TSTP Solution File: HEN009-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 13:00:54 EDT 2022
% Result : Unsatisfiable 0.99s 1.27s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n014.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 14:06:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.99/1.27 ============================== Prover9 ===============================
% 0.99/1.27 Prover9 (32) version 2009-11A, November 2009.
% 0.99/1.27 Process 20242 was started by sandbox on n014.cluster.edu,
% 0.99/1.27 Fri Jul 1 14:06:56 2022
% 0.99/1.27 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20088_n014.cluster.edu".
% 0.99/1.27 ============================== end of head ===========================
% 0.99/1.27
% 0.99/1.27 ============================== INPUT =================================
% 0.99/1.27
% 0.99/1.27 % Reading from file /tmp/Prover9_20088_n014.cluster.edu
% 0.99/1.27
% 0.99/1.27 set(prolog_style_variables).
% 0.99/1.27 set(auto2).
% 0.99/1.27 % set(auto2) -> set(auto).
% 0.99/1.27 % set(auto) -> set(auto_inference).
% 0.99/1.27 % set(auto) -> set(auto_setup).
% 0.99/1.27 % set(auto_setup) -> set(predicate_elim).
% 0.99/1.27 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.99/1.27 % set(auto) -> set(auto_limits).
% 0.99/1.27 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.99/1.27 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.99/1.27 % set(auto) -> set(auto_denials).
% 0.99/1.27 % set(auto) -> set(auto_process).
% 0.99/1.27 % set(auto2) -> assign(new_constants, 1).
% 0.99/1.27 % set(auto2) -> assign(fold_denial_max, 3).
% 0.99/1.27 % set(auto2) -> assign(max_weight, "200.000").
% 0.99/1.27 % set(auto2) -> assign(max_hours, 1).
% 0.99/1.27 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.99/1.27 % set(auto2) -> assign(max_seconds, 0).
% 0.99/1.27 % set(auto2) -> assign(max_minutes, 5).
% 0.99/1.27 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.99/1.27 % set(auto2) -> set(sort_initial_sos).
% 0.99/1.27 % set(auto2) -> assign(sos_limit, -1).
% 0.99/1.27 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.99/1.27 % set(auto2) -> assign(max_megs, 400).
% 0.99/1.27 % set(auto2) -> assign(stats, some).
% 0.99/1.27 % set(auto2) -> clear(echo_input).
% 0.99/1.27 % set(auto2) -> set(quiet).
% 0.99/1.27 % set(auto2) -> clear(print_initial_clauses).
% 0.99/1.27 % set(auto2) -> clear(print_given).
% 0.99/1.27 assign(lrs_ticks,-1).
% 0.99/1.27 assign(sos_limit,10000).
% 0.99/1.27 assign(order,kbo).
% 0.99/1.27 set(lex_order_vars).
% 0.99/1.27 clear(print_given).
% 0.99/1.27
% 0.99/1.27 % formulas(sos). % not echoed (13 formulas)
% 0.99/1.27
% 0.99/1.27 ============================== end of input ==========================
% 0.99/1.27
% 0.99/1.27 % From the command line: assign(max_seconds, 300).
% 0.99/1.27
% 0.99/1.27 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.99/1.27
% 0.99/1.27 % Formulas that are not ordinary clauses:
% 0.99/1.27
% 0.99/1.27 ============================== end of process non-clausal formulas ===
% 0.99/1.27
% 0.99/1.27 ============================== PROCESS INITIAL CLAUSES ===============
% 0.99/1.27
% 0.99/1.27 ============================== PREDICATE ELIMINATION =================
% 0.99/1.27
% 0.99/1.27 ============================== end predicate elimination =============
% 0.99/1.27
% 0.99/1.27 Auto_denials:
% 0.99/1.27 % copying label prove_one_inversion_equals_three to answer in negative clause
% 0.99/1.27
% 0.99/1.27 Term ordering decisions:
% 0.99/1.27 Function symbol KB weights: identity=1. zero=1. idQ_idQa=1. idQa=1. a=1. idQ__idQ_idQa=1. divide=1.
