TSTP Solution File: GRP772-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP772-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:21:00 EDT 2022
% Result : Unsatisfiable 6.12s 6.46s
% Output : Refutation 6.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : GRP772-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 06:55:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.36/4.68 ============================== Prover9 ===============================
% 4.36/4.68 Prover9 (32) version 2009-11A, November 2009.
% 4.36/4.68 Process 10520 was started by sandbox2 on n012.cluster.edu,
% 4.36/4.68 Tue Jun 14 06:55:56 2022
% 4.36/4.68 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10366_n012.cluster.edu".
% 4.36/4.68 ============================== end of head ===========================
% 4.36/4.68
% 4.36/4.68 ============================== INPUT =================================
% 4.36/4.68
% 4.36/4.68 % Reading from file /tmp/Prover9_10366_n012.cluster.edu
% 4.36/4.68
% 4.36/4.68 set(prolog_style_variables).
% 4.36/4.68 set(auto2).
% 4.36/4.68 % set(auto2) -> set(auto).
% 4.36/4.68 % set(auto) -> set(auto_inference).
% 4.36/4.68 % set(auto) -> set(auto_setup).
% 4.36/4.68 % set(auto_setup) -> set(predicate_elim).
% 4.36/4.68 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.36/4.68 % set(auto) -> set(auto_limits).
% 4.36/4.68 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.36/4.68 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.36/4.68 % set(auto) -> set(auto_denials).
% 4.36/4.68 % set(auto) -> set(auto_process).
% 4.36/4.68 % set(auto2) -> assign(new_constants, 1).
% 4.36/4.68 % set(auto2) -> assign(fold_denial_max, 3).
% 4.36/4.68 % set(auto2) -> assign(max_weight, "200.000").
% 4.36/4.68 % set(auto2) -> assign(max_hours, 1).
% 4.36/4.68 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.36/4.68 % set(auto2) -> assign(max_seconds, 0).
% 4.36/4.68 % set(auto2) -> assign(max_minutes, 5).
% 4.36/4.68 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.36/4.68 % set(auto2) -> set(sort_initial_sos).
% 4.36/4.68 % set(auto2) -> assign(sos_limit, -1).
% 4.36/4.68 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.36/4.68 % set(auto2) -> assign(max_megs, 400).
% 4.36/4.68 % set(auto2) -> assign(stats, some).
% 4.36/4.68 % set(auto2) -> clear(echo_input).
% 4.36/4.68 % set(auto2) -> set(quiet).
% 4.36/4.68 % set(auto2) -> clear(print_initial_clauses).
% 4.36/4.68 % set(auto2) -> clear(print_given).
% 4.36/4.68 assign(lrs_ticks,-1).
% 4.36/4.68 assign(sos_limit,10000).
% 4.36/4.68 assign(order,kbo).
% 4.36/4.68 set(lex_order_vars).
% 4.36/4.68 clear(print_given).
% 4.36/4.68
% 4.36/4.68 % formulas(sos). % not echoed (33 formulas)
% 4.36/4.68
% 4.36/4.68 ============================== end of input ==========================
% 4.36/4.68
% 4.36/4.68 % From the command line: assign(max_seconds, 300).
% 4.36/4.68
% 4.36/4.68 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.36/4.68
% 4.36/4.68 % Formulas that are not ordinary clauses:
% 4.36/4.68
% 4.36/4.68 ============================== end of process non-clausal formulas ===
% 4.36/4.68
% 4.36/4.68 ============================== PROCESS INITIAL CLAUSES ===============
% 4.36/4.68
% 4.36/4.68 ============================== PREDICATE ELIMINATION =================
% 4.36/4.68
% 4.36/4.68 ============================== end predicate elimination =============
% 4.36/4.68
% 4.36/4.68 Auto_denials:
% 4.36/4.68 % copying label goals to answer in negative clause
% 4.36/4.68
% 4.36/4.68 Term ordering decisions:
% 4.36/4.68 Function symbol KB weights: one=1. x0=1. x1=1. product=1. quotient=1. difference=1. c=1. t=1. j=1. i=1. eta=1. a=1.
% 4.36/4.68
% 4.36/4.68 ============================== end of process initial clauses ========
% 4.36/4.68
% 4.36/4.68 ============================== CLAUSES FOR SEARCH ====================
% 4.36/4.68
% 4.36/4.68 ============================== end of clauses for search =============
% 4.36/4.68
% 4.36/4.68 ============================== SEARCH ================================
% 4.36/4.68
% 4.36/4.68 % Starting search at 0.01 seconds.
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=53.000, iters=3340
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=49.000, iters=3339
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=47.000, iters=3356
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=43.000, iters=3370
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=41.000, iters=3390
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=40.000, iters=3333
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=39.000, iters=3404
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=37.000, iters=3338
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=35.000, iters=3340
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=34.000, iters=3385
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=33.000, iters=3373
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=32.000, iters=3345
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=31.000, iters=3341
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=30.000, iters=3333
% 4.36/4.68
% 4.36/4.68 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 35 (0.00 of 2.14 sec).
