TSTP Solution File: HEN010-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:00:57 EDT 2022
% Result : Unsatisfiable 0.99s 1.29s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.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 14:32:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.99/1.29 ============================== Prover9 ===============================
% 0.99/1.29 Prover9 (32) version 2009-11A, November 2009.
% 0.99/1.29 Process 22089 was started by sandbox2 on n011.cluster.edu,
% 0.99/1.29 Fri Jul 1 14:32:49 2022
% 0.99/1.29 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21936_n011.cluster.edu".
% 0.99/1.29 ============================== end of head ===========================
% 0.99/1.29
% 0.99/1.29 ============================== INPUT =================================
% 0.99/1.29
% 0.99/1.29 % Reading from file /tmp/Prover9_21936_n011.cluster.edu
% 0.99/1.29
% 0.99/1.29 set(prolog_style_variables).
% 0.99/1.29 set(auto2).
% 0.99/1.29 % set(auto2) -> set(auto).
% 0.99/1.29 % set(auto) -> set(auto_inference).
% 0.99/1.29 % set(auto) -> set(auto_setup).
% 0.99/1.29 % set(auto_setup) -> set(predicate_elim).
% 0.99/1.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.99/1.29 % set(auto) -> set(auto_limits).
% 0.99/1.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.99/1.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.99/1.29 % set(auto) -> set(auto_denials).
% 0.99/1.29 % set(auto) -> set(auto_process).
% 0.99/1.29 % set(auto2) -> assign(new_constants, 1).
% 0.99/1.29 % set(auto2) -> assign(fold_denial_max, 3).
% 0.99/1.29 % set(auto2) -> assign(max_weight, "200.000").
% 0.99/1.29 % set(auto2) -> assign(max_hours, 1).
% 0.99/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.99/1.29 % set(auto2) -> assign(max_seconds, 0).
% 0.99/1.29 % set(auto2) -> assign(max_minutes, 5).
% 0.99/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.99/1.29 % set(auto2) -> set(sort_initial_sos).
% 0.99/1.29 % set(auto2) -> assign(sos_limit, -1).
% 0.99/1.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.99/1.29 % set(auto2) -> assign(max_megs, 400).
% 0.99/1.29 % set(auto2) -> assign(stats, some).
% 0.99/1.29 % set(auto2) -> clear(echo_input).
% 0.99/1.29 % set(auto2) -> set(quiet).
% 0.99/1.29 % set(auto2) -> clear(print_initial_clauses).
% 0.99/1.29 % set(auto2) -> clear(print_given).
% 0.99/1.29 assign(lrs_ticks,-1).
% 0.99/1.29 assign(sos_limit,10000).
% 0.99/1.29 assign(order,kbo).
% 0.99/1.29 set(lex_order_vars).
% 0.99/1.29 clear(print_given).
% 0.99/1.29
% 0.99/1.29 % formulas(sos). % not echoed (13 formulas)
% 0.99/1.29
% 0.99/1.29 ============================== end of input ==========================
% 0.99/1.29
% 0.99/1.29 % From the command line: assign(max_seconds, 300).
% 0.99/1.29
% 0.99/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.99/1.29
% 0.99/1.29 % Formulas that are not ordinary clauses:
% 0.99/1.29
% 0.99/1.29 ============================== end of process non-clausal formulas ===
% 0.99/1.29
% 0.99/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.99/1.29
% 0.99/1.29 ============================== PREDICATE ELIMINATION =================
% 0.99/1.29
% 0.99/1.29 ============================== end predicate elimination =============
% 0.99/1.29
% 0.99/1.29 Auto_denials:
% 0.99/1.29 % copying label prove_idQa_equals_idQa_Q__idQ_idQa to answer in negative clause
% 0.99/1.29
% 0.99/1.29 Term ordering decisions:
% 0.99/1.29 Function symbol KB weights: idQa=1. identity=1. zero=1. idQ_idQa=1. a=1. idQa_Q__idQ_idQa=1. divide=1.
% 0.99/1.29
% 0.99/1.29 ============================== end of process initial clauses ========
% 0.99/1.29
% 0.99/1.29 ============================== CLAUSES FOR SEARCH ====================
% 0.99/1.29
% 0.99/1.29 ============================== end of clauses for search =============
% 0.99/1.29
% 0.99/1.29 ============================== SEARCH ================================
% 0.99/1.29
% 0.99/1.29 % Starting search at 0.01 seconds.
% 0.99/1.29
% 0.99/1.29 ============================== PROOF =================================
% 0.99/1.29 % SZS status Unsatisfiable
% 0.99/1.29 % SZS output start Refutation
% 0.99/1.29
% 0.99/1.29 % Proof 1 at 0.29 (+ 0.01) seconds: prove_idQa_equals_idQa_Q__idQ_idQa.
% 0.99/1.29 % Length of proof is 67.
% 0.99/1.29 % Level of proof is 18.
% 0.99/1.29 % Maximum clause weight is 23.000.
% 0.99/1.29 % Given clauses 186.
