TSTP Solution File: GRP779+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP779+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 11:21:02 EDT 2022
% Result : Theorem 6.13s 6.45s
% Output : Refutation 6.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP779+1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 05:41:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.47/1.04 ============================== Prover9 ===============================
% 0.47/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.04 Process 15220 was started by sandbox on n013.cluster.edu,
% 0.47/1.04 Mon Jun 13 05:41:44 2022
% 0.47/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15067_n013.cluster.edu".
% 0.47/1.04 ============================== end of head ===========================
% 0.47/1.04
% 0.47/1.04 ============================== INPUT =================================
% 0.47/1.04
% 0.47/1.04 % Reading from file /tmp/Prover9_15067_n013.cluster.edu
% 0.47/1.04
% 0.47/1.04 set(prolog_style_variables).
% 0.47/1.04 set(auto2).
% 0.47/1.04 % set(auto2) -> set(auto).
% 0.47/1.04 % set(auto) -> set(auto_inference).
% 0.47/1.04 % set(auto) -> set(auto_setup).
% 0.47/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.04 % set(auto) -> set(auto_limits).
% 0.47/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.04 % set(auto) -> set(auto_denials).
% 0.47/1.04 % set(auto) -> set(auto_process).
% 0.47/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.04 % set(auto2) -> assign(stats, some).
% 0.47/1.04 % set(auto2) -> clear(echo_input).
% 0.47/1.04 % set(auto2) -> set(quiet).
% 0.47/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.04 % set(auto2) -> clear(print_given).
% 0.47/1.04 assign(lrs_ticks,-1).
% 0.47/1.04 assign(sos_limit,10000).
% 0.47/1.04 assign(order,kbo).
% 0.47/1.04 set(lex_order_vars).
% 0.47/1.04 clear(print_given).
% 0.47/1.04
% 0.47/1.04 % formulas(sos). % not echoed (16 formulas)
% 0.47/1.04
% 0.47/1.04 ============================== end of input ==========================
% 0.47/1.04
% 0.47/1.04 % From the command line: assign(max_seconds, 300).
% 0.47/1.04
% 0.47/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.04
% 0.47/1.04 % Formulas that are not ordinary clauses:
% 0.47/1.04 1 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 4 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 5 (all D all C all B all A product(product(A,B),product(C,D)) = product(product(A,C),product(B,D))) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 6 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 7 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 8 (all X0 all X1 all X2 (d(X0,X1,X2) <-> product(X0,X1) = product(X1,X2))) # label(sos08) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 9 (all X3 all X4 all X5 (m(X3,X4,X5) <-> product(product(X3,X4),product(X4,X5)) = product(X3,X5))) # label(sos09) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04
% 0.47/1.04 ============================== end of process non-clausal formulas ===
% 0.47/1.04
% 0.47/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.47/1.04
% 0.47/1.04 ============================== PREDICATE ELIMINATION =================
% 0.47/1.04 10 -d(A,B,C) | product(B,C) = product(A,B) # label(sos08) # label(axiom). [clausify(8)].
% 0.47/1.04 11 d(b,bigA,c) # label(sos10) # label(axiom). [assumption].
% 0.47/1.04 12 d(bigB,a,c) # label(sos11) # label(axiom). [assumption].
% 0.47/1.04 13 d(b,a,bigC) # label(sos12) # label(axiom). [assumption].
% 0.47/1.04 14 d(a,b1,c1) # label(sos13) # label(axiom). [assumption].
% 0.47/1.04 15 d(a1,b,c1) # label(sos14) # label(axiom). [assumption].
% 0.47/1.04 16 d(a1,b1,c) # label(sos15) # label(axiom). [assumption].
% 0.47/1.04 Derived: product(bigA,c) = product(b,bigA). [resolve(10,a,11,a)].
% 0.47/1.04 Derived: product(a,c) = product(bigB,a). [resolve(10,a,12,a)].
% 0.47/1.04 Derived: product(a,bigC) = product(b,a). [resolve(10,a,13,a)].
% 6.13/6.45 Derived: product(b1,c1) = product(a,b1). [resolve(10,a,14,a)].