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=29.000, iters=3337
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=28.000, iters=3369
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=27.000, iters=3363
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=26.000, iters=3333
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=25.000, iters=3351
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=24.000, iters=3340
% 4.36/4.68
% 4.36/4.68 Low Water (keep): wt=23.000, iters=3342
% 4.36/4.68
% 4.36/4.68 Low Water (displace): id=6217, wt=91.000
% 4.36/4.68
% 4.36/4.68 Low Water (displace): id=6210, wt=89.000
% 4.36/4.68
% 4.36/4.68 Low Water (displace): id=5892, wt=85.000
% 4.36/4.68
% 4.36/4.68 Low Water (displace): id=6209, wt=79.000
% 4.36/4.68
% 4.36/4.68 Low Water (displace): id=6211, wt=76.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=8382, wt=75.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=5894, wt=73.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=6208, wt=71.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=10012, wt=69.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=17119, wt=20.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=17128, wt=19.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=17189, wt=18.000
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=17932, wt=17.000
% 6.12/6.46
% 6.12/6.46 Low Water (keep): wt=22.000, iters=3358
% 6.12/6.46
% 6.12/6.46 Low Water (displace): id=19855, wt=16.000
% 6.12/6.46
% 6.12/6.46 Low Water (keep): wt=21.000, iters=3335
% 6.12/6.46
% 6.12/6.46 ============================== PROOF =================================
% 6.12/6.46 % SZS status Unsatisfiable
% 6.12/6.46 % SZS output start Refutation
% 6.12/6.46
% 6.12/6.46 % Proof 1 at 5.30 (+ 0.17) seconds: goals.
% 6.12/6.46 % Length of proof is 195.
% 6.12/6.46 % Level of proof is 35.
% 6.12/6.46 % Maximum clause weight is 27.000.
% 6.12/6.46 % Given clauses 876.
% 6.12/6.46
% 6.12/6.46 1 product(A,one) = A # label(sos01) # label(axiom). [assumption].
% 6.12/6.46 2 product(one,A) = A # label(sos02) # label(axiom). [assumption].
% 6.12/6.46 3 i(A) = difference(A,one) # label(sos09) # label(axiom). [assumption].
% 6.12/6.46 4 j(A) = quotient(one,A) # label(sos10) # label(axiom). [assumption].
% 6.12/6.46 5 product(A,difference(A,B)) = B # label(sos03) # label(axiom). [assumption].
% 6.12/6.46 6 difference(A,product(A,B)) = B # label(sos04) # label(axiom). [assumption].
% 6.12/6.46 7 quotient(product(A,B),B) = A # label(sos05) # label(axiom). [assumption].
% 6.12/6.46 8 product(quotient(A,B),B) = A # label(sos06) # label(axiom). [assumption].
% 6.12/6.46 9 eta(A) = product(i(A),A) # label(sos12) # label(axiom). [assumption].
% 6.12/6.46 10 eta(A) = product(difference(A,one),A). [copy(9),rewrite([3(2)])].
% 6.12/6.46 11 product(i(A),A) = product(A,j(A)) # label(sos11) # label(axiom). [assumption].
% 6.12/6.46 12 product(difference(A,one),A) = product(A,quotient(one,A)). [copy(11),rewrite([3(1),4(4)])].
% 6.12/6.46 14 quotient(j(A),A) = product(j(A),i(A)) # label(sos17) # label(axiom). [assumption].
% 6.12/6.46 15 product(quotient(one,A),difference(A,one)) = quotient(quotient(one,A),A). [copy(14),rewrite([4(1),4(4),3(6)]),flip(a)].
% 6.12/6.46 16 a(j(A),B,C) = a(B,C,A) # label(sos32) # label(axiom). [assumption].
% 6.12/6.46 17 a(quotient(one,A),B,C) = a(B,C,A). [copy(16),rewrite([4(1)])].
% 6.12/6.46 18 product(i(product(A,B)),i(i(A))) = i(B) # label(sos21) # label(axiom). [assumption].
% 6.12/6.46 19 product(difference(product(A,B),one),difference(difference(A,one),one)) = difference(B,one). [copy(18),rewrite([3(2),3(4),3(6),3(9)])].
% 6.12/6.46 20 product(j(j(A)),j(product(B,A))) = j(B) # label(sos22) # label(axiom). [assumption].
% 6.12/6.46 21 product(quotient(one,quotient(one,A)),quotient(one,product(B,A))) = quotient(one,B). [copy(20),rewrite([4(1),4(3),4(6),4(9)])].
% 6.12/6.46 22 product(product(A,B),c(B,A)) = product(B,A) # label(sos24) # label(axiom). [assumption].
% 6.12/6.46 23 a(A,i(B),C) = a(A,j(B),C) # label(sos30) # label(axiom). [assumption].
% 6.12/6.46 24 a(A,difference(B,one),C) = a(A,quotient(one,B),C). [copy(23),rewrite([3(1),4(4)])].
% 6.12/6.46 25 a(i(A),B,C) = a(j(A),B,C) # label(sos31) # label(axiom). [assumption].
% 6.12/6.46 26 a(difference(A,one),B,C) = a(B,C,A). [copy(25),rewrite([3(1),4(4),17(6)])].
% 6.12/6.46 27 product(i(i(A)),B) = product(eta(A),product(A,B)) # label(sos13) # label(axiom). [assumption].
% 6.12/6.46 28 product(product(A,quotient(one,A)),product(A,B)) = product(difference(difference(A,one),one),B). [copy(27),rewrite([3(1),3(3),10(6),12(8)]),flip(a)].
