0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.34 % Computer : n020.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 : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Mon Jul 3 10:20:16 EDT 2023 0.12/0.34 % CPUTime : 0.74/1.01 ============================== Prover9 =============================== 0.74/1.01 Prover9 (32) version 2009-11A, November 2009. 0.74/1.01 Process 14037 was started by sandbox on n020.cluster.edu, 0.74/1.01 Mon Jul 3 10:20:16 2023 0.74/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_13884_n020.cluster.edu". 0.74/1.01 ============================== end of head =========================== 0.74/1.01 0.74/1.01 ============================== INPUT ================================= 0.74/1.01 0.74/1.01 % Reading from file /tmp/Prover9_13884_n020.cluster.edu 0.74/1.01 0.74/1.01 set(prolog_style_variables). 0.74/1.01 set(auto2). 0.74/1.01 % set(auto2) -> set(auto). 0.74/1.01 % set(auto) -> set(auto_inference). 0.74/1.01 % set(auto) -> set(auto_setup). 0.74/1.01 % set(auto_setup) -> set(predicate_elim). 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold). 0.74/1.01 % set(auto) -> set(auto_limits). 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000). 0.74/1.01 % set(auto) -> set(auto_denials). 0.74/1.01 % set(auto) -> set(auto_process). 0.74/1.01 % set(auto2) -> assign(new_constants, 1). 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3). 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000"). 0.74/1.01 % set(auto2) -> assign(max_hours, 1). 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.74/1.01 % set(auto2) -> assign(max_seconds, 0). 0.74/1.01 % set(auto2) -> assign(max_minutes, 5). 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.74/1.01 % set(auto2) -> set(sort_initial_sos). 0.74/1.01 % set(auto2) -> assign(sos_limit, -1). 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000). 0.74/1.01 % set(auto2) -> assign(max_megs, 400). 0.74/1.01 % set(auto2) -> assign(stats, some). 0.74/1.01 % set(auto2) -> clear(echo_input). 0.74/1.01 % set(auto2) -> set(quiet). 0.74/1.01 % set(auto2) -> clear(print_initial_clauses). 0.74/1.01 % set(auto2) -> clear(print_given). 0.74/1.01 assign(lrs_ticks,-1). 0.74/1.01 assign(sos_limit,10000). 0.74/1.01 assign(order,kbo). 0.74/1.01 set(lex_order_vars). 0.74/1.01 clear(print_given). 0.74/1.01 0.74/1.01 % formulas(sos). % not echoed (16 formulas) 0.74/1.01 0.74/1.01 ============================== end of input ========================== 0.74/1.01 0.74/1.01 % From the command line: assign(max_seconds, 1440). 0.74/1.01 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.74/1.01 0.74/1.01 % Formulas that are not ordinary clauses: 0.74/1.01 1 (all X3 all X4 all X5 (m(X3,X4,X5) <-> product(X3,X5) = product(product(X3,X4),product(X4,X5)))) # label(sos09) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 2 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 3 (all A A = product(A,A)) # label(sos06) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 4 (all B all A B = difference(A,product(A,B))) # label(sos01) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 5 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 6 (all X0 all X1 all X2 (product(X0,X1) = product(X1,X2) <-> d(X0,X1,X2))) # label(sos08) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 7 (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]. 