% 6.13/6.45 Derived: product(b,c1) = product(a1,b). [resolve(10,a,15,a)].
% 6.13/6.45 Derived: product(b1,c) = product(a1,b1). [resolve(10,a,16,a)].
% 6.13/6.45 17 d(A,B,C) | product(B,C) != product(A,B) # label(sos08) # label(axiom). [clausify(8)].
% 6.13/6.45
% 6.13/6.45 ============================== end predicate elimination =============
% 6.13/6.45
% 6.13/6.45 Auto_denials:
% 6.13/6.45 % copying label goals to answer in negative clause
% 6.13/6.45
% 6.13/6.45 Term ordering decisions:
% 6.13/6.45 Function symbol KB weights: a=1. b=1. b1=1. c=1. a1=1. bigA=1. c1=1. bigB=1. bigC=1. product=1. difference=1. quotient=1.
% 6.13/6.45
% 6.13/6.45 ============================== end of process initial clauses ========
% 6.13/6.45
% 6.13/6.45 ============================== CLAUSES FOR SEARCH ====================
% 6.13/6.45
% 6.13/6.45 ============================== end of clauses for search =============
% 6.13/6.45
% 6.13/6.45 ============================== SEARCH ================================
% 6.13/6.45
% 6.13/6.45 % Starting search at 0.01 seconds.
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=55.000, iters=3352
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=51.000, iters=3375
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=45.000, iters=3361
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=43.000, iters=3345
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=41.000, iters=3351
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=39.000, iters=3344
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=37.000, iters=3438
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=35.000, iters=3370
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=33.000, iters=3333
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=31.000, iters=3345
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=29.000, iters=3367
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=27.000, iters=3333
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=25.000, iters=3335
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=23.000, iters=3336
% 6.13/6.45
% 6.13/6.45 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 117 (0.00 of 1.68 sec).
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=21.000, iters=3335
% 6.13/6.45
% 6.13/6.45 Low Water (displace): id=3089, wt=67.000
% 6.13/6.45
% 6.13/6.45 Low Water (displace): id=15482, wt=17.000
% 6.13/6.45
% 6.13/6.45 Low Water (displace): id=15497, wt=15.000
% 6.13/6.45
% 6.13/6.45 Low Water (displace): id=16364, wt=13.000
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=19.000, iters=3333
% 6.13/6.45
% 6.13/6.45 Low Water (displace): id=19276, wt=11.000
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=17.000, iters=3345
% 6.13/6.45
% 6.13/6.45 Low Water (keep): wt=15.000, iters=4826
% 6.13/6.45
% 6.13/6.45 ============================== PROOF =================================
% 6.13/6.45 % SZS status Theorem
% 6.13/6.45 % SZS output start Refutation
% 6.13/6.45
% 6.13/6.45 % Proof 1 at 5.28 (+ 0.14) seconds: goals.
% 6.13/6.45 % Length of proof is 142.
% 6.13/6.45 % Level of proof is 26.
% 6.13/6.45 % Maximum clause weight is 21.000.
% 6.13/6.45 % Given clauses 1297.
% 6.13/6.45
% 6.13/6.45 1 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 4 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 5 (all D all C all B all A product(product(A,B),product(C,D)) = product(product(A,C),product(B,D))) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 6 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 7 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 8 (all X0 all X1 all X2 (d(X0,X1,X2) <-> product(X0,X1) = product(X1,X2))) # label(sos08) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 9 (all X3 all X4 all X5 (m(X3,X4,X5) <-> product(product(X3,X4),product(X4,X5)) = product(X3,X5))) # label(sos09) # label(axiom) # label(non_clause). [assumption].
% 6.13/6.45 10 -d(A,B,C) | product(B,C) = product(A,B) # label(sos08) # label(axiom). [clausify(8)].
% 6.13/6.45 11 d(b,bigA,c) # label(sos10) # label(axiom). [assumption].
% 6.13/6.45 13 d(b,a,bigC) # label(sos12) # label(axiom). [assumption].
% 6.13/6.45 14 d(a,b1,c1) # label(sos13) # label(axiom). [assumption].
