TSTP Solution File: HEN011-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN011-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 13:00:59 EDT 2022
% Result : Unsatisfiable 1.32s 1.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN011-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 14:10:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.32/1.65 ============================== Prover9 ===============================
% 1.32/1.65 Prover9 (32) version 2009-11A, November 2009.
% 1.32/1.65 Process 21558 was started by sandbox on n029.cluster.edu,
% 1.32/1.65 Fri Jul 1 14:10:10 2022
% 1.32/1.65 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21405_n029.cluster.edu".
% 1.32/1.65 ============================== end of head ===========================
% 1.32/1.65
% 1.32/1.65 ============================== INPUT =================================
% 1.32/1.65
% 1.32/1.65 % Reading from file /tmp/Prover9_21405_n029.cluster.edu
% 1.32/1.65
% 1.32/1.65 set(prolog_style_variables).
% 1.32/1.65 set(auto2).
% 1.32/1.65 % set(auto2) -> set(auto).
% 1.32/1.65 % set(auto) -> set(auto_inference).
% 1.32/1.65 % set(auto) -> set(auto_setup).
% 1.32/1.65 % set(auto_setup) -> set(predicate_elim).
% 1.32/1.65 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.32/1.65 % set(auto) -> set(auto_limits).
% 1.32/1.65 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.32/1.65 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.32/1.65 % set(auto) -> set(auto_denials).
% 1.32/1.65 % set(auto) -> set(auto_process).
% 1.32/1.65 % set(auto2) -> assign(new_constants, 1).
% 1.32/1.65 % set(auto2) -> assign(fold_denial_max, 3).
% 1.32/1.65 % set(auto2) -> assign(max_weight, "200.000").
% 1.32/1.65 % set(auto2) -> assign(max_hours, 1).
% 1.32/1.65 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.32/1.65 % set(auto2) -> assign(max_seconds, 0).
% 1.32/1.65 % set(auto2) -> assign(max_minutes, 5).
% 1.32/1.65 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.32/1.65 % set(auto2) -> set(sort_initial_sos).
% 1.32/1.65 % set(auto2) -> assign(sos_limit, -1).
% 1.32/1.65 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.32/1.65 % set(auto2) -> assign(max_megs, 400).
% 1.32/1.65 % set(auto2) -> assign(stats, some).
% 1.32/1.65 % set(auto2) -> clear(echo_input).
% 1.32/1.65 % set(auto2) -> set(quiet).
% 1.32/1.65 % set(auto2) -> clear(print_initial_clauses).
% 1.32/1.65 % set(auto2) -> clear(print_given).
% 1.32/1.65 assign(lrs_ticks,-1).
% 1.32/1.65 assign(sos_limit,10000).
% 1.32/1.65 assign(order,kbo).
% 1.32/1.65 set(lex_order_vars).
% 1.32/1.65 clear(print_given).
% 1.32/1.65
% 1.32/1.65 % formulas(sos). % not echoed (13 formulas)
% 1.32/1.65
% 1.32/1.65 ============================== end of input ==========================
% 1.32/1.65
% 1.32/1.65 % From the command line: assign(max_seconds, 300).
% 1.32/1.65
% 1.32/1.65 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.32/1.65
% 1.32/1.65 % Formulas that are not ordinary clauses:
% 1.32/1.65
% 1.32/1.65 ============================== end of process non-clausal formulas ===
% 1.32/1.65
% 1.32/1.65 ============================== PROCESS INITIAL CLAUSES ===============
% 1.32/1.65
% 1.32/1.65 ============================== PREDICATE ELIMINATION =================
% 1.32/1.65
% 1.32/1.65 ============================== end predicate elimination =============
% 1.32/1.65
% 1.32/1.65 Auto_denials:
% 1.32/1.65 % copying label prove_commutativity to answer in negative clause
% 1.32/1.65 % copying label part_of_theorem to answer in negative clause
% 1.32/1.65 % assign(max_proofs, 2). % (Horn set with more than one neg. clause)
% 1.32/1.65
% 1.32/1.65 Term ordering decisions:
% 1.32/1.65 Function symbol KB weights: identity=1. zero=1. c=1. d=1. a=1. b=1. e=1. g=1. divide=1.
