TSTP Solution File: HEN011-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : HEN011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 1.80s 2.07s
% Output : Refutation 1.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.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 14:25:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/2.07 ============================== Prover9 ===============================
% 1.80/2.07 Prover9 (32) version 2009-11A, November 2009.
% 1.80/2.07 Process 22939 was started by sandbox2 on n021.cluster.edu,
% 1.80/2.07 Fri Jul 1 14:25:14 2022
% 1.80/2.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22786_n021.cluster.edu".
% 1.80/2.07 ============================== end of head ===========================
% 1.80/2.07
% 1.80/2.07 ============================== INPUT =================================
% 1.80/2.07
% 1.80/2.07 % Reading from file /tmp/Prover9_22786_n021.cluster.edu
% 1.80/2.07
% 1.80/2.07 set(prolog_style_variables).
% 1.80/2.07 set(auto2).
% 1.80/2.07 % set(auto2) -> set(auto).
% 1.80/2.07 % set(auto) -> set(auto_inference).
% 1.80/2.07 % set(auto) -> set(auto_setup).
% 1.80/2.07 % set(auto_setup) -> set(predicate_elim).
% 1.80/2.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.80/2.07 % set(auto) -> set(auto_limits).
% 1.80/2.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.80/2.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.80/2.07 % set(auto) -> set(auto_denials).
% 1.80/2.07 % set(auto) -> set(auto_process).
% 1.80/2.07 % set(auto2) -> assign(new_constants, 1).
% 1.80/2.07 % set(auto2) -> assign(fold_denial_max, 3).
% 1.80/2.07 % set(auto2) -> assign(max_weight, "200.000").
% 1.80/2.07 % set(auto2) -> assign(max_hours, 1).
% 1.80/2.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.80/2.07 % set(auto2) -> assign(max_seconds, 0).
% 1.80/2.07 % set(auto2) -> assign(max_minutes, 5).
% 1.80/2.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.80/2.07 % set(auto2) -> set(sort_initial_sos).
% 1.80/2.07 % set(auto2) -> assign(sos_limit, -1).
% 1.80/2.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.80/2.07 % set(auto2) -> assign(max_megs, 400).
% 1.80/2.07 % set(auto2) -> assign(stats, some).
% 1.80/2.07 % set(auto2) -> clear(echo_input).
% 1.80/2.07 % set(auto2) -> set(quiet).
% 1.80/2.07 % set(auto2) -> clear(print_initial_clauses).
% 1.80/2.07 % set(auto2) -> clear(print_given).
% 1.80/2.07 assign(lrs_ticks,-1).
% 1.80/2.07 assign(sos_limit,10000).
% 1.80/2.07 assign(order,kbo).
% 1.80/2.07 set(lex_order_vars).
% 1.80/2.07 clear(print_given).
% 1.80/2.07
% 1.80/2.07 % formulas(sos). % not echoed (16 formulas)
% 1.80/2.07
% 1.80/2.07 ============================== end of input ==========================
% 1.80/2.07
% 1.80/2.07 % From the command line: assign(max_seconds, 300).
% 1.80/2.07
% 1.80/2.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.80/2.07
% 1.80/2.07 % Formulas that are not ordinary clauses:
% 1.80/2.07
% 1.80/2.07 ============================== end of process non-clausal formulas ===
% 1.80/2.07
% 1.80/2.07 ============================== PROCESS INITIAL CLAUSES ===============
% 1.80/2.07
% 1.80/2.07 ============================== PREDICATE ELIMINATION =================
% 1.80/2.07
% 1.80/2.07 ============================== end predicate elimination =============
% 1.80/2.07
% 1.80/2.07 Auto_denials:
% 1.80/2.07 % copying label prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa to answer in negative clause
% 1.80/2.07
% 1.80/2.07 Term ordering decisions:
% 1.80/2.07 Function symbol KB weights: identity=1. idQa=1. idQb=1. zero=1. idQ_idQa=1. idQ_idQb=1. a=1. b=1. idQa_Q__idQ_idQb=1. idQb_Q__idQ_idQa=1. divide=1.
