TSTP Solution File: GRP775+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 11:21:01 EDT 2022
% Result : Theorem 6.63s 6.90s
% Output : Refutation 6.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n007.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 13:11:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 23321 was started by sandbox on n007.cluster.edu,
% 0.43/0.98 Tue Jun 14 13:11:25 2022
% 0.43/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23167_n007.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_23167_n007.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (6 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98 1 (all C all B all A product(product(A,B),C) = product(A,product(B,C))) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 2 (all A product(A,A) = A) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 3 (all X0 all X1 (l(X0,X1) <-> product(X0,X1) = X0 & product(X1,X0) = X1)) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 4 (all X2 all X3 (r(X2,X3) <-> product(X2,X3) = X3 & product(X3,X2) = X2)) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 5 (all X4 all X5 (d(X4,X5) <-> (exists X6 (r(X4,X6) & l(X6,X5))))) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 6 -(all X7 all X8 (d(X7,X8) <-> product(X7,product(X8,X7)) = X7 & product(X8,product(X7,X8)) = X8)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.98
% 0.43/0.98 ============================== end of process non-clausal formulas ===
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.98
% 0.43/0.98 ============================== PREDICATE ELIMINATION =================
% 0.43/0.98 7 -d(A,B) | l(f1(A,B),B) # label(sos05) # label(axiom). [clausify(5)].
% 0.43/0.98 8 -l(A,B) | product(A,B) = A # label(sos03) # label(axiom). [clausify(3)].
% 0.43/0.98 9 -l(A,B) | product(B,A) = B # label(sos03) # label(axiom). [clausify(3)].
% 0.43/0.98 Derived: -d(A,B) | product(f1(A,B),B) = f1(A,B). [resolve(7,b,8,a)].
% 0.43/0.98 Derived: -d(A,B) | product(B,f1(A,B)) = B. [resolve(7,b,9,a)].
% 0.43/0.98 10 d(A,B) | -r(A,C) | -l(C,B) # label(sos05) # label(axiom). [clausify(5)].
% 0.43/0.98 Derived: d(A,B) | -r(A,f1(C,B)) | -d(C,B). [resolve(10,c,7,b)].
% 0.43/0.98 11 l(A,B) | product(A,B) != A | product(B,A) != B # label(sos03) # label(axiom). [clausify(3)].
% 0.43/0.98 Derived: product(A,B) != A | product(B,A) != B | d(C,B) | -r(C,A). [resolve(11,a,10,c)].
% 0.43/0.98
% 0.43/0.98 ============================== end predicate elimination =============
% 0.43/0.98
% 0.43/0.98 Auto_denials: (non-Horn, no changes).
% 0.43/0.98
% 0.43/0.98 Term ordering decisions:
% 0.43/0.98 Function symbol KB weights: c1=1. c2=1. product=1. f1=1.
% 0.43/0.98
% 0.43/0.98 ============================== end of process initial clauses ========
% 6.63/6.90
% 6.63/6.90 ============================== CLAUSES FOR SEARCH ====================
% 6.63/6.90
% 6.63/6.90 ============================== end of clauses for search =============
% 6.63/6.90
% 6.63/6.90 ============================== SEARCH ================================
% 6.63/6.90
% 6.63/6.90 % Starting search at 0.01 seconds.
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=54.000, iters=3417
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=51.000, iters=3361
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=46.000, iters=3472
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=44.000, iters=3389
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=43.000, iters=3388
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=42.000, iters=3370
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=40.000, iters=3341
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=39.000, iters=3340
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=38.000, iters=3385
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=37.000, iters=3345
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=36.000, iters=3350
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=35.000, iters=3358
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=34.000, iters=3333
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=33.000, iters=3381
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=32.000, iters=3391
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=31.000, iters=3341
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=30.000, iters=3347
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=29.000, iters=3335
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=28.000, iters=3405
% 6.63/6.90
% 6.63/6.90 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 1.56 sec).
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=27.000, iters=3403
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=26.000, iters=3359
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=4102, wt=70.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=3834, wt=69.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=5358, wt=66.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=2534, wt=65.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=13037, wt=25.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=13126, wt=24.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=13236, wt=22.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=13575, wt=21.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=13947, wt=20.000
% 6.63/6.90
% 6.63/6.90 Low Water (displace): id=14017, wt=18.000
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=25.000, iters=3380
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=24.000, iters=3333
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=23.000, iters=3355
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=22.000, iters=3335
% 6.63/6.90
% 6.63/6.90 Low Water (keep): wt=21.000, iters=3333
% 6.63/6.90
% 6.63/6.90 ============================== PROOF =================================
% 6.63/6.90 % SZS status Theorem
% 6.63/6.90 % SZS output start Refutation
% 6.63/6.90
% 6.63/6.90 % Proof 1 at 5.77 (+ 0.16) seconds.
