TSTP Solution File: HEN007-5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN007-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 13:00:52 EDT 2022
% Result : Unsatisfiable 0.68s 0.98s
% 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
% 0.06/0.11 % Problem : HEN007-5 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 14:48:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.68/0.98 ============================== Prover9 ===============================
% 0.68/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.98 Process 8296 was started by sandbox on n028.cluster.edu,
% 0.68/0.98 Fri Jul 1 14:48:16 2022
% 0.68/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8142_n028.cluster.edu".
% 0.68/0.98 ============================== end of head ===========================
% 0.68/0.98
% 0.68/0.98 ============================== INPUT =================================
% 0.68/0.98
% 0.68/0.98 % Reading from file /tmp/Prover9_8142_n028.cluster.edu
% 0.68/0.98
% 0.68/0.98 set(prolog_style_variables).
% 0.68/0.98 set(auto2).
% 0.68/0.98 % set(auto2) -> set(auto).
% 0.68/0.98 % set(auto) -> set(auto_inference).
% 0.68/0.98 % set(auto) -> set(auto_setup).
% 0.68/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.98 % set(auto) -> set(auto_limits).
% 0.68/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.98 % set(auto) -> set(auto_denials).
% 0.68/0.98 % set(auto) -> set(auto_process).
% 0.68/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.98 % set(auto2) -> assign(stats, some).
% 0.68/0.98 % set(auto2) -> clear(echo_input).
% 0.68/0.98 % set(auto2) -> set(quiet).
% 0.68/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.98 % set(auto2) -> clear(print_given).
% 0.68/0.98 assign(lrs_ticks,-1).
% 0.68/0.98 assign(sos_limit,10000).
% 0.68/0.98 assign(order,kbo).
% 0.68/0.98 set(lex_order_vars).
% 0.68/0.98 clear(print_given).
% 0.68/0.98
% 0.68/0.98 % formulas(sos). % not echoed (8 formulas)
% 0.68/0.98
% 0.68/0.98 ============================== end of input ==========================
% 0.68/0.98
% 0.68/0.98 % From the command line: assign(max_seconds, 300).
% 0.68/0.98
% 0.68/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.98
% 0.68/0.98 % Formulas that are not ordinary clauses:
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% 0.68/0.98 ============================== end of process non-clausal formulas ===
% 0.68/0.98
% 0.68/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.68/0.98
% 0.68/0.98 ============================== PREDICATE ELIMINATION =================
% 0.68/0.98
% 0.68/0.98 ============================== end predicate elimination =============
% 0.68/0.98
% 0.68/0.98 Auto_denials:
% 0.68/0.98 % copying label prove_property_of_divide2 to answer in negative clause
% 0.68/0.98
% 0.68/0.98 Term ordering decisions:
% 0.68/0.98 Function symbol KB weights: zero=1. a=1. b=1. identity=1. c=1. divide=1.
% 0.68/0.98
% 0.68/0.98 ============================== end of process initial clauses ========
% 0.68/0.98
% 0.68/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.68/0.98
% 0.68/0.98 ============================== end of clauses for search =============
% 0.68/0.98
% 0.68/0.98 ============================== SEARCH ================================
% 0.68/0.98
% 0.68/0.98 % Starting search at 0.01 seconds.
% 0.68/0.98
% 0.68/0.98 ============================== PROOF =================================
% 0.68/0.98 % SZS status Unsatisfiable
% 0.68/0.98 % SZS output start Refutation
% 0.68/0.98
% 0.68/0.98 % Proof 1 at 0.04 (+ 0.00) seconds: prove_property_of_divide2.
% 0.68/0.98 % Length of proof is 39.
% 0.68/0.98 % Level of proof is 9.
% 0.68/0.98 % Maximum clause weight is 24.000.
% 0.68/0.98 % Given clauses 65.
% 0.68/0.98
% 0.68/0.98 1 divide(zero,A) = zero # label(zero_is_smallest) # label(axiom). [assumption].
% 0.68/0.98 2 divide(A,identity) = zero # label(identity_is_largest) # label(axiom). [assumption].
% 0.68/0.98 3 divide(a,b) = zero # label(a_divide_b_is_zero) # label(hypothesis). [assumption].
% 0.68/0.98 4 zero = divide(a,b). [copy(3),flip(a)].
% 0.68/0.98 5 divide(divide(A,B),A) = zero # label(quotient_smaller_than_numerator) # label(axiom). [assumption].
% 0.68/0.98 6 divide(divide(A,B),A) = divide(a,b). [copy(5),rewrite([4(3)])].
% 0.68/0.98 7 divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero # label(quotient_property) # label(axiom). [assumption].
% 0.68/0.98 8 divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = divide(a,b). [copy(7),rewrite([4(7)])].
% 0.68/0.98 9 divide(divide(c,b),divide(c,a)) != zero # label(prove_property_of_divide2) # label(negated_conjecture) # answer(prove_property_of_divide2). [assumption].
% 0.68/0.98 10 divide(divide(c,b),divide(c,a)) != divide(a,b) # answer(prove_property_of_divide2). [copy(9),rewrite([4(8)])].
% 0.68/0.98 11 divide(A,B) != zero | divide(B,A) != zero | A = B # label(divide_and_equal) # label(axiom). [assumption].
% 0.68/0.98 12 divide(a,b) != divide(A,B) | divide(a,b) != divide(B,A) | A = B. [copy(11),rewrite([4(2),4(7)]),flip(a),flip(b)].
% 0.68/0.98 13 divide(A,B) != zero | divide(B,C) != zero | divide(A,C) = zero # label(transitivity_of_divide_to_zero) # label(axiom). [assumption].
