0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.33 % Computer : n015.cluster.edu 0.10/0.33 % Model : x86_64 x86_64 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.33 % Memory : 8042.1875MB 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.33 % CPULimit : 1440 0.10/0.33 % WCLimit : 180 0.10/0.33 % DateTime : Mon Jul 3 10:44:55 EDT 2023 0.10/0.33 % CPUTime : 0.73/1.11 ============================== Prover9 =============================== 0.73/1.11 Prover9 (32) version 2009-11A, November 2009. 0.73/1.11 Process 24990 was started by sandbox2 on n015.cluster.edu, 0.73/1.11 Mon Jul 3 10:44:55 2023 0.73/1.11 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_24837_n015.cluster.edu". 0.73/1.11 ============================== end of head =========================== 0.73/1.11 0.73/1.11 ============================== INPUT ================================= 0.73/1.11 0.73/1.11 % Reading from file /tmp/Prover9_24837_n015.cluster.edu 0.73/1.11 0.73/1.11 set(prolog_style_variables). 0.73/1.11 set(auto2). 0.73/1.11 % set(auto2) -> set(auto). 0.73/1.11 % set(auto) -> set(auto_inference). 0.73/1.11 % set(auto) -> set(auto_setup). 0.73/1.11 % set(auto_setup) -> set(predicate_elim). 0.73/1.11 % set(auto_setup) -> assign(eq_defs, unfold). 0.73/1.11 % set(auto) -> set(auto_limits). 0.73/1.11 % set(auto_limits) -> assign(max_weight, "100.000"). 0.73/1.11 % set(auto_limits) -> assign(sos_limit, 20000). 0.73/1.11 % set(auto) -> set(auto_denials). 0.73/1.11 % set(auto) -> set(auto_process). 0.73/1.11 % set(auto2) -> assign(new_constants, 1). 0.73/1.11 % set(auto2) -> assign(fold_denial_max, 3). 0.73/1.11 % set(auto2) -> assign(max_weight, "200.000"). 0.73/1.11 % set(auto2) -> assign(max_hours, 1). 0.73/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.73/1.11 % set(auto2) -> assign(max_seconds, 0). 0.73/1.11 % set(auto2) -> assign(max_minutes, 5). 0.73/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.73/1.11 % set(auto2) -> set(sort_initial_sos). 0.73/1.11 % set(auto2) -> assign(sos_limit, -1). 0.73/1.11 % set(auto2) -> assign(lrs_ticks, 3000). 0.73/1.11 % set(auto2) -> assign(max_megs, 400). 0.73/1.11 % set(auto2) -> assign(stats, some). 0.73/1.11 % set(auto2) -> clear(echo_input). 0.73/1.11 % set(auto2) -> set(quiet). 0.73/1.11 % set(auto2) -> clear(print_initial_clauses). 0.73/1.11 % set(auto2) -> clear(print_given). 0.73/1.11 assign(lrs_ticks,-1). 0.73/1.11 assign(sos_limit,10000). 0.73/1.11 assign(order,kbo). 0.73/1.11 set(lex_order_vars). 0.73/1.11 clear(print_given). 0.73/1.11 0.73/1.11 % formulas(sos). % not echoed (16 formulas) 0.73/1.11 0.73/1.11 ============================== end of input ========================== 0.73/1.11 0.73/1.11 % From the command line: assign(max_seconds, 1440). 0.73/1.11 0.73/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.73/1.11 0.73/1.11 % Formulas that are not ordinary clauses: 0.73/1.11 1 (all B all A B = product(product(product(A,B),B),product(B,product(B,A)))) # label(sos07) # label(axiom) # label(non_clause). [assumption]. 0.73/1.11 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption]. 