% 1.80/2.07
% 1.80/2.07 ============================== end of process initial clauses ========
% 1.80/2.07
% 1.80/2.07 ============================== CLAUSES FOR SEARCH ====================
% 1.80/2.07
% 1.80/2.07 ============================== end of clauses for search =============
% 1.80/2.07
% 1.80/2.07 ============================== SEARCH ================================
% 1.80/2.07
% 1.80/2.07 % Starting search at 0.01 seconds.
% 1.80/2.07
% 1.80/2.07 ============================== PROOF =================================
% 1.80/2.07 % SZS status Unsatisfiable
% 1.80/2.07 % SZS output start Refutation
% 1.80/2.07
% 1.80/2.07 % Proof 1 at 1.08 (+ 0.03) seconds: prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa.
% 1.80/2.07 % Length of proof is 127.
% 1.80/2.07 % Level of proof is 32.
% 1.80/2.07 % Maximum clause weight is 23.000.
% 1.80/2.07 % Given clauses 643.
% 1.80/2.07
% 1.80/2.07 1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom). [assumption].
% 1.80/2.07 2 less_equal(A,identity) # label(identity_is_largest) # label(axiom). [assumption].
% 1.80/2.07 3 quotient(identity,a,idQa) # label(identity_divide_a) # label(hypothesis). [assumption].
% 1.80/2.07 4 quotient(identity,b,idQb) # label(identity_divide_b) # label(hypothesis). [assumption].
% 1.80/2.07 5 quotient(identity,idQb,idQ_idQb) # label(identity_divide_idQb) # label(hypothesis). [assumption].
% 1.80/2.07 6 quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb) # label(idQa_divide_idQ_idQb) # label(hypothesis). [assumption].
% 1.80/2.07 7 quotient(identity,idQa,idQ_idQa) # label(identity_divide_idQa) # label(hypothesis). [assumption].
% 1.80/2.07 8 quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa) # label(idQb_divide_idQ_idQa) # label(hypothesis). [assumption].
% 1.80/2.07 9 quotient(A,B,divide(A,B)) # label(closure) # label(axiom). [assumption].
% 1.80/2.07 10 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].
% 1.80/2.07 11 idQb_Q__idQ_idQa != idQa_Q__idQ_idQb # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [copy(10),flip(a)].
% 1.80/2.07 12 -less_equal(A,B) | quotient(A,B,zero) # label(quotient_less_equal) # label(axiom). [assumption].
% 1.80/2.07 13 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom). [assumption].
% 1.80/2.07 14 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom). [assumption].
% 1.80/2.07 15 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom). [assumption].
% 1.80/2.07 16 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom). [assumption].
% 1.80/2.07 17 -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].
% 1.80/2.07 18 quotient(A,identity,zero). [hyper(12,a,2,a)].
% 1.80/2.07 19 quotient(zero,A,zero). [hyper(12,a,1,a)].
% 1.80/2.07 20 less_equal(divide(A,B),A). [hyper(14,a,9,a)].
% 1.80/2.07 23 divide(idQb,idQ_idQa) = idQb_Q__idQ_idQa. [hyper(16,a,9,a,b,8,a)].
% 1.80/2.07 25 divide(idQa,idQ_idQb) = idQa_Q__idQ_idQb. [hyper(16,a,9,a,b,6,a)].
% 1.80/2.07 27 divide(identity,b) = idQb. [hyper(16,a,9,a,b,4,a)].
% 1.80/2.07 28 divide(identity,a) = idQa. [hyper(16,a,9,a,b,3,a)].
% 1.80/2.07 31 less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)). [hyper(17,a,9,a,b,9,a,c,9,a,d,9,a,e,9,a)].
% 1.80/2.07 57 less_equal(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)). [hyper(17,a,7,a,b,6,a,c,9,a,d,9,a,e,9,a)].