0.74/1.01 8 (all B all A A = product(quotient(A,B),B)) # label(sos04) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 9 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 0.74/1.01 ============================== end of process non-clausal formulas === 0.74/1.01 0.74/1.01 ============================== PROCESS INITIAL CLAUSES =============== 0.74/1.01 0.74/1.01 ============================== PREDICATE ELIMINATION ================= 0.74/1.01 10 product(A,B) = product(C,A) | -d(C,A,B) # label(sos08) # label(axiom). [clausify(6)]. 0.74/1.01 11 d(a1,b2,c1) # label(sos14) # label(axiom). [assumption]. 0.74/1.01 12 d(a1,b,c) # label(sos10) # label(axiom). [assumption]. 0.74/1.01 13 d(a1,b1,c2) # label(sos15) # label(axiom). [assumption]. 0.74/1.01 14 d(a,b1,c) # label(sos11) # label(axiom). [assumption]. 0.74/1.01 15 d(a2,b1,c1) # label(sos13) # label(axiom). [assumption]. 0.74/1.01 16 d(a,b,c1) # label(sos12) # label(axiom). [assumption]. 0.74/1.01 17 product(A,B) != product(C,A) | d(C,A,B) # label(sos08) # label(axiom). [clausify(6)]. 0.74/1.01 Derived: product(b2,c1) = product(a1,b2). [resolve(10,b,11,a)]. 11.95/12.25 Derived: product(b,c) = product(a1,b). [resolve(10,b,12,a)]. 11.95/12.25 Derived: product(b1,c2) = product(a1,b1). [resolve(10,b,13,a)]. 11.95/12.25 Derived: product(b1,c) = product(a,b1). [resolve(10,b,14,a)]. 11.95/12.25 Derived: product(b1,c1) = product(a2,b1). [resolve(10,b,15,a)]. 11.95/12.25 Derived: product(b,c1) = product(a,b). [resolve(10,b,16,a)]. 11.95/12.25 11.95/12.25 ============================== end predicate elimination ============= 11.95/12.25 11.95/12.25 Auto_denials: 11.95/12.25 % copying label goals to answer in negative clause 11.95/12.25 11.95/12.25 Term ordering decisions: 11.95/12.25 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. 11.95/12.25 11.95/12.25 ============================== end of process initial clauses ======== 11.95/12.25 11.95/12.25 ============================== CLAUSES FOR SEARCH ==================== 11.95/12.25 11.95/12.25 ============================== end of clauses for search ============= 11.95/12.25 11.95/12.25 ============================== SEARCH ================================ 11.95/12.25 11.95/12.25 % Starting search at 0.01 seconds. 11.95/12.25 11.95/12.25 Low Water (keep): wt=57.000, iters=3403 11.95/12.25 11.95/12.25 Low Water (keep): wt=51.000, iters=3338 11.95/12.25 11.95/12.25 Low Water (keep): wt=47.000, iters=3398 11.95/12.25 11.95/12.25 Low Water (keep): wt=41.000, iters=3350 11.95/12.25 11.95/12.25 Low Water (keep): wt=39.000, iters=3525 11.95/12.25 11.95/12.25 Low Water (keep): wt=37.000, iters=3363 11.95/12.25 11.95/12.25 Low Water (keep): wt=35.000, iters=3360 11.95/12.25 11.95/12.25 Low Water (keep): wt=33.000, iters=3335 11.95/12.25 11.95/12.25 Low Water (keep): wt=31.000, iters=3396 11.95/12.25 11.95/12.25 Low Water (keep): wt=29.000, iters=3346 11.95/12.25 11.95/12.25 Low Water (keep): wt=27.000, iters=3343 11.95/12.25 11.95/12.25 Low Water (keep): wt=25.000, iters=3346 11.95/12.25 11.95/12.25 Low Water (keep): wt=23.000, iters=3334 11.95/12.25 11.95/12.25 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 118 (0.00 of 1.58 sec). 