% 1.32/1.65
% 1.32/1.65 ============================== end of process initial clauses ========
% 1.32/1.65
% 1.32/1.65 ============================== CLAUSES FOR SEARCH ====================
% 1.32/1.65
% 1.32/1.65 ============================== end of clauses for search =============
% 1.32/1.65
% 1.32/1.65 ============================== SEARCH ================================
% 1.32/1.65
% 1.32/1.65 % Starting search at 0.01 seconds.
% 1.32/1.65
% 1.32/1.65 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 0.29 sec).
% 1.32/1.65
% 1.32/1.65 ============================== PROOF =================================
% 1.32/1.65 % SZS status Unsatisfiable
% 1.32/1.65 % SZS output start Refutation
% 1.32/1.65
% 1.32/1.65 % Proof 1 at 0.62 (+ 0.02) seconds: prove_commutativity.
% 1.32/1.65 % Length of proof is 121.
% 1.32/1.65 % Level of proof is 27.
% 1.32/1.65 % Maximum clause weight is 25.000.
% 1.32/1.65 % Given clauses 840.
% 1.32/1.65
% 1.32/1.65 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 1.32/1.65 2 less_equal(A,identity) # label(identity_is_largest) # label(axiom). [assumption].
% 1.32/1.65 3 less_equal(divide(A,B),A) # label(quotient_smaller_than_numerator) # label(axiom). [assumption].
% 1.32/1.65 4 divide(identity,a) = c # label(identity_divide_a) # label(hypothesis). [assumption].
% 1.32/1.65 5 divide(identity,b) = d # label(identity_divide_b) # label(hypothesis). [assumption].
% 1.32/1.65 6 divide(identity,c) = e # label(identity_divide_c) # label(hypothesis). [assumption].
% 1.32/1.65 7 divide(identity,d) = g # label(identity_divide_d) # label(hypothesis). [assumption].
% 1.32/1.65 8 less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) # label(quotient_property) # label(axiom). [assumption].
% 1.32/1.65 9 divide(c,g) != divide(d,e) # label(prove_commutativity) # label(negated_conjecture) # answer(prove_commutativity). [assumption].
% 1.32/1.65 10 divide(d,e) != divide(c,g) # answer(prove_commutativity). [copy(9),flip(a)].
% 1.32/1.65 12 -less_equal(A,B) | divide(A,B) = zero # label(quotient_less_equal1) # label(axiom). [assumption].
% 1.32/1.65 13 divide(A,B) != zero | less_equal(A,B) # label(quotient_less_equal2) # label(axiom). [assumption].
% 1.32/1.65 14 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 1.32/1.65 15 divide(d,e) = c_0. [new_symbol(10)].
% 1.32/1.65 16 divide(c,g) != c_0 # answer(prove_commutativity). [back_rewrite(10),rewrite([15(3)]),flip(a)].
% 1.32/1.65 17 less_equal(divide(c,divide(A,a)),divide(divide(identity,A),a)). [para(4(a,1),8(a,1,1))].
% 1.32/1.65 18 less_equal(divide(divide(A,a),c),divide(divide(A,identity),a)). [para(4(a,1),8(a,1,2))].
% 1.32/1.65 19 less_equal(divide(divide(identity,A),divide(a,A)),divide(c,A)). [para(4(a,1),8(a,2,1))].
% 1.32/1.65 20 less_equal(divide(d,divide(A,b)),divide(divide(identity,A),b)). [para(5(a,1),8(a,1,1))].
% 1.32/1.65 22 less_equal(divide(divide(identity,A),divide(b,A)),divide(d,A)). [para(5(a,1),8(a,2,1))].
% 1.32/1.65 24 less_equal(divide(divide(A,c),e),divide(divide(A,identity),c)). [para(6(a,1),8(a,1,2))].
% 1.32/1.65 27 less_equal(divide(divide(A,d),g),divide(divide(A,identity),d)). [para(7(a,1),8(a,1,2))].
