TSTP Solution File: GRP778+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP778+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 6.57s 6.90s
% Output : Refutation 6.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP778+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n013.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 : Tue Jun 14 04:09:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.00 ============================== Prover9 ===============================
% 0.42/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.00 Process 20943 was started by sandbox2 on n013.cluster.edu,
% 0.42/1.00 Tue Jun 14 04:09:14 2022
% 0.42/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20790_n013.cluster.edu".
% 0.42/1.00 ============================== end of head ===========================
% 0.42/1.00
% 0.42/1.00 ============================== INPUT =================================
% 0.42/1.00
% 0.42/1.00 % Reading from file /tmp/Prover9_20790_n013.cluster.edu
% 0.42/1.00
% 0.42/1.00 set(prolog_style_variables).
% 0.42/1.00 set(auto2).
% 0.42/1.00 % set(auto2) -> set(auto).
% 0.42/1.00 % set(auto) -> set(auto_inference).
% 0.42/1.00 % set(auto) -> set(auto_setup).
% 0.42/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.00 % set(auto) -> set(auto_limits).
% 0.42/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.00 % set(auto) -> set(auto_denials).
% 0.42/1.00 % set(auto) -> set(auto_process).
% 0.42/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.00 % set(auto2) -> assign(stats, some).
% 0.42/1.00 % set(auto2) -> clear(echo_input).
% 0.42/1.00 % set(auto2) -> set(quiet).
% 0.42/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.00 % set(auto2) -> clear(print_given).
% 0.42/1.00 assign(lrs_ticks,-1).
% 0.42/1.00 assign(sos_limit,10000).
% 0.42/1.00 assign(order,kbo).
% 0.42/1.00 set(lex_order_vars).
% 0.42/1.00 clear(print_given).
% 0.42/1.00
% 0.42/1.00 % formulas(sos). % not echoed (16 formulas)
% 0.42/1.00
% 0.42/1.00 ============================== end of input ==========================
% 0.42/1.00
% 0.42/1.00 % From the command line: assign(max_seconds, 300).
% 0.42/1.00
% 0.42/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.00
% 0.42/1.00 % Formulas that are not ordinary clauses:
% 0.42/1.00 1 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 4 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 6 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00
% 0.42/1.00 ============================== end of process non-clausal formulas ===
% 0.42/1.00
% 0.42/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.00
% 0.42/1.00 ============================== PREDICATE ELIMINATION =================
% 0.42/1.00 10 -d(A,B,C) | product(B,C) = product(A,B) # label(sos08) # label(axiom). [clausify(8)].
% 0.42/1.00 11 d(a1,b,c) # label(sos10) # label(axiom). [assumption].
% 0.42/1.00 12 d(a,b1,c) # label(sos11) # label(axiom). [assumption].
% 0.42/1.00 13 d(a,b,c1) # label(sos12) # label(axiom). [assumption].
% 0.42/1.00 14 d(a2,b1,c1) # label(sos13) # label(axiom). [assumption].
% 0.42/1.00 15 d(a1,b2,c1) # label(sos14) # label(axiom). [assumption].
% 0.42/1.00 16 d(a1,b1,c2) # label(sos15) # label(axiom). [assumption].
% 0.42/1.00 Derived: product(b,c) = product(a1,b). [resolve(10,a,11,a)].
% 0.42/1.00 Derived: product(b1,c) = product(a,b1). [resolve(10,a,12,a)].
% 0.42/1.00 Derived: product(b,c1) = product(a,b). [resolve(10,a,13,a)].
% 6.57/6.90 Derived: product(b1,c1) = product(a2,b1). [resolve(10,a,14,a)].
% 6.57/6.90 Derived: product(b2,c1) = product(a1,b2). [resolve(10,a,15,a)].
% 6.57/6.90 Derived: product(b1,c2) = product(a1,b1). [resolve(10,a,16,a)].
% 6.57/6.90 17 d(A,B,C) | product(B,C) != product(A,B) # label(sos08) # label(axiom). [clausify(8)].