11.95/12.25 11.95/12.25 Low Water (keep): wt=21.000, iters=3341 11.95/12.25 11.95/12.25 Low Water (displace): id=2771, wt=67.000 11.95/12.25 11.95/12.25 Low Water (displace): id=14843, wt=17.000 11.95/12.25 11.95/12.25 Low Water (displace): id=14867, wt=15.000 11.95/12.25 11.95/12.25 Low Water (displace): id=15384, wt=13.000 11.95/12.25 11.95/12.25 Low Water (keep): wt=19.000, iters=3353 11.95/12.25 11.95/12.25 Low Water (displace): id=18287, wt=11.000 11.95/12.25 11.95/12.25 Low Water (keep): wt=17.000, iters=3351 11.95/12.25 11.95/12.25 Low Water (displace): id=21474, wt=9.000 11.95/12.25 11.95/12.25 Low Water (keep): wt=16.000, iters=3360 11.95/12.25 11.95/12.25 Low Water (keep): wt=15.000, iters=3333 11.95/12.25 11.95/12.25 ============================== PROOF ================================= 11.95/12.25 % SZS status Theorem 11.95/12.25 % SZS output start Refutation 11.95/12.25 11.95/12.25 % Proof 1 at 10.92 (+ 0.33) seconds: goals. 11.95/12.25 % Length of proof is 165. 11.95/12.25 % Level of proof is 32. 11.95/12.25 % Maximum clause weight is 21.000. 11.95/12.25 % Given clauses 1954. 11.95/12.25 11.95/12.25 1 (all X3 all X4 all X5 (m(X3,X4,X5) <-> product(X3,X5) = product(product(X3,X4),product(X4,X5)))) # label(sos09) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 2 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 3 (all A A = product(A,A)) # label(sos06) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 4 (all B all A B = difference(A,product(A,B))) # label(sos01) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 5 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 6 (all X0 all X1 all X2 (product(X0,X1) = product(X1,X2) <-> d(X0,X1,X2))) # label(sos08) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 7 (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]. 11.95/12.25 8 (all B all A A = product(quotient(A,B),B)) # label(sos04) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 9 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption]. 11.95/12.25 10 product(A,B) = product(C,A) | -d(C,A,B) # label(sos08) # label(axiom). [clausify(6)]. 11.95/12.25 11 d(a1,b2,c1) # label(sos14) # label(axiom). [assumption]. 11.95/12.25 12 d(a1,b,c) # label(sos10) # label(axiom). [assumption]. 11.95/12.25 13 d(a1,b1,c2) # label(sos15) # label(axiom). [assumption]. 11.95/12.25 14 d(a,b1,c) # label(sos11) # label(axiom). [assumption]. 11.95/12.25 16 d(a,b,c1) # label(sos12) # label(axiom). [assumption]. 11.95/12.25 18 product(A,A) = A # label(sos06) # label(axiom). [clausify(3)]. 11.95/12.25 19 difference(A,product(A,B)) = B # label(sos01) # label(axiom). [clausify(4)]. 11.95/12.25 20 product(A,difference(A,B)) = B # label(sos02) # label(axiom). [clausify(5)]. 11.95/12.25 21 product(quotient(A,B),B) = A # label(sos04) # label(axiom). [clausify(8)]. 11.95/12.25 22 quotient(product(A,B),B) = A # label(sos03) # label(axiom). [clausify(9)]. 11.95/12.25 23 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom). [clausify(2)]. 