TSTP Solution File: HEN011-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN011-2 : 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 13:00:59 EDT 2022
% Result : Unsatisfiable 1.12s 1.52s
% Output : Refutation 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.09 % Problem : HEN011-2 : TPTP v8.1.0. Released v1.0.0.
% 0.01/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.06/0.29 % Computer : n004.cluster.edu
% 0.06/0.29 % Model : x86_64 x86_64
% 0.06/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.29 % Memory : 8042.1875MB
% 0.06/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.29 % CPULimit : 300
% 0.06/0.29 % WCLimit : 600
% 0.06/0.29 % DateTime : Fri Jul 1 14:54:53 EDT 2022
% 0.06/0.29 % CPUTime :
% 1.12/1.51 ============================== Prover9 ===============================
% 1.12/1.51 Prover9 (32) version 2009-11A, November 2009.
% 1.12/1.51 Process 13660 was started by sandbox on n004.cluster.edu,
% 1.12/1.51 Fri Jul 1 14:54:53 2022
% 1.12/1.51 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13506_n004.cluster.edu".
% 1.12/1.51 ============================== end of head ===========================
% 1.12/1.51
% 1.12/1.51 ============================== INPUT =================================
% 1.12/1.51
% 1.12/1.51 % Reading from file /tmp/Prover9_13506_n004.cluster.edu
% 1.12/1.51
% 1.12/1.51 set(prolog_style_variables).
% 1.12/1.51 set(auto2).
% 1.12/1.51 % set(auto2) -> set(auto).
% 1.12/1.51 % set(auto) -> set(auto_inference).
% 1.12/1.51 % set(auto) -> set(auto_setup).
% 1.12/1.51 % set(auto_setup) -> set(predicate_elim).
% 1.12/1.51 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.12/1.51 % set(auto) -> set(auto_limits).
% 1.12/1.51 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.12/1.51 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.12/1.51 % set(auto) -> set(auto_denials).
% 1.12/1.51 % set(auto) -> set(auto_process).
% 1.12/1.51 % set(auto2) -> assign(new_constants, 1).
% 1.12/1.51 % set(auto2) -> assign(fold_denial_max, 3).
% 1.12/1.51 % set(auto2) -> assign(max_weight, "200.000").
% 1.12/1.51 % set(auto2) -> assign(max_hours, 1).
% 1.12/1.51 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.12/1.51 % set(auto2) -> assign(max_seconds, 0).
% 1.12/1.51 % set(auto2) -> assign(max_minutes, 5).
% 1.12/1.51 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.12/1.51 % set(auto2) -> set(sort_initial_sos).
% 1.12/1.51 % set(auto2) -> assign(sos_limit, -1).
% 1.12/1.51 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.12/1.51 % set(auto2) -> assign(max_megs, 400).
% 1.12/1.51 % set(auto2) -> assign(stats, some).
% 1.12/1.51 % set(auto2) -> clear(echo_input).
% 1.12/1.51 % set(auto2) -> set(quiet).
% 1.12/1.51 % set(auto2) -> clear(print_initial_clauses).
% 1.12/1.51 % set(auto2) -> clear(print_given).
% 1.12/1.51 assign(lrs_ticks,-1).
% 1.12/1.51 assign(sos_limit,10000).
% 1.12/1.51 assign(order,kbo).
% 1.12/1.51 set(lex_order_vars).
% 1.12/1.51 clear(print_given).
% 1.12/1.51
% 1.12/1.51 % formulas(sos). % not echoed (26 formulas)
% 1.12/1.51
% 1.12/1.51 ============================== end of input ==========================
% 1.12/1.51
% 1.12/1.51 % From the command line: assign(max_seconds, 300).
% 1.12/1.51
% 1.12/1.51 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.12/1.51
% 1.12/1.51 % Formulas that are not ordinary clauses:
% 1.12/1.51
% 1.12/1.51 ============================== end of process non-clausal formulas ===
% 1.12/1.51
% 1.12/1.51 ============================== PROCESS INITIAL CLAUSES ===============
% 1.12/1.51
% 1.12/1.51 ============================== PREDICATE ELIMINATION =================
% 1.12/1.51
% 1.12/1.51 ============================== end predicate elimination =============
% 1.12/1.51
% 1.12/1.51 Auto_denials:
% 1.12/1.51 % copying label prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa to answer in negative clause
% 1.12/1.51
% 1.12/1.51 Term ordering decisions:
% 1.12/1.51 Function symbol KB weights: identity=1. zero=1. idQa=1. idQb=1. idQ_idQa=1. idQ_idQb=1. a=1. b=1. idQa_Q__idQ_idQb=1. idQb_Q__idQ_idQa=1. divide=1.
% 1.12/1.51
% 1.12/1.51 ============================== end of process initial clauses ========
% 1.12/1.51
% 1.12/1.51 ============================== CLAUSES FOR SEARCH ====================
% 1.12/1.51
% 1.12/1.51 ============================== end of clauses for search =============
% 1.12/1.51
% 1.12/1.51 ============================== SEARCH ================================
% 1.12/1.51
% 1.12/1.51 % Starting search at 0.01 seconds.
% 1.12/1.51
% 1.12/1.51 ============================== PROOF =================================
% 1.12/1.52 % SZS status Unsatisfiable
% 1.12/1.52 % SZS output start Refutation
% 1.12/1.52
% 1.12/1.52 % Proof 1 at 0.66 (+ 0.03) seconds: prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa.
% 1.12/1.52 % Length of proof is 30.
