TSTP Solution File: HEN006-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 13:00:49 EDT 2022
% Result : Unsatisfiable 0.82s 1.11s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HEN006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n013.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 13:34:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.82/1.11 ============================== Prover9 ===============================
% 0.82/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.11 Process 2350 was started by sandbox on n013.cluster.edu,
% 0.82/1.11 Fri Jul 1 13:34:30 2022
% 0.82/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2196_n013.cluster.edu".
% 0.82/1.11 ============================== end of head ===========================
% 0.82/1.11
% 0.82/1.11 ============================== INPUT =================================
% 0.82/1.11
% 0.82/1.11 % Reading from file /tmp/Prover9_2196_n013.cluster.edu
% 0.82/1.11
% 0.82/1.11 set(prolog_style_variables).
% 0.82/1.11 set(auto2).
% 0.82/1.11 % set(auto2) -> set(auto).
% 0.82/1.11 % set(auto) -> set(auto_inference).
% 0.82/1.11 % set(auto) -> set(auto_setup).
% 0.82/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.11 % set(auto) -> set(auto_limits).
% 0.82/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.11 % set(auto) -> set(auto_denials).
% 0.82/1.11 % set(auto) -> set(auto_process).
% 0.82/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.11 % set(auto2) -> assign(stats, some).
% 0.82/1.11 % set(auto2) -> clear(echo_input).
% 0.82/1.11 % set(auto2) -> set(quiet).
% 0.82/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.11 % set(auto2) -> clear(print_given).
% 0.82/1.11 assign(lrs_ticks,-1).
% 0.82/1.11 assign(sos_limit,10000).
% 0.82/1.11 assign(order,kbo).
% 0.82/1.11 set(lex_order_vars).
% 0.82/1.11 clear(print_given).
% 0.82/1.11
% 0.82/1.11 % formulas(sos). % not echoed (13 formulas)
% 0.82/1.11
% 0.82/1.11 ============================== end of input ==========================
% 0.82/1.11
% 0.82/1.11 % From the command line: assign(max_seconds, 300).
% 0.82/1.11
% 0.82/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.11
% 0.82/1.11 % Formulas that are not ordinary clauses:
% 0.82/1.11
% 0.82/1.11 ============================== end of process non-clausal formulas ===
% 0.82/1.11
% 0.82/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.11
% 0.82/1.11 ============================== PREDICATE ELIMINATION =================
% 0.82/1.11
% 0.82/1.11 ============================== end predicate elimination =============
% 0.82/1.11
% 0.82/1.11 Auto_denials:
% 0.82/1.11 % copying label prove_xQzLEy to answer in negative clause
% 0.82/1.11
% 0.82/1.11 Term ordering decisions:
% 0.82/1.11 Function symbol KB weights: zero=1. x=1. xQy=1. z=1. identity=1. xQz=1. y=1. divide=1.
% 0.82/1.11
% 0.82/1.11 ============================== end of process initial clauses ========
% 0.82/1.11
% 0.82/1.11 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.11
% 0.82/1.11 ============================== end of clauses for search =============
% 0.82/1.11
% 0.82/1.11 ============================== SEARCH ================================
% 0.82/1.11
% 0.82/1.11 % Starting search at 0.01 seconds.
% 0.82/1.11
% 0.82/1.11 ============================== PROOF =================================
% 0.82/1.11 % SZS status Unsatisfiable
% 0.82/1.11 % SZS output start Refutation
% 0.82/1.11
% 0.82/1.11 % Proof 1 at 0.08 (+ 0.01) seconds: prove_xQzLEy.
% 0.82/1.11 % Length of proof is 28.
% 0.82/1.11 % Level of proof is 11.
% 0.82/1.11 % Maximum clause weight is 23.000.
% 0.82/1.11 % Given clauses 74.
% 0.82/1.11
% 0.82/1.11 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 0.82/1.11 3 less_equal(xQy,z) # label(xQyLEz) # label(hypothesis). [assumption].
% 0.82/1.11 4 quotient(x,y,xQy) # label(xQy) # label(hypothesis). [assumption].