11.95/12.25 24 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom). [clausify(7)]. 11.95/12.25 25 -m(b1,b,b2) # label(goals) # label(negated_conjecture) # answer(goals). [assumption]. 11.95/12.25 27 m(A,B,C) | product(product(A,B),product(B,C)) != product(A,C) # label(sos09) # label(axiom). [clausify(1)]. 11.95/12.25 28 product(b2,c1) = product(a1,b2). [resolve(10,b,11,a)]. 11.95/12.25 29 product(b,c) = product(a1,b). [resolve(10,b,12,a)]. 11.95/12.25 30 product(a1,b) = product(b,c). [copy(29),flip(a)]. 11.95/12.25 31 product(b1,c2) = product(a1,b1). [resolve(10,b,13,a)]. 11.95/12.25 32 product(a1,b1) = product(b1,c2). [copy(31),flip(a)]. 11.95/12.25 33 product(b1,c) = product(a,b1). [resolve(10,b,14,a)]. 11.95/12.25 34 product(a,b1) = product(b1,c). [copy(33),flip(a)]. 11.95/12.25 37 product(b,c1) = product(a,b). [resolve(10,b,16,a)]. 11.95/12.25 38 product(a,b) = product(b,c1). [copy(37),flip(a)]. 11.95/12.25 39 difference(A,A) = A. [para(18(a,1),19(a,1,2))]. 11.95/12.25 40 difference(quotient(A,B),A) = B. [para(21(a,1),19(a,1,2))]. 11.95/12.25 41 quotient(A,A) = A. [para(18(a,1),22(a,1,1))]. 11.95/12.25 43 difference(product(product(A,B),B),B) = product(B,product(B,A)). [para(23(a,1),19(a,1,2))]. 11.95/12.25 51 product(product(A,B),product(A,C)) = product(A,product(B,C)). [para(18(a,1),24(a,1,1)),flip(a)]. 11.95/12.25 52 product(product(A,B),product(C,B)) = product(product(A,C),B). [para(18(a,1),24(a,1,2)),flip(a)]. 11.95/12.25 53 difference(product(A,B),product(product(A,C),product(B,D))) = product(C,D). [para(24(a,1),19(a,1,2))]. 11.95/12.25 54 product(product(A,B),product(difference(A,C),D)) = product(C,product(B,D)). [para(20(a,1),24(a,1,1)),flip(a)]. 11.95/12.25 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)]. 11.95/12.25 57 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B). [para(21(a,1),24(a,1,2)),flip(a)]. 11.95/12.25 87 product(product(product(a1,b2),c1),product(c1,product(c1,b2))) = c1. [para(28(a,1),23(a,1,1,1))]. 11.95/12.25 89 product(product(b2,A),product(c1,B)) = product(product(a1,b2),product(A,B)). [para(28(a,1),24(a,1,1)),flip(a)]. 11.95/12.25 90 product(product(A,b2),product(B,c1)) = product(product(A,B),product(a1,b2)). [para(28(a,1),24(a,1,2)),flip(a)]. 11.95/12.25 95 quotient(product(b,c),b) = a1. [para(30(a,1),22(a,1,1))]. 11.95/12.25 104 quotient(product(b1,c2),b1) = a1. [para(32(a,1),22(a,1,1))]. 11.95/12.25 113 quotient(product(b1,c),b1) = a. [para(34(a,1),22(a,1,1))]. 11.95/12.25 117 product(product(A,a),product(B,b1)) = product(product(A,B),product(b1,c)). [para(34(a,1),24(a,1,2)),flip(a)]. 11.95/12.25 131 quotient(product(b,c1),b) = a. [para(38(a,1),22(a,1,1))]. 11.95/12.25 134 product(product(a,A),product(b,B)) = product(product(b,c1),product(A,B)). [para(38(a,1),24(a,1,1)),flip(a)]. 11.95/12.25 140 product(A,product(A,quotient(B,A))) = difference(product(B,A),A). [para(21(a,1),43(a,1,1,1)),flip(a)]. 11.95/12.25 188 product(product(A,B),A) = product(A,product(B,A)). [para(18(a,1),51(a,1,2))]. 11.95/12.25 192 product(A,product(B,difference(A,C))) = product(product(A,B),C). [para(20(a,1),51(a,1,2)),flip(a)]. 11.95/12.25 194 product(quotient(A,B),product(C,B)) = product(product(quotient(A,B),C),A). [para(21(a,1),51(a,1,2)),flip(a)]. 