% 1.32/1.65 29 divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero. [hyper(12,a,8,a)].
% 1.32/1.65 30 divide(divide(A,B),A) = zero. [hyper(12,a,3,a)].
% 1.32/1.65 31 divide(A,identity) = zero. [hyper(12,a,2,a)].
% 1.32/1.65 32 divide(zero,A) = zero. [hyper(12,a,1,a)].
% 1.32/1.65 33 less_equal(divide(divide(A,d),g),zero). [back_rewrite(27),rewrite([31(6),32(7)])].
% 1.32/1.65 34 less_equal(divide(divide(A,c),e),zero). [back_rewrite(24),rewrite([31(6),32(7)])].
% 1.32/1.65 36 less_equal(divide(divide(A,a),c),zero). [back_rewrite(18),rewrite([31(6),32(7)])].
% 1.32/1.65 42 less_equal(divide(c_0,divide(A,e)),divide(divide(d,A),e)). [para(15(a,1),8(a,1,1))].
% 1.32/1.65 43 less_equal(divide(divide(A,e),c_0),divide(divide(A,d),e)). [para(15(a,1),8(a,1,2))].
% 1.32/1.65 47 less_equal(divide(c,c),zero). [para(4(a,1),17(a,1,2)),rewrite([31(6),32(6)])].
% 1.32/1.65 54 less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)). [para(32(a,1),8(a,1,2))].
% 1.32/1.65 56 divide(c,c) = zero. [hyper(14,a,1,a,b,47,a),flip(a)].
% 1.32/1.65 59 less_equal(divide(e,divide(a,c)),zero). [para(6(a,1),19(a,1,1)),rewrite([56(8)])].
% 1.32/1.65 66 divide(divide(d,divide(A,b)),divide(divide(identity,A),b)) = zero. [hyper(12,a,20,a)].
% 1.32/1.65 67 less_equal(divide(d,d),zero). [para(5(a,1),20(a,1,2)),rewrite([31(6),32(6)])].
% 1.32/1.65 72 divide(d,d) = zero. [hyper(14,a,1,a,b,67,a),flip(a)].
% 1.32/1.65 78 less_equal(divide(g,divide(b,d)),zero). [para(7(a,1),22(a,1,1)),rewrite([72(8)])].
% 1.32/1.65 80 less_equal(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)). [para(30(a,1),8(a,1,2))].
% 1.32/1.65 81 less_equal(divide(divide(divide(A,B),C),divide(A,C)),zero). [para(30(a,1),8(a,2,1)),rewrite([32(6)])].
% 1.32/1.65 95 divide(divide(A,d),g) = zero. [hyper(14,a,1,a,b,33,a),flip(a)].
% 1.32/1.65 104 divide(divide(A,c),e) = zero. [hyper(14,a,1,a,b,34,a),flip(a)].
% 1.32/1.65 111 divide(divide(A,a),c) = zero. [hyper(14,a,1,a,b,36,a),flip(a)].
% 1.32/1.65 112 divide(e,divide(a,c)) = zero. [hyper(14,a,1,a,b,59,a),flip(a)].
% 1.32/1.65 113 divide(g,divide(b,d)) = zero. [hyper(14,a,1,a,b,78,a),flip(a)].
% 1.32/1.65 118 less_equal(divide(A,d),g). [hyper(13,a,95,a)].
% 1.32/1.65 122 less_equal(divide(A,c),e). [hyper(13,a,104,a)].
% 1.32/1.65 125 less_equal(divide(divide(A,e),divide(c,e)),zero). [para(104(a,1),8(a,2))].
% 1.32/1.65 130 divide(divide(divide(A,e),c_0),divide(divide(A,d),e)) = zero. [para(15(a,1),29(a,1,1,2))].
% 1.32/1.65 169 less_equal(divide(c_0,zero),divide(divide(d,divide(e,A)),e)). [para(30(a,1),42(a,1,2))].
% 1.32/1.65 171 less_equal(divide(c_0,divide(c,e)),zero). [para(104(a,1),42(a,2))].