0.73/1.11 3 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption]. 0.73/1.11 4 (all A A = product(A,A)) # label(sos06) # label(axiom) # label(non_clause). [assumption]. 0.73/1.11 5 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption]. 0.73/1.11 6 (all X0 all X1 all X2 (d(X0,X1,X2) <-> product(X0,X1) = product(X1,X2))) # label(sos08) # label(axiom) # label(non_clause). [assumption]. 0.73/1.11 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]. 0.73/1.11 8 (all B all A A = quotient(product(A,B),B)) # label(sos03) # label(axiom) # label(non_clause). [assumption]. 0.73/1.11 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]. 0.73/1.11 0.73/1.11 ============================== end of process non-clausal formulas === 0.73/1.11 0.73/1.11 ============================== PROCESS INITIAL CLAUSES =============== 0.73/1.11 0.73/1.11 ============================== PREDICATE ELIMINATION ================= 0.73/1.11 10 -d(A,B,C) | product(B,C) = product(A,B) # label(sos08) # label(axiom). [clausify(6)]. 0.73/1.11 11 d(bigB,a,c) # label(sos11) # label(axiom). [assumption]. 0.73/1.11 12 d(a1,b1,c) # label(sos15) # label(axiom). [assumption]. 0.73/1.11 13 d(b,a,bigC) # label(sos12) # label(axiom). [assumption]. 0.73/1.11 14 d(b,bigA,c) # label(sos10) # label(axiom). [assumption]. 0.73/1.11 15 d(a1,b,c1) # label(sos14) # label(axiom). [assumption]. 0.73/1.11 16 d(a,b1,c1) # label(sos13) # label(axiom). [assumption]. 0.73/1.11 Derived: product(a,c) = product(bigB,a). [resolve(10,a,11,a)]. 0.73/1.11 Derived: product(b1,c) = product(a1,b1). [resolve(10,a,12,a)]. 0.73/1.11 Derived: product(a,bigC) = product(b,a). [resolve(10,a,13,a)]. 21.39/22.44 Derived: product(bigA,c) = product(b,bigA). [resolve(10,a,14,a)]. 21.39/22.44 Derived: product(b,c1) = product(a1,b). [resolve(10,a,15,a)]. 21.39/22.44 Derived: product(b1,c1) = product(a,b1). [resolve(10,a,16,a)]. 21.39/22.44 17 d(A,B,C) | product(B,C) != product(A,B) # label(sos08) # label(axiom). [clausify(6)]. 21.39/22.44 21.39/22.44 ============================== end predicate elimination ============= 21.39/22.44 21.39/22.44 Auto_denials: 21.39/22.44 % copying label goals to answer in negative clause 21.39/22.44 21.39/22.44 Term ordering decisions: 21.39/22.44 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. 21.39/22.44 21.39/22.44 ============================== end of process initial clauses ======== 21.39/22.44 21.39/22.44 ============================== CLAUSES FOR SEARCH ==================== 21.39/22.44 21.39/22.44 ============================== end of clauses for search ============= 21.39/22.44 21.39/22.44 ============================== SEARCH ================================ 21.39/22.44 21.39/22.44 % Starting search at 0.01 seconds. 