% 6.57/6.90
% 6.57/6.90 ============================== end predicate elimination =============
% 6.57/6.90
% 6.57/6.90 Auto_denials:
% 6.57/6.90 % copying label goals to answer in negative clause
% 6.57/6.90
% 6.57/6.90 Term ordering decisions:
% 6.57/6.90 Function symbol KB weights: b1=1. b=1. a1=1. c1=1. a=1. b2=1. c=1. a2=1. c2=1. product=1. difference=1. quotient=1.
% 6.57/6.90
% 6.57/6.90 ============================== end of process initial clauses ========
% 6.57/6.90
% 6.57/6.90 ============================== CLAUSES FOR SEARCH ====================
% 6.57/6.90
% 6.57/6.90 ============================== end of clauses for search =============
% 6.57/6.90
% 6.57/6.90 ============================== SEARCH ================================
% 6.57/6.90
% 6.57/6.90 % Starting search at 0.01 seconds.
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=57.000, iters=3381
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=51.000, iters=3349
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=47.000, iters=3433
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=45.000, iters=3360
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=43.000, iters=3353
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=39.000, iters=3355
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=37.000, iters=3360
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=35.000, iters=3381
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=33.000, iters=3355
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=31.000, iters=3346
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=29.000, iters=3361
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=27.000, iters=3335
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=25.000, iters=3335
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=23.000, iters=3338
% 6.57/6.90
% 6.57/6.90 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 104 (0.00 of 1.52 sec).
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=21.000, iters=3350
% 6.57/6.90
% 6.57/6.90 Low Water (displace): id=2993, wt=67.000
% 6.57/6.90
% 6.57/6.90 Low Water (displace): id=14728, wt=17.000
% 6.57/6.90
% 6.57/6.90 Low Water (displace): id=14735, wt=15.000
% 6.57/6.90
% 6.57/6.90 Low Water (displace): id=15307, wt=13.000
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=19.000, iters=3334
% 6.57/6.90
% 6.57/6.90 Low Water (displace): id=17242, wt=11.000
% 6.57/6.90
% 6.57/6.90 Low Water (keep): wt=17.000, iters=3345
% 6.57/6.90
% 6.57/6.90 ============================== PROOF =================================
% 6.57/6.90 % SZS status Theorem
% 6.57/6.90 % SZS output start Refutation
% 6.57/6.90
% 6.57/6.90 % Proof 1 at 5.75 (+ 0.16) seconds: goals.
% 6.57/6.90 % Length of proof is 116.
% 6.57/6.90 % Level of proof is 25.
% 6.57/6.90 % Maximum clause weight is 21.000.
% 6.57/6.90 % Given clauses 1477.
% 6.57/6.90
% 6.57/6.90 1 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 6.57/6.90 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 6.57/6.90 3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 6.57/6.90 4 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 6.57/6.90 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].
% 6.57/6.90 6 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 6.57/6.90 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].
% 6.57/6.90 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].
% 6.57/6.90 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].
% 6.57/6.90 10 -d(A,B,C) | product(B,C) = product(A,B) # label(sos08) # label(axiom). [clausify(8)].
% 6.57/6.90 11 d(a1,b,c) # label(sos10) # label(axiom). [assumption].
% 6.57/6.90 12 d(a,b1,c) # label(sos11) # label(axiom). [assumption].
% 6.57/6.90 13 d(a,b,c1) # label(sos12) # label(axiom). [assumption].
% 6.57/6.90 15 d(a1,b2,c1) # label(sos14) # label(axiom). [assumption].
% 6.57/6.90 16 d(a1,b1,c2) # label(sos15) # label(axiom). [assumption].
% 6.57/6.90 18 product(A,A) = A # label(sos06) # label(axiom). [clausify(6)].
% 6.57/6.90 19 difference(A,product(A,B)) = B # label(sos01) # label(axiom). [clausify(1)].
% 6.57/6.90 20 product(A,difference(A,B)) = B # label(sos02) # label(axiom). [clausify(2)].