% 0.99/1.27
% 0.99/1.27 ============================== end of process initial clauses ========
% 0.99/1.27
% 0.99/1.27 ============================== CLAUSES FOR SEARCH ====================
% 0.99/1.27
% 0.99/1.27 ============================== end of clauses for search =============
% 0.99/1.27
% 0.99/1.27 ============================== SEARCH ================================
% 0.99/1.27
% 0.99/1.27 % Starting search at 0.01 seconds.
% 0.99/1.27
% 0.99/1.27 ============================== PROOF =================================
% 0.99/1.27 % SZS status Unsatisfiable
% 0.99/1.27 % SZS output start Refutation
% 0.99/1.27
% 0.99/1.27 % Proof 1 at 0.28 (+ 0.01) seconds: prove_one_inversion_equals_three.
% 0.99/1.27 % Length of proof is 80.
% 0.99/1.27 % Level of proof is 23.
% 0.99/1.27 % Maximum clause weight is 23.000.
% 0.99/1.27 % Given clauses 204.
% 0.99/1.27
% 0.99/1.27 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 0.99/1.27 2 less_equal(A,identity) # label(identity_is_largest) # label(axiom). [assumption].
% 0.99/1.27 3 quotient(identity,a,idQa) # label(identity_divide_a) # label(hypothesis). [assumption].
% 0.99/1.27 4 quotient(identity,idQa,idQ_idQa) # label(identity_divide_idQa) # label(hypothesis). [assumption].
% 0.99/1.27 5 quotient(identity,idQ_idQa,idQ__idQ_idQa) # label(identity_divide_idQ_idQa) # label(hypothesis). [assumption].
% 0.99/1.27 6 quotient(A,B,divide(A,B)) # label(closure) # label(axiom). [assumption].
% 0.99/1.27 7 idQa != idQ__idQ_idQa # label(prove_one_inversion_equals_three) # label(negated_conjecture) # answer(prove_one_inversion_equals_three). [assumption].
% 0.99/1.27 8 idQ__idQ_idQa != idQa # answer(prove_one_inversion_equals_three). [copy(7),flip(a)].
% 0.99/1.27 9 -less_equal(A,B) | quotient(A,B,zero) # label(quotient_less_equal) # label(axiom). [assumption].
% 0.99/1.27 10 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom). [assumption].
% 0.99/1.27 11 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom). [assumption].
% 0.99/1.27 12 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 0.99/1.27 13 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom). [assumption].
% 0.99/1.27 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].
% 0.99/1.27 15 quotient(A,identity,zero). [hyper(9,a,2,a)].
% 0.99/1.27 16 quotient(zero,A,zero). [hyper(9,a,1,a)].
% 0.99/1.27 17 less_equal(divide(A,B),A). [hyper(11,a,6,a)].
% 0.99/1.27 19 divide(identity,idQa) = idQ_idQa. [hyper(13,a,6,a,b,4,a)].
% 0.99/1.27 20 divide(identity,a) = idQa. [hyper(13,a,6,a,b,3,a)].
% 0.99/1.27 23 less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)). [hyper(14,a,6,a,b,6,a,c,6,a,d,6,a,e,6,a)].
% 0.99/1.27 38 less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),divide(idQ_idQa,idQ_idQa)). [hyper(14,a,4,a,b,6,a,c,5,a,d,6,a,e,6,a)].
% 0.99/1.27 43 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)].
% 0.99/1.27 76 less_equal(divide(divide(A,B),divide(identity,B)),zero). [hyper(14,a,15,a,b,6,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.27 78 less_equal(divide(idQ_idQa,idQ_idQa),zero). [hyper(14,a,15,a,b,6,a,c,4,a,d,6,a,e,16,a),rewrite([19(4)])].
% 0.99/1.27 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([20(4)])].
% 0.99/1.27 80 less_equal(divide(divide(A,idQ_idQa),idQ__idQ_idQa),zero). [hyper(14,a,15,a,b,5,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.27 81 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)].
% 0.99/1.27 95 quotient(divide(A,B),A,zero). [hyper(9,a,17,a)].
% 0.99/1.27 97 divide(idQ_idQa,idQ_idQa) = zero. [hyper(12,a,1,a,b,78,a),flip(a)].
% 0.99/1.27 98 less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero). [back_rewrite(38),rewrite([97(8)])].