% 1.12/1.52 % Level of proof is 8.
% 1.12/1.52 % Maximum clause weight is 23.000.
% 1.12/1.52 % Given clauses 214.
% 1.12/1.52
% 1.12/1.52 7 quotient(identity,a,idQa) # label(identity_divide_a) # label(hypothesis). [assumption].
% 1.12/1.52 8 quotient(identity,b,idQb) # label(identity_divide_b) # label(hypothesis). [assumption].
% 1.12/1.52 9 quotient(identity,idQb,idQ_idQb) # label(identity_divide_idQb) # label(hypothesis). [assumption].
% 1.12/1.52 10 quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb) # label(idQa_divide_idQ_idQb) # label(hypothesis). [assumption].
% 1.12/1.52 11 quotient(identity,idQa,idQ_idQa) # label(identity_divide_idQa) # label(hypothesis). [assumption].
% 1.12/1.52 12 quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa) # label(idQb_divide_idQ_idQa) # label(hypothesis). [assumption].
% 1.12/1.52 13 quotient(A,B,divide(A,B)) # label(closure) # label(axiom). [assumption].
% 1.12/1.52 14 idQa_Q__idQ_idQb != idQb_Q__idQ_idQa # label(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) # label(negated_conjecture) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [assumption].
% 1.12/1.52 15 idQb_Q__idQ_idQa != idQa_Q__idQ_idQb # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [copy(14),flip(a)].
% 1.12/1.52 18 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom). [assumption].
% 1.12/1.52 19 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 1.12/1.52 20 -less_equal(A,B) | -less_equal(B,C) | less_equal(A,C) # label(transitivity_of_less_equal) # label(axiom). [assumption].
% 1.12/1.52 21 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom). [assumption].
% 1.12/1.52 22 -quotient(A,B,C) | -less_equal(C,D) | -quotient(A,D,E) | less_equal(E,B) # label(xQyLEz_implies_xQzLEy) # label(axiom). [assumption].
% 1.12/1.52 25 -quotient(identity,A,B) | -quotient(identity,B,C) | -quotient(identity,C,D) | B = D # label(one_inversion_equals_three) # label(axiom). [assumption].
% 1.12/1.52 27 -quotient(A,B,C) | -quotient(B,D,E) | -quotient(A,D,F) | -quotient(F,E,V6) | -quotient(C,D,V7) | less_equal(V6,V7) # label(quotient_property) # label(axiom). [assumption].
% 1.12/1.52 29 less_equal(divide(A,B),A). [hyper(18,a,13,a)].
% 1.12/1.52 32 divide(idQb,idQ_idQa) = idQb_Q__idQ_idQa. [hyper(21,a,13,a,b,12,a)].
% 1.12/1.52 33 divide(identity,idQa) = idQ_idQa. [hyper(21,a,13,a,b,11,a)].
% 1.12/1.52 35 divide(identity,idQb) = idQ_idQb. [hyper(21,a,13,a,b,9,a)].
% 1.12/1.52 56 divide(identity,idQ_idQb) = idQb. [hyper(25,a,8,a,b,13,a,c,13,a),rewrite([35(5)]),flip(a)].
% 1.12/1.52 57 divide(identity,idQ_idQa) = idQa. [hyper(25,a,7,a,b,13,a,c,13,a),rewrite([33(5)]),flip(a)].
% 1.12/1.52 90 less_equal(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)). [hyper(27,a,11,a,b,10,a,c,13,a,d,13,a,e,13,a),rewrite([56(3)])].
% 1.12/1.52 97 less_equal(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)). [hyper(27,a,9,a,b,12,a,c,13,a,d,13,a,e,13,a),rewrite([57(3)])].
% 1.12/1.52 1061 less_equal(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa). [hyper(20,a,90,a,b,29,a)].
% 1.12/1.52 1078 less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb). [hyper(22,a,13,a,b,1061,a,c,13,a),rewrite([32(3)])].
% 1.12/1.52 1092 -less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [ur(19,b,1078,a,c,15,a(flip))].
% 1.12/1.52 1175 -less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [ur(22,a,13,a,c,10,a,d,1092,a)].
% 1.12/1.52 3771 less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb). [hyper(20,a,97,a,b,29,a)].
% 1.12/1.52 3772 $F # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [resolve(3771,a,1175,a)].
% 1.12/1.52
% 1.12/1.52 % SZS output end Refutation
% 1.12/1.52 ============================== end of proof ==========================
% 1.12/1.52
% 1.12/1.52 ============================== STATISTICS ============================
% 1.12/1.52
% 1.12/1.52 Given=214. Generated=45532. Kept=3770. proofs=1.
% 1.12/1.52 Usable=189. Sos=2761. Demods=57. Limbo=8, Disabled=837. Hints=0.
% 1.12/1.52 Megabytes=1.99.
% 1.12/1.52 User_CPU=0.66, System_CPU=0.03, Wall_clock=1.
% 1.12/1.52
% 1.12/1.52 ============================== end of statistics =====================
% 1.12/1.52
% 1.12/1.52 ============================== end of search =========================
% 1.12/1.52
% 1.12/1.52 THEOREM PROVED
% 1.12/1.52 % SZS status Unsatisfiable
% 1.12/1.52
% 1.12/1.52 Exiting with 1 proof.
% 1.12/1.52
% 1.12/1.52 Process 13660 exit (max_proofs) Fri Jul 1 14:54:54 2022
% 1.12/1.52 Prover9 interrupted
%------------------------------------------------------------------------------