% 6.13/6.45 15 d(a1,b,c1) # label(sos14) # label(axiom). [assumption].
% 6.13/6.45 16 d(a1,b1,c) # label(sos15) # label(axiom). [assumption].
% 6.13/6.45 18 product(A,A) = A # label(sos06) # label(axiom). [clausify(6)].
% 6.13/6.45 19 difference(A,product(A,B)) = B # label(sos01) # label(axiom). [clausify(1)].
% 6.13/6.45 20 product(A,difference(A,B)) = B # label(sos02) # label(axiom). [clausify(2)].
% 6.13/6.45 21 quotient(product(A,B),B) = A # label(sos03) # label(axiom). [clausify(3)].
% 6.13/6.45 22 product(quotient(A,B),B) = A # label(sos04) # label(axiom). [clausify(4)].
% 6.13/6.45 23 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom). [clausify(7)].
% 6.13/6.45 24 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom). [clausify(5)].
% 6.13/6.45 25 -m(bigA,b1,bigC) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 6.13/6.45 27 m(A,B,C) | product(product(A,B),product(B,C)) != product(A,C) # label(sos09) # label(axiom). [clausify(9)].
% 6.13/6.45 28 product(bigA,c) = product(b,bigA). [resolve(10,a,11,a)].
% 6.13/6.45 31 product(a,bigC) = product(b,a). [resolve(10,a,13,a)].
% 6.13/6.45 32 product(b,a) = product(a,bigC). [copy(31),flip(a)].
% 6.13/6.45 33 product(b1,c1) = product(a,b1). [resolve(10,a,14,a)].
% 6.13/6.45 34 product(b,c1) = product(a1,b). [resolve(10,a,15,a)].
% 6.13/6.45 35 product(a1,b) = product(b,c1). [copy(34),flip(a)].
% 6.13/6.45 36 product(b1,c) = product(a1,b1). [resolve(10,a,16,a)].
% 6.13/6.45 37 product(a1,b1) = product(b1,c). [copy(36),flip(a)].
% 6.13/6.45 38 difference(A,A) = A. [para(18(a,1),19(a,1,2))].
% 6.13/6.45 39 quotient(A,A) = A. [para(18(a,1),21(a,1,1))].
% 6.13/6.45 40 quotient(A,difference(B,A)) = B. [para(20(a,1),21(a,1,1))].
% 6.13/6.45 41 difference(quotient(A,B),A) = B. [para(22(a,1),19(a,1,2))].
% 6.13/6.45 42 difference(product(product(A,B),B),B) = product(B,product(B,A)). [para(23(a,1),19(a,1,2))].
% 6.13/6.45 43 product(product(A,difference(B,A)),product(difference(B,A),product(difference(B,A),B))) = difference(B,A). [para(20(a,1),23(a,1,1,1))].
% 6.13/6.45 50 product(product(A,B),product(A,C)) = product(A,product(B,C)). [para(18(a,1),24(a,1,1)),flip(a)].
% 6.13/6.45 51 product(product(A,B),product(C,B)) = product(product(A,C),B). [para(18(a,1),24(a,1,2)),flip(a)].
% 6.13/6.45 52 difference(product(A,B),product(product(A,C),product(B,D))) = product(C,D). [para(24(a,1),19(a,1,2))].
% 6.13/6.45 53 product(product(A,B),product(difference(A,C),D)) = product(C,product(B,D)). [para(20(a,1),24(a,1,1)),flip(a)].
% 6.13/6.45 55 quotient(product(product(A,B),product(C,D)),product(B,D)) = product(A,C). [para(24(a,1),21(a,1,1))].
% 6.13/6.45 57 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B). [para(22(a,1),24(a,1,2)),flip(a)].
% 6.13/6.45 67 product(product(bigA,b1),product(b1,bigC)) != product(bigA,bigC) # answer(goals). [ur(27,a,25,a)].
% 6.13/6.45 89 product(product(A,bigA),product(B,c)) = product(product(A,B),product(b,bigA)). [para(28(a,1),24(a,1,2)),flip(a)].
% 6.13/6.45 103 quotient(product(a,bigC),a) = b. [para(32(a,1),21(a,1,1))].