% 6.57/6.90 21 quotient(product(A,B),B) = A # label(sos03) # label(axiom). [clausify(3)].
% 6.57/6.90 22 product(quotient(A,B),B) = A # label(sos04) # label(axiom). [clausify(4)].
% 6.57/6.90 23 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom). [clausify(7)].
% 6.57/6.90 24 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom). [clausify(5)].
% 6.57/6.90 25 -m(b1,b,b2) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 6.57/6.90 27 m(A,B,C) | product(product(A,B),product(B,C)) != product(A,C) # label(sos09) # label(axiom). [clausify(9)].
% 6.57/6.90 28 product(b,c) = product(a1,b). [resolve(10,a,11,a)].
% 6.57/6.90 29 product(a1,b) = product(b,c). [copy(28),flip(a)].
% 6.57/6.90 30 product(b1,c) = product(a,b1). [resolve(10,a,12,a)].
% 6.57/6.90 31 product(a,b1) = product(b1,c). [copy(30),flip(a)].
% 6.57/6.90 32 product(b,c1) = product(a,b). [resolve(10,a,13,a)].
% 6.57/6.90 33 product(a,b) = product(b,c1). [copy(32),flip(a)].
% 6.57/6.90 36 product(b2,c1) = product(a1,b2). [resolve(10,a,15,a)].
% 6.57/6.90 37 product(b1,c2) = product(a1,b1). [resolve(10,a,16,a)].
% 6.57/6.90 38 product(a1,b1) = product(b1,c2). [copy(37),flip(a)].
% 6.57/6.90 39 difference(A,A) = A. [para(18(a,1),19(a,1,2))].
% 6.57/6.90 42 difference(quotient(A,B),A) = B. [para(22(a,1),19(a,1,2))].
% 6.57/6.90 43 difference(product(product(A,B),B),B) = product(B,product(B,A)). [para(23(a,1),19(a,1,2))].
% 6.57/6.90 51 product(product(A,B),product(A,C)) = product(A,product(B,C)). [para(18(a,1),24(a,1,1)),flip(a)].
% 6.57/6.90 52 product(product(A,B),product(C,B)) = product(product(A,C),B). [para(18(a,1),24(a,1,2)),flip(a)].
% 6.57/6.90 53 difference(product(A,B),product(product(A,C),product(B,D))) = product(C,D). [para(24(a,1),19(a,1,2))].
% 6.57/6.90 55 product(product(A,B),product(C,difference(B,D))) = product(product(A,C),D). [para(20(a,1),24(a,1,2)),flip(a)].
% 6.57/6.90 58 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B). [para(22(a,1),24(a,1,2)),flip(a)].
% 6.57/6.90 68 product(product(b1,b),product(b,b2)) != product(b1,b2) # answer(goals). [ur(27,a,25,a)].
% 6.57/6.90 86 quotient(product(b,c),b) = a1. [para(29(a,1),21(a,1,1))].
% 6.57/6.90 90 product(product(A,a1),product(B,b)) = product(product(A,B),product(b,c)). [para(29(a,1),24(a,1,2)),flip(a)].
% 6.57/6.90 95 quotient(product(b1,c),b1) = a. [para(31(a,1),21(a,1,1))].
% 6.57/6.90 98 product(product(b1,c),product(A,B)) = product(product(a,A),product(b1,B)). [para(31(a,1),24(a,1,1))].
% 6.57/6.90 104 quotient(product(b,c1),b) = a. [para(33(a,1),21(a,1,1))].
% 6.57/6.90 107 product(product(a,A),product(b,B)) = product(product(b,c1),product(A,B)). [para(33(a,1),24(a,1,1)),flip(a)].
% 6.57/6.90 131 quotient(product(b1,c2),b1) = a1. [para(38(a,1),21(a,1,1))].
% 6.57/6.90 140 product(A,product(A,quotient(B,A))) = difference(product(B,A),A). [para(22(a,1),43(a,1,1,1)),flip(a)].