% 6.12/6.46 29 product(A,product(eta(A),B)) = product(j(j(A)),B) # label(sos14) # label(axiom). [assumption].
% 6.12/6.46 30 product(A,product(product(A,quotient(one,A)),B)) = product(quotient(one,quotient(one,A)),B). [copy(29),rewrite([10(1),12(3),4(6),4(8)])].
% 6.12/6.46 31 product(A,product(B,eta(A))) = product(product(A,B),eta(A)) # label(sos15) # label(axiom). [assumption].
% 6.12/6.46 32 product(product(A,B),product(A,quotient(one,A))) = product(A,product(B,product(A,quotient(one,A)))). [copy(31),rewrite([10(1),12(3),10(7),12(9)]),flip(a)].
% 6.12/6.46 35 difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) # label(sos07) # label(axiom). [assumption].
% 6.12/6.46 36 product(c(A,B),product(C,D)) = product(product(c(A,B),C),D) # label(sos25) # label(axiom). [assumption].
% 6.12/6.46 37 product(product(c(A,B),C),D) = product(c(A,B),product(C,D)). [copy(36),flip(a)].
% 6.12/6.46 38 product(product(A,B),c(C,D)) = product(A,product(B,c(C,D))) # label(sos26) # label(axiom). [assumption].
% 6.12/6.46 39 product(a(A,B,C),difference(C,product(a(C,A,B),C))) = one # label(sos29) # label(axiom). [assumption].
% 6.12/6.46 42 product(product(A,product(B,C)),a(A,B,C)) = product(product(A,B),C) # label(sos23) # label(axiom). [assumption].
% 6.12/6.46 43 product(a(A,B,C),product(D,E)) = product(product(a(A,B,C),D),E) # label(sos27) # label(axiom). [assumption].
% 6.12/6.46 44 product(product(a(A,B,C),D),E) = product(a(A,B,C),product(D,E)). [copy(43),flip(a)].
% 6.12/6.46 45 product(product(A,B),a(C,D,E)) = product(A,product(B,a(C,D,E))) # label(sos28) # label(axiom). [assumption].
% 6.12/6.46 46 difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) # label(sos08) # label(axiom). [assumption].
% 6.12/6.46 49 a(x0,x1,x1) != a(x1,x1,x0) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 6.12/6.46 50 a(x1,x1,x0) != a(x0,x1,x1) # answer(goals). [copy(49),flip(a)].
% 6.12/6.46 52 product(A,product(B,c(B,A))) = product(B,A). [back_rewrite(22),rewrite([38(3)])].
% 6.12/6.46 53 product(A,product(B,product(C,a(A,B,C)))) = product(product(A,B),C). [back_rewrite(42),rewrite([45(4),45(3)])].
% 6.12/6.46 55 difference(A,A) = one. [para(1(a,1),6(a,1,2))].
% 6.12/6.46 57 quotient(A,A) = one. [para(2(a,1),7(a,1,1))].
% 6.12/6.46 58 quotient(A,difference(B,A)) = B. [para(5(a,1),7(a,1,1))].
% 6.12/6.46 59 difference(quotient(A,B),A) = B. [para(8(a,1),6(a,1,2))].
% 6.12/6.46 60 difference(difference(A,one),product(A,quotient(one,A))) = A. [para(12(a,1),6(a,1,2))].
% 6.12/6.46 61 quotient(product(A,quotient(one,A)),A) = difference(A,one). [para(12(a,1),7(a,1,1))].
% 6.12/6.46 64 product(difference(A,one),difference(difference(B,one),one)) = difference(difference(B,A),one). [para(5(a,1),19(a,1,1,1))].
% 6.12/6.46 66 quotient(difference(A,one),difference(difference(B,one),one)) = difference(product(B,A),one). [para(19(a,1),7(a,1,1))].
% 6.12/6.46 70 quotient(quotient(one,A),quotient(one,product(A,B))) = quotient(one,quotient(one,B)). [para(21(a,1),7(a,1,1))].
% 6.12/6.46 71 product(quotient(one,quotient(one,A)),quotient(one,B)) = quotient(one,quotient(B,A)). [para(8(a,1),21(a,1,2,2))].
% 6.12/6.46 73 product(product(A,quotient(one,A)),A) = difference(difference(A,one),one). [para(1(a,1),28(a,1,2)),rewrite([1(10)])].
% 6.12/6.46 81 product(A,product(A,quotient(one,A))) = quotient(one,quotient(one,A)). [para(1(a,1),30(a,1,2)),rewrite([1(10)])].
% 6.12/6.46 83 difference(A,product(quotient(one,quotient(one,A)),B)) = product(product(A,quotient(one,A)),B). [para(30(a,1),6(a,1,2))].
% 6.12/6.46 85 quotient(quotient(one,quotient(one,A)),quotient(one,A)) = product(A,difference(difference(A,one),one)). [para(15(a,1),30(a,2)),rewrite([59(7),73(4)]),flip(a)].
% 6.12/6.46 93 quotient(difference(difference(A,one),one),A) = product(A,quotient(one,A)). [para(32(a,1),6(a,1,2)),rewrite([46(7),28(5),7(6)])].
% 6.12/6.46 120 quotient(product(difference(A,B),product(C,A)),A) = difference(A,product(B,C)). [para(5(a,1),35(a,1,2,1)),flip(a)].
