TSTP Solution File: NUN088+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUN088+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 : 300s
% DateTime : Wed Jul 27 13:10:34 EDT 2022
% Result : Theorem 1.78s 1.95s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 4
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 7 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 3 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(20,axiom,
( ~ id(A,B)
| ~ r1(A)
| ~ r2(C,B) ),
file('NUN088+1.p',unknown),
[] ).
cnf(62,axiom,
id(dollar_c2,dollar_c4),
file('NUN088+1.p',unknown),
[] ).
cnf(63,axiom,
r1(dollar_c2),
file('NUN088+1.p',unknown),
[] ).
cnf(65,axiom,
r2(dollar_c3,dollar_c4),
file('NUN088+1.p',unknown),
[] ).
cnf(84,plain,
$false,
inference(hyper,[status(thm)],[65,20,62,63]),
[iquote('hyper,65,20,62,63')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN088+1 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 02:32:05 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.78/1.95 ----- Otter 3.3f, August 2004 -----
% 1.78/1.95 The process was started by sandbox2 on n005.cluster.edu,
% 1.78/1.95 Wed Jul 27 02:32:05 2022
% 1.78/1.95 The command was "./otter". The process ID is 9483.
% 1.78/1.95
% 1.78/1.95 set(prolog_style_variables).
% 1.78/1.95 set(auto).
% 1.78/1.95 dependent: set(auto1).
% 1.78/1.95 dependent: set(process_input).
% 1.78/1.95 dependent: clear(print_kept).
% 1.78/1.95 dependent: clear(print_new_demod).
% 1.78/1.95 dependent: clear(print_back_demod).
% 1.78/1.95 dependent: clear(print_back_sub).
% 1.78/1.95 dependent: set(control_memory).
% 1.78/1.95 dependent: assign(max_mem, 12000).
% 1.78/1.95 dependent: assign(pick_given_ratio, 4).
% 1.78/1.95 dependent: assign(stats_level, 1).
% 1.78/1.95 dependent: assign(max_seconds, 10800).
% 1.78/1.95 clear(print_given).
% 1.78/1.95
% 1.78/1.95 formula_list(usable).
% 1.78/1.95 exists Y24 all X19 (id(X19,Y24)&r1(X19)| -r1(X19)& -id(X19,Y24)).
% 1.78/1.95 all X11 exists Y21 all X12 (id(X12,Y21)&r2(X11,X12)| -r2(X11,X12)& -id(X12,Y21)).
% 1.78/1.95 all X13 X14 exists Y22 all X15 (id(X15,Y22)&r3(X13,X14,X15)| -r3(X13,X14,X15)& -id(X15,Y22)).
% 1.78/1.95 all X16 X17 exists Y23 all X18 (id(X18,Y23)&r4(X16,X17,X18)| -r4(X16,X17,X18)& -id(X18,Y23)).
% 1.78/1.95 all X20 id(X20,X20).
% 1.78/1.95 all X21 X22 (-id(X21,X22)|id(X22,X21)).
% 1.78/1.95 all X23 X24 X25 (-id(X23,X24)|id(X23,X25)| -id(X24,X25)).
% 1.78/1.95 all X26 X27 (-id(X26,X27)| -r1(X26)& -r1(X27)|r1(X26)&r1(X27)).
% 1.78/1.95 all X28 X29 X30 X31 (-id(X28,X30)| -id(X29,X31)| -r2(X28,X29)& -r2(X30,X31)|r2(X28,X29)&r2(X30,X31)).
% 1.78/1.95 all X32 X33 X34 X35 X36 X37 (-id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X32,X33,X34)& -r3(X35,X36,X37)|r3(X32,X33,X34)&r3(X35,X36,X37)).
% 1.78/1.95 all X38 X39 X40 X41 X42 X43 (-id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X38,X39,X40)& -r4(X41,X42,X43)|r4(X38,X39,X40)&r4(X41,X42,X43)).
% 1.78/1.95 all X1 X8 exists Y4 ((exists Y5 (id(Y5,Y4)& (exists Y15 (r2(X8,Y15)&r3(X1,Y15,Y5)))))& (exists Y7 (r2(Y7,Y4)&r3(X1,X8,Y7)))).
