TSTP Solution File: GRP770-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP770-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:20:59 EDT 2022
% Result : Unsatisfiable 2.67s 2.99s
% Output : Refutation 2.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP770-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 20:01:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.67/2.99 ============================== Prover9 ===============================
% 2.67/2.99 Prover9 (32) version 2009-11A, November 2009.
% 2.67/2.99 Process 24724 was started by sandbox2 on n009.cluster.edu,
% 2.67/2.99 Mon Jun 13 20:01:53 2022
% 2.67/2.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24571_n009.cluster.edu".
% 2.67/2.99 ============================== end of head ===========================
% 2.67/2.99
% 2.67/2.99 ============================== INPUT =================================
% 2.67/2.99
% 2.67/2.99 % Reading from file /tmp/Prover9_24571_n009.cluster.edu
% 2.67/2.99
% 2.67/2.99 set(prolog_style_variables).
% 2.67/2.99 set(auto2).
% 2.67/2.99 % set(auto2) -> set(auto).
% 2.67/2.99 % set(auto) -> set(auto_inference).
% 2.67/2.99 % set(auto) -> set(auto_setup).
% 2.67/2.99 % set(auto_setup) -> set(predicate_elim).
% 2.67/2.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.67/2.99 % set(auto) -> set(auto_limits).
% 2.67/2.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.67/2.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.67/2.99 % set(auto) -> set(auto_denials).
% 2.67/2.99 % set(auto) -> set(auto_process).
% 2.67/2.99 % set(auto2) -> assign(new_constants, 1).
% 2.67/2.99 % set(auto2) -> assign(fold_denial_max, 3).
% 2.67/2.99 % set(auto2) -> assign(max_weight, "200.000").
% 2.67/2.99 % set(auto2) -> assign(max_hours, 1).
% 2.67/2.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.67/2.99 % set(auto2) -> assign(max_seconds, 0).
% 2.67/2.99 % set(auto2) -> assign(max_minutes, 5).
% 2.67/2.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.67/2.99 % set(auto2) -> set(sort_initial_sos).
% 2.67/2.99 % set(auto2) -> assign(sos_limit, -1).
% 2.67/2.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.67/2.99 % set(auto2) -> assign(max_megs, 400).
% 2.67/2.99 % set(auto2) -> assign(stats, some).
% 2.67/2.99 % set(auto2) -> clear(echo_input).
% 2.67/2.99 % set(auto2) -> set(quiet).
% 2.67/2.99 % set(auto2) -> clear(print_initial_clauses).
% 2.67/2.99 % set(auto2) -> clear(print_given).
% 2.67/2.99 assign(lrs_ticks,-1).
% 2.67/2.99 assign(sos_limit,10000).
% 2.67/2.99 assign(order,kbo).
% 2.67/2.99 set(lex_order_vars).
% 2.67/2.99 clear(print_given).
% 2.67/2.99
% 2.67/2.99 % formulas(sos). % not echoed (25 formulas)
% 2.67/2.99
% 2.67/2.99 ============================== end of input ==========================
% 2.67/2.99
% 2.67/2.99 % From the command line: assign(max_seconds, 300).
% 2.67/2.99
% 2.67/2.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.67/2.99
% 2.67/2.99 % Formulas that are not ordinary clauses:
% 2.67/2.99
% 2.67/2.99 ============================== end of process non-clausal formulas ===
% 2.67/2.99
% 2.67/2.99 ============================== PROCESS INITIAL CLAUSES ===============
% 2.67/2.99
% 2.67/2.99 ============================== PREDICATE ELIMINATION =================
% 2.67/2.99
% 2.67/2.99 ============================== end predicate elimination =============
% 2.67/2.99
% 2.67/2.99 Auto_denials:
% 2.67/2.99 % copying label goals to answer in negative clause
% 2.67/2.99
% 2.67/2.99 Term ordering decisions:
% 2.67/2.99 Function symbol KB weights: one=1. x0=1. x1=1. x2=1. product=1. quotient=1. difference=1. t=1. j=1. i=1. eta=1.
% 2.67/2.99
% 2.67/2.99 ============================== end of process initial clauses ========
% 2.67/2.99
% 2.67/2.99 ============================== CLAUSES FOR SEARCH ====================
% 2.67/2.99
% 2.67/2.99 ============================== end of clauses for search =============
% 2.67/2.99
% 2.67/2.99 ============================== SEARCH ================================
% 2.67/2.99
% 2.67/2.99 % Starting search at 0.01 seconds.