% 6.12/6.46 122 quotient(product(A,product(B,quotient(C,A))),quotient(C,A)) = difference(quotient(C,A),product(C,B)). [para(8(a,1),35(a,1,2,1)),flip(a)].
% 6.12/6.46 123 difference(difference(A,one),product(product(A,quotient(one,A)),B)) = quotient(product(A,product(B,difference(A,one))),difference(A,one)). [para(12(a,1),35(a,1,2,1))].
% 6.12/6.46 139 quotient(product(c(A,B),product(C,D)),D) = product(c(A,B),C). [para(37(a,1),7(a,1,1))].
% 6.12/6.46 149 quotient(product(A,product(B,c(C,D))),c(C,D)) = product(A,B). [para(37(a,1),35(a,1,2)),rewrite([6(5)]),flip(a)].
% 6.12/6.46 151 product(A,product(difference(A,B),c(C,D))) = product(B,c(C,D)). [para(5(a,1),38(a,1,1)),flip(a)].
% 6.12/6.46 161 quotient(product(A,product(c(B,C),D)),D) = product(A,c(B,C)). [para(38(a,1),35(a,1,2)),rewrite([6(4)]),flip(a)].
% 6.12/6.46 165 difference(A,product(a(A,B,C),A)) = difference(a(B,C,A),one). [para(39(a,1),6(a,1,2)),flip(a)].
% 6.12/6.46 169 quotient(A,difference(a(B,C,D),one)) = product(A,a(B,C,D)). [para(39(a,1),35(a,2,1,2)),rewrite([165(3),165(6),45(9),6(10),1(4),165(5)]),flip(a)].
% 6.12/6.46 201 quotient(product(A,product(B,a(C,D,E))),a(C,D,E)) = product(A,B). [para(44(a,1),35(a,1,2)),rewrite([6(5)]),flip(a)].
% 6.12/6.46 203 product(A,product(difference(A,B),a(C,D,E))) = product(B,a(C,D,E)). [para(5(a,1),45(a,1,1)),flip(a)].
% 6.12/6.46 204 product(quotient(A,B),product(B,a(C,D,E))) = product(A,a(C,D,E)). [para(8(a,1),45(a,1,1)),flip(a)].
% 6.12/6.46 220 difference(product(A,B),product(A,C)) = quotient(difference(B,product(C,A)),A). [para(5(a,1),46(a,1,2,2)),rewrite([120(7)])].
% 6.12/6.46 267 difference(A,product(B,A)) = product(B,c(B,A)). [para(52(a,1),6(a,1,2))].
% 6.12/6.46 268 quotient(product(A,B),product(A,c(A,B))) = B. [para(52(a,1),7(a,1,1))].
% 6.12/6.46 281 quotient(product(A,B),c(A,B)) = product(B,A). [para(52(a,1),35(a,2,1)),rewrite([37(4),6(5)]),flip(a)].
% 6.12/6.46 295 quotient(product(A,product(B,C)),C) = product(A,product(B,a(C,A,B))). [para(53(a,1),6(a,1,2)),rewrite([35(3)])].
% 6.12/6.46 300 product(A,product(difference(B,one),product(C,a(A,quotient(one,B),C)))) = product(product(A,difference(B,one)),C). [para(24(a,1),53(a,1,2,2,2))].
% 6.12/6.46 336 product(A,difference(difference(A,one),one)) = quotient(A,difference(A,one)). [para(58(a,1),15(a,1,1)),rewrite([58(9)])].
% 6.12/6.46 337 a(A,B,difference(C,one)) = a(C,A,B). [para(58(a,1),17(a,1,1)),flip(a)].
% 6.12/6.46 343 quotient(quotient(one,quotient(one,A)),quotient(one,A)) = quotient(A,difference(A,one)). [back_rewrite(85),rewrite([336(12)])].
% 6.12/6.46 345 product(quotient(one,A),quotient(one,quotient(one,A))) = product(A,quotient(one,A)). [para(59(a,1),12(a,1,1)),flip(a)].
% 6.12/6.46 346 product(quotient(one,quotient(one,A)),A) = quotient(A,difference(A,one)). [para(59(a,1),15(a,1,2)),rewrite([343(12)])].
% 6.12/6.46 348 a(A,B,quotient(one,C)) = a(C,A,B). [para(59(a,1),26(a,1,1)),flip(a)].
% 6.12/6.46 349 product(product(A,quotient(one,A)),product(quotient(one,A),B)) = product(difference(A,one),B). [para(59(a,1),28(a,2,1,1)),rewrite([345(7)])].
% 6.12/6.46 370 difference(A,difference(B,product(A,B))) = c(A,B). [para(267(a,2),6(a,1,2))].
% 6.12/6.46 385 quotient(product(A,difference(B,product(C,B))),c(C,B)) = product(A,C). [para(267(a,2),35(a,2,1,2)),rewrite([37(4),6(5)]),flip(a)].
% 6.12/6.46 399 quotient(difference(c(A,B),product(B,A)),A) = product(B,c(B,product(A,c(A,B)))). [para(52(a,1),267(a,1,2)),rewrite([220(4)])].
% 6.12/6.46 436 difference(product(A,B),product(B,A)) = c(B,A). [para(281(a,1),59(a,1,1))].