% 6.63/6.90 % Length of proof is 91.
% 6.63/6.90 % Level of proof is 25.
% 6.63/6.90 % Maximum clause weight is 29.000.
% 6.63/6.90 % Given clauses 2278.
% 6.63/6.90
% 6.63/6.90 1 (all C all B all A product(product(A,B),C) = product(A,product(B,C))) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 6.63/6.90 2 (all A product(A,A) = A) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 6.63/6.90 3 (all X0 all X1 (l(X0,X1) <-> product(X0,X1) = X0 & product(X1,X0) = X1)) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 6.63/6.90 4 (all X2 all X3 (r(X2,X3) <-> product(X2,X3) = X3 & product(X3,X2) = X2)) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 6.63/6.90 5 (all X4 all X5 (d(X4,X5) <-> (exists X6 (r(X4,X6) & l(X6,X5))))) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 6.63/6.90 6 -(all X7 all X8 (d(X7,X8) <-> product(X7,product(X8,X7)) = X7 & product(X8,product(X7,X8)) = X8)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.63/6.90 7 -d(A,B) | l(f1(A,B),B) # label(sos05) # label(axiom). [clausify(5)].
% 6.63/6.90 8 -l(A,B) | product(A,B) = A # label(sos03) # label(axiom). [clausify(3)].
% 6.63/6.90 9 -l(A,B) | product(B,A) = B # label(sos03) # label(axiom). [clausify(3)].
% 6.63/6.90 10 d(A,B) | -r(A,C) | -l(C,B) # label(sos05) # label(axiom). [clausify(5)].
% 6.63/6.90 11 l(A,B) | product(A,B) != A | product(B,A) != B # label(sos03) # label(axiom). [clausify(3)].
% 6.63/6.90 12 product(A,A) = A # label(sos02) # label(axiom). [clausify(2)].
% 6.63/6.90 13 d(c1,c2) | product(c1,product(c2,c1)) = c1 # label(goals) # label(negated_conjecture). [clausify(6)].
% 6.63/6.90 14 d(c1,c2) | product(c2,product(c1,c2)) = c2 # label(goals) # label(negated_conjecture). [clausify(6)].
% 6.63/6.90 15 product(product(A,B),C) = product(A,product(B,C)) # label(sos01) # label(axiom). [clausify(1)].
% 6.63/6.90 16 -d(c1,c2) | product(c1,product(c2,c1)) != c1 | product(c2,product(c1,c2)) != c2 # label(goals) # label(negated_conjecture). [clausify(6)].
% 6.63/6.90 17 -r(A,B) | product(A,B) = B # label(sos04) # label(axiom). [clausify(4)].
% 6.63/6.90 18 -r(A,B) | product(B,A) = A # label(sos04) # label(axiom). [clausify(4)].
% 6.63/6.90 19 -d(A,B) | r(A,f1(A,B)) # label(sos05) # label(axiom). [clausify(5)].
% 6.63/6.90 20 r(A,B) | product(A,B) != B | product(B,A) != A # label(sos04) # label(axiom). [clausify(4)].
% 6.63/6.90 21 -d(A,B) | product(f1(A,B),B) = f1(A,B). [resolve(7,b,8,a)].
% 6.63/6.90 22 -d(A,B) | product(B,f1(A,B)) = B. [resolve(7,b,9,a)].
% 6.63/6.90 23 d(A,B) | -r(A,f1(C,B)) | -d(C,B). [resolve(10,c,7,b)].
% 6.63/6.90 24 product(A,B) != A | product(B,A) != B | d(C,B) | -r(C,A). [resolve(11,a,10,c)].
% 6.63/6.90 26 d(A,B) | -r(A,B). [factor(24,a,b),rewrite([12(1)]),xx(a)].
% 6.63/6.90 27 product(A,product(B,product(A,B))) = product(A,B). [para(15(a,1),12(a,1))].
% 6.63/6.90 28 product(A,product(A,B)) = product(A,B). [para(12(a,1),15(a,1,1)),flip(a)].