% 6.57/6.90 177 product(product(A,B),A) = product(A,product(B,A)). [para(18(a,1),51(a,1,2))].
% 6.57/6.90 180 product(A,product(difference(A,B),C)) = product(B,product(A,C)). [para(20(a,1),51(a,1,1)),flip(a)].
% 6.57/6.90 187 product(product(product(A,B),C),product(product(A,D),E)) = product(product(A,product(B,D)),product(C,E)). [para(51(a,1),24(a,1,1)),flip(a)].
% 6.57/6.90 226 quotient(product(A,product(B,A)),A) = product(A,B). [para(177(a,1),21(a,1,1))].
% 6.57/6.90 339 difference(product(A,B),product(C,product(B,D))) = product(difference(A,C),D). [para(20(a,1),53(a,1,2,1))].
% 6.57/6.90 443 product(product(A,B),product(product(C,difference(B,D)),E)) = product(product(A,product(C,B)),product(D,E)). [para(55(a,1),51(a,1,1)),rewrite([187(5)]),flip(a)].
% 6.57/6.90 501 quotient(product(A,B),A) = product(A,quotient(B,A)). [para(22(a,1),226(a,1,1,2))].
% 6.57/6.90 516 product(b1,quotient(c2,b1)) = a1. [back_rewrite(131),rewrite([501(5)])].
% 6.57/6.90 518 product(b,quotient(c1,b)) = a. [back_rewrite(104),rewrite([501(5)])].
% 6.57/6.90 519 product(b1,quotient(c,b1)) = a. [back_rewrite(95),rewrite([501(5)])].
% 6.57/6.90 520 product(b,quotient(c,b)) = a1. [back_rewrite(86),rewrite([501(5)])].
% 6.57/6.90 564 product(product(b1,A),c2) = product(a1,product(A,b1)). [para(516(a,1),58(a,1,1)),flip(a)].
% 6.57/6.90 570 product(product(b,A),c1) = product(a,product(A,b)). [para(518(a,1),58(a,1,1)),flip(a)].
% 6.57/6.90 573 product(product(b1,A),c) = product(a,product(A,b1)). [para(519(a,1),58(a,1,1)),flip(a)].
% 6.57/6.90 669 quotient(c,b) = difference(b,a1). [para(520(a,1),19(a,1,2)),flip(a)].
% 6.57/6.90 671 product(product(b,A),c) = product(a1,product(A,b)). [para(520(a,1),58(a,1,1)),flip(a)].
% 6.57/6.90 778 product(difference(b,a1),b) = c. [para(669(a,1),22(a,1,1))].
% 6.57/6.90 1813 product(A,quotient(difference(A,B),A)) = quotient(B,A). [para(20(a,1),501(a,1,1)),flip(a)].
% 6.57/6.90 1821 product(b2,quotient(c1,b2)) = a1. [para(36(a,1),501(a,1,1)),rewrite([21(5)]),flip(a)].
% 6.57/6.90 1823 difference(product(A,quotient(B,A)),product(A,B)) = A. [para(501(a,1),42(a,1,1))].
% 6.57/6.90 1913 product(product(b2,A),c1) = product(a1,product(A,b2)). [para(1821(a,1),58(a,1,1)),flip(a)].
% 6.57/6.90 2028 product(a1,product(difference(b1,A),b1)) = product(A,c2). [para(20(a,1),564(a,1,1)),flip(a)].
% 6.57/6.90 2552 quotient(product(a,product(A,b)),c1) = product(b,A). [para(570(a,1),21(a,1,1))].
% 6.57/6.90 2575 product(a,c) = product(a1,c1). [para(778(a,1),570(a,2,2)),rewrite([20(5)]),flip(a)].
% 6.57/6.90 2880 product(a,product(difference(b1,A),b1)) = product(A,c). [para(20(a,1),573(a,1,1)),flip(a)].
% 6.57/6.90 2883 product(product(a1,c1),product(c,b1)) = c. [para(573(a,1),23(a,1,1)),rewrite([52(11),2575(3)])].