% 6.12/6.46 447 a(A,quotient(one,B),C) = a(C,quotient(one,A),B). [para(337(a,1),17(a,1)),rewrite([24(6)])].
% 6.12/6.46 468 difference(quotient(A,B),difference(B,A)) = c(quotient(A,B),B). [para(8(a,1),370(a,1,2,2))].
% 6.12/6.46 504 difference(A,product(difference(B,A),B)) = c(difference(B,A),B). [para(5(a,1),436(a,1,1))].
% 6.12/6.46 506 difference(A,product(B,quotient(A,B))) = c(B,quotient(A,B)). [para(8(a,1),436(a,1,1))].
% 6.12/6.46 643 difference(difference(c(A,B),one),one) = c(A,B). [para(73(a,1),37(a,1)),rewrite([8(11),1(8)])].
% 6.12/6.46 645 difference(difference(a(A,B,C),one),one) = a(A,B,C). [para(73(a,1),44(a,1)),rewrite([8(11),1(8)])].
% 6.12/6.46 671 product(c(A,B),quotient(one,c(A,B))) = one. [para(643(a,1),5(a,1,2)),rewrite([12(5)])].
% 6.12/6.46 673 difference(c(A,B),one) = quotient(one,c(A,B)). [para(643(a,1),58(a,1,2)),flip(a)].
% 6.12/6.46 674 quotient(one,quotient(one,c(A,B))) = c(A,B). [para(643(a,1),61(a,2)),rewrite([673(3),673(7),345(9),671(5),673(4)])].
% 6.12/6.46 678 difference(product(c(A,B),C),one) = quotient(difference(C,one),c(A,B)). [para(643(a,1),66(a,1,2)),flip(a)].
% 6.12/6.46 691 product(quotient(one,c(A,B)),C) = difference(c(A,B),C). [para(671(a,1),35(a,1,2,1)),rewrite([2(3),149(10)]),flip(a)].
% 6.12/6.46 692 difference(quotient(one,c(A,B)),product(difference(c(A,B),C),c(A,B))) = quotient(C,quotient(one,c(A,B))). [para(671(a,1),35(a,2,1,2)),rewrite([691(7),1(10)])].
% 6.12/6.46 713 quotient(quotient(one,A),quotient(one,B)) = quotient(one,quotient(one,difference(A,B))). [para(5(a,1),70(a,1,2,2))].
% 6.12/6.46 718 quotient(A,quotient(one,product(difference(A,one),B))) = quotient(one,quotient(one,B)). [para(58(a,1),70(a,1,1))].
% 6.12/6.46 721 quotient(one,quotient(one,difference(quotient(one,A),A))) = quotient(A,difference(A,one)). [back_rewrite(343),rewrite([713(7)])].
% 6.12/6.46 729 difference(quotient(one,A),A) = quotient(A,difference(A,one)). [para(81(a,1),35(a,2,1)),rewrite([8(5),2(4),713(10),721(10)])].
% 6.12/6.46 743 difference(product(A,A),one) = difference(A,difference(A,one)). [para(58(a,1),729(a,1,1)),rewrite([66(10)]),flip(a)].
% 6.12/6.46 782 quotient(one,quotient(A,c(B,C))) = product(c(B,C),quotient(one,A)). [para(674(a,1),71(a,1,1)),flip(a)].
% 6.12/6.46 787 product(product(A,A),difference(A,difference(A,one))) = one. [para(743(a,1),5(a,1,2))].
% 6.12/6.46 788 product(difference(A,difference(A,one)),product(A,A)) = product(product(A,A),quotient(one,product(A,A))). [para(743(a,1),12(a,1,1))].
% 6.12/6.46 797 quotient(one,difference(A,difference(A,one))) = product(A,A). [para(743(a,1),58(a,1,2))].
% 6.12/6.46 800 a(A,B,difference(C,difference(C,one))) = a(product(C,C),A,B). [para(743(a,1),337(a,1,3))].
% 6.12/6.46 822 a(product(A,A),A,A) = one. [para(787(a,1),53(a,2)),rewrite([800(7),203(7),203(6),2(4)])].
% 6.12/6.46 837 a(A,A,quotient(quotient(one,A),A)) = one. [para(71(a,1),822(a,1,1)),rewrite([348(14),348(12),348(10),348(8),348(6)])].
% 6.12/6.46 839 product(product(A,A),quotient(quotient(one,A),A)) = product(A,product(A,quotient(quotient(one,A),A))). [para(837(a,1),53(a,1,2,2,2)),rewrite([1(5)]),flip(a)].
% 6.12/6.46 860 difference(difference(difference(A,difference(A,one)),one),product(product(A,A),quotient(one,product(A,A)))) = difference(A,difference(A,one)). [para(797(a,1),60(a,1,2,2)),rewrite([788(10)])].
% 6.12/6.46 907 quotient(difference(difference(A,difference(A,one)),one),product(A,A)) = product(product(A,A),quotient(one,product(A,A))). [para(743(a,1),93(a,1,1,1))].
% 6.12/6.46 908 product(product(A,quotient(one,A)),quotient(A,difference(A,one))) = difference(difference(A,difference(A,one)),one). [para(336(a,1),28(a,1,2)),rewrite([64(16)])].
% 6.12/6.46 930 difference(difference(A,difference(A,one)),one) = product(A,A). [para(346(a,1),28(a,1,2)),rewrite([345(11),345(7),908(7),59(11),59(9)])].
