TSTP Solution File: HEN009-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 13:00:55 EDT 2022
% Result : Unsatisfiable 0.69s 1.04s
% Output : Refutation 0.69s
% 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 : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.32 % Computer : n018.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Fri Jul 1 13:37:02 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.69/1.04 ============================== Prover9 ===============================
% 0.69/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.69/1.04 Process 16963 was started by sandbox on n018.cluster.edu,
% 0.69/1.04 Fri Jul 1 13:37:03 2022
% 0.69/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16810_n018.cluster.edu".
% 0.69/1.04 ============================== end of head ===========================
% 0.69/1.04
% 0.69/1.04 ============================== INPUT =================================
% 0.69/1.04
% 0.69/1.04 % Reading from file /tmp/Prover9_16810_n018.cluster.edu
% 0.69/1.04
% 0.69/1.04 set(prolog_style_variables).
% 0.69/1.04 set(auto2).
% 0.69/1.04 % set(auto2) -> set(auto).
% 0.69/1.04 % set(auto) -> set(auto_inference).
% 0.69/1.04 % set(auto) -> set(auto_setup).
% 0.69/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.69/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/1.04 % set(auto) -> set(auto_limits).
% 0.69/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/1.04 % set(auto) -> set(auto_denials).
% 0.69/1.04 % set(auto) -> set(auto_process).
% 0.69/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.69/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.69/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.69/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.69/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.69/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.69/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.69/1.04 % set(auto2) -> assign(stats, some).
% 0.69/1.04 % set(auto2) -> clear(echo_input).
% 0.69/1.04 % set(auto2) -> set(quiet).
% 0.69/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.69/1.04 % set(auto2) -> clear(print_given).
% 0.69/1.04 assign(lrs_ticks,-1).
% 0.69/1.04 assign(sos_limit,10000).
% 0.69/1.04 assign(order,kbo).
% 0.69/1.04 set(lex_order_vars).
% 0.69/1.04 clear(print_given).
% 0.69/1.04
% 0.69/1.04 % formulas(sos). % not echoed (12 formulas)
% 0.69/1.04
% 0.69/1.04 ============================== end of input ==========================
% 0.69/1.04
% 0.69/1.04 % From the command line: assign(max_seconds, 300).
% 0.69/1.04
% 0.69/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/1.04
% 0.69/1.04 % Formulas that are not ordinary clauses:
% 0.69/1.04
% 0.69/1.04 ============================== end of process non-clausal formulas ===
% 0.69/1.04
% 0.69/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.69/1.04
% 0.69/1.04 ============================== PREDICATE ELIMINATION =================
% 0.69/1.04
% 0.69/1.04 ============================== end predicate elimination =============
% 0.69/1.04
% 0.69/1.04 Auto_denials:
% 0.69/1.04 % copying label prove_b_equals_d to answer in negative clause
% 0.69/1.04 % copying label part_of_theorem to answer in negative clause
% 0.69/1.04 % assign(max_proofs, 2). % (Horn set with more than one neg. clause)
% 0.69/1.04
% 0.69/1.04 Term ordering decisions:
% 0.69/1.04 Function symbol KB weights: identity=1. zero=1. b=1. c=1. a=1. d=1. divide=1.
% 0.69/1.04
% 0.69/1.04 ============================== end of process initial clauses ========
% 0.69/1.04
% 0.69/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.69/1.04
% 0.69/1.04 ============================== end of clauses for search =============
% 0.69/1.04
% 0.69/1.04 ============================== SEARCH ================================
% 0.69/1.04
% 0.69/1.04 % Starting search at 0.01 seconds.
% 0.69/1.04
% 0.69/1.04 ============================== PROOF =================================
% 0.69/1.04 % SZS status Unsatisfiable
% 0.69/1.04 % SZS output start Refutation
% 0.69/1.04
% 0.69/1.04 % Proof 1 at 0.09 (+ 0.01) seconds: prove_b_equals_d.
% 0.69/1.04 % Length of proof is 62.
% 0.69/1.04 % Level of proof is 16.
% 0.69/1.04 % Maximum clause weight is 13.000.