% 0.99/1.27 100 divide(idQa,idQa) = zero. [hyper(12,a,1,a,b,79,a),flip(a)].
% 0.99/1.27 101 less_equal(divide(idQ_idQa,divide(a,idQa)),zero). [back_rewrite(43),rewrite([100(8)])].
% 0.99/1.27 131 divide(divide(A,idQ_idQa),idQ__idQ_idQa) = zero. [hyper(12,a,1,a,b,80,a),flip(a)].
% 0.99/1.27 133 divide(divide(A,idQa),idQ_idQa) = zero. [hyper(12,a,1,a,b,81,a),flip(a)].
% 0.99/1.27 135 divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)) = zero. [hyper(12,a,1,a,b,98,a),flip(a)].
% 0.99/1.27 138 divide(idQ_idQa,divide(a,idQa)) = zero. [hyper(12,a,1,a,b,101,a),flip(a)].
% 0.99/1.27 142 quotient(divide(A,idQ_idQa),idQ__idQ_idQa,zero). [para(131(a,1),6(a,3))].
% 0.99/1.27 145 less_equal(divide(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa)),zero). [para(131(a,1),23(a,2))].
% 0.99/1.27 147 less_equal(divide(A,idQ_idQa),idQ__idQ_idQa). [hyper(10,a,142,a)].
% 0.99/1.27 148 quotient(divide(A,idQa),idQ_idQa,zero). [para(133(a,1),6(a,3))].
% 0.99/1.27 155 less_equal(divide(A,idQa),idQ_idQa). [hyper(10,a,148,a)].
% 0.99/1.27 164 quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero). [para(135(a,1),6(a,3))].
% 0.99/1.27 171 less_equal(idQ__idQ_idQa,divide(idQa,idQ_idQa)). [hyper(10,a,164,a)].
% 0.99/1.27 172 divide(idQa,idQ_idQa) = idQ__idQ_idQa. [hyper(12,a,147,a,b,171,a)].
% 0.99/1.27 175 less_equal(idQ__idQ_idQa,idQa). [para(172(a,1),17(a,1))].
% 0.99/1.27 178 quotient(idQ__idQ_idQa,idQa,zero). [para(172(a,1),95(a,1))].
% 0.99/1.27 182 -less_equal(idQa,idQ__idQ_idQa) # answer(prove_one_inversion_equals_three). [ur(12,b,175,a,c,8,a(flip))].
% 0.99/1.27 188 less_equal(divide(divide(divide(idQ__idQ_idQa,A),idQa),zero),zero). [hyper(14,a,95,a,b,178,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.27 194 -quotient(idQ__idQ_idQa,A,idQa) # answer(prove_one_inversion_equals_three). [ur(11,b,182,a)].
% 0.99/1.27 196 quotient(idQ_idQa,divide(a,idQa),zero). [para(138(a,1),6(a,3))].
% 0.99/1.27 205 less_equal(idQ_idQa,divide(a,idQa)). [hyper(10,a,196,a)].
% 0.99/1.27 206 divide(a,idQa) = idQ_idQa. [hyper(12,a,155,a,b,205,a)].
% 0.99/1.27 212 quotient(idQ_idQa,a,zero). [para(206(a,1),95(a,1))].
% 0.99/1.27 224 less_equal(divide(divide(divide(idQ_idQa,A),a),zero),zero). [hyper(14,a,95,a,b,212,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.27 227 divide(divide(A,B),divide(identity,B)) = zero. [hyper(12,a,1,a,b,76,a),flip(a)].
% 0.99/1.27 327 divide(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa)) = zero. [hyper(12,a,1,a,b,145,a),flip(a)].
% 0.99/1.27 340 divide(divide(divide(idQ__idQ_idQa,A),idQa),zero) = zero. [hyper(12,a,1,a,b,188,a),flip(a)].
% 0.99/1.27 357 divide(divide(divide(idQ_idQa,A),a),zero) = zero. [hyper(12,a,1,a,b,224,a),flip(a)].
% 0.99/1.27 359 quotient(divide(A,B),divide(identity,B),zero). [para(227(a,1),6(a,3))].