% 0.99/1.29
% 0.99/1.29 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 0.99/1.29 2 less_equal(A,identity) # label(identity_is_largest) # label(axiom). [assumption].
% 0.99/1.29 3 quotient(identity,a,idQa) # label(identity_divide_a) # label(hypothesis). [assumption].
% 0.99/1.29 4 quotient(identity,idQa,idQ_idQa) # label(identity_divide_idQa) # label(hypothesis). [assumption].
% 0.99/1.29 5 quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) # label(identity_divide_idQ_idQa) # label(hypothesis). [assumption].
% 0.99/1.29 6 quotient(A,B,divide(A,B)) # label(closure) # label(axiom). [assumption].
% 0.99/1.29 7 idQa != idQa_Q__idQ_idQa # label(prove_idQa_equals_idQa_Q__idQ_idQa) # label(negated_conjecture) # answer(prove_idQa_equals_idQa_Q__idQ_idQa). [assumption].
% 0.99/1.29 8 idQa_Q__idQ_idQa != idQa # answer(prove_idQa_equals_idQa_Q__idQ_idQa). [copy(7),flip(a)].
% 0.99/1.29 9 -less_equal(A,B) | quotient(A,B,zero) # label(quotient_less_equal) # label(axiom). [assumption].
% 0.99/1.29 10 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom). [assumption].
% 0.99/1.29 11 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom). [assumption].
% 0.99/1.29 12 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.99/1.29 13 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom). [assumption].
% 0.99/1.29 14 -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].
% 0.99/1.29 15 quotient(A,identity,zero). [hyper(9,a,2,a)].
% 0.99/1.29 16 quotient(zero,A,zero). [hyper(9,a,1,a)].
% 0.99/1.29 17 less_equal(divide(A,B),A). [hyper(11,a,6,a)].
% 0.99/1.29 18 less_equal(idQa_Q__idQ_idQa,idQa). [hyper(11,a,5,a)].
% 0.99/1.29 21 divide(identity,a) = idQa. [hyper(13,a,6,a,b,3,a)].
% 0.99/1.29 28 less_equal(divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(A,idQa),idQ_idQa)). [hyper(14,a,6,a,b,5,a,c,6,a,d,6,a,e,6,a)].
% 0.99/1.29 42 less_equal(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)). [hyper(14,a,3,a,b,6,a,c,4,a,d,6,a,e,6,a)].
% 0.99/1.29 70 -less_equal(idQa,idQa_Q__idQ_idQa) # answer(prove_idQa_equals_idQa_Q__idQ_idQa). [ur(12,b,18,a,c,8,a(flip))].
% 0.99/1.29 77 less_equal(divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),zero). [hyper(14,a,15,a,b,6,a,c,5,a,d,6,a,e,16,a)].
% 0.99/1.29 79 less_equal(divide(idQa,idQa),zero). [hyper(14,a,15,a,b,6,a,c,3,a,d,6,a,e,16,a),rewrite([21(4)])].
% 0.99/1.29 80 less_equal(divide(divide(A,idQa),idQ_idQa),zero). [hyper(14,a,15,a,b,4,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.29 90 less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)). [hyper(14,a,6,a,b,16,a,c,6,a,d,6,a,e,6,a)].
% 0.99/1.29 101 quotient(divide(A,B),A,zero). [hyper(9,a,17,a)].
% 0.99/1.29 104 -quotient(idQa,idQa_Q__idQ_idQa,zero) # answer(prove_idQa_equals_idQa_Q__idQ_idQa). [ur(10,b,70,a)].
% 0.99/1.29 109 divide(idQa,idQa) = zero. [hyper(12,a,1,a,b,79,a),flip(a)].
% 0.99/1.29 110 less_equal(divide(idQ_idQa,divide(a,idQa)),zero). [back_rewrite(42),rewrite([109(8)])].
% 0.99/1.29 130 less_equal(divide(divide(A,A),zero),zero). [hyper(14,a,6,a,b,101,a,c,6,a,d,6,a,e,101,a)].
% 0.99/1.29 144 divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)) = zero. [hyper(12,a,1,a,b,77,a),flip(a)].
% 0.99/1.29 145 divide(divide(A,idQa),idQ_idQa) = zero. [hyper(12,a,1,a,b,80,a),flip(a)].
% 0.99/1.29 146 less_equal(divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa),zero). [back_rewrite(28),rewrite([145(8)])].
% 0.99/1.29 150 divide(idQ_idQa,divide(a,idQa)) = zero. [hyper(12,a,1,a,b,110,a),flip(a)].
% 0.99/1.29 153 divide(divide(A,A),zero) = zero. [hyper(12,a,1,a,b,130,a),flip(a)].
% 0.99/1.29 154 quotient(idQa_Q__idQ_idQa,divide(identity,idQ_idQa),zero). [para(144(a,1),6(a,3))].
% 0.99/1.29 159 less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)). [hyper(10,a,154,a)].
% 0.99/1.29 161 quotient(divide(A,idQa),idQ_idQa,zero). [para(145(a,1),6(a,3))].