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=69.000, iters=3385
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=55.000, iters=3359
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=53.000, iters=3340
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=47.000, iters=3349
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=45.000, iters=3465
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=39.000, iters=3333
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=37.000, iters=3450
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=35.000, iters=3353
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=33.000, iters=3340
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=31.000, iters=3361
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=29.000, iters=3344
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=27.000, iters=3344
% 2.67/2.99
% 2.67/2.99 Low Water (keep): wt=25.000, iters=3343
% 2.67/2.99
% 2.67/2.99 ============================== PROOF =================================
% 2.67/2.99 % SZS status Unsatisfiable
% 2.67/2.99 % SZS output start Refutation
% 2.67/2.99
% 2.67/2.99 % Proof 1 at 2.00 (+ 0.05) seconds: goals.
% 2.67/2.99 % Length of proof is 110.
% 2.67/2.99 % Level of proof is 20.
% 2.67/2.99 % Maximum clause weight is 37.000.
% 2.67/2.99 % Given clauses 361.
% 2.67/2.99
% 2.67/2.99 1 product(A,one) = A # label(sos01) # label(axiom). [assumption].
% 2.67/2.99 2 product(one,A) = A # label(sos02) # label(axiom). [assumption].
% 2.67/2.99 3 i(A) = difference(A,one) # label(sos09) # label(axiom). [assumption].
% 2.67/2.99 4 j(A) = quotient(one,A) # label(sos10) # label(axiom). [assumption].
% 2.67/2.99 5 product(A,difference(A,B)) = B # label(sos03) # label(axiom). [assumption].
% 2.67/2.99 6 difference(A,product(A,B)) = B # label(sos04) # label(axiom). [assumption].
% 2.67/2.99 7 quotient(product(A,B),B) = A # label(sos05) # label(axiom). [assumption].
% 2.67/2.99 8 product(quotient(A,B),B) = A # label(sos06) # label(axiom). [assumption].
% 2.67/2.99 9 eta(A) = product(i(A),A) # label(sos12) # label(axiom). [assumption].
% 2.67/2.99 10 eta(A) = product(difference(A,one),A). [copy(9),rewrite([3(2)])].
% 2.67/2.99 11 product(i(A),A) = product(A,j(A)) # label(sos11) # label(axiom). [assumption].
% 2.67/2.99 12 product(difference(A,one),A) = product(A,quotient(one,A)). [copy(11),rewrite([3(1),4(4)])].
% 2.67/2.99 14 product(A,i(product(B,A))) = i(B) # label(sos23) # label(axiom). [assumption].
% 2.67/2.99 15 product(A,difference(product(B,A),one)) = difference(B,one). [copy(14),rewrite([3(2),3(5)])].
% 2.67/2.99 16 product(j(product(A,B)),A) = j(B) # label(sos24) # label(axiom). [assumption].
% 2.67/2.99 17 product(quotient(one,product(A,B)),A) = quotient(one,B). [copy(16),rewrite([4(2),4(5)])].
% 2.67/2.99 18 quotient(j(A),A) = product(j(A),i(A)) # label(sos17) # label(axiom). [assumption].
% 2.67/2.99 19 product(quotient(one,A),difference(A,one)) = quotient(quotient(one,A),A). [copy(18),rewrite([4(1),4(4),3(6)]),flip(a)].
% 2.67/2.99 22 product(j(j(A)),j(product(B,A))) = j(B) # label(sos22) # label(axiom). [assumption].
% 2.67/2.99 23 product(quotient(one,quotient(one,A)),quotient(one,product(B,A))) = quotient(one,B). [copy(22),rewrite([4(1),4(3),4(6),4(9)])].
% 2.67/2.99 24 product(i(i(A)),B) = product(eta(A),product(A,B)) # label(sos13) # label(axiom). [assumption].
% 2.67/2.99 25 product(product(A,quotient(one,A)),product(A,B)) = product(difference(difference(A,one),one),B). [copy(24),rewrite([3(1),3(3),10(6),12(8)]),flip(a)].
% 2.67/2.99 26 product(A,product(eta(A),B)) = product(j(j(A)),B) # label(sos14) # label(axiom). [assumption].
% 2.67/2.99 27 product(A,product(product(A,quotient(one,A)),B)) = product(quotient(one,quotient(one,A)),B). [copy(26),rewrite([10(1),12(3),4(6),4(8)])].
