TSTP Solution File: HEN009-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN009-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 0.73s 1.03s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN009-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n004.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 14:22:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.73/1.03 ============================== Prover9 ===============================
% 0.73/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.03 Process 3406 was started by sandbox on n004.cluster.edu,
% 0.73/1.03 Fri Jul 1 14:22:38 2022
% 0.73/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3252_n004.cluster.edu".
% 0.73/1.03 ============================== end of head ===========================
% 0.73/1.03
% 0.73/1.03 ============================== INPUT =================================
% 0.73/1.03
% 0.73/1.03 % Reading from file /tmp/Prover9_3252_n004.cluster.edu
% 0.73/1.03
% 0.73/1.03 set(prolog_style_variables).
% 0.73/1.03 set(auto2).
% 0.73/1.03 % set(auto2) -> set(auto).
% 0.73/1.03 % set(auto) -> set(auto_inference).
% 0.73/1.03 % set(auto) -> set(auto_setup).
% 0.73/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.03 % set(auto) -> set(auto_limits).
% 0.73/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.03 % set(auto) -> set(auto_denials).
% 0.73/1.03 % set(auto) -> set(auto_process).
% 0.73/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.03 % set(auto2) -> assign(stats, some).
% 0.73/1.03 % set(auto2) -> clear(echo_input).
% 0.73/1.03 % set(auto2) -> set(quiet).
% 0.73/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.03 % set(auto2) -> clear(print_given).
% 0.73/1.03 assign(lrs_ticks,-1).
% 0.73/1.03 assign(sos_limit,10000).
% 0.73/1.03 assign(order,kbo).
% 0.73/1.03 set(lex_order_vars).
% 0.73/1.03 clear(print_given).
% 0.73/1.03
% 0.73/1.03 % formulas(sos). % not echoed (21 formulas)
% 0.73/1.03
% 0.73/1.03 ============================== end of input ==========================
% 0.73/1.03
% 0.73/1.03 % From the command line: assign(max_seconds, 300).
% 0.73/1.03
% 0.73/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.03
% 0.73/1.03 % Formulas that are not ordinary clauses:
% 0.73/1.03
% 0.73/1.03 ============================== end of process non-clausal formulas ===
% 0.73/1.03
% 0.73/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.03
% 0.73/1.03 ============================== PREDICATE ELIMINATION =================
% 0.73/1.03
% 0.73/1.03 ============================== end predicate elimination =============
% 0.73/1.03
% 0.73/1.03 Auto_denials:
% 0.73/1.03 % copying label prove_one_inversion_equals_three to answer in negative clause
% 0.73/1.03
% 0.73/1.03 Term ordering decisions:
% 0.73/1.03 Function symbol KB weights: zero=1. identity=1. idQ_idQa=1. idQa=1. a=1. idQ__idQ_idQa=1. divide=1.
% 0.73/1.03
% 0.73/1.03 ============================== end of process initial clauses ========
% 0.73/1.03
% 0.73/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.03
% 0.73/1.03 ============================== end of clauses for search =============
% 0.73/1.03
% 0.73/1.03 ============================== SEARCH ================================
% 0.73/1.03
% 0.73/1.03 % Starting search at 0.01 seconds.
% 0.73/1.03
% 0.73/1.03 ============================== PROOF =================================
% 0.73/1.03 % SZS status Unsatisfiable
% 0.73/1.03 % SZS output start Refutation
% 0.73/1.03
% 0.73/1.03 % Proof 1 at 0.04 (+ 0.00) seconds: prove_one_inversion_equals_three.
% 0.73/1.03 % Length of proof is 21.
% 0.73/1.03 % Level of proof is 4.
% 0.73/1.03 % Maximum clause weight is 14.000.
% 0.73/1.03 % Given clauses 28.
% 0.73/1.03
% 0.73/1.03 5 quotient(A,A,zero) # label(x_divide_x_is_zero) # label(axiom). [assumption].