% 6.13/6.45 121 quotient(product(b,c1),b) = a1. [para(35(a,1),21(a,1,1))].
% 6.13/6.45 130 quotient(product(b1,c),b1) = a1. [para(37(a,1),21(a,1,1))].
% 6.13/6.45 139 product(A,product(A,quotient(B,A))) = difference(product(B,A),A). [para(22(a,1),42(a,1,1,1)),flip(a)].
% 6.13/6.45 176 product(product(A,B),A) = product(A,product(B,A)). [para(18(a,1),50(a,1,2))].
% 6.13/6.45 182 product(quotient(A,B),product(B,C)) = product(A,product(quotient(A,B),C)). [para(22(a,1),50(a,1,1)),flip(a)].
% 6.13/6.45 186 product(product(product(A,B),C),product(product(A,D),E)) = product(product(A,product(B,D)),product(C,E)). [para(50(a,1),24(a,1,1)),flip(a)].
% 6.13/6.45 223 quotient(product(A,product(B,A)),A) = product(A,B). [para(176(a,1),21(a,1,1))].
% 6.13/6.45 304 product(product(A,product(B,C)),product(D,B)) = product(product(A,B),product(D,product(C,B))). [para(51(a,1),50(a,1,2)),rewrite([186(5)])].
% 6.13/6.45 337 difference(product(A,B),product(C,product(B,D))) = product(difference(A,C),D). [para(20(a,1),52(a,1,2,1))].
% 6.13/6.45 468 quotient(product(A,B),A) = product(A,quotient(B,A)). [para(22(a,1),223(a,1,1,2))].
% 6.13/6.45 472 product(product(A,difference(B,A)),quotient(product(difference(B,A),A),product(A,difference(B,A)))) = difference(B,A). [para(43(a,1),223(a,2)),rewrite([304(9),18(5),20(5),18(4),468(8)])].
% 6.13/6.45 483 product(b1,quotient(c,b1)) = a1. [back_rewrite(130),rewrite([468(5)])].
% 6.13/6.45 484 product(b,quotient(c1,b)) = a1. [back_rewrite(121),rewrite([468(5)])].
% 6.13/6.45 485 product(a,quotient(bigC,a)) = b. [back_rewrite(103),rewrite([468(5)])].
% 6.13/6.45 487 quotient(c,b1) = difference(b1,a1). [para(483(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 489 quotient(product(A,product(B,C)),product(D,C)) = product(quotient(A,D),B). [para(22(a,1),55(a,1,1,1))].
% 6.13/6.45 500 quotient(c1,b) = difference(b,a1). [para(484(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 502 quotient(bigC,a) = difference(a,b). [para(485(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 506 product(difference(b1,a1),b1) = c. [para(487(a,1),22(a,1,1))].
% 6.13/6.45 549 product(difference(b,a1),b) = c1. [para(500(a,1),22(a,1,1))].
% 6.13/6.45 552 product(difference(a,b),a) = bigC. [para(502(a,1),22(a,1,1))].
% 6.13/6.45 570 product(product(b1,A),c) = product(a1,product(A,b1)). [para(506(a,1),53(a,1,2))].
% 6.13/6.45 681 product(product(b,A),c1) = product(a1,product(A,b)). [para(549(a,1),53(a,1,2))].
% 6.13/6.45 700 product(product(a,A),bigC) = product(b,product(A,a)). [para(552(a,1),53(a,1,2))].
% 6.13/6.45 1749 product(A,quotient(difference(A,B),A)) = quotient(B,A). [para(20(a,1),468(a,1,1)),flip(a)].
% 6.13/6.45 1753 product(bigA,quotient(c,bigA)) = b. [para(28(a,1),468(a,1,1)),rewrite([21(5)]),flip(a)].
% 6.13/6.45 1755 quotient(product(a,bigC),b) = product(b,quotient(a,b)). [para(32(a,1),468(a,1,1))].
% 6.13/6.45 1756 product(b1,quotient(c1,b1)) = a. [para(33(a,1),468(a,1,1)),rewrite([21(5)]),flip(a)].