11.95/12.25 195 quotient(product(A,product(B,C)),product(A,C)) = product(A,B). [para(51(a,1),22(a,1,1))]. 11.95/12.25 198 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)]. 11.95/12.25 200 product(product(A,product(B,C)),product(product(C,D),E)) = product(product(A,C),product(product(B,D),E)). [para(24(a,1),51(a,1,1)),rewrite([198(6)])]. 11.95/12.25 241 quotient(product(A,product(B,A)),A) = product(A,B). [para(188(a,1),22(a,1,1))]. 11.95/12.25 262 product(product(A,B),difference(A,C)) = product(C,product(B,difference(A,C))). [para(20(a,1),52(a,1,1)),flip(a)]. 11.95/12.25 322 difference(product(A,B),product(C,product(B,D))) = product(difference(A,C),D). [para(20(a,1),53(a,1,2,1))]. 11.95/12.25 403 product(product(quotient(A,B),C),D) = product(A,product(C,difference(B,D))). [para(21(a,1),55(a,1,1)),flip(a)]. 11.95/12.25 445 product(quotient(A,B),product(C,B)) = product(A,product(C,difference(B,A))). [back_rewrite(194),rewrite([403(6)])]. 11.95/12.25 722 quotient(product(A,B),A) = product(A,quotient(B,A)). [para(21(a,1),241(a,1,1,2))]. 11.95/12.25 739 product(b,quotient(c1,b)) = a. [back_rewrite(131),rewrite([722(5)])]. 11.95/12.25 741 product(b1,quotient(c,b1)) = a. [back_rewrite(113),rewrite([722(5)])]. 11.95/12.25 742 product(b1,quotient(c2,b1)) = a1. [back_rewrite(104),rewrite([722(5)])]. 11.95/12.25 743 product(b,quotient(c,b)) = a1. [back_rewrite(95),rewrite([722(5)])]. 11.95/12.25 744 quotient(c1,b) = difference(b,a). [para(739(a,1),19(a,1,2)),flip(a)]. 11.95/12.25 746 product(product(b,A),c1) = product(a,product(A,b)). [para(739(a,1),57(a,1,1)),flip(a)]. 11.95/12.25 750 quotient(c,b1) = difference(b1,a). [para(741(a,1),19(a,1,2)),flip(a)]. 11.95/12.25 752 product(product(b1,A),c) = product(a,product(A,b1)). [para(741(a,1),57(a,1,1)),flip(a)]. 11.95/12.25 823 product(product(b1,A),c2) = product(a1,product(A,b1)). [para(742(a,1),57(a,1,1)),flip(a)]. 11.95/12.25 824 quotient(c,b) = difference(b,a1). [para(743(a,1),19(a,1,2)),flip(a)]. 11.95/12.25 826 product(product(b,A),c) = product(a1,product(A,b)). [para(743(a,1),57(a,1,1)),flip(a)]. 11.95/12.25 827 product(difference(b,a),b) = c1. [para(744(a,1),21(a,1,1))]. 11.95/12.25 901 product(difference(b1,a),b1) = c. [para(750(a,1),21(a,1,1))]. 11.95/12.25 907 product(difference(b,a1),b) = c. [para(824(a,1),21(a,1,1))]. 11.95/12.25 1982 product(A,quotient(difference(A,B),A)) = quotient(B,A). [para(20(a,1),722(a,1,1)),flip(a)]. 11.95/12.25 1986 product(b2,quotient(c1,b2)) = a1. [para(28(a,1),722(a,1,1)),rewrite([22(5)]),flip(a)]. 11.95/12.25 1987 quotient(product(b,c),a1) = product(a1,quotient(b,a1)). [para(30(a,1),722(a,1,1))]. 11.95/12.25 1992 difference(product(A,quotient(B,A)),product(A,B)) = A. [para(722(a,1),40(a,1,1))]. 11.95/12.25 2026 quotient(c1,b2) = difference(b2,a1). [para(1986(a,1),19(a,1,2)),flip(a)]. 11.95/12.25 2028 product(product(b2,A),c1) = product(a1,product(A,b2)). [para(1986(a,1),57(a,1,1)),flip(a)]. 11.95/12.25 2031 product(difference(b2,a1),b2) = c1. [para(2026(a,1),21(a,1,1))]. 11.95/12.25 2124 product(a,product(difference(b,A),b)) = product(A,c1). [para(20(a,1),746(a,1,1)),flip(a)]. 11.95/12.25 2125 quotient(product(a,product(A,b)),c1) = product(b,A). [para(746(a,1),22(a,1,1))]. 