% 1.78/1.95 all X2 X9 exists Y2 ((exists Y3 (id(Y3,Y2)& (exists Y14 (r2(X9,Y14)&r4(X2,Y14,Y3)))))& (exists Y6 (r3(Y6,X2,Y2)&r4(X2,X9,Y6)))).
% 1.78/1.95 all X3 X10 ((all Y12 ((all Y13 (-id(Y13,Y12)| -r2(X3,Y13)))| -r2(X10,Y12)))|id(X3,X10)).
% 1.78/1.95 all X4 exists Y9 (id(Y9,X4)& (exists Y16 (r1(Y16)&r3(X4,Y16,Y9)))).
% 1.78/1.95 all X5 exists Y8 ((exists Y17 (r1(Y17)&r4(X5,Y17,Y8)))& (exists Y18 (id(Y8,Y18)&r1(Y18)))).
% 1.78/1.95 all X6 ((exists Y19 (id(X6,Y19)&r1(Y19)))| (exists Y1 Y11 (id(X6,Y11)&r2(Y1,Y11)))).
% 1.78/1.95 all X7 Y10 ((all Y20 (-id(Y20,Y10)| -r1(Y20)))| -r2(X7,Y10)).
% 1.78/1.95 -(all Y1 ((all Y2 (-id(Y2,Y1)| -r1(Y2)))| (all Y3 (-r1(Y3)| -r2(Y3,Y1))))).
% 1.78/1.95 end_of_list.
% 1.78/1.95
% 1.78/1.95 -------> usable clausifies to:
% 1.78/1.95
% 1.78/1.95 list(usable).
% 1.78/1.95 0 [] id(X19,$c1)| -r1(X19).
% 1.78/1.95 0 [] r1(X19)| -id(X19,$c1).
% 1.78/1.95 0 [] id(X12,$f1(X11))| -r2(X11,X12).
% 1.78/1.95 0 [] r2(X11,X12)| -id(X12,$f1(X11)).
% 1.78/1.95 0 [] id(X15,$f2(X13,X14))| -r3(X13,X14,X15).
% 1.78/1.95 0 [] r3(X13,X14,X15)| -id(X15,$f2(X13,X14)).
% 1.78/1.95 0 [] id(X18,$f3(X16,X17))| -r4(X16,X17,X18).
% 1.78/1.95 0 [] r4(X16,X17,X18)| -id(X18,$f3(X16,X17)).
% 1.78/1.95 0 [] id(X20,X20).
% 1.78/1.95 0 [] -id(X21,X22)|id(X22,X21).
% 1.78/1.95 0 [] -id(X23,X24)|id(X23,X25)| -id(X24,X25).
% 1.78/1.95 0 [] -id(X26,X27)| -r1(X26)|r1(X27).
% 1.78/1.95 0 [] -id(X26,X27)| -r1(X27)|r1(X26).
% 1.78/1.95 0 [] -id(X28,X30)| -id(X29,X31)| -r2(X28,X29)|r2(X30,X31).
% 1.78/1.95 0 [] -id(X28,X30)| -id(X29,X31)| -r2(X30,X31)|r2(X28,X29).
% 1.78/1.95 0 [] -id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X32,X33,X34)|r3(X35,X36,X37).
% 1.78/1.95 0 [] -id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X35,X36,X37)|r3(X32,X33,X34).
% 1.78/1.95 0 [] -id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X38,X39,X40)|r4(X41,X42,X43).
% 1.78/1.95 0 [] -id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X41,X42,X43)|r4(X38,X39,X40).
% 1.78/1.95 0 [] id($f5(X1,X8),$f7(X1,X8)).
% 1.78/1.95 0 [] r2(X8,$f4(X1,X8)).
% 1.78/1.95 0 [] r3(X1,$f4(X1,X8),$f5(X1,X8)).
% 1.78/1.95 0 [] r2($f6(X1,X8),$f7(X1,X8)).
% 1.78/1.95 0 [] r3(X1,X8,$f6(X1,X8)).
% 1.78/1.95 0 [] id($f9(X2,X9),$f11(X2,X9)).
% 1.78/1.95 0 [] r2(X9,$f8(X2,X9)).
% 1.78/1.95 0 [] r4(X2,$f8(X2,X9),$f9(X2,X9)).
% 1.78/1.95 0 [] r3($f10(X2,X9),X2,$f11(X2,X9)).
% 1.78/1.95 0 [] r4(X2,X9,$f10(X2,X9)).