% 6.13/6.45 1759 difference(product(A,quotient(B,A)),product(A,B)) = A. [para(468(a,1),41(a,1,1))].
% 6.13/6.45 1846 product(product(bigA,A),c) = product(b,product(A,bigA)). [para(1753(a,1),57(a,1,1)),flip(a)].
% 6.13/6.45 1849 quotient(c1,b1) = difference(b1,a). [para(1756(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 1851 product(product(b1,A),c1) = product(a,product(A,b1)). [para(1756(a,1),57(a,1,1)),flip(a)].
% 6.13/6.45 1857 product(difference(b1,a),b1) = c1. [para(1849(a,1),22(a,1,1))].
% 6.13/6.45 1858 difference(difference(b1,a),c1) = b1. [para(1849(a,1),41(a,1,1))].
% 6.13/6.45 2084 product(a1,product(difference(b1,A),b1)) = product(A,c). [para(20(a,1),570(a,1,1)),flip(a)].
% 6.13/6.45 2085 quotient(product(a1,product(A,b1)),c) = product(b1,A). [para(570(a,1),21(a,1,1))].
% 6.13/6.45 2125 product(a1,c1) = product(a,c). [para(1857(a,1),570(a,2,2)),rewrite([20(5)]),flip(a)].
% 6.13/6.45 2373 product(product(a,c),product(c1,b)) = c1. [para(681(a,1),23(a,1,1)),rewrite([51(11),2125(3)])].
% 6.13/6.45 2423 product(product(a,c1),product(c,b)) = c1. [para(2373(a,1),24(a,1)),flip(a)].
% 6.13/6.45 2510 difference(product(a,c1),c1) = product(c,b). [para(2423(a,1),19(a,1,2))].
% 6.13/6.45 3464 quotient(difference(A,B),A) = difference(A,quotient(B,A)). [para(1749(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 3963 difference(difference(product(A,B),B),product(B,product(B,A))) = B. [para(468(a,1),1759(a,1,1,2)),rewrite([139(3)])].
% 6.13/6.45 4040 quotient(product(b,product(A,bigA)),c) = product(bigA,A). [para(1846(a,1),21(a,1,1))].
% 6.13/6.45 4042 product(product(b,c),product(c,bigA)) = c. [para(1846(a,1),23(a,1,1)),rewrite([51(11)])].
% 6.13/6.45 4114 quotient(c,product(c,bigA)) = product(b,c). [para(4042(a,1),21(a,1,1))].
% 6.13/6.45 4407 product(product(c,bigA),product(b,c)) = product(c,b). [para(4114(a,1),468(a,2,2)),rewrite([176(5),28(4),489(9),39(3)]),flip(a)].
% 6.13/6.45 4416 product(product(a,c1),product(c1,b1)) = c1. [para(1851(a,1),23(a,1,1)),rewrite([51(11)])].
% 6.13/6.45 4607 product(c1,b1) = product(c,b). [para(4416(a,1),19(a,1,2)),rewrite([2510(5)]),flip(a)].
% 6.13/6.45 4799 product(product(A,bigA),product(B,c)) = product(product(A,b),product(B,bigA)). [para(89(a,2),24(a,1))].
% 6.13/6.45 4930 product(product(c,b),product(b,bigA)) = product(c,b). [back_rewrite(4407),rewrite([4799(7)])].
% 6.13/6.45 5753 difference(a1,product(A,c)) = product(difference(b1,A),b1). [para(2084(a,1),19(a,1,2))].
% 6.13/6.45 5857 quotient(product(a1,A),c) = product(b1,quotient(A,b1)). [para(22(a,1),2085(a,1,1,2))].
% 6.13/6.45 6443 product(difference(A,quotient(B,A)),A) = difference(A,B). [para(3464(a,1),22(a,1,1))].
% 6.13/6.45 6831 quotient(product(b,A),c) = product(bigA,quotient(A,bigA)). [para(22(a,1),4040(a,1,1,2))].
% 6.13/6.45 7482 product(c,b) = product(b,bigA). [para(4930(a,1),19(a,1,2)),rewrite([38(7)])].