% 6.12/6.46 932 difference(A,difference(A,one)) = quotient(quotient(one,A),A). [para(58(a,1),346(a,1,1,2)),rewrite([15(5),66(10),743(6)]),flip(a)].
% 6.12/6.46 943 quotient(difference(quotient(quotient(one,A),A),one),product(A,A)) = product(product(A,A),quotient(one,product(A,A))). [back_rewrite(907),rewrite([932(3)])].
% 6.12/6.46 951 difference(difference(quotient(quotient(one,A),A),one),product(product(A,A),quotient(one,product(A,A)))) = quotient(quotient(one,A),A). [back_rewrite(860),rewrite([932(3),932(14)])].
% 6.12/6.46 962 difference(quotient(quotient(one,A),A),one) = product(A,A). [back_rewrite(930),rewrite([932(3)])].
% 6.12/6.46 1022 quotient(quotient(one,A),A) = quotient(one,product(A,A)). [back_rewrite(951),rewrite([962(5),6(7)]),flip(a)].
% 6.12/6.46 1026 product(product(A,A),quotient(one,product(A,A))) = one. [back_rewrite(943),rewrite([1022(3),59(5),57(3)]),flip(a)].
% 6.12/6.46 1053 product(A,product(A,quotient(one,product(A,A)))) = one. [back_rewrite(839),rewrite([1022(4),1026(5),1022(4)]),flip(a)].
% 6.12/6.46 1299 product(A,quotient(one,product(A,A))) = difference(A,one). [para(1053(a,1),6(a,1,2)),flip(a)].
% 6.12/6.46 1302 product(c(A,B),product(C,product(c(A,B),product(C,quotient(one,product(c(A,B),product(C,product(c(A,B),C)))))))) = one. [para(1053(a,1),37(a,1)),rewrite([37(10),37(12)]),flip(a)].
% 6.12/6.46 1362 product(c(A,B),product(C,quotient(one,product(c(A,B),product(C,product(c(A,B),C)))))) = quotient(difference(C,one),c(A,B)). [para(1299(a,1),37(a,1)),rewrite([678(4),37(11)]),flip(a)].
% 6.12/6.46 1370 product(c(A,B),product(C,quotient(difference(C,one),c(A,B)))) = one. [back_rewrite(1302),rewrite([1362(11)])].
% 6.12/6.46 1906 product(A,c(difference(B,A),B)) = product(difference(B,A),B). [para(504(a,1),5(a,1,2))].
% 6.12/6.46 2170 product(a(A,B,C),quotient(one,a(A,B,C))) = one. [para(645(a,1),5(a,1,2)),rewrite([12(5)])].
% 6.12/6.46 2171 difference(a(A,B,C),one) = quotient(one,a(A,B,C)). [para(645(a,1),58(a,1,2)),flip(a)].
% 6.12/6.46 2177 quotient(A,quotient(one,a(B,C,D))) = product(A,a(B,C,D)). [back_rewrite(169),rewrite([2171(3)])].
% 6.12/6.46 2178 difference(A,product(a(A,B,C),A)) = quotient(one,a(B,C,A)). [back_rewrite(165),rewrite([2171(6)])].
% 6.12/6.46 2226 quotient(difference(c(A,B),C),C) = quotient(one,c(A,B)). [para(691(a,1),7(a,1,1))].
% 6.12/6.46 2573 product(difference(A,product(B,C)),A) = product(difference(A,B),product(C,A)). [para(120(a,1),8(a,1,1))].
% 6.12/6.46 2590 difference(c(A,B),product(C,A)) = product(difference(c(A,B),C),A). [para(267(a,2),120(a,1,1,2)),rewrite([385(7)]),flip(a)].
% 6.12/6.46 2656 product(A,c(A,product(B,c(B,A)))) = difference(c(B,A),A). [back_rewrite(399),rewrite([2590(3),7(4)]),flip(a)].
% 6.12/6.46 3389 product(difference(A,product(B,A)),c(c(B,A),B)) = product(c(B,A),B). [para(370(a,1),1906(a,1,2,1)),rewrite([370(8)])].
% 6.12/6.46 3424 difference(quotient(A,c(B,C)),product(A,D)) = product(c(B,C),D). [para(139(a,1),122(a,1)),flip(a)].
% 6.12/6.46 3425 difference(quotient(one,c(A,B)),C) = product(c(A,B),C). [para(139(a,1),123(a,2)),rewrite([673(3),671(8),2(5)])].
% 6.12/6.46 3494 quotient(A,quotient(one,c(B,C))) = product(A,c(B,C)). [back_rewrite(692),rewrite([3425(8),151(6)]),flip(a)].
% 6.12/6.46 3536 product(quotient(one,a(A,B,C)),D) = difference(a(A,B,C),D). [para(2170(a,1),35(a,1,2,1)),rewrite([2(3),201(10)]),flip(a)].
% 6.12/6.46 3625 quotient(A,product(c(B,C),A)) = quotient(one,c(B,C)). [para(6(a,1),2226(a,1,1))].
% 6.12/6.46 3828 quotient(product(A,B),c(C,D)) = product(A,quotient(B,c(C,D))). [para(8(a,1),149(a,1,1,2))].