% 1.80/2.07 65 less_equal(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)). [hyper(17,a,5,a,b,8,a,c,9,a,d,9,a,e,9,a)].
% 1.80/2.07 69 less_equal(divide(idQ_idQb,divide(b,idQb)),divide(idQb,idQb)). [hyper(17,a,4,a,b,9,a,c,5,a,d,9,a,e,9,a)].
% 1.80/2.07 74 less_equal(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)). [hyper(17,a,3,a,b,9,a,c,7,a,d,9,a,e,9,a)].
% 1.80/2.07 132 less_equal(divide(idQb,idQb),zero). [hyper(17,a,18,a,b,9,a,c,4,a,d,9,a,e,19,a),rewrite([27(4)])].
% 1.80/2.07 133 less_equal(divide(idQa,idQa),zero). [hyper(17,a,18,a,b,9,a,c,3,a,d,9,a,e,19,a),rewrite([28(4)])].
% 1.80/2.07 134 less_equal(divide(divide(A,idQa),idQ_idQa),zero). [hyper(17,a,18,a,b,7,a,c,9,a,d,9,a,e,19,a)].
% 1.80/2.07 135 less_equal(divide(divide(A,idQb),idQ_idQb),zero). [hyper(17,a,18,a,b,5,a,c,9,a,d,9,a,e,19,a)].
% 1.80/2.07 136 less_equal(divide(divide(A,b),idQb),zero). [hyper(17,a,18,a,b,4,a,c,9,a,d,9,a,e,19,a)].
% 1.80/2.07 137 less_equal(divide(divide(A,a),idQa),zero). [hyper(17,a,18,a,b,3,a,c,9,a,d,9,a,e,19,a)].
% 1.80/2.07 157 divide(zero,A) = zero. [hyper(16,a,9,a,b,19,a)].
% 1.80/2.07 164 quotient(divide(A,B),A,zero). [hyper(12,a,20,a)].
% 1.80/2.07 173 quotient(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B),zero). [hyper(12,a,31,a)].
% 1.80/2.07 176 divide(idQb,idQb) = zero. [hyper(15,a,1,a,b,132,a),flip(a)].
% 1.80/2.07 177 less_equal(divide(idQ_idQb,divide(b,idQb)),zero). [back_rewrite(69),rewrite([176(8)])].
% 1.80/2.07 180 divide(idQa,idQa) = zero. [hyper(15,a,1,a,b,133,a),flip(a)].
% 1.80/2.07 181 less_equal(divide(idQ_idQa,divide(a,idQa)),zero). [back_rewrite(74),rewrite([180(8)])].
% 1.80/2.07 220 less_equal(divide(divide(A,A),zero),zero). [hyper(17,a,9,a,b,164,a,c,9,a,d,9,a,e,164,a)].
% 1.80/2.07 223 less_equal(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)). [hyper(17,a,9,a,b,164,a,c,9,a,d,9,a,e,9,a)].
% 1.80/2.07 245 divide(divide(A,idQa),idQ_idQa) = zero. [hyper(15,a,1,a,b,134,a),flip(a)].
% 1.80/2.07 246 divide(divide(A,idQb),idQ_idQb) = zero. [hyper(15,a,1,a,b,135,a),flip(a)].
% 1.80/2.07 247 divide(divide(A,b),idQb) = zero. [hyper(15,a,1,a,b,136,a),flip(a)].
% 1.80/2.07 249 divide(divide(A,a),idQa) = zero. [hyper(15,a,1,a,b,137,a),flip(a)].
% 1.80/2.07 252 divide(idQ_idQb,divide(b,idQb)) = zero. [hyper(15,a,1,a,b,177,a),flip(a)].
% 1.80/2.07 255 divide(idQ_idQa,divide(a,idQa)) = zero. [hyper(15,a,1,a,b,181,a),flip(a)].
% 1.80/2.07 257 divide(divide(A,A),zero) = zero. [hyper(15,a,1,a,b,220,a),flip(a)].