% 6.57/6.90 3067 product(product(a1,c),product(c1,b1)) = c. [para(2883(a,1),24(a,1)),flip(a)].
% 6.57/6.90 3107 difference(product(a1,c),c) = product(c1,b1). [para(3067(a,1),19(a,1,2))].
% 6.57/6.90 3245 product(a1,product(difference(b,A),b)) = product(A,c). [para(20(a,1),671(a,1,1)),flip(a)].
% 6.57/6.90 3246 quotient(product(a1,product(A,b)),c) = product(b,A). [para(671(a,1),21(a,1,1))].
% 6.57/6.90 3248 product(product(a1,c),product(c,b)) = c. [para(671(a,1),23(a,1,1)),rewrite([52(11)])].
% 6.57/6.90 3422 product(c,b) = product(c1,b1). [para(3248(a,1),19(a,1,2)),rewrite([3107(5)]),flip(a)].
% 6.57/6.90 4914 product(product(A,a1),product(c1,b1)) = product(product(A,b),c). [para(90(a,2),52(a,1)),rewrite([3422(5)])].
% 6.57/6.90 5105 quotient(difference(A,B),A) = difference(A,quotient(B,A)). [para(1813(a,1),19(a,1,2)),flip(a)].
% 6.57/6.90 5144 difference(difference(product(A,B),B),product(B,product(B,A))) = B. [para(501(a,1),1823(a,1,1,2)),rewrite([140(3)])].
% 6.57/6.90 5250 product(a1,product(difference(b2,A),b2)) = product(A,c1). [para(20(a,1),1913(a,1,1)),flip(a)].
% 6.57/6.90 5513 product(product(b,c1),product(b1,A)) = product(product(b1,c),product(b,A)). [para(33(a,1),98(a,2,1)),flip(a)].
% 6.57/6.90 5920 product(product(a,A),product(b,B)) = product(product(b,A),product(c1,B)). [para(107(a,2),24(a,1))].
% 6.57/6.90 5923 product(product(b1,c),product(b,c2)) = product(b,c). [para(38(a,1),107(a,2,2)),rewrite([5920(7),4914(7),18(3),5513(10)]),flip(a)].
% 6.57/6.90 6433 quotient(product(a,A),c1) = product(b,quotient(A,b)). [para(22(a,1),2552(a,1,1,2))].
% 6.57/6.90 6571 difference(a1,product(A,c)) = product(difference(b,A),b). [para(3245(a,1),19(a,1,2))].
% 6.57/6.90 6624 quotient(product(a1,A),c) = product(b,quotient(A,b)). [para(22(a,1),3246(a,1,1,2))].
% 6.57/6.90 7613 product(difference(A,quotient(B,A)),A) = difference(A,B). [para(5105(a,1),22(a,1,1))].
% 6.57/6.90 7956 difference(a1,product(A,c1)) = product(difference(b2,A),b2). [para(5250(a,1),19(a,1,2))].
% 6.57/6.90 8384 quotient(difference(product(A,B),B),B) = difference(A,B). [para(140(a,1),501(a,1,1)),rewrite([501(6),140(7),22(5)])].
% 6.57/6.90 17800 difference(product(A,B),product(C,D)) = product(difference(A,C),difference(B,D)). [para(20(a,1),339(a,1,2,2))].
% 6.57/6.90 17801 difference(A,product(B,product(C,D))) = product(difference(quotient(A,C),B),D). [para(22(a,1),339(a,1,1))].
% 6.57/6.90 17964 product(difference(difference(A,B),B),A) = B. [back_rewrite(5144),rewrite([17801(5),8384(3)])].
% 6.57/6.90 18095 difference(difference(A,B),B) = quotient(B,A). [para(17964(a,1),21(a,1,1)),flip(a)].
% 6.57/6.90 18393 difference(A,product(B,A)) = product(B,quotient(A,B)). [para(19(a,1),18095(a,1,1)),rewrite([501(4)])].