% 6.12/6.46 3830 product(A,quotient(one,c(B,C))) = quotient(A,c(B,C)). [para(12(a,1),149(a,1,1,2)),rewrite([671(5),1(2),673(5)]),flip(a)].
% 6.12/6.46 3887 product(A,quotient(B,c(A,B))) = product(B,A). [back_rewrite(281),rewrite([3828(3)])].
% 6.12/6.46 3910 quotient(A,c(B,A)) = difference(B,product(A,B)). [para(3887(a,1),6(a,1,2)),flip(a)].
% 6.12/6.46 3930 product(A,c(A,quotient(B,c(A,B)))) = product(c(A,B),A). [para(3887(a,1),267(a,1,2)),rewrite([3424(4)]),flip(a)].
% 6.12/6.46 3993 product(difference(A,product(B,A)),c(A,B)) = B. [para(3910(a,1),8(a,1,1))].
% 6.12/6.46 4004 quotient(A,c(B,A)) = product(A,c(A,B)). [para(3910(a,2),267(a,1))].
% 6.12/6.46 4005 quotient(one,difference(A,product(B,A))) = product(c(A,B),quotient(one,B)). [para(3910(a,1),71(a,2,2)),rewrite([3494(5),2(3)]),flip(a)].
% 6.12/6.46 4015 c(difference(A,product(B,A)),c(A,B)) = difference(product(B,c(B,A)),difference(c(A,B),B)). [para(3910(a,1),468(a,2,1)),rewrite([4004(2)]),flip(a)].
% 6.12/6.46 4036 difference(c(A,B),B) = product(c(B,A),B). [back_rewrite(3930),rewrite([4004(2),2656(4)])].
% 6.12/6.46 4050 c(difference(A,product(B,A)),c(A,B)) = c(c(B,A),B). [back_rewrite(4015),rewrite([4036(8),436(9)])].
% 6.12/6.46 4075 quotient(one,c(A,B)) = c(B,A). [para(3993(a,1),268(a,1,1)),rewrite([4050(6),3389(5),3625(3)])].
% 6.12/6.46 4113 quotient(A,c(B,C)) = product(A,c(C,B)). [back_rewrite(3830),rewrite([4075(3)]),flip(a)].
% 6.12/6.46 4243 product(c(A,B),c(B,A)) = one. [back_rewrite(1370),rewrite([4113(5),151(6),2(4)])].
% 6.12/6.46 4254 quotient(one,product(A,c(B,C))) = product(c(C,B),quotient(one,A)). [back_rewrite(782),rewrite([4113(3)])].
% 6.12/6.46 4681 product(difference(A,c(B,C)),c(C,B)) = difference(A,one). [para(4243(a,1),120(a,2,2)),rewrite([161(6)])].
% 6.12/6.46 5382 difference(quotient(c(A,B),C),one) = product(C,c(B,A)). [para(59(a,1),4681(a,1,1)),flip(a)].
% 6.12/6.46 5960 product(c(A,B),quotient(one,C)) = quotient(c(A,B),C). [para(5382(a,1),58(a,1,2)),rewrite([4254(4)])].
% 6.12/6.46 6054 quotient(c(A,B),B) = quotient(one,difference(A,product(B,A))). [back_rewrite(4005),rewrite([5960(8)]),flip(a)].
% 6.12/6.46 6374 quotient(c(A,quotient(B,A)),quotient(B,A)) = quotient(one,difference(A,B)). [para(8(a,1),6054(a,2,2,2))].
% 6.12/6.46 6544 product(A,quotient(one,a(B,C,D))) = quotient(A,a(B,C,D)). [para(12(a,1),201(a,1,1,2)),rewrite([2170(5),1(2),2171(5)]),flip(a)].
% 6.12/6.46 6662 difference(A,product(B,a(C,D,E))) = product(difference(A,B),a(C,D,E)). [para(203(a,1),6(a,1,2))].
% 6.12/6.46 6835 product(difference(A,one),a(B,C,D)) = difference(A,a(B,C,D)). [para(204(a,1),83(a,1,2)),rewrite([2(3),349(10)]),flip(a)].
% 6.12/6.46 8244 difference(product(quotient(A,B),A),A) = quotient(one,difference(B,A)). [para(506(a,1),220(a,2,1)),rewrite([8(4),6374(7)])].
% 6.12/6.46 9324 quotient(A,quotient(one,difference(B,A))) = product(quotient(A,B),A). [para(8244(a,1),58(a,1,2))].
% 6.12/6.46 10798 product(quotient(A,quotient(A,B)),A) = quotient(A,quotient(one,B)). [para(59(a,1),9324(a,1,2,2)),flip(a)].
% 6.12/6.46 11373 quotient(quotient(A,quotient(one,B)),A) = quotient(A,quotient(A,B)). [para(10798(a,1),7(a,1,1))].
% 6.12/6.46 11591 quotient(A,quotient(A,difference(B,one))) = quotient(quotient(A,B),A). [para(58(a,1),11373(a,1,1,2)),flip(a)].
% 6.12/6.46 11910 product(A,a(a(B,C,D),E,difference(E,A))) = A. [para(203(a,1),295(a,1,1)),rewrite([7(4),203(6)]),flip(a)].