% 1.80/2.07 272 quotient(divide(A,idQa),idQ_idQa,zero). [para(245(a,1),9(a,3))].
% 1.80/2.07 275 less_equal(divide(divide(A,idQ_idQa),divide(idQa,idQ_idQa)),zero). [para(245(a,1),31(a,2))].
% 1.80/2.07 280 less_equal(divide(A,idQa),idQ_idQa). [hyper(13,a,272,a)].
% 1.80/2.07 281 quotient(divide(A,idQb),idQ_idQb,zero). [para(246(a,1),9(a,3))].
% 1.80/2.07 284 less_equal(divide(divide(A,idQ_idQb),divide(idQb,idQ_idQb)),zero). [para(246(a,1),31(a,2))].
% 1.80/2.07 288 less_equal(divide(A,idQb),idQ_idQb). [hyper(13,a,281,a)].
% 1.80/2.07 290 quotient(divide(A,b),idQb,zero). [para(247(a,1),9(a,3))].
% 1.80/2.07 297 less_equal(divide(A,b),idQb). [hyper(13,a,290,a)].
% 1.80/2.07 298 quotient(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb),zero). [hyper(12,a,57,a)].
% 1.80/2.07 299 quotient(divide(A,a),idQa,zero). [para(249(a,1),9(a,3))].
% 1.80/2.07 306 less_equal(divide(A,a),idQa). [hyper(13,a,299,a)].
% 1.80/2.07 307 quotient(idQ_idQb,divide(b,idQb),zero). [para(252(a,1),9(a,3))].
% 1.80/2.07 316 less_equal(idQ_idQb,divide(b,idQb)). [hyper(13,a,307,a)].
% 1.80/2.07 317 divide(b,idQb) = idQ_idQb. [hyper(15,a,288,a,b,316,a)].
% 1.80/2.07 322 quotient(idQ_idQb,b,zero). [para(317(a,1),164(a,1))].
% 1.80/2.07 334 less_equal(divide(idQb,zero),divide(divide(identity,idQ_idQb),b)). [hyper(17,a,9,a,b,322,a,c,4,a,d,9,a,e,9,a)].
% 1.80/2.07 337 quotient(idQ_idQa,divide(a,idQa),zero). [para(255(a,1),9(a,3))].
% 1.80/2.07 346 less_equal(idQ_idQa,divide(a,idQa)). [hyper(13,a,337,a)].
% 1.80/2.07 347 divide(a,idQa) = idQ_idQa. [hyper(15,a,280,a,b,346,a)].
% 1.80/2.07 352 quotient(idQ_idQa,a,zero). [para(347(a,1),164(a,1))].
% 1.80/2.07 365 less_equal(divide(idQa,zero),divide(divide(identity,idQ_idQa),a)). [hyper(17,a,9,a,b,352,a,c,3,a,d,9,a,e,9,a)].
% 1.80/2.07 368 quotient(divide(A,A),zero,zero). [para(257(a,1),9(a,3))].
% 1.80/2.07 372 quotient(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa),zero). [hyper(12,a,65,a)].
% 1.80/2.07 374 less_equal(divide(A,A),zero). [hyper(13,a,368,a)].
% 1.80/2.07 375 divide(A,A) = zero. [hyper(15,a,1,a,b,374,a),flip(a)].
% 1.80/2.07 378 quotient(A,A,zero). [para(375(a,1),9(a,3))].
% 1.80/2.07 381 less_equal(divide(divide(A,divide(A,zero)),zero),zero). [hyper(17,a,9,a,b,19,a,c,9,a,d,9,a,e,378,a)].
% 1.80/2.07 551 divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero. [hyper(16,a,9,a,b,173,a)].
% 1.80/2.07 596 divide(divide(A,idQ_idQa),divide(idQa,idQ_idQa)) = zero. [hyper(15,a,1,a,b,275,a),flip(a)].
% 1.80/2.07 597 divide(divide(A,idQ_idQb),divide(idQb,idQ_idQb)) = zero. [hyper(15,a,1,a,b,284,a),flip(a)].