11.95/12.25 2127 product(product(a,c1),product(c1,b)) = c1. [para(746(a,1),23(a,1,1)),rewrite([52(11)])]. 11.95/12.25 2160 product(a,c) = product(a1,c1). [para(907(a,1),746(a,2,2)),rewrite([20(5)]),flip(a)]. 11.95/12.25 2833 quotient(product(a,product(A,b1)),c) = product(b1,A). [para(752(a,1),22(a,1,1))]. 11.95/12.25 2835 product(product(a1,c1),product(c,b1)) = c. [para(752(a,1),23(a,1,1)),rewrite([52(11),2160(3)])]. 11.95/12.25 3038 product(product(a1,c),product(c1,b1)) = c. [para(2835(a,1),24(a,1)),flip(a)]. 11.95/12.25 3080 difference(product(a1,c),c) = product(c1,b1). [para(3038(a,1),19(a,1,2))]. 11.95/12.25 3231 quotient(product(a1,product(A,b1)),c2) = product(b1,A). [para(823(a,1),22(a,1,1))]. 11.95/12.25 3786 product(product(a1,c),product(c,b)) = c. [para(826(a,1),23(a,1,1)),rewrite([52(11)])]. 11.95/12.25 3853 product(c,b) = product(c1,b1). [para(3786(a,1),19(a,1,2)),rewrite([3080(5)]),flip(a)]. 11.95/12.25 3924 quotient(product(c1,b1),b) = c. [para(3853(a,1),22(a,1,1))]. 11.95/12.25 4529 product(product(a1,b2),c1) = product(a1,product(c1,b2)). [para(2031(a,1),89(a,2,2)),rewrite([20(5)]),flip(a)]. 11.95/12.25 4636 product(product(a1,c1),product(c1,b2)) = c1. [back_rewrite(87),rewrite([4529(5),52(11)])]. 11.95/12.25 4638 quotient(c1,product(c1,b2)) = product(a1,c1). [para(4636(a,1),22(a,1,1))]. 11.95/12.25 4696 product(product(A,b2),product(B,c1)) = product(product(A,a1),product(B,b2)). [para(90(a,2),24(a,1))]. 11.95/12.25 4842 product(product(c1,a1),product(a1,b2)) = product(c1,a1). [para(4638(a,1),722(a,2,2)),rewrite([188(5),28(4),195(9),4696(10)]),flip(a)]. 11.95/12.25 5633 quotient(difference(A,B),A) = difference(A,quotient(B,A)). [para(1982(a,1),19(a,1,2)),flip(a)]. 11.95/12.25 5732 difference(difference(product(A,B),B),product(B,product(B,A))) = B. [para(722(a,1),1992(a,1,1,2)),rewrite([140(3)])]. 11.95/12.25 5763 quotient(product(a1,product(A,b2)),c1) = product(b2,A). [para(2028(a,1),22(a,1,1))]. 11.95/12.25 6025 difference(a,product(A,c1)) = product(difference(b,A),b). [para(2124(a,1),19(a,1,2))]. 11.95/12.25 6078 quotient(product(a,A),c1) = product(b,quotient(A,b)). [para(21(a,1),2125(a,1,1,2))]. 11.95/12.25 6548 quotient(product(a,A),c) = product(b1,quotient(A,b1)). [para(21(a,1),2833(a,1,1,2))]. 11.95/12.25 6676 quotient(product(a1,A),c2) = product(b1,quotient(A,b1)). [para(21(a,1),3231(a,1,1,2))]. 11.95/12.25 7126 product(product(a,product(c1,a)),product(product(c1,b),b1)) = product(c1,product(b1,c)). [para(2127(a,1),117(a,2,1)),rewrite([188(5)])]. 11.95/12.25 7400 product(c1,a1) = product(a1,b2). [para(4842(a,1),19(a,1,2)),rewrite([39(7)])]. 11.95/12.25 8079 product(product(a,A),product(b,B)) = product(product(b,A),product(c1,B)). [para(134(a,2),24(a,1))]. 11.95/12.25 8150 product(product(b,c1),product(c1,b1)) = product(product(a1,c1),b). [para(3853(a,1),134(a,2,2)),rewrite([2160(3),18(6)]),flip(a)]. 11.95/12.25 8477 product(difference(A,quotient(B,A)),A) = difference(A,B). [para(5633(a,1),21(a,1,1))]. 11.95/12.25 8539 product(b,quotient(a,b)) = difference(c1,b). [para(827(a,1),140(a,2,1)),rewrite([5633(7),20(8)])]. 11.95/12.25 8545 product(b1,quotient(a,b1)) = difference(c,b1). [para(901(a,1),140(a,2,1)),rewrite([5633(7),20(8)])]. 