% 2.67/2.99 28 product(A,product(B,eta(A))) = product(product(A,B),eta(A)) # label(sos15) # label(axiom). [assumption].
% 2.67/2.99 29 product(product(A,B),product(A,quotient(one,A))) = product(A,product(B,product(A,quotient(one,A)))). [copy(28),rewrite([10(1),12(3),10(7),12(9)]),flip(a)].
% 2.67/2.99 30 product(eta(A),product(B,C)) = product(product(eta(A),B),C) # label(sos16) # label(axiom). [assumption].
% 2.67/2.99 31 product(product(product(A,quotient(one,A)),B),C) = product(product(A,quotient(one,A)),product(B,C)). [copy(30),rewrite([10(1),12(3),10(6),12(8)]),flip(a)].
% 2.67/2.99 32 difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) # label(sos07) # label(axiom). [assumption].
% 2.67/2.99 35 difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) # label(sos08) # label(axiom). [assumption].
% 2.67/2.99 38 product(x0,product(x1,x2)) != product(quotient(product(x0,x1),x0),product(x0,x2)) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 2.67/2.99 39 product(quotient(product(x0,x1),x0),product(x0,x2)) != product(x0,product(x1,x2)) # answer(goals). [copy(38),flip(a)].
% 2.67/2.99 45 quotient(A,difference(B,A)) = B. [para(5(a,1),7(a,1,1))].
% 2.67/2.99 46 difference(quotient(A,B),A) = B. [para(8(a,1),6(a,1,2))].
% 2.67/2.99 48 quotient(product(A,quotient(one,A)),A) = difference(A,one). [para(12(a,1),7(a,1,1))].
% 2.67/2.99 49 product(difference(A,B),difference(B,one)) = difference(A,one). [para(5(a,1),15(a,1,2,1))].
% 2.67/2.99 50 difference(product(A,B),one) = difference(B,difference(A,one)). [para(15(a,1),6(a,1,2)),flip(a)].
% 2.67/2.99 51 difference(quotient(A,B),one) = product(B,difference(A,one)). [para(8(a,1),15(a,1,2,1)),flip(a)].
% 2.67/2.99 52 product(A,difference(quotient(one,A),difference(A,one))) = difference(difference(A,one),one). [para(12(a,1),15(a,1,2,1)),rewrite([50(5)])].
% 2.67/2.99 53 quotient(one,difference(A,B)) = product(quotient(one,B),A). [para(5(a,1),17(a,1,1,2)),flip(a)].
% 2.67/2.99 55 quotient(quotient(one,A),B) = quotient(one,product(B,A)). [para(17(a,1),7(a,1,1))].
% 2.67/2.99 56 product(quotient(one,A),quotient(A,B)) = quotient(one,B). [para(8(a,1),17(a,1,1,2))].
% 2.67/2.99 58 product(quotient(one,A),difference(A,one)) = quotient(one,product(A,A)). [back_rewrite(19),rewrite([55(8)])].
% 2.67/2.99 60 product(quotient(one,quotient(one,A)),quotient(one,B)) = quotient(one,quotient(B,A)). [para(8(a,1),23(a,1,2,2))].
% 2.67/2.99 61 product(product(A,quotient(one,A)),A) = difference(difference(A,one),one). [para(1(a,1),25(a,1,2)),rewrite([1(10)])].
% 2.67/2.99 63 difference(product(A,quotient(one,A)),product(difference(difference(A,one),one),B)) = product(A,B). [para(25(a,1),6(a,1,2))].
% 2.67/2.99 70 product(A,product(A,quotient(one,A))) = quotient(one,quotient(one,A)). [para(1(a,1),27(a,1,2)),rewrite([1(10)])].
% 2.67/2.99 76 product(product(A,quotient(one,A)),product(quotient(one,quotient(one,A)),B)) = product(A,B). [para(27(a,1),25(a,2)),rewrite([45(13),12(10),45(9),12(6),27(8),45(16),45(13)])].
% 2.67/2.99 86 product(difference(difference(A,one),one),product(A,quotient(one,A))) = A. [para(12(a,1),29(a,2,2)),rewrite([50(5),52(6),27(18),60(18),48(13),45(12)])].
% 2.67/2.99 113 quotient(product(difference(A,B),product(C,A)),A) = difference(A,product(B,C)). [para(5(a,1),32(a,1,2,1)),flip(a)].