% 0.68/0.98 14 divide(a,b) != divide(A,B) | divide(a,b) != divide(B,C) | divide(a,b) = divide(A,C). [copy(13),rewrite([4(2),4(7),4(12)]),flip(a),flip(b),flip(c)].
% 0.68/0.98 15 divide(a,b) = divide(A,identity). [back_rewrite(2),rewrite([4(3)]),flip(a)].
% 0.68/0.98 16 divide(divide(a,b),A) = divide(a,b). [back_rewrite(1),rewrite([4(1),4(5)])].
% 0.68/0.98 34 divide(divide(divide(A,B),C),D) != divide(a,b) | divide(divide(divide(A,C),divide(B,C)),D) = divide(a,b). [para(8(a,1),14(a,2)),flip(b),flip(c),xx(a)].
% 0.68/0.98 39 divide(divide(divide(A,b),divide(B,identity)),divide(divide(A,a),b)) = divide(a,b). [para(15(a,1),8(a,1,1,2))].
% 0.68/0.98 43 divide(divide(c,b),divide(c,a)) != divide(A,identity) # answer(prove_property_of_divide2). [para(15(a,1),10(a,2))].
% 0.68/0.98 44 divide(A,identity) != divide(B,C) | divide(a,b) != divide(C,B) | B = C. [para(15(a,1),12(a,1))].
% 0.68/0.98 48 divide(A,identity) != divide(B,C) | divide(a,b) != divide(C,D) | divide(a,b) = divide(B,D). [para(15(a,1),14(a,1))].
% 0.68/0.98 53 divide(A,identity) = divide(B,identity). [para(15(a,1),15(a,1))].
% 0.68/0.98 54 divide(A,identity) = c_0. [new_symbol(53)].
% 0.68/0.98 58 divide(A,B) != c_0 | divide(a,b) != divide(B,C) | divide(a,b) = divide(A,C). [back_rewrite(48),rewrite([54(2)]),flip(a)].
% 0.68/0.98 61 divide(A,B) != c_0 | divide(a,b) != divide(B,A) | A = B. [back_rewrite(44),rewrite([54(2)]),flip(a)].
% 0.68/0.98 62 divide(divide(c,b),divide(c,a)) != c_0 # answer(prove_property_of_divide2). [back_rewrite(43),rewrite([54(9)])].
% 0.68/0.98 65 divide(divide(divide(A,b),c_0),divide(divide(A,a),b)) = divide(a,b). [back_rewrite(39),rewrite([54(4)])].
% 0.68/0.98 68 divide(a,b) = c_0. [back_rewrite(15),rewrite([54(5)])].
% 0.68/0.98 70 divide(divide(divide(A,b),c_0),divide(divide(A,a),b)) = c_0. [back_rewrite(65),rewrite([68(12)])].
% 0.68/0.99 72 divide(A,B) != c_0 | divide(B,A) != c_0 | A = B. [back_rewrite(61),rewrite([68(6)]),flip(b)].
% 0.68/0.99 74 divide(A,B) != c_0 | divide(B,C) != c_0 | divide(A,C) = c_0. [back_rewrite(58),rewrite([68(6),68(9)]),flip(b),flip(c)].
% 0.68/0.99 81 divide(divide(divide(A,B),C),D) != c_0 | divide(divide(divide(A,C),divide(B,C)),D) = c_0. [back_rewrite(34),rewrite([68(6),68(12)])].
% 0.68/0.99 99 divide(c_0,A) = c_0. [back_rewrite(16),rewrite([68(3),68(5)])].
% 0.68/0.99 101 divide(divide(A,B),A) = c_0. [back_rewrite(6),rewrite([68(5)])].
% 0.68/0.99 111 divide(divide(divide(c,b),divide(c,a)),c_0) != c_0 # answer(prove_property_of_divide2). [ur(72,b,99,a,c,62,a)].
% 0.68/0.99 119 divide(divide(divide(divide(c,b),divide(c,a)),c_0),c_0) != c_0 # answer(prove_property_of_divide2). [ur(72,b,99,a,c,111,a)].
% 0.68/0.99 128 divide(divide(divide(A,b),c_0),divide(A,a)) = c_0. [hyper(74,a,70,a,b,101,a)].
% 0.68/0.99 265 divide(divide(divide(divide(A,b),divide(A,a)),c_0),B) = c_0. [para(128(a,1),81(a,1,1)),rewrite([99(2),99(12)]),xx(a)].
% 0.68/0.99 266 $F # answer(prove_property_of_divide2). [resolve(265,a,119,a)].
% 0.68/0.99
% 0.68/0.99 % SZS output end Refutation
% 0.68/0.99 ============================== end of proof ==========================
% 0.68/0.99
% 0.68/0.99 ============================== STATISTICS ============================
% 0.68/0.99
% 0.68/0.99 Given=65. Generated=1258. Kept=259. proofs=1.
% 0.68/0.99 Usable=51. Sos=119. Demods=60. Limbo=11, Disabled=85. Hints=0.
% 0.68/0.99 Megabytes=0.23.
% 0.68/0.99 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.68/0.99
% 0.68/0.99 ============================== end of statistics =====================
% 0.68/0.99
% 0.68/0.99 ============================== end of search =========================
% 0.68/0.99
% 0.68/0.99 THEOREM PROVED
% 0.68/0.99 % SZS status Unsatisfiable
% 0.68/0.99
% 0.68/0.99 Exiting with 1 proof.
% 0.68/0.99
% 0.68/0.99 Process 8296 exit (max_proofs) Fri Jul 1 14:48:16 2022
% 0.68/0.99 Prover9 interrupted
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