% 6.63/6.90 29 r(c1,f1(c1,c2)) | product(c2,product(c1,c2)) = c2. [resolve(19,a,14,a)].
% 6.63/6.90 30 r(c1,f1(c1,c2)) | product(c1,product(c2,c1)) = c1. [resolve(19,a,13,a)].
% 6.63/6.90 34 product(f1(c1,c2),c2) = f1(c1,c2) | product(c1,product(c2,c1)) = c1. [resolve(21,a,13,a)].
% 6.63/6.90 35 product(c2,f1(c1,c2)) = c2 | product(c2,product(c1,c2)) = c2. [resolve(22,a,14,a)].
% 6.63/6.90 40 product(A,product(B,product(A,product(B,C)))) = product(A,product(B,C)). [para(27(a,1),15(a,1,1)),rewrite([15(2),15(5),15(4)]),flip(a)].
% 6.63/6.90 52 r(product(A,B),A) | product(A,product(B,A)) != A. [resolve(28,a,20,c),rewrite([15(4)])].
% 6.63/6.90 57 product(c2,product(c1,c2)) = c2 | product(c1,f1(c1,c2)) = f1(c1,c2). [resolve(29,a,17,a)].
% 6.63/6.90 60 product(c1,product(c2,c1)) = c1 | product(f1(c1,c2),c1) = c1. [resolve(30,a,18,a)].
% 6.63/6.90 77 r(product(A,B),product(A,product(B,A))). [para(27(a,1),52(b,1,2)),rewrite([15(3),15(2),27(3),15(8),12(7)]),xx(b)].
% 6.63/6.90 78 r(product(A,product(B,A)),product(A,B)). [para(28(a,1),52(b,1,2)),rewrite([15(2),12(7)]),xx(b)].
% 6.63/6.90 79 d(product(A,B),product(A,product(B,A))). [resolve(77,a,26,b)].
% 6.63/6.90 80 product(A,product(B,product(A,C))) != product(A,product(B,A)) | product(C,product(A,product(B,A))) != C | d(product(A,B),C). [resolve(77,a,24,d),rewrite([15(3),15(2)])].
% 6.63/6.90 82 r(product(A,product(B,C)),product(A,product(B,product(C,A)))). [para(15(a,1),77(a,2,2))].
% 6.63/6.90 84 product(A,product(B,C)) != product(A,B) | product(C,product(A,B)) != C | d(product(A,product(B,A)),C). [resolve(78,a,24,d),rewrite([15(2)])].
% 6.63/6.90 86 r(product(A,product(B,product(C,product(A,B)))),product(A,product(B,C))). [para(15(a,1),78(a,1)),rewrite([15(6)])].
% 6.63/6.90 89 product(f1(product(A,B),product(A,product(B,A))),product(A,product(B,A))) = f1(product(A,B),product(A,product(B,A))). [resolve(79,a,21,a)].
% 6.63/6.90 90 r(product(A,B),f1(product(A,B),product(A,product(B,A)))). [resolve(79,a,19,a)].
% 6.63/6.90 151 product(f1(product(A,B),product(A,product(B,A))),product(A,B)) = product(A,B). [resolve(90,a,18,a)].
% 6.63/6.90 158 product(c1,product(c2,c1)) = c1 | product(f1(c1,c2),product(c2,A)) = product(f1(c1,c2),A). [para(34(a,1),15(a,1,1)),flip(b)].
% 6.63/6.90 308 product(c1,product(c2,c1)) = c1 | product(f1(c1,c2),product(c1,A)) = product(c1,A). [para(60(b,1),15(a,1,1)),flip(b)].
% 6.63/6.90 346 product(A,product(B,product(C,product(A,product(B,product(C,D)))))) = product(A,product(B,product(C,D))). [para(40(a,1),15(a,1)),rewrite([15(3),15(6)]),flip(a)].
% 6.63/6.90 1397 d(product(A,B),product(B,A)). [resolve(80,a,40,a),rewrite([15(4),28(3),27(3)]),xx(a)].
% 6.63/6.90 1456 d(product(A,product(B,C)),product(C,product(A,B))). [para(15(a,1),1397(a,1))].
% 6.63/6.90 1570 d(product(A,B),product(B,product(A,B))). [para(12(a,1),1456(a,1,2))].