% 1.32/1.65 178 less_equal(divide(A,a),c). [hyper(13,a,111,a)].
% 1.32/1.65 186 less_equal(divide(divide(divide(d,A),e),c_0),zero). [para(30(a,1),43(a,2,1)),rewrite([32(9)])].
% 1.32/1.65 188 less_equal(e,divide(a,c)). [hyper(13,a,112,a)].
% 1.32/1.65 194 divide(a,c) = e. [hyper(14,a,122,a,b,188,a)].
% 1.32/1.65 199 divide(e,a) = zero. [para(194(a,1),30(a,1,1))].
% 1.32/1.65 206 less_equal(divide(c,zero),divide(divide(identity,e),a)). [para(199(a,1),17(a,1,2))].
% 1.32/1.65 210 less_equal(g,divide(b,d)). [hyper(13,a,113,a)].
% 1.32/1.65 229 divide(b,d) = g. [hyper(14,a,118,a,b,210,a)].
% 1.32/1.65 234 divide(g,b) = zero. [para(229(a,1),30(a,1,1))].
% 1.32/1.65 239 less_equal(divide(divide(A,b),zero),divide(divide(A,g),b)). [para(234(a,1),8(a,1,2))].
% 1.32/1.65 246 divide(c_0,divide(c,e)) = zero. [hyper(14,a,1,a,b,171,a),flip(a)].
% 1.32/1.65 282 less_equal(divide(divide(A,A),zero),zero). [para(30(a,1),54(a,2))].
% 1.32/1.65 291 divide(divide(A,A),zero) = zero. [hyper(14,a,1,a,b,282,a),flip(a)].
% 1.32/1.65 292 less_equal(divide(A,A),zero). [hyper(13,a,291,a)].
% 1.32/1.65 297 divide(A,A) = zero. [hyper(14,a,1,a,b,292,a),flip(a)].
% 1.32/1.65 303 less_equal(divide(divide(A,divide(A,zero)),zero),zero). [para(297(a,1),54(a,2))].
% 1.32/1.65 325 divide(divide(divide(A,divide(divide(identity,B),b)),zero),divide(divide(A,divide(d,divide(B,b))),divide(divide(identity,B),b))) = zero. [para(66(a,1),29(a,1,1,2))].
% 1.32/1.65 346 divide(divide(A,e),divide(c,e)) = zero. [hyper(14,a,1,a,b,125,a),flip(a)].
% 1.32/1.65 358 less_equal(divide(divide(c_0,c),zero),zero). [para(246(a,1),80(a,2,1)),rewrite([32(8)])].
% 1.32/1.65 364 divide(divide(c_0,c),zero) = zero. [hyper(14,a,1,a,b,358,a),flip(a)].
% 1.32/1.65 365 less_equal(divide(c_0,c),zero). [hyper(13,a,364,a)].
% 1.32/1.65 372 divide(c_0,c) = zero. [hyper(14,a,1,a,b,365,a),flip(a)].
% 1.32/1.65 375 less_equal(divide(divide(c_0,A),divide(c,A)),zero). [para(372(a,1),8(a,2,1)),rewrite([32(7)])].
% 1.32/1.65 380 divide(divide(divide(A,B),C),divide(A,C)) = zero. [hyper(14,a,1,a,b,81,a),flip(a)].
% 1.32/1.65 398 divide(divide(divide(d,A),e),c_0) = zero. [hyper(14,a,1,a,b,186,a),flip(a)].
% 1.32/1.65 434 divide(divide(A,divide(A,zero)),zero) = zero. [hyper(14,a,1,a,b,303,a),flip(a)].
% 1.32/1.65 521 less_equal(divide(divide(divide(A,e),c),zero),zero). [para(346(a,1),80(a,2,1)),rewrite([32(9)])].
% 1.32/1.65 558 divide(divide(c_0,A),divide(c,A)) = zero. [hyper(14,a,1,a,b,375,a),flip(a)].
% 1.32/1.65 636 less_equal(divide(divide(d,A),e),c_0). [hyper(13,a,398,a)].