% 2.67/2.99 147 difference(A,product(B,product(difference(B,A),C))) = quotient(quotient(product(C,A),difference(B,A)),B). [para(5(a,1),35(a,1,1)),rewrite([5(6)])].
% 2.67/2.99 148 difference(product(A,B),product(A,C)) = quotient(difference(B,product(C,A)),A). [para(5(a,1),35(a,1,2,2)),rewrite([113(7)])].
% 2.67/2.99 149 difference(A,product(quotient(A,B),product(B,C))) = quotient(quotient(product(C,A),B),quotient(A,B)). [para(8(a,1),35(a,1,1)),rewrite([8(6)])].
% 2.67/2.99 157 quotient(quotient(product(A,product(quotient(one,quotient(one,B)),C)),product(product(B,quotient(one,B)),C)),B) = quotient(quotient(product(A,product(quotient(one,quotient(one,B)),C)),C),quotient(one,quotient(one,B))). [para(27(a,1),35(a,1,1)),rewrite([31(10),27(11),148(12),32(7),27(17)]),flip(a)].
% 2.67/2.99 168 product(quotient(one,A),quotient(one,quotient(one,A))) = product(A,quotient(one,A)). [para(46(a,1),12(a,1,1)),flip(a)].
% 2.67/2.99 176 difference(difference(A,B),difference(A,one)) = difference(B,one). [para(49(a,1),6(a,1,2))].
% 2.67/2.99 177 quotient(difference(A,one),difference(B,one)) = difference(A,B). [para(49(a,1),7(a,1,1))].
% 2.67/2.99 203 quotient(one,product(A,difference(B,one))) = quotient(B,A). [para(51(a,1),45(a,1,2))].
% 2.67/2.99 223 product(product(A,quotient(one,A)),quotient(one,B)) = product(difference(A,one),quotient(A,B)). [para(56(a,1),25(a,1,2)),rewrite([168(7),46(10)])].
% 2.67/2.99 248 difference(quotient(one,A),B) = quotient(A,difference(B,one)). [para(46(a,1),177(a,1,1)),flip(a)].
% 2.67/2.99 249 difference(A,quotient(one,B)) = quotient(difference(A,one),B). [para(46(a,1),177(a,1,2)),flip(a)].
% 2.67/2.99 300 quotient(one,product(quotient(one,A),quotient(one,A))) = product(A,difference(difference(A,one),one)). [para(58(a,1),27(a,2)),rewrite([46(7),61(4)]),flip(a)].
% 2.67/2.99 305 product(A,difference(difference(A,one),one)) = quotient(A,difference(A,one)). [para(45(a,1),58(a,1,1)),rewrite([203(12)])].
% 2.67/2.99 306 product(quotient(one,quotient(one,A)),A) = quotient(A,difference(A,one)). [para(46(a,1),58(a,1,2)),rewrite([300(12),305(10)])].
% 2.67/2.99 307 difference(difference(A,one),A) = product(A,A). [para(58(a,1),50(a,1,1)),rewrite([46(5),46(7)]),flip(a)].
% 2.67/2.99 311 quotient(one,quotient(one,product(A,A))) = quotient(A,quotient(one,A)). [para(58(a,1),55(a,2,2)),rewrite([45(4)]),flip(a)].
% 2.67/2.99 321 product(quotient(one,A),quotient(one,A)) = quotient(difference(A,one),A). [para(46(a,1),307(a,1,1)),rewrite([249(3)]),flip(a)].
% 2.67/2.99 335 quotient(A,quotient(one,product(difference(A,one),B))) = quotient(one,quotient(one,B)). [para(17(a,1),203(a,1,2)),flip(a)].
% 2.67/2.99 361 product(quotient(one,quotient(one,A)),product(quotient(one,B),C)) = quotient(one,quotient(difference(C,B),A)). [para(53(a,1),60(a,1,2))].
% 2.67/2.99 395 difference(A,product(quotient(one,B),C)) = quotient(difference(A,one),difference(C,B)). [para(53(a,1),249(a,1,2))].
% 2.67/2.99 452 product(quotient(A,difference(A,one)),product(A,quotient(one,A))) = product(A,A). [para(86(a,1),29(a,2,2)),rewrite([305(5)])].
% 2.67/2.99 490 quotient(A,quotient(one,A)) = product(A,A). [para(306(a,1),29(a,1,1)),rewrite([168(14),168(10),452(7),168(16),168(12),70(9),321(10),46(5)]),flip(a)].
