0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n014.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   : 960
0.12/0.33	% DateTime   : Thu Jul  2 08:48:40 EDT 2020
0.12/0.33	% CPUTime    : 
2.46/2.75	============================== Prover9 ===============================
2.46/2.75	Prover9 (32) version 2009-11A, November 2009.
2.46/2.75	Process 18840 was started by sandbox on n014.cluster.edu,
2.46/2.75	Thu Jul  2 08:48:40 2020
2.46/2.75	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_18685_n014.cluster.edu".
2.46/2.75	============================== end of head ===========================
2.46/2.75	
2.46/2.75	============================== INPUT =================================
2.46/2.75	
2.46/2.75	% Reading from file /tmp/Prover9_18685_n014.cluster.edu
2.46/2.75	
2.46/2.75	set(prolog_style_variables).
2.46/2.75	set(auto2).
2.46/2.75	    % set(auto2) -> set(auto).
2.46/2.75	    % set(auto) -> set(auto_inference).
2.46/2.75	    % set(auto) -> set(auto_setup).
2.46/2.75	    % set(auto_setup) -> set(predicate_elim).
2.46/2.75	    % set(auto_setup) -> assign(eq_defs, unfold).
2.46/2.75	    % set(auto) -> set(auto_limits).
2.46/2.75	    % set(auto_limits) -> assign(max_weight, "100.000").
2.46/2.75	    % set(auto_limits) -> assign(sos_limit, 20000).
2.46/2.75	    % set(auto) -> set(auto_denials).
2.46/2.75	    % set(auto) -> set(auto_process).
2.46/2.75	    % set(auto2) -> assign(new_constants, 1).
2.46/2.75	    % set(auto2) -> assign(fold_denial_max, 3).
2.46/2.75	    % set(auto2) -> assign(max_weight, "200.000").
2.46/2.75	    % set(auto2) -> assign(max_hours, 1).
2.46/2.75	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
2.46/2.75	    % set(auto2) -> assign(max_seconds, 0).
2.46/2.75	    % set(auto2) -> assign(max_minutes, 5).
2.46/2.75	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
2.46/2.75	    % set(auto2) -> set(sort_initial_sos).
2.46/2.75	    % set(auto2) -> assign(sos_limit, -1).
2.46/2.75	    % set(auto2) -> assign(lrs_ticks, 3000).
2.46/2.75	    % set(auto2) -> assign(max_megs, 400).
2.46/2.75	    % set(auto2) -> assign(stats, some).
2.46/2.75	    % set(auto2) -> clear(echo_input).
2.46/2.75	    % set(auto2) -> set(quiet).
2.46/2.75	    % set(auto2) -> clear(print_initial_clauses).
2.46/2.75	    % set(auto2) -> clear(print_given).
2.46/2.75	assign(lrs_ticks,-1).
2.46/2.75	assign(sos_limit,10000).
2.46/2.75	assign(order,kbo).
2.46/2.75	set(lex_order_vars).
2.46/2.75	clear(print_given).
2.46/2.75	
2.46/2.75	% formulas(sos).  % not echoed (4 formulas)
2.46/2.75	
2.46/2.75	============================== end of input ==========================
2.46/2.75	
2.46/2.75	% From the command line: assign(max_seconds, 960).
2.46/2.75	
2.46/2.75	============================== PROCESS NON-CLAUSAL FORMULAS ==========
2.46/2.75	
2.46/2.75	% Formulas that are not ordinary clauses:
2.46/2.75	1 (all C all B all A product(A,product(B,C)) = product(product(A,B),C)) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
2.46/2.75	2 (all X0 all X1 (X1 = product(X1,product(X0,X1)) & product(X0,product(X1,X0)) = X0 <-> d(X0,X1))) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
2.46/2.75	3 (all A A = product(A,A)) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
2.46/2.75	4 -(all X2 all X3 all X4 all X5 (d(X4,X5) & d(X2,X3) -> d(product(X2,X4),product(X3,X5)))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
2.46/2.75	
2.46/2.75	============================== end of process non-clausal formulas ===
2.46/2.75	
2.46/2.75	============================== PROCESS INITIAL CLAUSES ===============
2.46/2.75	
2.46/2.75	============================== PREDICATE ELIMINATION =================
2.46/2.75	
2.46/2.75	============================== end predicate elimination =============
2.46/2.75	
2.46/2.75	Auto_denials:
2.46/2.75	  % copying label goals to answer in negative clause
2.46/2.75	
2.46/2.75	Term ordering decisions:
2.46/2.75	Function symbol KB weights:  c1=1. c2=1. c3=1. c4=1. product=1.