% 0.82/1.11 5 quotient(x,z,xQz) # label(xQz) # label(hypothesis). [assumption].
% 0.82/1.11 6 quotient(A,B,divide(A,B)) # label(closure) # label(axiom). [assumption].
% 0.82/1.11 7 -less_equal(xQz,y) # label(prove_xQzLEy) # label(negated_conjecture) # answer(prove_xQzLEy). [assumption].
% 0.82/1.11 8 -less_equal(A,B) | quotient(A,B,zero) # label(quotient_less_equal) # label(axiom). [assumption].
% 0.82/1.11 9 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom). [assumption].
% 0.82/1.11 10 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom). [assumption].
% 0.82/1.11 11 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.82/1.11 12 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom). [assumption].
% 0.82/1.11 13 -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].
% 0.82/1.11 14 quotient(xQy,z,zero). [hyper(8,a,3,a)].
% 0.82/1.11 16 quotient(zero,A,zero). [hyper(8,a,1,a)].
% 0.82/1.11 17 -quotient(xQz,y,zero) # answer(prove_xQzLEy). [ur(9,b,7,a)].
% 0.82/1.11 18 less_equal(divide(A,B),A). [hyper(10,a,6,a)].
% 0.82/1.11 22 divide(x,z) = xQz. [hyper(12,a,6,a,b,5,a)].
% 0.82/1.11 37 less_equal(divide(xQz,divide(y,z)),zero). [hyper(13,a,4,a,b,6,a,c,6,a,d,6,a,e,14,a),rewrite([22(3)])].
% 0.82/1.11 92 quotient(divide(A,B),A,zero). [hyper(8,a,18,a)].
% 0.82/1.11 121 divide(xQz,divide(y,z)) = zero. [hyper(11,a,1,a,b,37,a),flip(a)].
% 0.82/1.11 130 quotient(xQz,divide(y,z),zero). [para(121(a,1),6(a,3))].
% 0.82/1.11 135 less_equal(divide(divide(xQz,y),zero),zero). [hyper(13,a,130,a,b,92,a,c,6,a,d,6,a,e,16,a)].
% 0.82/1.11 178 divide(divide(xQz,y),zero) = zero. [hyper(11,a,1,a,b,135,a),flip(a)].
% 0.82/1.11 181 quotient(divide(xQz,y),zero,zero). [para(178(a,1),6(a,3))].
% 0.82/1.11 187 less_equal(divide(xQz,y),zero). [hyper(9,a,181,a)].
% 0.82/1.11 188 divide(xQz,y) = zero. [hyper(11,a,1,a,b,187,a),flip(a)].
% 0.82/1.11 191 quotient(xQz,y,zero). [para(188(a,1),6(a,3))].
% 0.82/1.11 192 $F # answer(prove_xQzLEy). [resolve(191,a,17,a)].
% 0.82/1.11
% 0.82/1.11 % SZS output end Refutation
% 0.82/1.11 ============================== end of proof ==========================
% 0.82/1.11
% 0.82/1.11 ============================== STATISTICS ============================
% 0.82/1.11
% 0.82/1.11 Given=74. Generated=3132. Kept=191. proofs=1.
% 0.82/1.11 Usable=54. Sos=51. Demods=13. Limbo=0, Disabled=98. Hints=0.
% 0.82/1.11 Megabytes=0.15.
% 0.82/1.11 User_CPU=0.08, System_CPU=0.01, Wall_clock=0.
% 0.82/1.11
% 0.82/1.11 ============================== end of statistics =====================
% 0.82/1.11
% 0.82/1.11 ============================== end of search =========================
% 0.82/1.11
% 0.82/1.11 THEOREM PROVED
% 0.82/1.11 % SZS status Unsatisfiable
% 0.82/1.11
% 0.82/1.11 Exiting with 1 proof.
% 0.82/1.11
% 0.82/1.11 Process 2350 exit (max_proofs) Fri Jul 1 13:34:30 2022
% 0.82/1.11 Prover9 interrupted
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