% 1.80/2.07 667 divide(divide(A,divide(A,zero)),zero) = zero. [hyper(15,a,1,a,b,381,a),flip(a)].
% 1.80/2.07 871 less_equal(divide(divide(divide(A,idQ_idQa),idQa),zero),zero). [para(596(a,1),223(a,2,1)),rewrite([157(9)])].
% 1.80/2.07 957 less_equal(divide(divide(divide(A,idQ_idQb),idQb),zero),zero). [para(597(a,1),223(a,2,1)),rewrite([157(9)])].
% 1.80/2.07 1173 quotient(divide(A,divide(A,zero)),zero,zero). [para(667(a,1),9(a,3))].
% 1.80/2.07 1188 less_equal(divide(A,divide(A,zero)),zero). [hyper(13,a,1173,a)].
% 1.80/2.07 1189 divide(A,divide(A,zero)) = zero. [hyper(15,a,1,a,b,1188,a),flip(a)].
% 1.80/2.07 1190 quotient(A,divide(A,zero),zero). [para(1189(a,1),9(a,3))].
% 1.80/2.07 1302 less_equal(A,divide(A,zero)). [hyper(13,a,1190,a)].
% 1.80/2.07 1304 divide(A,zero) = A. [hyper(15,a,20,a,b,1302,a)].
% 1.80/2.07 1386 less_equal(divide(divide(A,idQ_idQb),idQb),zero). [back_rewrite(957),rewrite([1304(6)])].
% 1.80/2.07 1408 less_equal(divide(divide(A,idQ_idQa),idQa),zero). [back_rewrite(871),rewrite([1304(6)])].
% 1.80/2.07 1549 less_equal(idQa,divide(divide(identity,idQ_idQa),a)). [back_rewrite(365),rewrite([1304(3)])].
% 1.80/2.07 1555 less_equal(idQb,divide(divide(identity,idQ_idQb),b)). [back_rewrite(334),rewrite([1304(3)])].
% 1.80/2.07 1591 less_equal(divide(divide(divide(identity,idQ_idQb),idQa_Q__idQ_idQb),idQ_idQa),zero). [hyper(17,a,298,a,b,164,a,c,9,a,d,9,a,e,19,a),rewrite([1304(9)])].
% 1.80/2.07 1594 quotient(A,zero,A). [para(1304(a,1),9(a,3))].
% 1.80/2.07 1633 divide(divide(A,idQ_idQb),idQb) = zero. [hyper(15,a,1,a,b,1386,a),flip(a)].
% 1.80/2.07 1636 divide(divide(A,idQ_idQa),idQa) = zero. [hyper(15,a,1,a,b,1408,a),flip(a)].
% 1.80/2.07 1691 divide(divide(identity,idQ_idQa),a) = idQa. [hyper(15,a,306,a,b,1549,a)].
% 1.80/2.07 1694 divide(divide(identity,idQ_idQb),b) = idQb. [hyper(15,a,297,a,b,1555,a)].
% 1.80/2.07 1732 less_equal(divide(divide(divide(identity,idQ_idQa),idQb_Q__idQ_idQa),idQ_idQb),zero). [hyper(17,a,372,a,b,164,a,c,9,a,d,1594,a,e,19,a)].
% 1.80/2.07 1895 quotient(divide(A,idQ_idQb),idQb,zero). [para(1633(a,1),9(a,3))].
% 1.80/2.07 1909 less_equal(divide(A,idQ_idQb),idQb). [hyper(13,a,1895,a)].
% 1.80/2.07 2065 quotient(divide(A,idQ_idQa),idQa,zero). [para(1636(a,1),9(a,3))].
% 1.80/2.07 2079 less_equal(divide(A,idQ_idQa),idQa). [hyper(13,a,2065,a)].
% 1.80/2.07 2270 less_equal(idQa,divide(identity,idQ_idQa)). [para(1691(a,1),20(a,1))].