% 6.63/6.90 1607 d(product(c1,product(c2,c1)),c2) | product(c1,f1(c1,c2)) = f1(c1,c2). [resolve(84,b,57,a),rewrite([12(4)]),xx(a)].
% 6.63/6.90 1608 product(A,product(B,A)) != A | d(product(B,product(A,B)),A). [para(12(a,1),84(a,1,2)),xx(a)].
% 6.63/6.90 1665 product(A,product(B,product(A,f1(product(B,A),product(A,product(B,A)))))) = product(A,product(B,A)). [resolve(1570,a,22,a),rewrite([15(7),15(6)])].
% 6.63/6.90 1667 r(product(A,B),f1(product(A,B),product(B,product(A,B)))). [resolve(1570,a,19,a)].
% 6.63/6.90 1925 product(A,product(B,f1(product(A,B),product(B,product(A,B))))) = f1(product(A,B),product(B,product(A,B))). [resolve(1667,a,17,a),rewrite([15(6)])].
% 6.63/6.90 1959 product(A,f1(product(B,A),product(A,product(B,A)))) = product(A,product(B,A)). [back_rewrite(1665),rewrite([1925(6)])].
% 6.63/6.90 1960 f1(product(A,B),product(B,product(A,B))) = product(A,B). [back_rewrite(1925),rewrite([1959(5),27(3)]),flip(a)].
% 6.63/6.90 1973 product(f1(product(A,B),product(A,product(B,A))),product(A,product(B,product(A,C)))) = product(f1(product(A,B),product(A,product(B,A))),C). [para(89(a,1),15(a,1,1)),rewrite([15(12),15(11)]),flip(a)].
% 6.63/6.90 2285 d(A,product(B,product(C,B))) | -r(A,product(C,B)). [para(1960(a,1),23(b,2)),unit_del(c,1570)].
% 6.63/6.90 2323 d(A,product(B,product(C,product(D,B)))) | -r(A,product(C,product(D,B))). [para(15(a,1),2285(b,2)),rewrite([15(2)])].
% 6.63/6.90 8868 product(c1,f1(c1,c2)) = f1(c1,c2) | r(product(c1,product(c2,c1)),f1(product(c1,product(c2,c1)),c2)). [resolve(1607,a,19,a)].
% 6.63/6.90 9319 product(f1(product(A,B),product(A,product(B,A))),product(A,product(B,C))) = product(A,product(B,C)). [para(151(a,1),15(a,1,1)),rewrite([15(2),15(8)]),flip(a)].
% 6.63/6.90 9342 r(product(A,product(B,product(C,product(A,f1(product(B,C),product(B,product(C,B))))))),product(A,product(B,C))). [para(151(a,1),86(a,2,2)),rewrite([15(11),9319(12)])].
% 6.63/6.90 9430 product(f1(product(A,B),product(A,product(B,A))),C) = product(A,product(B,product(A,C))). [back_rewrite(1973),rewrite([9319(8)]),flip(a)].
% 6.63/6.90 9431 f1(product(A,B),product(A,product(B,A))) = product(A,product(B,A)). [back_rewrite(89),rewrite([9430(7),28(3),27(3)]),flip(a)].
% 6.63/6.90 9444 r(product(A,product(B,product(C,B))),product(A,product(B,C))). [back_rewrite(9342),rewrite([9431(4),346(6)])].
% 6.63/6.90 9863 product(c1,product(c2,c1)) = c1 | product(f1(c1,c2),product(c2,c1)) = c1. [para(60(b,1),158(b,2)),merge(b)].
% 6.63/6.90 10495 d(product(A,product(B,C)),product(C,product(A,product(B,product(C,A))))). [resolve(2323,b,82,a),rewrite([15(7),28(6)])].
% 6.63/6.90 11650 product(c1,product(c2,c1)) = c1 | r(product(f1(c1,c2),product(c2,product(c1,c2))),c1). [para(9863(b,1),9444(a,2))].
% 6.63/6.90 19859 product(c1,product(c2,c1)) = c1 | r(product(f1(c1,c2),product(c1,c2)),c1). [para(158(b,1),11650(b,1)),merge(b)].
% 6.63/6.90 19862 product(c1,product(c2,c1)) = c1 | r(product(c1,c2),c1). [para(308(b,1),19859(b,1)),merge(b)].
% 6.63/6.90 19865 product(c1,product(c2,c1)) = c1. [resolve(19862,b,17,a),rewrite([15(12)]),merge(b)].