21.39/22.44 21.39/22.44 Low Water (keep): wt=55.000, iters=3348 21.39/22.44 21.39/22.44 Low Water (keep): wt=53.000, iters=3463 21.39/22.44 21.39/22.44 Low Water (keep): wt=47.000, iters=3396 21.39/22.44 21.39/22.44 Low Water (keep): wt=43.000, iters=3465 21.39/22.44 21.39/22.44 Low Water (keep): wt=39.000, iters=3467 21.39/22.44 21.39/22.44 Low Water (keep): wt=37.000, iters=3345 21.39/22.44 21.39/22.44 Low Water (keep): wt=35.000, iters=3361 21.39/22.44 21.39/22.44 Low Water (keep): wt=33.000, iters=3346 21.39/22.44 21.39/22.44 Low Water (keep): wt=31.000, iters=3338 21.39/22.44 21.39/22.44 Low Water (keep): wt=29.000, iters=3372 21.39/22.44 21.39/22.44 Low Water (keep): wt=27.000, iters=3365 21.39/22.44 21.39/22.44 Low Water (keep): wt=25.000, iters=3351 21.39/22.44 21.39/22.44 Low Water (keep): wt=23.000, iters=3335 21.39/22.44 21.39/22.44 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 113 (0.00 of 3.32 sec). 21.39/22.44 21.39/22.44 Low Water (keep): wt=21.000, iters=3352 21.39/22.44 21.39/22.44 Low Water (displace): id=2808, wt=67.000 21.39/22.44 21.39/22.44 Low Water (displace): id=15641, wt=19.000 21.39/22.44 21.39/22.44 Low Water (displace): id=15645, wt=15.000 21.39/22.44 21.39/22.44 Low Water (displace): id=16201, wt=13.000 21.39/22.44 21.39/22.44 Low Water (keep): wt=19.000, iters=3336 21.39/22.44 21.39/22.44 Low Water (displace): id=18264, wt=11.000 21.39/22.44 21.39/22.44 Low Water (displace): id=20839, wt=10.000 21.39/22.44 21.39/22.44 Low Water (keep): wt=17.000, iters=3335 21.39/22.44 21.39/22.44 Low Water (keep): wt=16.000, iters=3335 21.39/22.44 21.39/22.44 Low Water (keep): wt=15.000, iters=3340 21.39/22.44 21.39/22.44 ============================== PROOF ================================= 21.39/22.44 % SZS status Theorem 21.39/22.44 % SZS output start Refutation 21.39/22.44 21.39/22.44 % Proof 1 at 20.17 (+ 0.53) seconds: goals. 21.39/22.44 % Length of proof is 127. 21.39/22.44 % Level of proof is 25. 21.39/22.44 % Maximum clause weight is 19.000. 21.39/22.44 % Given clauses 1901. 21.39/22.44 21.39/22.44 1 (all B all A B = product(product(product(A,B),B),product(B,product(B,A)))) # label(sos07) # label(axiom) # label(non_clause). [assumption]. 21.39/22.44 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption]. 21.39/22.44 3 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption]. 21.39/22.44 4 (all A A = product(A,A)) # label(sos06) # label(axiom) # label(non_clause). [assumption]. 21.39/22.44 5 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption]. 21.39/22.44 6 (all X0 all X1 all X2 (d(X0,X1,X2) <-> product(X0,X1) = product(X1,X2))) # label(sos08) # label(axiom) # label(non_clause). [assumption]. 21.39/22.44 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]. 21.39/22.44 8 (all B all A A = quotient(product(A,B),B)) # label(sos03) # label(axiom) # label(non_clause). [assumption]. 21.39/22.44 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]. 21.39/22.44 10 -d(A,B,C) | product(B,C) = product(A,B) # label(sos08) # label(axiom). [clausify(6)]. 21.39/22.44 12 d(a1,b1,c) # label(sos15) # label(axiom). [assumption]. 21.39/22.44 13 d(b,a,bigC) # label(sos12) # label(axiom). [assumption]. 21.39/22.44 14 d(b,bigA,c) # label(sos10) # label(axiom). [assumption]. 21.39/22.44 15 d(a1,b,c1) # label(sos14) # label(axiom). [assumption]. 21.39/22.44 16 d(a,b1,c1) # label(sos13) # label(axiom). [assumption]. 21.39/22.44 18 product(A,A) = A # label(sos06) # label(axiom). [clausify(4)]. 