% 0.69/1.04 % Given clauses 126.
% 0.69/1.04
% 0.69/1.04 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 0.69/1.04 2 less_equal(A,identity) # label(identity_is_largest) # label(axiom). [assumption].
% 0.69/1.04 3 less_equal(divide(A,B),A) # label(quotient_smaller_than_numerator) # label(axiom). [assumption].
% 0.69/1.04 4 divide(identity,a) = b # label(id_divide_a_is_b) # label(hypothesis). [assumption].
% 0.69/1.04 5 b = divide(identity,a). [copy(4),flip(a)].
% 0.69/1.04 6 divide(identity,b) = c # label(id_divide_b_is_c) # label(hypothesis). [assumption].
% 0.69/1.04 7 divide(identity,divide(identity,a)) = c. [copy(6),rewrite([5(2)])].
% 0.69/1.04 8 divide(identity,c) = d # label(id_divide_c_is_d) # label(hypothesis). [assumption].
% 0.69/1.04 9 d = divide(identity,c). [copy(8),flip(a)].
% 0.69/1.04 10 less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) # label(quotient_property) # label(axiom). [assumption].
% 0.69/1.04 11 b != d # label(prove_b_equals_d) # label(negated_conjecture) # answer(prove_b_equals_d). [assumption].
% 0.69/1.04 12 divide(identity,a) != divide(identity,c) # answer(prove_b_equals_d). [copy(11),rewrite([5(1),9(4)])].
% 0.69/1.04 14 -less_equal(A,B) | divide(A,B) = zero # label(quotient_less_equal1) # label(axiom). [assumption].
% 0.69/1.04 15 divide(A,B) != zero | less_equal(A,B) # label(quotient_less_equal2) # label(axiom). [assumption].
% 0.69/1.04 16 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.69/1.04 17 divide(identity,a) = c_0. [new_symbol(12)].
% 0.69/1.04 18 divide(identity,c) != c_0 # answer(prove_b_equals_d). [back_rewrite(12),rewrite([17(3)]),flip(a)].
% 0.69/1.04 19 divide(identity,c_0) = c. [back_rewrite(7),rewrite([17(4)])].
% 0.69/1.04 22 divide(divide(A,B),A) = zero. [hyper(14,a,3,a)].
% 0.69/1.04 23 divide(A,identity) = zero. [hyper(14,a,2,a)].
% 0.69/1.04 24 divide(zero,A) = zero. [hyper(14,a,1,a)].
% 0.69/1.04 25 less_equal(divide(c_0,divide(A,a)),divide(divide(identity,A),a)). [para(17(a,1),10(a,1,1))].
% 0.69/1.04 26 less_equal(divide(divide(A,a),c_0),zero). [para(17(a,1),10(a,1,2)),rewrite([23(6),24(7)])].
% 0.69/1.04 27 less_equal(divide(divide(identity,A),divide(a,A)),divide(c_0,A)). [para(17(a,1),10(a,2,1))].
% 0.69/1.04 30 less_equal(divide(divide(A,c_0),c),zero). [para(19(a,1),10(a,1,2)),rewrite([23(6),24(7)])].
% 0.69/1.04 45 less_equal(divide(divide(A,B),divide(identity,B)),zero). [para(23(a,1),10(a,2,1)),rewrite([24(6)])].
% 0.69/1.04 47 less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)). [para(24(a,1),10(a,1,2))].
% 0.69/1.04 51 less_equal(divide(divide(A,A),divide(B,A)),zero). [para(22(a,1),10(a,2))].
% 0.69/1.04 55 divide(divide(A,a),c_0) = zero. [hyper(16,a,1,a,b,26,a),flip(a)].
% 0.69/1.04 56 less_equal(divide(c_0,c_0),zero). [para(17(a,1),26(a,1,1))].
% 0.69/1.04 57 divide(c_0,c_0) = zero. [hyper(16,a,1,a,b,56,a),flip(a)].
% 0.69/1.04 67 divide(divide(A,c_0),c) = zero. [hyper(16,a,1,a,b,30,a),flip(a)].