2.46/2.75	
2.46/2.75	============================== end of process initial clauses ========
2.46/2.75	
2.46/2.75	============================== CLAUSES FOR SEARCH ====================
2.46/2.75	
2.46/2.75	============================== end of clauses for search =============
2.46/2.75	
2.46/2.75	============================== SEARCH ================================
2.46/2.75	
2.46/2.75	% Starting search at 0.01 seconds.
2.46/2.75	
2.46/2.75	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 0.54 sec).
2.46/2.75	
2.46/2.75	Low Water (keep): wt=107.000, iters=3370
2.46/2.75	
2.46/2.75	Low Water (keep): wt=91.000, iters=3336
2.46/2.75	
2.46/2.75	Low Water (keep): wt=89.000, iters=3336
2.46/2.75	
2.46/2.75	Low Water (keep): wt=71.000, iters=3388
2.46/2.75	
2.46/2.75	Low Water (keep): wt=65.000, iters=3383
2.46/2.75	
2.46/2.75	Low Water (keep): wt=61.000, iters=3348
2.46/2.75	
2.46/2.75	Low Water (keep): wt=60.000, iters=3421
2.46/2.75	
2.46/2.75	Low Water (keep): wt=59.000, iters=3405
2.46/2.75	
2.46/2.75	Low Water (keep): wt=58.000, iters=3373
2.46/2.75	
2.46/2.75	Low Water (keep): wt=57.000, iters=3356
2.46/2.75	
2.46/2.75	Low Water (keep): wt=56.000, iters=3350
2.46/2.75	
2.46/2.75	Low Water (keep): wt=55.000, iters=3445
2.46/2.75	
2.46/2.75	Low Water (keep): wt=49.000, iters=3353
2.46/2.75	
2.46/2.75	Low Water (keep): wt=48.000, iters=3343
9.46/9.75	
9.46/9.75	Low Water (keep): wt=46.000, iters=3338
9.46/9.75	
9.46/9.75	Low Water (keep): wt=45.000, iters=3396
9.46/9.75	
9.46/9.75	Low Water (keep): wt=43.000, iters=3336
9.46/9.75	
9.46/9.75	Low Water (keep): wt=40.000, iters=3376
9.46/9.75	
9.46/9.75	Low Water (keep): wt=37.000, iters=3463
9.46/9.75	
9.46/9.75	Low Water (keep): wt=35.000, iters=3343
9.46/9.75	
9.46/9.75	Low Water (keep): wt=33.000, iters=3483
9.46/9.75	
9.46/9.75	Low Water (keep): wt=32.000, iters=3390
9.46/9.75	
9.46/9.75	Low Water (keep): wt=31.000, iters=3437
9.46/9.75	
9.46/9.75	Low Water (keep): wt=29.000, iters=3353
9.46/9.75	
9.46/9.75	Low Water (keep): wt=28.000, iters=3384
9.46/9.75	
9.46/9.75	Low Water (keep): wt=27.000, iters=3341
9.46/9.75	
9.46/9.75	Low Water (keep): wt=26.000, iters=3366
9.46/9.75	
9.46/9.75	Low Water (keep): wt=25.000, iters=3335
9.46/9.75	
9.46/9.75	Low Water (keep): wt=24.000, iters=3338
9.46/9.75	
9.46/9.75	Low Water (displace): id=4513, wt=121.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=4509, wt=115.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=4550, wt=111.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=4344, wt=109.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=6215, wt=107.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=6677, wt=105.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=6664, wt=99.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=12604, wt=23.000
9.46/9.75	
9.46/9.75	Low Water (keep): wt=23.000, iters=3353
9.46/9.75	
9.46/9.75	Low Water (displace): id=12680, wt=21.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=12718, wt=17.000
9.46/9.75	
9.46/9.75	Low Water (displace): id=13548, wt=15.000
9.46/9.75	
9.46/9.75	Low Water (keep): wt=22.000, iters=3338
9.46/9.75	
9.46/9.75	Low Water (keep): wt=21.000, iters=3336
9.46/9.75	
9.46/9.75	============================== PROOF =================================
9.46/9.75	% SZS status Theorem
9.46/9.75	% SZS output start Refutation
9.46/9.75	
9.46/9.75	% Proof 1 at 8.57 (+ 0.23) seconds: goals.
9.46/9.75	% Length of proof is 40.
9.46/9.75	% Level of proof is 10.
9.46/9.75	% Maximum clause weight is 59.000.