11.95/12.25 8552 product(b,quotient(a1,b)) = difference(c,b). [para(907(a,1),140(a,2,1)),rewrite([5633(7),20(8)])]. 11.95/12.25 8559 quotient(difference(product(A,B),B),B) = difference(A,B). [para(140(a,1),722(a,1,1)),rewrite([722(6),140(7),21(5)])]. 11.95/12.25 8645 product(difference(c1,b),c1) = a. [para(8539(a,1),746(a,1,1)),rewrite([21(11),18(8)])]. 11.95/12.25 8677 product(c1,a) = product(b,c1). [para(8645(a,1),188(a,2,2)),rewrite([20(5)]),flip(a)]. 11.95/12.25 8724 product(product(a1,c1),b) = product(c1,product(b1,c)). [back_rewrite(7126),rewrite([8677(4),200(11),18(6),8079(7),8150(7)])]. 11.95/12.25 9364 product(difference(c,b1),c) = a. [para(8545(a,1),752(a,1,1)),rewrite([21(11),18(8)])]. 11.95/12.25 9391 product(product(c,A),a) = product(b1,product(A,c)). [para(9364(a,1),54(a,1,2))]. 11.95/12.25 10159 product(difference(c,b),c) = a1. [para(8552(a,1),826(a,1,1)),rewrite([21(11),18(8)])]. 11.95/12.25 10177 product(c,a1) = product(b,c). [para(10159(a,1),188(a,2,2)),rewrite([20(5)]),flip(a)]. 11.95/12.25 10201 product(c,quotient(b,c)) = difference(a1,c). [para(10159(a,1),140(a,2,1)),rewrite([5633(7),20(8)])]. 11.95/12.25 10266 product(a1,quotient(b,a1)) = c. [para(10177(a,1),22(a,1,1)),rewrite([1987(5)])]. 11.95/12.25 10347 quotient(b,a1) = difference(a1,c). [para(10266(a,1),19(a,1,2)),flip(a)]. 11.95/12.25 10349 product(product(a1,A),b) = product(c,product(A,a1)). [para(10266(a,1),57(a,1,1)),flip(a)]. 11.95/12.25 10354 product(c,product(a1,b2)) = product(c1,product(b1,c)). [back_rewrite(8724),rewrite([10349(5),7400(4)])]. 11.95/12.25 10363 product(difference(a1,c),a1) = b. [para(10347(a,1),21(a,1,1))]. 11.95/12.25 10375 product(difference(a1,c),c) = product(b,difference(a1,c)). [para(10363(a,1),188(a,1,1)),rewrite([20(13)]),flip(a)]. 11.95/12.25 11614 difference(A,product(product(A,B),C)) = product(B,difference(A,C)). [para(192(a,1),19(a,1,2))]. 11.95/12.25 12197 quotient(product(A,B),product(A,C)) = product(A,quotient(B,C)). [para(21(a,1),195(a,1,1,2))]. 11.95/12.25 13318 product(b,difference(a1,c)) = product(c1,b1). [para(10201(a,1),188(a,1,1)),rewrite([10375(5),21(11),3853(8)])]. 11.95/12.25 14763 m(product(A,B),B,product(B,difference(A,B))). [hyper(27,b,262,a(flip)),rewrite([11614(4)])]. 11.95/12.25 14765 product(A,product(difference(B,C),difference(B,A))) = product(C,difference(B,A)). [para(20(a,1),262(a,1,1)),flip(a)]. 11.95/12.25 15221 difference(b,product(c1,b1)) = difference(a1,c). [para(13318(a,1),19(a,1,2))]. 11.95/12.25 15545 quotient(difference(a1,c),b) = difference(b,c). [para(15221(a,1),5633(a,1,1)),rewrite([3924(11)])]. 11.95/12.25 16160 product(difference(b,c),b) = difference(a1,c). [para(15545(a,1),21(a,1,1))]. 11.95/12.25 16408 difference(A,product(B,product(C,D))) = product(difference(quotient(A,C),B),D). [para(21(a,1),322(a,1,1))]. 11.95/12.25 16576 product(difference(difference(A,B),B),A) = B. [back_rewrite(5732),rewrite([16408(5),8559(3)])]. 11.95/12.25 16777 product(a,difference(a1,c)) = product(c,c1). [para(16160(a,1),746(a,2,2)),rewrite([20(5)]),flip(a)]. 11.95/12.25 16990 difference(difference(A,B),B) = quotient(B,A). [para(16576(a,1),22(a,1,1)),flip(a)]. 