% 0.73/1.03 7 quotient(identity,a,idQa) # label(identity_divide_a) # label(hypothesis). [assumption].
% 0.73/1.03 8 quotient(identity,idQa,idQ_idQa) # label(identity_divide_idQa) # label(hypothesis). [assumption].
% 0.73/1.03 9 quotient(identity,idQ_idQa,idQ__idQ_idQa) # label(identity_divide_idQ_idQa) # label(hypothesis). [assumption].
% 0.73/1.03 10 quotient(A,B,divide(A,B)) # label(closure) # label(axiom). [assumption].
% 0.73/1.03 11 idQa != idQ__idQ_idQa # label(prove_one_inversion_equals_three) # label(negated_conjecture) # answer(prove_one_inversion_equals_three). [assumption].
% 0.73/1.03 12 idQ__idQ_idQa != idQa # answer(prove_one_inversion_equals_three). [copy(11),flip(a)].
% 0.73/1.03 14 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom). [assumption].
% 0.73/1.03 16 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.73/1.03 18 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom). [assumption].
% 0.73/1.03 19 -quotient(A,B,C) | -less_equal(C,D) | -quotient(A,D,E) | less_equal(E,B) # label(xQyLEz_implies_xQzLEy) # label(axiom). [assumption].
% 0.73/1.03 20 -less_equal(A,B) | -quotient(C,B,D) | -quotient(C,A,E) | less_equal(D,E) # label(xLEy_implies_zQyLEzQx) # label(axiom). [assumption].
% 0.73/1.03 23 less_equal(A,A). [hyper(14,a,5,a)].
% 0.73/1.03 25 divide(identity,idQ_idQa) = idQ__idQ_idQa. [hyper(18,a,10,a,b,9,a)].
% 0.73/1.03 26 divide(identity,idQa) = idQ_idQa. [hyper(18,a,10,a,b,8,a)].
% 0.73/1.03 27 divide(identity,a) = idQa. [hyper(18,a,10,a,b,7,a)].
% 0.73/1.03 65 less_equal(idQ__idQ_idQa,idQa). [hyper(19,a,8,a,b,23,a,c,10,a),rewrite([25(3)])].
% 0.73/1.03 66 less_equal(idQ_idQa,a). [hyper(19,a,7,a,b,23,a,c,10,a),rewrite([26(3)])].
% 0.73/1.03 72 -less_equal(idQa,idQ__idQ_idQa) # answer(prove_one_inversion_equals_three). [ur(16,b,65,a,c,12,a(flip))].
% 0.73/1.03 76 less_equal(idQa,idQ__idQ_idQa). [hyper(20,a,66,a,b,10,a,c,9,a),rewrite([27(3)])].
% 0.73/1.03 77 $F # answer(prove_one_inversion_equals_three). [resolve(76,a,72,a)].
% 0.73/1.03
% 0.73/1.03 % SZS output end Refutation
% 0.73/1.03 ============================== end of proof ==========================
% 0.73/1.03
% 0.73/1.03 ============================== STATISTICS ============================
% 0.73/1.03
% 0.73/1.03 Given=28. Generated=1948. Kept=75. proofs=1.
% 0.73/1.03 Usable=28. Sos=43. Demods=7. Limbo=3, Disabled=21. Hints=0.
% 0.73/1.03 Megabytes=0.08.
% 0.73/1.03 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.73/1.03
% 0.73/1.03 ============================== end of statistics =====================
% 0.73/1.03
% 0.73/1.03 ============================== end of search =========================
% 0.73/1.03
% 0.73/1.03 THEOREM PROVED
% 0.73/1.03 % SZS status Unsatisfiable
% 0.73/1.03
% 0.73/1.03 Exiting with 1 proof.
% 0.73/1.03
% 0.73/1.03 Process 3406 exit (max_proofs) Fri Jul 1 14:22:38 2022
% 0.73/1.03 Prover9 interrupted
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