9.46/9.75	% Given clauses 4495.
9.46/9.75	
9.46/9.75	1 (all C all B all A product(A,product(B,C)) = product(product(A,B),C)) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
9.46/9.75	2 (all X0 all X1 (X1 = product(X1,product(X0,X1)) & product(X0,product(X1,X0)) = X0 <-> d(X0,X1))) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
9.46/9.75	3 (all A A = product(A,A)) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
9.46/9.75	4 -(all X2 all X3 all X4 all X5 (d(X4,X5) & d(X2,X3) -> d(product(X2,X4),product(X3,X5)))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
9.46/9.75	5 d(c3,c4) # label(goals) # label(negated_conjecture).  [clausify(4)].
9.46/9.75	6 d(c1,c2) # label(goals) # label(negated_conjecture).  [clausify(4)].
9.46/9.75	7 product(A,A) = A # label(sos02) # label(axiom).  [clausify(3)].
9.46/9.75	8 product(product(A,B),C) = product(A,product(B,C)) # label(sos01) # label(axiom).  [clausify(1)].
9.46/9.75	9 -d(product(c1,c3),product(c2,c4)) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(4)].
9.46/9.75	10 product(A,product(B,A)) = A | -d(B,A) # label(sos03) # label(axiom).  [clausify(2)].
9.46/9.75	11 product(A,product(B,A)) = A | -d(A,B) # label(sos03) # label(axiom).  [clausify(2)].
9.46/9.75	12 product(A,product(B,A)) != A | product(B,product(A,B)) != B | d(B,A) # label(sos03) # label(axiom).  [clausify(2)].
9.46/9.75	13 product(A,product(B,product(A,B))) = product(A,B).  [para(8(a,1),7(a,1))].
9.46/9.75	15 product(c2,product(c1,c2)) = c2.  [hyper(10,b,6,a)].
9.46/9.75	16 product(c4,product(c3,c4)) = c4.  [hyper(10,b,5,a)].
9.46/9.75	17 product(c1,product(c2,c1)) = c1.  [hyper(11,b,6,a)].
9.46/9.75	18 product(c3,product(c4,c3)) = c3.  [hyper(11,b,5,a)].
9.46/9.75	20 product(A,product(B,product(C,A))) != A | product(B,product(C,product(A,product(B,C)))) != product(B,C) | d(product(B,C),A).  [para(8(a,1),12(a,1,2)),rewrite([8(8)])].
9.46/9.75	21 product(A,product(B,product(C,product(A,B)))) != product(A,B) | product(C,product(A,product(B,C))) != C | d(C,product(A,B)).  [para(8(a,1),12(a,1)),rewrite([8(8)])].
9.46/9.75	22 product(A,product(B,product(A,product(B,C)))) = product(A,product(B,C)).  [para(13(a,1),8(a,1,1)),rewrite([8(2),8(5),8(4)]),flip(a)].
9.46/9.75	23 product(A,product(B,product(C,product(A,product(B,C))))) = product(A,product(B,C)).  [para(13(a,1),8(a,1)),rewrite([8(2),8(4)]),flip(a)].
9.46/9.75	26 product(c2,product(c1,product(c2,A))) = product(c2,A).  [para(15(a,1),8(a,1,1)),rewrite([8(7)]),flip(a)].
9.46/9.75	36 product(c1,product(c2,product(c1,A))) = product(c1,A).  [para(17(a,1),8(a,1,1)),rewrite([8(7)]),flip(a)].
9.46/9.75	43 product(A,product(B,product(C,product(D,A)))) != A | product(B,product(C,product(D,product(A,product(B,product(C,D)))))) != product(B,product(C,D)) | d(product(B,product(C,D)),A).  [para(8(a,1),20(a,1,2,2)),rewrite([8(10)])].
9.46/9.75	67 product(A,product(B,product(C,product(A,product(B,product(C,D)))))) = product(A,product(B,product(C,D))).  [para(22(a,1),8(a,1)),rewrite([8(3),8(6)]),flip(a)].
9.46/9.75	86 product(A,product(B,product(C,product(D,product(A,product(B,product(C,D))))))) = product(A,product(B,product(C,D))).  [para(23(a,1),8(a,1)),rewrite([8(3),8(6)]),flip(a)].
9.46/9.75	91 product(A,product(B,product(C,product(D,product(A,B))))) != product(A,B) | product(C,product(D,product(B,product(C,product(D,product(A,product(B,product(C,D)))))))) != product(C,product(D,product(B,product(C,D)))) | d(product(C,product(D,product(B,product(C,D)))),product(A,B)).  [para(23(a,1),21(b,1,2,2)),rewrite([8(6),8(5),8(4),8(3),67(7),8(15),8(14),8(13),8(12)])].