21.39/22.44 19 product(A,difference(A,B)) = B # label(sos02) # label(axiom). [clausify(2)]. 21.39/22.44 20 difference(A,product(A,B)) = B # label(sos01) # label(axiom). [clausify(3)]. 21.39/22.44 21 product(quotient(A,B),B) = A # label(sos04) # label(axiom). [clausify(5)]. 21.39/22.44 22 quotient(product(A,B),B) = A # label(sos03) # label(axiom). [clausify(8)]. 21.39/22.44 23 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom). [clausify(1)]. 21.39/22.44 24 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom). [clausify(7)]. 21.39/22.44 25 -m(bigA,b1,bigC) # label(goals) # label(negated_conjecture) # answer(goals). [assumption]. 21.39/22.44 27 m(A,B,C) | product(product(A,B),product(B,C)) != product(A,C) # label(sos09) # label(axiom). [clausify(9)]. 21.39/22.44 30 product(b1,c) = product(a1,b1). [resolve(10,a,12,a)]. 21.39/22.44 31 product(a1,b1) = product(b1,c). [copy(30),flip(a)]. 21.39/22.44 32 product(a,bigC) = product(b,a). [resolve(10,a,13,a)]. 21.39/22.44 33 product(b,a) = product(a,bigC). [copy(32),flip(a)]. 21.39/22.44 34 product(bigA,c) = product(b,bigA). [resolve(10,a,14,a)]. 21.39/22.44 35 product(b,c1) = product(a1,b). [resolve(10,a,15,a)]. 21.39/22.44 36 product(a1,b) = product(b,c1). [copy(35),flip(a)]. 21.39/22.44 37 product(b1,c1) = product(a,b1). [resolve(10,a,16,a)]. 21.39/22.44 39 difference(quotient(A,B),A) = B. [para(21(a,1),20(a,1,2))]. 21.39/22.44 40 quotient(A,A) = A. [para(18(a,1),22(a,1,1))]. 21.39/22.44 42 product(product(A,difference(B,A)),product(difference(B,A),product(difference(B,A),B))) = difference(B,A). [para(19(a,1),23(a,1,1,1))]. 21.39/22.44 44 difference(product(product(A,B),B),B) = product(B,product(B,A)). [para(23(a,1),20(a,1,2))]. 21.39/22.44 50 product(product(A,B),product(A,C)) = product(A,product(B,C)). [para(18(a,1),24(a,1,1)),flip(a)]. 21.39/22.44 51 product(product(A,B),product(C,B)) = product(product(A,C),B). [para(18(a,1),24(a,1,2)),flip(a)]. 21.39/22.44 52 product(product(A,B),product(difference(A,C),D)) = product(C,product(B,D)). [para(19(a,1),24(a,1,1)),flip(a)]. 21.39/22.44 56 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B). [para(21(a,1),24(a,1,2)),flip(a)]. 21.39/22.44 94 quotient(product(b1,c),b1) = a1. [para(31(a,1),22(a,1,1))]. 21.39/22.44 103 quotient(product(a,bigC),a) = b. [para(33(a,1),22(a,1,1))]. 21.39/22.44 121 quotient(product(b,c1),b) = a1. [para(36(a,1),22(a,1,1))]. 21.39/22.44 132 product(product(product(c1,b1),b1),product(b1,product(a,b1))) = b1. [para(37(a,1),23(a,1,2,2))]. 21.39/22.44 138 difference(product(A,difference(B,A)),difference(B,A)) = product(difference(B,A),product(difference(B,A),B)). [para(42(a,1),20(a,1,2))]. 21.39/22.44 153 product(A,product(A,quotient(B,A))) = difference(product(B,A),A). [para(21(a,1),44(a,1,1,1)),flip(a)]. 21.39/22.44 187 product(product(A,B),A) = product(A,product(B,A)). [para(18(a,1),50(a,1,2))]. 21.39/22.44 190 product(A,product(B,difference(A,C))) = product(product(A,B),C). [para(19(a,1),50(a,1,2)),flip(a)]. 21.39/22.44 238 quotient(product(A,product(B,A)),A) = product(A,B). [para(187(a,1),22(a,1,1))]. 