% 6.57/6.90 19438 product(difference(b1,b),c) = product(b,c2). [para(5923(a,1),19(a,1,2)),rewrite([17800(7),39(6)])].
% 6.57/6.90 19456 quotient(product(b,c2),c) = difference(b1,b). [para(19438(a,1),21(a,1,1))].
% 6.57/6.90 19671 product(b,quotient(product(difference(b1,A),b1),b)) = quotient(product(A,c),c1). [para(2880(a,1),6433(a,1,1)),flip(a)].
% 6.57/6.90 22148 quotient(product(A,c2),c) = quotient(product(A,c),c1). [para(2028(a,1),6624(a,1,1)),rewrite([19671(12)])].
% 6.57/6.90 22162 quotient(product(b,c),c1) = difference(b1,b). [back_rewrite(19456),rewrite([22148(5)])].
% 6.57/6.90 22193 product(difference(b1,b),c1) = product(b,c). [para(22162(a,1),22(a,1,1))].
% 6.57/6.90 22342 difference(A,product(B,A)) = product(difference(A,B),A). [para(21(a,1),7613(a,1,1,2)),flip(a)].
% 6.57/6.90 22496 product(difference(A,B),A) = product(B,quotient(A,B)). [back_rewrite(18393),rewrite([22342(2)])].
% 6.57/6.90 23661 product(difference(b2,difference(b1,b)),b2) = b. [para(22193(a,1),7956(a,1,2)),rewrite([6571(5),39(3),18(3)]),flip(a)].
% 6.57/6.90 23666 difference(b2,difference(b1,b)) = quotient(b,b2). [para(23661(a,1),21(a,1,1)),flip(a)].
% 6.57/6.90 23673 product(difference(b1,b),b2) = product(b2,b). [para(23661(a,1),180(a,1,2)),rewrite([18(9)]),flip(a)].
% 6.57/6.90 23776 difference(difference(b1,b),product(b2,b)) = b2. [para(23673(a,1),19(a,1,2))].
% 6.57/6.90 23781 quotient(product(b2,b),difference(b1,b)) = b. [para(23673(a,1),501(a,1,1)),rewrite([22496(16,R),23666(12),22(12)])].
% 6.57/6.90 23945 product(quotient(b,b1),difference(b1,b)) = b2. [para(23776(a,1),7613(a,2)),rewrite([23781(10),18095(5)])].
% 6.57/6.90 24221 product(product(A,b),product(b,B)) = product(product(A,b1),product(b2,B)). [para(23945(a,1),443(a,1,2,1)),rewrite([22(10)]),flip(a)].
% 6.57/6.90 24230 $F # answer(goals). [back_rewrite(68),rewrite([24221(7),18(3),18(4)]),xx(a)].
% 6.57/6.90
% 6.57/6.90 % SZS output end Refutation
% 6.57/6.90 ============================== end of proof ==========================
% 6.57/6.90
% 6.57/6.90 ============================== STATISTICS ============================
% 6.57/6.90
% 6.57/6.90 Given=1477. Generated=286156. Kept=24207. proofs=1.
% 6.57/6.90 Usable=1167. Sos=9999. Demods=6619. Limbo=19, Disabled=13046. Hints=0.
% 6.57/6.90 Megabytes=20.95.
% 6.57/6.90 User_CPU=5.75, System_CPU=0.16, Wall_clock=6.
% 6.57/6.90
% 6.57/6.90 ============================== end of statistics =====================
% 6.57/6.90
% 6.57/6.90 ============================== end of search =========================
% 6.57/6.90
% 6.57/6.90 THEOREM PROVED
% 6.57/6.90 % SZS status Theorem
% 6.57/6.90
% 6.57/6.90 Exiting with 1 proof.
% 6.57/6.90
% 6.57/6.90 Process 20943 exit (max_proofs) Tue Jun 14 04:09:20 2022
% 6.57/6.90 Prover9 interrupted
%------------------------------------------------------------------------------