9.46/9.75	93 product(c2,product(A,product(c1,product(c2,A)))) = product(c2,A).  [para(23(a,1),26(a,1,2)),rewrite([26(6)]),flip(a)].
9.46/9.75	193 product(A,product(B,product(A,product(C,product(D,product(E,product(B,product(A,C)))))))) != product(A,product(B,product(A,C))) | product(D,product(E,product(B,product(A,product(C,product(D,product(E,B))))))) != product(D,product(E,B)) | d(product(D,product(E,B)),product(A,product(B,product(A,C)))).  [para(22(a,1),43(a,1,2,2,2)),rewrite([8(8),8(7),8(6),8(18),8(17),8(16),22(19)])].
9.46/9.75	236 product(c2,product(A,product(c1,product(c2,product(A,B))))) = product(c2,product(A,B)).  [para(93(a,1),8(a,1,1)),rewrite([8(3),8(10),8(9),8(8)]),flip(a)].
9.46/9.75	237 product(c2,product(A,product(B,product(c1,product(c2,product(A,B)))))) = product(c2,product(A,B)).  [para(8(a,1),93(a,1,2))].
9.46/9.75	544 product(A,product(c4,product(c3,product(A,c4)))) = product(A,c4).  [para(16(a,1),67(a,1,2,2,2,2)),rewrite([16(12)])].
9.46/9.75	546 product(A,product(c3,product(c4,product(A,c3)))) = product(A,c3).  [para(18(a,1),67(a,1,2,2,2,2)),rewrite([18(12)])].
9.46/9.75	554 product(A,product(c1,product(c2,product(A,product(c1,B))))) = product(A,product(c1,B)).  [para(36(a,1),67(a,1,2,2,2,2)),rewrite([36(14)])].
9.46/9.75	1407 product(c2,product(A,product(B,product(C,product(c2,A))))) != product(c2,A) | d(product(B,product(C,product(A,product(c1,product(c2,product(A,product(B,C))))))),product(c2,A)).  [para(93(a,1),91(a,1,2,2,2,2)),rewrite([8(11),8(10),8(9),236(12),93(14),8(23),8(22),8(21),236(24),8(22),8(21),8(20),86(20),8(26),8(25),8(24),8(36),8(35),8(34),93(45)]),xx(b)].
9.46/9.75	3298 d(product(c2,product(A,B)),product(c1,product(B,product(c1,product(c2,product(A,B)))))).  [para(237(a,1),193(a,1,2,2,2,2)),rewrite([7(9),7(26),237(26)]),xx(a),xx(b)].
9.46/9.75	18285 d(product(c2,c4),product(c1,product(c3,product(c2,c4)))).  [para(544(a,1),3298(a,1)),rewrite([544(19),8(15),8(14),93(14)])].
9.46/9.75	18294 product(c2,product(c4,product(c1,product(c3,product(c2,c4))))) = product(c2,c4).  [hyper(11,b,18285,a),rewrite([8(14),8(13),7(12),8(11)])].
9.46/9.75	18318 d(product(c1,c3),product(c2,c4)).  [hyper(1407,a,18294,a),rewrite([554(13),546(9)])].
9.46/9.75	18319 $F # answer(goals).  [resolve(18318,a,9,a)].
9.46/9.75	
9.46/9.75	% SZS output end Refutation
9.46/9.75	============================== end of proof ==========================
9.46/9.75	
9.46/9.75	============================== STATISTICS ============================
9.46/9.75	
9.46/9.75	Given=4495. Generated=380136. Kept=18314. proofs=1.
9.46/9.75	Usable=4346. Sos=9996. Demods=237. Limbo=2, Disabled=3977. Hints=0.
9.46/9.75	Megabytes=18.37.
9.46/9.75	User_CPU=8.57, System_CPU=0.23, Wall_clock=9.
9.46/9.75	
9.46/9.75	============================== end of statistics =====================
9.46/9.75	
9.46/9.75	============================== end of search =========================
9.46/9.75	
9.46/9.75	THEOREM PROVED
9.46/9.75	% SZS status Theorem
9.46/9.75	
9.46/9.75	Exiting with 1 proof.
9.46/9.75	
9.46/9.75	Process 18840 exit (max_proofs) Thu Jul  2 08:48:49 2020
9.46/9.75	Prover9 interrupted
9.46/9.75	EOF