11.95/12.25 17489 difference(A,product(B,A)) = product(B,quotient(A,B)). [para(19(a,1),16990(a,1,1)),rewrite([722(4)])]. 11.95/12.25 17490 quotient(A,quotient(A,B)) = difference(B,A). [para(40(a,1),16990(a,1,1)),flip(a)]. 11.95/12.25 19612 product(quotient(A,b1),c) = product(a,difference(b1,A)). [para(901(a,1),445(a,1,2)),rewrite([14765(11)])]. 11.95/12.25 20033 quotient(product(a1,A),c1) = product(b2,quotient(A,b2)). [para(21(a,1),5763(a,1,1,2))]. 11.95/12.25 21115 product(b1,quotient(difference(a1,c),b1)) = product(c,quotient(c1,c)). [para(16777(a,1),6548(a,1,1)),rewrite([722(5)]),flip(a)]. 11.95/12.25 21135 product(b1,quotient(difference(a1,A),b1)) = quotient(A,c2). [para(20(a,1),6676(a,1,1)),flip(a)]. 11.95/12.25 21153 product(c,quotient(c1,c)) = quotient(c,c2). [back_rewrite(21115),rewrite([21135(7)]),flip(a)]. 11.95/12.25 23446 difference(A,product(B,A)) = product(difference(A,B),A). [para(22(a,1),8477(a,1,1,2)),flip(a)]. 11.95/12.25 23655 product(difference(A,B),A) = product(B,quotient(A,B)). [back_rewrite(17489),rewrite([23446(2)])]. 11.95/12.25 24280 quotient(difference(A,B),B) = difference(quotient(A,B),B). [para(21(a,1),8559(a,1,1,1))]. 11.95/12.25 25947 product(quotient(c,c2),a) = product(b1,c1). [para(21153(a,1),9391(a,1,1)),rewrite([21(11)])]. 11.95/12.25 25971 difference(quotient(c,c2),product(b1,c1)) = a. [para(25947(a,1),19(a,1,2))]. 11.95/12.25 26000 quotient(product(b1,c1),quotient(c,c2)) = product(b1,quotient(b,b1)). [para(25971(a,1),16990(a,1,1)),rewrite([6025(5),23655(5)]),flip(a)]. 11.95/12.25 26002 product(b1,quotient(c1,quotient(b,b1))) = a. [para(25971(a,1),17490(a,2)),rewrite([26000(10),12197(9)])]. 11.95/12.25 26018 quotient(c1,quotient(b,b1)) = difference(b1,a). [para(26002(a,1),19(a,1,2)),flip(a)]. 11.95/12.25 26030 difference(difference(b1,a),c1) = quotient(b,b1). [para(26018(a,1),40(a,1,1))]. 11.95/12.25 26347 product(a,difference(b1,b)) = product(a1,b2). [para(10354(a,1),19(a,1,2)),rewrite([16408(7),750(3),26030(5),19612(5)])]. 11.95/12.25 26363 product(b,difference(quotient(b1,b),b)) = b2. [para(26347(a,1),6078(a,1,1)),rewrite([20033(5),41(4),18(3),24280(7)]),flip(a)]. 11.95/12.25 26404 m(b1,b,b2). [para(26363(a,1),14763(a,3)),rewrite([21(5)])]. 11.95/12.25 26405 $F # answer(goals). [resolve(26404,a,25,a)]. 11.95/12.25 11.95/12.25 % SZS output end Refutation 11.95/12.25 ============================== end of proof ========================== 11.95/12.25 11.95/12.25 ============================== STATISTICS ============================ 11.95/12.25 11.95/12.25 Given=1954. Generated=576174. Kept=26382. proofs=1. 11.95/12.25 Usable=1551. Sos=9998. Demods=6960. Limbo=8, Disabled=14848. Hints=0. 11.95/12.25 Megabytes=21.86. 11.95/12.25 User_CPU=10.92, System_CPU=0.33, Wall_clock=12. 11.95/12.25 11.95/12.25 ============================== end of statistics ===================== 11.95/12.25 11.95/12.25 ============================== end of search ========================= 11.95/12.25 11.95/12.25 THEOREM PROVED 11.95/12.25 % SZS status Theorem 11.95/12.25 11.95/12.25 Exiting with 1 proof. 11.95/12.25 11.95/12.25 Process 14037 exit (max_proofs) Mon Jul 3 10:20:28 2023 11.95/12.25 Prover9 interrupted 11.95/12.25 EOF