% 6.13/6.45 7932 product(c1,b1) = product(b,bigA). [back_rewrite(4607),rewrite([7482(6)])].
% 6.13/6.45 9045 product(a,quotient(b,a)) = difference(bigC,a). [para(552(a,1),139(a,2,1)),rewrite([3464(7),20(8)])].
% 6.13/6.45 9058 quotient(difference(product(A,B),B),B) = difference(A,B). [para(139(a,1),468(a,1,1)),rewrite([468(6),139(7),22(5)])].
% 6.13/6.45 9937 product(difference(bigC,a),bigC) = b. [para(9045(a,1),700(a,1,1)),rewrite([22(11),18(8)])].
% 6.13/6.45 9962 product(bigC,b) = product(a,bigC). [para(9937(a,1),176(a,2,2)),rewrite([20(5)]),flip(a)].
% 6.13/6.45 10042 product(b,quotient(a,b)) = bigC. [para(9962(a,1),21(a,1,1)),rewrite([1755(5)])].
% 6.13/6.45 10120 quotient(a,b) = difference(b,bigC). [para(10042(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 18129 difference(A,product(B,product(C,D))) = product(difference(quotient(A,C),B),D). [para(22(a,1),337(a,1,1))].
% 6.13/6.45 18322 product(difference(difference(A,B),B),A) = B. [back_rewrite(3963),rewrite([18129(5),9058(3)])].
% 6.13/6.45 18509 difference(difference(A,B),B) = quotient(B,A). [para(18322(a,1),21(a,1,1)),flip(a)].
% 6.13/6.45 18736 difference(A,product(B,A)) = product(B,quotient(A,B)). [para(19(a,1),18509(a,1,1)),rewrite([468(4)])].
% 6.13/6.45 18759 quotient(quotient(A,B),difference(B,A)) = difference(difference(B,A),B). [para(18509(a,1),3464(a,1,1)),rewrite([40(6)])].
% 6.13/6.45 20140 difference(a1,product(b,bigA)) = product(difference(b1,bigA),b1). [para(28(a,1),5753(a,1,2))].
% 6.13/6.45 20364 difference(A,product(B,A)) = product(difference(A,B),A). [para(21(a,1),6443(a,1,1,2)),flip(a)].
% 6.13/6.45 20500 product(difference(A,B),A) = product(B,quotient(A,B)). [back_rewrite(18736),rewrite([20364(2)])].
% 6.13/6.45 20562 difference(a1,product(b,bigA)) = product(bigA,quotient(b1,bigA)). [back_rewrite(20140),rewrite([20500(10)])].
% 6.13/6.45 21482 product(product(b,bigA),quotient(product(a,b1),product(b,bigA))) = b1. [para(1858(a,1),472(a,1,1,2)),rewrite([7932(3),1858(8),33(6),1858(12),7932(9),1858(16)])].
% 6.13/6.45 21820 quotient(product(A,B),product(C,D)) = product(quotient(A,C),quotient(B,D)). [para(22(a,1),489(a,1,1,2))].
% 6.13/6.45 21822 quotient(product(A,product(B,C)),D) = product(quotient(A,quotient(D,C)),B). [para(22(a,1),489(a,1,2))].
% 6.13/6.45 21891 product(bigC,product(bigA,quotient(b1,bigA))) = b1. [back_rewrite(21482),rewrite([21820(10),10120(6),53(11)])].
% 6.13/6.45 22436 product(bigA,quotient(b1,bigA)) = difference(bigC,b1). [para(21891(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 22438 product(product(b1,quotient(bigC,b1)),difference(bigC,b1)) = product(difference(bigC,b1),b1). [para(21891(a,1),176(a,2,2)),rewrite([22436(5),20500(5),22436(10),22436(14)])].
% 6.13/6.45 22443 difference(a1,product(b,bigA)) = difference(bigC,b1). [back_rewrite(20562),rewrite([22436(10)])].
% 6.13/6.45 22620 difference(bigA,difference(bigC,b1)) = quotient(b1,bigA). [para(22436(a,1),19(a,1,2))].