% 2.67/2.99 500 quotient(one,quotient(one,product(A,A))) = product(A,A). [back_rewrite(311),rewrite([490(8)])].
% 2.67/2.99 526 quotient(quotient(A,difference(A,B)),A) = quotient(one,quotient(B,A)). [para(60(a,1),63(a,2)),rewrite([168(11),168(7),46(9),46(7),148(7),395(6),46(4)])].
% 2.67/2.99 551 quotient(one,quotient(A,product(B,B))) = product(product(B,B),quotient(one,A)). [para(500(a,1),60(a,1,1)),flip(a)].
% 2.67/2.99 733 quotient(one,quotient(product(A,B),A)) = quotient(quotient(A,B),A). [para(6(a,1),526(a,1,1,2)),flip(a)].
% 2.67/2.99 734 product(quotient(one,quotient(A,B)),B) = quotient(B,difference(B,A)). [para(526(a,1),8(a,1,1))].
% 2.67/2.99 776 product(difference(A,one),quotient(A,B)) = product(A,quotient(one,product(B,A))). [para(56(a,1),76(a,1,2)),rewrite([223(6),55(7)])].
% 2.67/2.99 798 product(product(A,quotient(one,A)),quotient(one,B)) = product(A,quotient(one,product(B,A))). [back_rewrite(223),rewrite([776(10)])].
% 2.67/2.99 815 product(A,product(B,difference(A,one))) = quotient(product(A,B),A). [para(733(a,1),46(a,1,1)),rewrite([51(4),51(3)])].
% 2.67/2.99 868 quotient(A,difference(A,product(B,A))) = product(quotient(one,B),A). [para(7(a,1),734(a,1,1,2)),flip(a)].
% 2.67/2.99 875 product(difference(A,B),difference(A,one)) = difference(A,quotient(B,A)). [para(734(a,1),50(a,1,1)),rewrite([51(4),46(9)])].
% 2.67/2.99 979 quotient(product(A,difference(B,A)),A) = product(A,difference(B,one)). [para(49(a,1),815(a,1,2)),flip(a)].
% 2.67/2.99 1012 quotient(A,quotient(product(B,product(A,A)),A)) = quotient(one,B). [para(17(a,1),868(a,2)),rewrite([32(3)])].
% 2.67/2.99 1235 quotient(difference(difference(A,one),product(difference(A,B),B)),B) = B. [para(979(a,1),46(a,1,1)),rewrite([148(6)])].
% 2.67/2.99 1358 product(product(A,A),quotient(one,B)) = quotient(A,quotient(B,A)). [para(8(a,1),1012(a,1,2,1)),rewrite([551(6)]),flip(a)].
% 2.67/2.99 1363 quotient(product(A,product(B,B)),B) = quotient(A,difference(B,one)). [para(1012(a,1),46(a,1,1)),rewrite([248(3)]),flip(a)].
% 2.67/2.99 1709 difference(difference(A,one),product(difference(A,B),B)) = product(B,B). [para(1235(a,1),8(a,1,1)),flip(a)].
% 2.67/2.99 1895 quotient(difference(A,one),difference(B,A)) = product(quotient(difference(A,one),A),B). [para(177(a,1),1358(a,2,2)),rewrite([875(5),249(3),45(7)]),flip(a)].
% 2.67/2.99 1926 product(quotient(A,difference(B,one)),B) = product(A,product(B,B)). [para(1363(a,1),8(a,1,1))].
% 2.67/2.99 2579 quotient(difference(difference(A,one),product(A,B)),B) = product(A,A). [para(46(a,1),1709(a,1,2,1)),rewrite([51(3),148(5)])].
% 2.67/2.99 3047 product(quotient(A,B),quotient(one,B)) = product(A,quotient(difference(B,one),B)). [para(46(a,1),1926(a,1,1,2)),rewrite([321(9)])].
% 2.67/2.99 3762 difference(difference(A,one),product(A,B)) = product(product(A,A),B). [para(2579(a,1),8(a,1,1)),flip(a)].
% 2.67/2.99 4959 product(quotient(difference(A,one),A),quotient(A,B)) = quotient(difference(A,one),B). [para(56(a,1),3762(a,1,2)),rewrite([46(4),249(3),3047(8),2(8)]),flip(a)].