21.39/22.44 258 product(product(A,B),difference(A,C)) = product(C,product(B,difference(A,C))). [para(19(a,1),51(a,1,1)),flip(a)]. 21.39/22.44 296 product(product(A,B),product(B,product(C,B))) = product(product(A,product(B,C)),B). [para(187(a,1),51(a,1,2))]. 21.39/22.44 302 product(product(product(c1,b1),product(b1,a)),b1) = b1. [back_rewrite(132),rewrite([296(11)])]. 21.39/22.44 322 difference(product(A,B),product(C,product(B,D))) = product(difference(A,C),D). [para(52(a,1),20(a,1,2))]. 21.39/22.44 323 product(A,product(difference(quotient(A,B),C),D)) = product(C,product(B,D)). [para(21(a,1),52(a,1,1))]. 21.39/22.44 324 quotient(product(A,product(B,C)),product(difference(D,A),C)) = product(D,B). [para(52(a,1),22(a,1,1))]. 21.39/22.44 594 quotient(product(A,B),A) = product(A,quotient(B,A)). [para(21(a,1),238(a,1,1,2))]. 21.39/22.44 609 product(b,quotient(c1,b)) = a1. [back_rewrite(121),rewrite([594(5)])]. 21.39/22.44 610 product(a,quotient(bigC,a)) = b. [back_rewrite(103),rewrite([594(5)])]. 21.39/22.44 611 product(b1,quotient(c,b1)) = a1. [back_rewrite(94),rewrite([594(5)])]. 21.39/22.44 706 product(product(b,A),c1) = product(a1,product(A,b)). [para(609(a,1),56(a,1,1)),flip(a)]. 21.39/22.44 707 quotient(bigC,a) = difference(a,b). [para(610(a,1),20(a,1,2)),flip(a)]. 21.39/22.44 709 product(product(a,A),bigC) = product(b,product(A,a)). [para(610(a,1),56(a,1,1)),flip(a)]. 21.39/22.44 710 quotient(c,b1) = difference(b1,a1). [para(611(a,1),20(a,1,2)),flip(a)]. 21.39/22.44 712 product(product(b1,A),c) = product(a1,product(A,b1)). [para(611(a,1),56(a,1,1)),flip(a)]. 21.39/22.44 788 product(difference(a,b),a) = bigC. [para(707(a,1),21(a,1,1))]. 21.39/22.44 791 product(difference(b1,a1),b1) = c. [para(710(a,1),21(a,1,1))]. 21.39/22.44 1686 product(product(c1,b1),product(b1,a)) = b1. [para(302(a,1),22(a,1,1)),rewrite([40(3)]),flip(a)]. 21.39/22.44 1939 product(A,quotient(difference(A,B),A)) = quotient(B,A). [para(19(a,1),594(a,1,1)),flip(a)]. 21.39/22.44 1944 quotient(product(b1,c),a1) = product(a1,quotient(b1,a1)). [para(31(a,1),594(a,1,1))]. 21.39/22.44 1946 product(bigA,quotient(c,bigA)) = b. [para(34(a,1),594(a,1,1)),rewrite([22(5)]),flip(a)]. 21.39/22.44 1948 product(b1,quotient(c1,b1)) = a. [para(37(a,1),594(a,1,1)),rewrite([22(5)]),flip(a)]. 21.39/22.44 1949 difference(product(A,quotient(B,A)),product(A,B)) = A. [para(594(a,1),39(a,1,1))]. 21.39/22.44 1982 quotient(c,bigA) = difference(bigA,b). [para(1946(a,1),20(a,1,2)),flip(a)]. 21.39/22.44 1984 product(product(bigA,A),c) = product(b,product(A,bigA)). [para(1946(a,1),56(a,1,1)),flip(a)]. 21.39/22.44 1987 quotient(c1,b1) = difference(b1,a). [para(1948(a,1),20(a,1,2)),flip(a)]. 21.39/22.44 1989 product(product(b1,A),c1) = product(a,product(A,b1)). [para(1948(a,1),56(a,1,1)),flip(a)]. 21.39/22.44 1992 product(difference(bigA,b),bigA) = c. [para(1982(a,1),21(a,1,1))]. 21.39/22.44 2054 product(difference(b1,a),b1) = c1. [para(1987(a,1),21(a,1,1))]. 21.39/22.44 2162 product(product(a1,c1),product(c1,b)) = c1. [para(706(a,1),23(a,1,1)),rewrite([51(11)])]. 21.39/22.44 2652 product(a1,c1) = product(a,c). [para(2054(a,1),712(a,2,2)),rewrite([19(5)]),flip(a)]. 