% 6.13/6.45 22623 product(difference(bigC,b1),product(bigA,A)) = product(bigA,product(quotient(b1,bigA),A)). [para(22436(a,1),50(a,1,1))].
% 6.13/6.45 22625 product(difference(bigC,b1),bigA) = product(bigA,b1). [para(22436(a,1),176(a,1,1)),rewrite([22(11)])].
% 6.13/6.45 22645 product(a1,difference(bigC,b1)) = product(b,bigA). [para(22443(a,1),20(a,1,2))].
% 6.13/6.45 22812 difference(difference(bigC,b1),product(bigA,b1)) = bigA. [para(22625(a,1),19(a,1,2))].
% 6.13/6.45 22852 product(b1,quotient(difference(bigC,b1),b1)) = bigA. [para(22645(a,1),5857(a,1,1)),rewrite([6831(5),39(4),18(3)]),flip(a)].
% 6.13/6.45 23013 quotient(product(bigA,b1),difference(bigC,b1)) = b1. [para(22812(a,1),18509(a,1,1)),rewrite([19(5)]),flip(a)].
% 6.13/6.45 23016 product(quotient(b1,bigC),difference(bigC,b1)) = bigA. [para(22812(a,1),6443(a,2)),rewrite([23013(10),18509(5)])].
% 6.13/6.45 23027 quotient(difference(bigC,b1),b1) = difference(b1,bigA). [para(22852(a,1),19(a,1,2)),flip(a)].
% 6.13/6.45 23031 product(product(b1,A),difference(bigC,b1)) = product(bigA,product(A,b1)). [para(22852(a,1),57(a,1,1)),flip(a)].
% 6.13/6.45 23038 product(difference(bigC,b1),b1) = product(bigA,bigC). [back_rewrite(22438),rewrite([23031(9),22(6)]),flip(a)].
% 6.13/6.45 23232 product(b1,quotient(b1,bigA)) = product(bigA,bigC). [para(23013(a,1),468(a,2,2)),rewrite([22623(7),21822(11),23027(6),40(5),23038(10)])].
% 6.13/6.45 23234 product(product(bigA,b1),product(b1,A)) = product(b1,product(difference(bigC,b1),A)). [para(23013(a,1),182(a,1,1)),rewrite([23013(16)]),flip(a)].
% 6.13/6.45 23249 difference(product(bigC,b1),b1) != product(bigA,bigC) # answer(goals). [back_rewrite(67),rewrite([23234(7),20500(6),139(7)])].
% 6.13/6.45 23254 product(b1,quotient(bigC,b1)) = quotient(b1,bigA). [para(23016(a,1),139(a,2,1)),rewrite([18759(13),20(12),20500(5),22620(10)])].
% 6.13/6.45 23725 difference(product(bigC,b1),b1) = product(bigA,bigC). [para(23254(a,1),139(a,1,2)),rewrite([23232(5)]),flip(a)].
% 6.13/6.45 23726 $F # answer(goals). [resolve(23725,a,23249,a)].
% 6.13/6.45
% 6.13/6.45 % SZS output end Refutation
% 6.13/6.45 ============================== end of proof ==========================
% 6.13/6.45
% 6.13/6.45 ============================== STATISTICS ============================
% 6.13/6.45
% 6.13/6.45 Given=1297. Generated=241654. Kept=23704. proofs=1.
% 6.13/6.45 Usable=1001. Sos=9999. Demods=6563. Limbo=14, Disabled=12713. Hints=0.
% 6.13/6.45 Megabytes=20.77.
% 6.13/6.45 User_CPU=5.28, System_CPU=0.14, Wall_clock=6.
% 6.13/6.45
% 6.13/6.45 ============================== end of statistics =====================
% 6.13/6.45
% 6.13/6.45 ============================== end of search =========================
% 6.13/6.45
% 6.13/6.45 THEOREM PROVED
% 6.13/6.45 % SZS status Theorem
% 6.13/6.45
% 6.13/6.45 Exiting with 1 proof.
% 6.13/6.45
% 6.13/6.45 Process 15220 exit (max_proofs) Mon Jun 13 05:41:50 2022
% 6.13/6.45 Prover9 interrupted
%------------------------------------------------------------------------------