% 6.63/6.90 19878 product(c1,f1(c1,c2)) = f1(c1,c2) | r(c1,f1(c1,c2)). [back_rewrite(8868),rewrite([19865(14),19865(15)])].
% 6.63/6.90 19887 -d(c1,c2) | product(c2,product(c1,c2)) != c2. [back_rewrite(16),rewrite([19865(8)]),xx(b)].
% 6.63/6.90 19894 product(c1,product(c2,product(c1,A))) = product(c1,A). [para(19865(a,1),15(a,1,1)),rewrite([15(7)]),flip(a)].
% 6.63/6.90 19954 d(product(A,c1),product(c2,product(c1,A))). [para(19865(a,1),10495(a,1,2)),rewrite([15(10),19894(11),15(9),27(8)])].
% 6.63/6.90 25247 product(c1,f1(c1,c2)) = f1(c1,c2). [resolve(19878,b,17,a),merge(b)].
% 6.63/6.90 25564 r(product(f1(c1,c2),c1),f1(c1,c2)). [para(25247(a,1),52(b,1,2)),rewrite([12(16)]),xx(b)].
% 6.63/6.90 25709 d(product(f1(c1,c2),c1),product(c2,f1(c1,c2))). [para(25247(a,1),19954(a,2,2))].
% 6.63/6.90 25712 product(c1,product(c2,f1(c1,c2))) = f1(c1,c2). [para(25247(a,1),19894(a,1,2,2)),rewrite([25247(12)])].
% 6.63/6.90 25896 d(product(f1(c1,c2),c1),c2) | -d(c1,c2). [resolve(25564,a,23,b)].
% 6.63/6.90 25908 d(product(f1(c1,c2),c1),c2) | product(c2,product(c1,c2)) = c2. [resolve(25896,b,14,a)].
% 6.63/6.90 25922 product(c2,product(c1,c2)) = c2 | f1(c1,c2) = product(c1,c2). [para(35(a,1),25712(a,1,2)),flip(b)].
% 6.63/6.90 26716 product(c2,product(c1,c2)) = c2 | product(c2,f1(product(f1(c1,c2),c1),c2)) = c2. [resolve(25908,a,22,a)].
% 6.63/6.90 26724 f1(c1,c2) = product(c1,c2) | d(c1,c2). [resolve(25922,a,1608,a),rewrite([19865(12)])].
% 6.63/6.90 26936 f1(c1,c2) = product(c1,c2) | product(c2,product(c1,c2)) != c2. [resolve(26724,b,19887,a)].
% 6.63/6.90 29991 f1(c1,c2) = product(c1,c2). [resolve(26936,b,25922,a),merge(b)].
% 6.63/6.90 30043 product(c2,product(c1,c2)) = c2. [back_rewrite(26716),rewrite([29991(11),15(13),19865(13),29991(11)]),merge(b)].
% 6.63/6.90 30122 d(c1,c2). [back_rewrite(25709),rewrite([29991(3),15(5),19865(5),29991(5),30043(6)])].
% 6.63/6.90 30256 $F. [back_rewrite(19887),rewrite([30043(8)]),xx(b),unit_del(a,30122)].
% 6.63/6.90
% 6.63/6.90 % SZS output end Refutation
% 6.63/6.90 ============================== end of proof ==========================
% 6.63/6.90
% 6.63/6.90 ============================== STATISTICS ============================
% 6.63/6.90
% 6.63/6.90 Given=2278. Generated=252646. Kept=30244. proofs=1.
% 6.63/6.90 Usable=675. Sos=3310. Demods=314. Limbo=213, Disabled=26064. Hints=0.
% 6.63/6.90 Megabytes=26.40.
% 6.63/6.90 User_CPU=5.77, System_CPU=0.16, Wall_clock=6.
% 6.63/6.90
% 6.63/6.90 ============================== end of statistics =====================
% 6.63/6.90
% 6.63/6.90 ============================== end of search =========================
% 6.63/6.90
% 6.63/6.90 THEOREM PROVED
% 6.63/6.90 % SZS status Theorem
% 6.63/6.90
% 6.63/6.90 Exiting with 1 proof.
% 6.63/6.90
% 6.63/6.90 Process 23321 exit (max_proofs) Tue Jun 14 13:11:31 2022
% 6.63/6.90 Prover9 interrupted
%------------------------------------------------------------------------------