21.39/22.44 2698 product(product(a,c),product(c1,b)) = c1. [back_rewrite(2162),rewrite([2652(3)])]. 21.39/22.44 2998 product(product(a,c1),product(c,b)) = c1. [para(2698(a,1),24(a,1)),flip(a)]. 21.39/22.44 3114 difference(product(a,c1),c1) = product(c,b). [para(2998(a,1),20(a,1,2))]. 21.39/22.44 4593 quotient(difference(A,B),A) = difference(A,quotient(B,A)). [para(1939(a,1),20(a,1,2)),flip(a)]. 21.39/22.44 5119 product(product(a,c1),product(c1,b1)) = c1. [para(1989(a,1),23(a,1,1)),rewrite([51(11)])]. 21.39/22.44 5196 product(c1,b1) = product(c,b). [para(5119(a,1),20(a,1,2)),rewrite([3114(5)]),flip(a)]. 21.39/22.44 5307 product(product(c,b),product(b1,a)) = b1. [back_rewrite(1686),rewrite([5196(3)])]. 21.39/22.44 5404 product(product(c,b1),product(a,bigC)) = b1. [para(5307(a,1),24(a,1)),rewrite([33(7)]),flip(a)]. 21.39/22.44 5428 product(product(c,a),product(b1,bigC)) = b1. [para(5404(a,1),24(a,1)),flip(a)]. 21.39/22.44 5736 quotient(b1,product(b1,bigC)) = product(c,a). [para(5428(a,1),22(a,1,1))]. 21.39/22.44 7405 product(difference(A,quotient(B,A)),A) = difference(A,B). [para(4593(a,1),21(a,1,1))]. 21.39/22.44 8332 difference(product(A,product(B,A)),A) = product(A,difference(product(B,A),A)). [para(1949(a,1),138(a,1,1,2)),rewrite([187(2),1949(6),1949(7),1949(7),153(6)])]. 21.39/22.44 9436 product(a,quotient(b,a)) = difference(bigC,a). [para(788(a,1),153(a,2,1)),rewrite([4593(7),19(8)])]. 21.39/22.44 9439 product(b1,quotient(a1,b1)) = difference(c,b1). [para(791(a,1),153(a,2,1)),rewrite([4593(7),19(8)])]. 21.39/22.44 9451 quotient(difference(product(A,B),B),B) = difference(A,B). [para(153(a,1),594(a,1,1)),rewrite([594(6),153(7),21(5)])]. 21.39/22.44 9452 product(bigA,quotient(b,bigA)) = difference(c,bigA). [para(1992(a,1),153(a,2,1)),rewrite([4593(7),19(8)])]. 21.39/22.44 9795 product(difference(bigC,a),bigC) = b. [para(9436(a,1),709(a,1,1)),rewrite([21(11),18(8)])]. 21.39/22.44 9810 product(product(A,difference(bigC,a)),product(B,bigC)) = product(product(A,B),b). [para(9795(a,1),24(a,1,2)),flip(a)]. 21.39/22.44 10221 product(difference(c,b1),c) = a1. [para(9439(a,1),712(a,1,1)),rewrite([21(11),18(8)])]. 21.39/22.44 10247 product(c,a1) = product(b1,c). [para(10221(a,1),187(a,2,2)),rewrite([19(5)]),flip(a)]. 21.39/22.44 10273 product(c,quotient(b1,c)) = difference(a1,c). [para(10221(a,1),153(a,2,1)),rewrite([4593(7),19(8)])]. 21.39/22.44 10315 product(a1,quotient(b1,a1)) = c. [para(10247(a,1),22(a,1,1)),rewrite([1944(5)])]. 21.39/22.44 10396 quotient(b1,a1) = difference(a1,c). [para(10315(a,1),20(a,1,2)),flip(a)]. 21.39/22.44 10415 product(difference(a1,c),a1) = b1. [para(10396(a,1),21(a,1,1))]. 21.39/22.44 10425 product(difference(a1,c),c) = product(b1,difference(a1,c)). [para(10415(a,1),187(a,1,1)),rewrite([19(13)]),flip(a)]. 21.39/22.44 10799 product(difference(c,bigA),c) = b. [para(9452(a,1),1984(a,1,1)),rewrite([21(11),18(8)])]. 21.39/22.44 10822 product(product(c,A),b) = product(bigA,product(A,c)). [para(10799(a,1),52(a,1,2))]. 21.39/22.44 11566 difference(A,product(product(A,B),C)) = product(B,difference(A,C)). [para(190(a,1),20(a,1,2))]. 