% 0.99/1.29 166 less_equal(divide(A,idQa),idQ_idQa). [hyper(10,a,161,a)].
% 0.99/1.29 168 divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa) = zero. [hyper(12,a,1,a,b,146,a),flip(a)].
% 0.99/1.29 177 quotient(idQ_idQa,divide(a,idQa),zero). [para(150(a,1),6(a,3))].
% 0.99/1.29 185 less_equal(idQ_idQa,divide(a,idQa)). [hyper(10,a,177,a)].
% 0.99/1.29 186 divide(a,idQa) = idQ_idQa. [hyper(12,a,166,a,b,185,a)].
% 0.99/1.29 191 quotient(idQ_idQa,a,zero). [para(186(a,1),101(a,1))].
% 0.99/1.29 203 less_equal(divide(idQa,zero),divide(divide(identity,idQ_idQa),a)). [hyper(14,a,6,a,b,191,a,c,3,a,d,6,a,e,6,a)].
% 0.99/1.29 207 quotient(divide(A,A),zero,zero). [para(153(a,1),6(a,3))].
% 0.99/1.29 212 less_equal(divide(A,A),zero). [hyper(10,a,207,a)].
% 0.99/1.29 213 divide(A,A) = zero. [hyper(12,a,1,a,b,212,a),flip(a)].
% 0.99/1.29 220 less_equal(divide(divide(A,divide(A,zero)),zero),zero). [para(213(a,1),90(a,2))].
% 0.99/1.29 222 quotient(divide(A,idQ_idQa),idQa_Q__idQ_idQa,zero). [para(168(a,1),6(a,3))].
% 0.99/1.29 228 less_equal(divide(A,idQ_idQa),idQa_Q__idQ_idQa). [hyper(10,a,222,a)].
% 0.99/1.29 230 divide(identity,idQ_idQa) = idQa_Q__idQ_idQa. [hyper(12,a,159,a,b,228,a),flip(a)].
% 0.99/1.29 231 less_equal(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a)). [back_rewrite(203),rewrite([230(6)])].
% 0.99/1.29 242 quotient(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a),zero). [hyper(9,a,231,a)].
% 0.99/1.29 292 less_equal(divide(divide(divide(idQa,zero),idQa_Q__idQ_idQa),zero),zero). [hyper(14,a,242,a,b,101,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.29 362 divide(divide(A,divide(A,zero)),zero) = zero. [hyper(12,a,1,a,b,220,a),flip(a)].
% 0.99/1.29 383 divide(divide(divide(idQa,zero),idQa_Q__idQ_idQa),zero) = zero. [hyper(12,a,1,a,b,292,a),flip(a)].
% 0.99/1.29 493 quotient(divide(A,divide(A,zero)),zero,zero). [para(362(a,1),6(a,3))].
% 0.99/1.29 505 less_equal(divide(A,divide(A,zero)),zero). [hyper(10,a,493,a)].
% 0.99/1.29 506 divide(A,divide(A,zero)) = zero. [hyper(12,a,1,a,b,505,a),flip(a)].
% 0.99/1.29 507 quotient(A,divide(A,zero),zero). [para(506(a,1),6(a,3))].
% 0.99/1.29 563 less_equal(A,divide(A,zero)). [hyper(10,a,507,a)].
% 0.99/1.29 565 divide(A,zero) = A. [hyper(12,a,17,a,b,563,a)].
% 0.99/1.29 611 divide(idQa,idQa_Q__idQ_idQa) = zero. [back_rewrite(383),rewrite([565(3),565(5)])].
% 0.99/1.29 693 quotient(idQa,idQa_Q__idQ_idQa,zero). [para(611(a,1),6(a,3))].
% 0.99/1.29 694 $F # answer(prove_idQa_equals_idQa_Q__idQ_idQa). [resolve(693,a,104,a)].
% 0.99/1.29
% 0.99/1.29 % SZS output end Refutation
% 0.99/1.29 ============================== end of proof ==========================
% 0.99/1.29
% 0.99/1.29 ============================== STATISTICS ============================
% 0.99/1.29
% 0.99/1.29 Given=186. Generated=16917. Kept=692. proofs=1.
% 0.99/1.29 Usable=90. Sos=172. Demods=37. Limbo=0, Disabled=442. Hints=0.
% 0.99/1.29 Megabytes=0.44.
% 0.99/1.29 User_CPU=0.29, System_CPU=0.01, Wall_clock=1.
% 0.99/1.29
% 0.99/1.29 ============================== end of statistics =====================
% 0.99/1.29
% 0.99/1.29 ============================== end of search =========================
% 0.99/1.29
% 0.99/1.29 THEOREM PROVED
% 0.99/1.29 % SZS status Unsatisfiable
% 0.99/1.29
% 0.99/1.29 Exiting with 1 proof.
% 0.99/1.29
% 0.99/1.29 Process 22089 exit (max_proofs) Fri Jul 1 14:32:50 2022
% 0.99/1.29 Prover9 interrupted
%------------------------------------------------------------------------------