% 2.67/2.99 5064 product(A,quotient(quotient(product(B,A),difference(C,A)),C)) = product(C,product(difference(C,A),B)). [para(147(a,1),5(a,1,2))].
% 2.67/2.99 5326 difference(product(A,B),A) = quotient(difference(B,A),A). [para(1(a,1),148(a,1,2)),rewrite([2(4)])].
% 2.67/2.99 5341 quotient(one,quotient(difference(A,product(B,C)),C)) = product(quotient(one,product(C,B)),product(C,A)). [para(148(a,1),53(a,1,2))].
% 2.67/2.99 5587 quotient(difference(difference(A,B),A),A) = difference(B,A). [para(5(a,1),5326(a,1,1)),flip(a)].
% 2.67/2.99 5591 quotient(A,quotient(difference(B,A),A)) = product(A,B). [para(5326(a,1),45(a,1,2))].
% 2.67/2.99 5645 difference(difference(A,B),A) = product(difference(B,A),A). [para(5587(a,1),8(a,1,1)),flip(a)].
% 2.67/2.99 5668 product(quotient(difference(A,one),A),B) = product(difference(A,one),difference(A,B)). [para(176(a,1),5591(a,1,2,1)),rewrite([177(7),1895(4)])].
% 2.67/2.99 5830 product(difference(A,one),difference(A,quotient(A,B))) = quotient(difference(A,one),B). [back_rewrite(4959),rewrite([5668(5)])].
% 2.67/2.99 5905 quotient(A,product(difference(B,A),A)) = difference(A,B). [para(5645(a,1),45(a,1,2))].
% 2.67/2.99 5988 product(A,quotient(quotient(product(B,A),C),quotient(A,C))) = product(quotient(A,C),product(C,B)). [para(149(a,1),5(a,1,2))].
% 2.67/2.99 6260 difference(A,quotient(A,B)) = quotient(A,product(B,A)). [para(46(a,1),5905(a,1,2,1)),flip(a)].
% 2.67/2.99 6320 product(A,quotient(one,product(product(B,A),A))) = quotient(difference(A,one),B). [back_rewrite(5830),rewrite([6260(4),776(5)])].
% 2.67/2.99 6764 quotient(quotient(product(A,B),quotient(one,product(difference(B,one),C))),quotient(one,quotient(one,C))) = quotient(quotient(product(A,B),difference(C,B)),C). [para(5(a,1),157(a,1,1,1,2)),rewrite([248(9),55(9),798(10),6320(8),177(6),248(13),55(13),60(14),7(9),45(8),248(10),55(10)]),flip(a)].
% 2.67/2.99 16176 quotient(quotient(product(A,B),difference(C,B)),C) = quotient(quotient(product(A,B),C),quotient(B,C)). [para(335(a,1),149(a,1,2,1)),rewrite([361(11),5341(7),203(5),149(4),335(17),6764(16)]),flip(a)].
% 2.67/2.99 16208 product(quotient(A,B),product(B,C)) = product(B,product(difference(B,A),C)). [back_rewrite(5064),rewrite([16176(4),5988(5)])].
% 2.67/2.99 16265 $F # answer(goals). [back_rewrite(39),rewrite([16208(9),6(6)]),xx(a)].
% 2.67/2.99
% 2.67/2.99 % SZS output end Refutation
% 2.67/2.99 ============================== end of proof ==========================
% 2.67/2.99
% 2.67/2.99 ============================== STATISTICS ============================
% 2.67/2.99
% 2.67/2.99 Given=361. Generated=64732. Kept=16250. proofs=1.
% 2.67/2.99 Usable=248. Sos=8024. Demods=8177. Limbo=57, Disabled=7946. Hints=0.
% 2.67/2.99 Megabytes=18.28.
% 2.67/2.99 User_CPU=2.00, System_CPU=0.05, Wall_clock=2.
% 2.67/2.99
% 2.67/2.99 ============================== end of statistics =====================
% 2.67/2.99
% 2.67/2.99 ============================== end of search =========================
% 2.67/2.99
% 2.67/2.99 THEOREM PROVED
% 2.67/2.99 % SZS status Unsatisfiable
% 2.67/2.99
% 2.67/2.99 Exiting with 1 proof.
% 2.67/2.99
% 2.67/2.99 Process 24724 exit (max_proofs) Mon Jun 13 20:01:55 2022
% 2.67/2.99 Prover9 interrupted
%------------------------------------------------------------------------------