21.39/22.44 14095 product(b1,difference(a1,c)) = product(c,b1). [para(10273(a,1),187(a,1,1)),rewrite([10425(5),21(11)])]. 21.39/22.44 15423 m(product(A,B),B,product(B,difference(A,B))). [hyper(27,b,258,a(flip)),rewrite([11566(4)])]. 21.39/22.44 16040 difference(b1,product(c,b1)) = difference(a1,c). [para(14095(a,1),20(a,1,2))]. 21.39/22.44 17328 quotient(difference(a1,c),b1) = difference(b1,c). [para(16040(a,1),4593(a,1,1)),rewrite([22(11)])]. 21.39/22.44 17698 difference(product(A,B),product(C,D)) = product(difference(A,C),difference(B,D)). [para(19(a,1),322(a,1,2,2))]. 21.39/22.44 17905 product(difference(b1,c),b1) = difference(a1,c). [para(17328(a,1),21(a,1,1))]. 21.39/22.44 17975 quotient(product(A,product(B,C)),product(D,C)) = product(quotient(A,D),B). [para(39(a,1),324(a,1,2,1))]. 21.39/22.44 18052 product(quotient(A,difference(B,C)),D) = product(B,difference(quotient(C,D),A)). [para(323(a,1),324(a,1,1)),rewrite([17975(5)])]. 21.39/22.44 20250 m(product(quotient(A,B),A),A,product(A,B)). [para(39(a,1),15423(a,3,2))]. 21.39/22.44 20687 m(product(A,difference(quotient(B,A),A)),A,B). [para(19(a,1),20250(a,3)),rewrite([18052(3)])]. 21.39/22.44 22582 difference(product(b1,bigC),b1) = product(difference(a1,c),b). [para(5736(a,1),7405(a,1,1,2)),rewrite([17698(7),9810(11),17905(5)]),flip(a)]. 21.39/22.44 25126 difference(product(A,B),B) = product(difference(A,B),B). [para(9451(a,1),21(a,1,1)),flip(a)]. 21.39/22.44 25127 quotient(difference(A,B),B) = difference(quotient(A,B),B). [para(21(a,1),9451(a,1,1,1))]. 21.39/22.44 25130 difference(product(A,B),A) = product(A,difference(B,A)). [para(187(a,1),9451(a,1,1,1)),rewrite([8332(3),25126(2),594(4),22(3)]),flip(a)]. 21.39/22.44 25287 product(difference(a1,c),b) = product(b1,difference(bigC,b1)). [back_rewrite(22582),rewrite([25130(5)]),flip(a)]. 21.39/22.44 28155 product(b1,difference(bigC,b1)) = product(bigA,b1). [para(10273(a,1),10822(a,1,1)),rewrite([25287(5),21(11)])]. 21.39/22.44 28185 product(b1,difference(quotient(bigC,b1),b1)) = bigA. [para(28155(a,1),594(a,1,1)),rewrite([22(5),25127(7)]),flip(a)]. 21.39/22.44 28301 m(bigA,b1,bigC). [para(28185(a,1),20687(a,1))]. 21.39/22.44 28302 $F # answer(goals). [resolve(28301,a,25,a)]. 21.39/22.44 21.39/22.44 % SZS output end Refutation 21.39/22.44 ============================== end of proof ========================== 21.39/22.44 21.39/22.44 ============================== STATISTICS ============================ 21.39/22.44 21.39/22.44 Given=1901. Generated=515471. Kept=28280. proofs=1. 21.39/22.44 Usable=1419. Sos=9999. Demods=7071. Limbo=11, Disabled=16874. Hints=0. 21.39/22.44 Megabytes=23.06. 21.39/22.44 User_CPU=20.17, System_CPU=0.53, Wall_clock=22. 21.39/22.44 21.39/22.44 ============================== end of statistics ===================== 21.39/22.44 21.39/22.44 ============================== end of search ========================= 21.39/22.44 21.39/22.44 THEOREM PROVED 21.39/22.44 % SZS status Theorem 21.39/22.44 21.39/22.44 Exiting with 1 proof. 21.39/22.44 21.39/22.44 Process 24990 exit (max_proofs) Mon Jul 3 10:45:17 2023 21.39/22.44 Prover9 interrupted 21.39/22.44 EOF