% 1.32/1.65 896 less_equal(divide(A,divide(A,zero)),zero). [hyper(13,a,434,a)].
% 1.32/1.65 906 less_equal(divide(divide(divide(divide(A,e),c_0),divide(A,d)),zero),zero). [para(130(a,1),80(a,2,1)),rewrite([32(13)])].
% 1.32/1.65 911 divide(A,divide(A,zero)) = zero. [hyper(14,a,1,a,b,896,a),flip(a)].
% 1.32/1.65 912 less_equal(A,divide(A,zero)). [hyper(13,a,911,a)].
% 1.32/1.65 959 divide(A,zero) = A. [hyper(14,a,3,a,b,912,a)].
% 1.32/1.65 969 less_equal(divide(divide(divide(A,e),c_0),divide(A,d)),zero). [back_rewrite(906),rewrite([959(9)])].
% 1.32/1.65 1192 less_equal(divide(divide(A,e),c),zero). [back_rewrite(521),rewrite([959(6)])].
% 1.32/1.65 1271 divide(divide(A,divide(divide(identity,B),b)),divide(divide(A,divide(d,divide(B,b))),divide(divide(identity,B),b))) = zero. [back_rewrite(325),rewrite([959(7)])].
% 1.32/1.65 1284 less_equal(divide(A,b),divide(divide(A,g),b)). [back_rewrite(239),rewrite([959(4)])].
% 1.32/1.65 1293 less_equal(c,divide(divide(identity,e),a)). [back_rewrite(206),rewrite([959(3)])].
% 1.32/1.65 1300 less_equal(c_0,divide(divide(d,divide(e,A)),e)). [back_rewrite(169),rewrite([959(3)])].
% 1.32/1.65 1367 divide(divide(A,e),c) = zero. [hyper(14,a,1,a,b,1192,a),flip(a)].
% 1.32/1.65 1391 divide(divide(identity,e),a) = c. [hyper(14,a,178,a,b,1293,a)].
% 1.32/1.65 1423 less_equal(divide(A,e),c). [hyper(13,a,1367,a)].
% 1.32/1.65 1544 less_equal(c,divide(identity,e)). [para(1391(a,1),3(a,1))].
% 1.32/1.65 1551 divide(identity,e) = c. [hyper(14,a,1423,a,b,1544,a)].
% 1.32/1.65 1661 less_equal(divide(c_0,A),divide(c,A)). [hyper(13,a,558,a)].
% 1.32/1.65 1690 less_equal(divide(divide(A,B),C),divide(A,C)). [hyper(13,a,380,a)].
% 1.32/1.65 1802 divide(divide(d,divide(e,A)),e) = c_0. [hyper(14,a,636,a,b,1300,a)].
% 1.32/1.65 2056 less_equal(divide(divide(c,c_0),g),zero). [para(7(a,1),969(a,1,2)),rewrite([1551(3)])].
% 1.32/1.65 2061 divide(divide(c,c_0),g) = zero. [hyper(14,a,1,a,b,2056,a),flip(a)].
% 1.32/1.65 2068 divide(divide(c,g),divide(c_0,g)) = zero. [para(2061(a,1),29(a,1,2)),rewrite([959(9)])].
% 1.32/1.65 2070 less_equal(divide(divide(c,c_0),b),zero). [para(2061(a,1),1284(a,2,1)),rewrite([32(8)])].
% 1.32/1.65 2072 divide(divide(c,c_0),b) = zero. [hyper(14,a,1,a,b,2070,a),flip(a)].
% 1.32/1.65 2093 divide(divide(c,b),divide(c_0,b)) = zero. [para(2072(a,1),29(a,1,2)),rewrite([959(9)])].
% 1.32/1.65 2471 divide(divide(A,g),b) = divide(A,b). [hyper(14,a,1284,a,b,1690,a),flip(a)].
% 1.32/1.65 2938 divide(c_0,divide(d,divide(e,A))) = zero. [para(1802(a,1),30(aCputime limit exceeded (core dumped)
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