% 6.12/6.46 12342 product(A,product(difference(a(B,C,D),E),a(A,quotient(one,a(B,C,D)),E))) = product(quotient(A,a(B,C,D)),E). [para(2171(a,1),300(a,1,2,1)),rewrite([3536(9),6662(7),2171(11),6544(12)])].
% 6.12/6.46 12355 a(a(A,B,C),D,difference(D,E)) = one. [para(11910(a,1),6(a,1,2)),rewrite([55(1)]),flip(a)].
% 6.12/6.46 12401 a(a(A,B,C),D,E) = one. [para(6(a,1),12355(a,1,3))].
% 6.12/6.46 12412 a(A,quotient(one,a(B,C,D)),E) = one. [para(12401(a,1),447(a,1)),flip(a)].
% 6.12/6.46 12414 product(quotient(A,a(B,C,D)),E) = product(A,difference(a(B,C,D),E)). [back_rewrite(12342),rewrite([12412(6),1(4)]),flip(a)].
% 6.12/6.46 18429 quotient(one,quotient(A,a(B,C,D))) = product(a(B,C,D),quotient(one,A)). [para(2177(a,1),71(a,1,1)),rewrite([2(3)]),flip(a)].
% 6.12/6.46 18444 quotient(A,product(a(B,C,D),A)) = quotient(one,a(B,C,D)). [para(2177(a,1),718(a,2,2)),rewrite([6544(7),18429(6),58(5),2(7)])].
% 6.12/6.46 18486 quotient(A,a(B,C,A)) = product(a(A,B,C),A). [para(2178(a,1),5(a,1,2)),rewrite([6544(4)])].
% 6.12/6.46 18545 difference(a(A,B,C),A) = product(A,a(B,C,A)). [para(18486(a,1),10798(a,1,1,2)),rewrite([18444(3),12414(4),2(4),2177(6)])].
% 6.12/6.46 18546 quotient(A,product(A,a(B,C,A))) = a(A,B,C). [para(18486(a,1),11591(a,2,1)),rewrite([2171(3),2177(4),7(6)])].
% 6.12/6.46 18609 product(A,a(B,quotient(one,C),A)) = difference(a(C,A,B),A). [para(24(a,1),18545(a,2,2)),rewrite([337(3)]),flip(a)].
% 6.12/6.46 18652 quotient(A,product(A,a(B,A,C))) = a(A,quotient(one,C),B). [para(17(a,1),18546(a,1,2,2))].
% 6.12/6.46 19034 product(difference(A,one),product(B,A)) = product(difference(A,B),A). [para(2(a,1),2573(a,1,1,2)),flip(a)].
% 6.12/6.46 19125 difference(difference(A,one),product(difference(A,B),A)) = product(B,A). [para(19034(a,1),6(a,1,2))].
% 6.12/6.46 19161 product(difference(A,one),difference(a(A,B,A),B)) = difference(A,B). [para(19034(a,1),295(a,1,1)),rewrite([7(3),24(6),18609(7)]),flip(a)].
% 6.12/6.46 19212 difference(difference(A,one),difference(A,B)) = product(product(B,A),difference(A,one)). [para(19125(a,1),2573(a,1,1)),rewrite([5(11),1(10)]),flip(a)].
% 6.12/6.46 20769 difference(a(A,B,A),B) = product(product(B,A),difference(A,one)). [para(19161(a,1),6(a,1,2)),rewrite([19212(4)]),flip(a)].
% 6.12/6.46 21548 difference(a(A,B,A),B) = product(B,a(A,B,A)). [para(20769(a,2),53(a,2)),rewrite([337(5),6835(4),5(3)]),flip(a)].
% 6.12/6.46 21625 a(A,quotient(one,B),B) = a(B,A,B). [para(21548(a,1),58(a,1,2)),rewrite([18652(3)])].
% 6.12/6.46 21680 a(A,quotient(one,B),A) = a(A,B,A). [para(21625(a,1),17(a,1)),rewrite([17(6)])].
% 6.12/6.46 21709 a(A,B,B) = a(B,B,A). [para(21680(a,1),18546(a,1,2,2)),rewrite([18546(3),348(4)]),flip(a)].
% 6.12/6.46 21710 $F # answer(goals). [resolve(21709,a,50,a(flip))].
% 6.12/6.46
% 6.12/6.46 % SZS output end Refutation
% 6.12/6.46 ============================== end of proof ==========================
% 6.12/6.46
% 6.12/6.46 ============================== STATISTICS ============================
% 6.12/6.46
% 6.12/6.46 Given=876. Generated=205171. Kept=21692. proofs=1.
% 6.12/6.46 Usable=586. Sos=9988. Demods=9244. Limbo=16, Disabled=11134. Hints=0.
% 6.12/6.46 Megabytes=25.70.
% 6.12/6.46 User_CPU=5.31, System_CPU=0.17, Wall_clock=5.
% 6.12/6.46
% 6.12/6.46 ============================== end of statistics =====================
% 6.12/6.46
% 6.12/6.46 ============================== end of search =========================
% 6.12/6.46
% 6.12/6.46 THEOREM PROVED
% 6.12/6.46 % SZS status Unsatisfiable
% 6.12/6.46
% 6.12/6.46 Exiting with 1 proof.
% 6.12/6.46
% 6.12/6.46 Process 10520 exit (max_proofs) Tue Jun 14 06:56:01 2022
% 6.12/6.46 Prover9 interrupted
%------------------------------------------------------------------------------