide(A,B),C),divide(A,C)). [hyper(8,a,197,a)].
% 0.82/1.14 258 less_equal(divide(A,divide(A,B)),divide(B,divide(A,B))). [hyper(8,a,163,a)].
% 0.82/1.14 268 divide(divide(A,divide(B,C)),B) = divide(A,B). [hyper(9,a,237,a,b,199,a)].
% 0.82/1.14 369 divide(identity,divide(identity,A)) = divide(A,divide(identity,A)). [hyper(9,a,79,a,b,258,a),flip(a)].
% 0.82/1.14 372 -less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) # answer(prove_property_of_inversion). [back_rewrite(14),rewrite([369(12,R)])].
% 0.82/1.14 374 less_equal(divide(A,B),divide(A,divide(B,C))). [para(268(a,1),3(a,1))].
% 0.82/1.14 545 less_equal(divide(A,B),divide(A,divide(identity,divide(identity,B)))). [para(369(a,2),374(a,2,2))].
% 0.82/1.14 546 $F # answer(prove_property_of_inversion). [resolve(545,a,372,a)].
% 0.82/1.14
% 0.82/1.14 % SZS output end Refutation
% 0.82/1.14 ============================== end of proof ==========================
% 0.82/1.14
% 0.82/1.14 ============================== STATISTICS ============================
% 0.82/1.14
% 0.82/1.14 Given=86. Generated=3622. Kept=544. proofs=1.
% 0.82/1.14 Usable=44. Sos=235. Demods=215. Limbo=60, Disabled=212. Hints=0.
% 0.82/1.14 Megabytes=0.92.
% 0.82/1.14 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.82/1.14
% 0.82/1.14 ============================== end of statistics =====================
% 0.82/1.14
% 0.82/1.14 ============================== end of search =========================
% 0.82/1.14
% 0.82/1.14 THEOREM PROVED
% 0.82/1.14 % SZS status Unsatisfiable
% 0.82/1.14
% 0.82/1.14 Exiting with 1 proof.
% 0.82/1.14
% 0.82/1.14 Process 25226 exit (max_proofs) Fri Jul 1 13:07:54 2022
% 0.82/1.14 Prover9 interrupted
%------------------------------------------------------------------------------