% 1.80/2.07 2277 divide(identity,idQ_idQa) = idQa. [hyper(15,a,2079,a,b,2270,a)].
% 1.80/2.07 2290 less_equal(divide(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),zero). [back_rewrite(1732),rewrite([2277(3)])].
% 1.80/2.07 2604 less_equal(idQb,divide(identity,idQ_idQb)). [para(1694(a,1),20(a,1))].
% 1.80/2.07 2613 divide(identity,idQ_idQb) = idQb. [hyper(15,a,1909,a,b,2604,a)].
% 1.80/2.07 2630 less_equal(divide(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa),zero). [back_rewrite(1591),rewrite([2613(3)])].
% 1.80/2.07 2892 divide(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb) = zero. [hyper(15,a,1,a,b,2290,a),flip(a)].
% 1.80/2.07 2907 divide(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa) = zero. [hyper(15,a,1,a,b,2630,a),flip(a)].
% 1.80/2.07 2938 divide(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb)) = zero. [para(2892(a,1),551(a,1,2)),rewrite([25(3),1304(7)])].
% 1.80/2.07 2994 divide(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,idQ_idQa)) = zero. [para(2907(a,1),551(a,1,2)),rewrite([23(3),1304(7)])].
% 1.80/2.07 3072 quotient(idQa_Q__idQ_idQb,divide(idQb_Q__idQ_idQa,idQ_idQb),zero). [para(2938(a,1),9(a,3))].
% 1.80/2.07 3085 less_equal(divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),zero). [hyper(17,a,3072,a,b,164,a,c,9,a,d,1594,a,e,19,a)].
% 1.80/2.07 3089 divide(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa) = zero. [hyper(15,a,1,a,b,3085,a),flip(a)].
% 1.80/2.07 3099 quotient(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa,zero). [para(3089(a,1),9(a,3))].
% 1.80/2.07 3110 less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa). [hyper(13,a,3099,a)].
% 1.80/2.07 3111 -less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [ur(15,b,3110,a,c,11,a)].
% 1.80/2.07 3144 -quotient(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb,zero) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [ur(13,b,3111,a)].
% 1.80/2.07 3163 quotient(idQb_Q__idQ_idQa,divide(idQa_Q__idQ_idQb,idQ_idQa),zero). [para(2994(a,1),9(a,3))].
% 1.80/2.07 3177 less_equal(divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),zero). [hyper(17,a,3163,a,b,164,a,c,9,a,d,1594,a,e,19,a)].
% 1.80/2.07 3182 divide(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb) = zero. [hyper(15,a,1,a,b,3177,a),flip(a)].
% 1.80/2.07 3192 quotient(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb,zero). [para(3182(a,1),9(a,3))].
% 1.80/2.07 3193 $F # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa). [resolve(3192,a,3144,a)].
% 1.80/2.07
% 1.80/2.07 % SZS output end Refutation
% 1.80/2.07 ============================== end of proof ==========================
% 1.80/2.07
% 1.80/2.07 ============================== STATISTICS ============================
% 1.80/2.07
% 1.80/2.07 Given=643. Generated=62325. Kept=3191. proofs=1.
% 1.80/2.07 Usable=319. Sos=1246. Demods=308. Limbo=0, Disabled=1641. Hints=0.
% 1.80/2.07 Megabytes=1.96.
% 1.80/2.07 User_CPU=1.08, System_CPU=0.03, Wall_clock=1.
% 1.80/2.07
% 1.80/2.07 ============================== end of statistics =====================
% 1.80/2.07
% 1.80/2.07 ============================== end of search =========================
% 1.80/2.07
% 1.80/2.07 THEOREM PROVED
% 1.80/2.07 % SZS status Unsatisfiable
% 1.80/2.07
% 1.80/2.07 Exiting with 1 proof.
% 1.80/2.07
% 1.80/2.07 Process 22939 exit (max_proofs) Fri Jul 1 14:25:15 2022
% 1.80/2.07 Prover9 interrupted
%------------------------------------------------------------------------------