% 0.99/1.27 369 less_equal(divide(A,B),divide(identity,B)). [hyper(10,a,359,a)].
% 0.99/1.27 381 quotient(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa),zero). [para(327(a,1),6(a,3))].
% 0.99/1.27 391 less_equal(divide(A,idQ__idQ_idQa),divide(idQ_idQa,idQ__idQ_idQa)). [hyper(10,a,381,a)].
% 0.99/1.27 393 divide(idQ_idQa,idQ__idQ_idQa) = divide(identity,idQ__idQ_idQa). [hyper(12,a,369,a,b,391,a)].
% 0.99/1.27 478 quotient(divide(divide(idQ__idQ_idQa,A),idQa),zero,zero). [para(340(a,1),6(a,3))].
% 0.99/1.27 486 less_equal(divide(divide(idQ__idQ_idQa,A),idQa),zero). [hyper(10,a,478,a)].
% 0.99/1.27 488 divide(divide(idQ__idQ_idQa,A),idQa) = zero. [hyper(12,a,1,a,b,486,a),flip(a)].
% 0.99/1.27 489 quotient(divide(idQ__idQ_idQa,A),idQa,zero). [para(488(a,1),6(a,3))].
% 0.99/1.27 500 less_equal(divide(idQ__idQ_idQa,A),idQa). [hyper(10,a,489,a)].
% 0.99/1.27 537 quotient(divide(divide(idQ_idQa,A),a),zero,zero). [para(357(a,1),6(a,3))].
% 0.99/1.27 546 less_equal(divide(divide(idQ_idQa,A),a),zero). [hyper(10,a,537,a)].
% 0.99/1.27 548 divide(divide(idQ_idQa,A),a) = zero. [hyper(12,a,1,a,b,546,a),flip(a)].
% 0.99/1.27 550 quotient(divide(idQ_idQa,A),a,zero). [para(548(a,1),6(a,3))].
% 0.99/1.27 561 quotient(divide(identity,idQ__idQ_idQa),a,zero). [para(393(a,1),550(a,1))].
% 0.99/1.27 564 less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero). [hyper(14,a,6,a,b,6,a,c,6,a,d,6,a,e,561,a),rewrite([20(3)])].
% 0.99/1.27 576 divide(idQa,divide(idQ__idQ_idQa,a)) = zero. [hyper(12,a,1,a,b,564,a),flip(a)].
% 0.99/1.27 577 quotient(idQa,divide(idQ__idQ_idQa,a),zero). [para(576(a,1),6(a,3))].
% 0.99/1.27 595 less_equal(idQa,divide(idQ__idQ_idQa,a)). [hyper(10,a,577,a)].
% 0.99/1.27 596 divide(idQ__idQ_idQa,a) = idQa. [hyper(12,a,500,a,b,595,a)].
% 0.99/1.27 597 quotient(idQ__idQ_idQa,a,idQa). [para(596(a,1),6(a,3))].
% 0.99/1.27 598 $F # answer(prove_one_inversion_equals_three). [resolve(597,a,194,a)].
% 0.99/1.27
% 0.99/1.27 % SZS output end Refutation
% 0.99/1.27 ============================== end of proof ==========================
% 0.99/1.27
% 0.99/1.27 ============================== STATISTICS ============================
% 0.99/1.27
% 0.99/1.27 Given=204. Generated=12501. Kept=596. proofs=1.
% 0.99/1.27 Usable=113. Sos=180. Demods=43. Limbo=0, Disabled=315. Hints=0.
% 0.99/1.27 Megabytes=0.40.
% 0.99/1.27 User_CPU=0.28, System_CPU=0.01, Wall_clock=0.
% 0.99/1.27
% 0.99/1.27 ============================== end of statistics =====================
% 0.99/1.27
% 0.99/1.27 ============================== end of search =========================
% 0.99/1.27
% 0.99/1.27 THEOREM PROVED
% 0.99/1.27 % SZS status Unsatisfiable
% 0.99/1.27
% 0.99/1.27 Exiting with 1 proof.
% 0.99/1.27
% 0.99/1.27 Process 20242 exit (max_proofs) Fri Jul 1 14:06:56 2022
% 0.99/1.27 Prover9 interrupted
%------------------------------------------------------------------------------