% 0.69/1.04 75 less_equal(divide(c,divide(a,c_0)),zero). [para(19(a,1),27(a,1,1)),rewrite([57(8)])].
% 0.69/1.04 76 less_equal(divide(A,a),c_0). [hyper(15,a,55,a)].
% 0.69/1.04 83 less_equal(divide(A,c_0),c). [hyper(15,a,67,a)].
% 0.69/1.04 86 less_equal(divide(divide(A,c),divide(c_0,c)),zero). [para(67(a,1),10(a,2))].
% 0.69/1.04 94 divide(c,divide(a,c_0)) = zero. [hyper(16,a,1,a,b,75,a),flip(a)].
% 0.69/1.04 96 less_equal(c,divide(a,c_0)). [hyper(15,a,94,a)].
% 0.69/1.04 101 divide(a,c_0) = c. [hyper(16,a,83,a,b,96,a)].
% 0.69/1.04 108 divide(c,a) = zero. [para(101(a,1),22(a,1,1))].
% 0.69/1.04 114 less_equal(divide(c_0,zero),divide(divide(identity,c),a)). [para(108(a,1),25(a,1,2))].
% 0.69/1.04 187 divide(divide(A,B),divide(identity,B)) = zero. [hyper(16,a,1,a,b,45,a),flip(a)].
% 0.69/1.04 189 less_equal(divide(divide(A,A),zero),zero). [para(24(a,1),51(a,1,2))].
% 0.69/1.04 190 divide(divide(A,A),zero) = zero. [hyper(16,a,1,a,b,189,a),flip(a)].
% 0.69/1.04 217 less_equal(divide(A,A),zero). [hyper(15,a,190,a)].
% 0.69/1.04 224 divide(A,A) = zero. [hyper(16,a,1,a,b,217,a),flip(a)].
% 0.69/1.04 241 divide(divide(A,c),divide(c_0,c)) = zero. [hyper(16,a,1,a,b,86,a),flip(a)].
% 0.69/1.04 259 less_equal(divide(A,B),divide(identity,B)). [hyper(15,a,187,a)].
% 0.69/1.04 277 less_equal(divide(A,c),divide(c_0,c)). [hyper(15,a,241,a)].
% 0.69/1.04 287 divide(c_0,c) = divide(identity,c). [hyper(16,a,259,a,b,277,a)].
% 0.69/1.04 288 less_equal(divide(identity,c),c_0). [para(287(a,1),3(a,1))].
% 0.69/1.04 297 -less_equal(c_0,divide(identity,c)) # answer(prove_b_equals_d). [ur(16,b,288,a,c,18,a(flip))].
% 0.69/1.04 397 less_equal(divide(divide(A,divide(A,zero)),zero),zero). [para(224(a,1),47(a,2))].
% 0.69/1.04 408 divide(divide(A,divide(A,zero)),zero) = zero. [hyper(16,a,1,a,b,397,a),flip(a)].
% 0.69/1.04 459 less_equal(divide(A,divide(A,zero)),zero). [hyper(15,a,408,a)].
% 0.69/1.04 468 divide(A,divide(A,zero)) = zero. [hyper(16,a,1,a,b,459,a),flip(a)].
% 0.69/1.04 469 less_equal(A,divide(A,zero)). [hyper(15,a,468,a)].
% 0.69/1.04 499 divide(A,zero) = A. [hyper(16,a,3,a,b,469,a)].
% 0.69/1.04 645 less_equal(c_0,divide(divide(identity,c),a)). [back_rewrite(114),rewrite([499(3)])].
% 0.69/1.04 665 divide(divide(identity,c),a) = c_0. [hyper(16,a,76,a,b,645,a)].
% 0.69/1.04 673 less_equal(c_0,divide(identity,c)). [para(665(a,1),3(a,1))].
% 0.69/1.04 674 $F # answer(prove_b_equals_d). [resolve(673,a,297,a)].
% 0.69/1.04
% 0.69/1.04 % SZS output end Refutation
% 0.69/1.04 ============================== end of proof ======================Cputime limit exceeded (core dumped)
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