% 1.78/1.95 0 [] -id(Y13,Y12)| -r2(X3,Y13)| -r2(X10,Y12)|id(X3,X10).
% 1.78/1.95 0 [] id($f13(X4),X4).
% 1.78/1.95 0 [] r1($f12(X4)).
% 1.78/1.95 0 [] r3(X4,$f12(X4),$f13(X4)).
% 1.78/1.95 0 [] r1($f14(X5)).
% 1.78/1.95 0 [] r4(X5,$f14(X5),$f16(X5)).
% 1.78/1.95 0 [] id($f16(X5),$f15(X5)).
% 1.78/1.95 0 [] r1($f15(X5)).
% 1.78/1.95 0 [] id(X6,$f17(X6))|id(X6,$f18(X6)).
% 1.78/1.95 0 [] id(X6,$f17(X6))|r2($f19(X6),$f18(X6)).
% 1.78/1.95 0 [] r1($f17(X6))|id(X6,$f18(X6)).
% 1.78/1.95 0 [] r1($f17(X6))|r2($f19(X6),$f18(X6)).
% 1.78/1.95 0 [] -id(Y20,Y10)| -r1(Y20)| -r2(X7,Y10).
% 1.78/1.95 0 [] id($c2,$c4).
% 1.78/1.95 0 [] r1($c2).
% 1.78/1.95 0 [] r1($c3).
% 1.78/1.95 0 [] r2($c3,$c4).
% 1.78/1.95 end_of_list.
% 1.78/1.95
% 1.78/1.95 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.78/1.95
% 1.78/1.95 This is a non-Horn set without equality. The strategy will
% 1.78/1.95 be ordered hyper_res, unit deletion, and factoring, with
% 1.78/1.95 satellites in sos and with nuclei in usable.
% 1.78/1.95
% 1.78/1.95 dependent: set(hyper_res).
% 1.78/1.95 dependent: set(factor).
% 1.78/1.95 dependent: set(unit_deletion).
% 1.78/1.95
% 1.78/1.95 ------------> process usable:
% 1.78/1.95 ** KEPT (pick-wt=5): 1 [] id(A,$c1)| -r1(A).
% 1.78/1.95 ** KEPT (pick-wt=5): 2 [] r1(A)| -id(A,$c1).
% 1.78/1.95 ** KEPT (pick-wt=7): 3 [] id(A,$f1(B))| -r2(B,A).
% 1.78/1.95 ** KEPT (pick-wt=7): 4 [] r2(A,B)| -id(B,$f1(A)).
% 1.78/1.95 ** KEPT (pick-wt=9): 5 [] id(A,$f2(B,C))| -r3(B,C,A).
% 1.78/1.95 ** KEPT (pick-wt=9): 6 [] r3(A,B,C)| -id(C,$f2(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=9): 7 [] id(A,$f3(B,C))| -r4(B,C,A).
% 1.78/1.95 ** KEPT (pick-wt=9): 8 [] r4(A,B,C)| -id(C,$f3(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=6): 9 [] -id(A,B)|id(B,A).
% 1.78/1.95 ** KEPT (pick-wt=9): 10 [] -id(A,B)|id(A,C)| -id(B,C).
% 1.78/1.95 ** KEPT (pick-wt=7): 11 [] -id(A,B)| -r1(A)|r1(B).
% 1.78/1.95 ** KEPT (pick-wt=7): 12 [] -id(A,B)| -r1(B)|r1(A).
% 1.78/1.95 ** KEPT (pick-wt=12): 13 [] -id(A,B)| -id(C,D)| -r2(A,C)|r2(B,D).
% 1.78/1.95 ** KEPT (pick-wt=12): 14 [] -id(A,B)| -id(C,D)| -r2(B,D)|r2(A,C).
% 1.78/1.95 ** KEPT (pick-wt=17): 15 [] -id(A,B)| -id(C,D)| -id(E,F)| -r3(A,C,E)|r3(B,D,F).
% 1.78/1.95 ** KEPT (pick-wt=17): 16 [] -id(A,B)| -id(C,D)| -id(E,F)| -r3(B,D,F)|r3(A,C,E).
% 1.78/1.95 ** KEPT (pick-wt=17): 17 [] -id(A,B)| -id(C,D)| -id(E,F)| -r4(A,C,E)|r4(B,D,F).
% 1.78/1.95 ** KEPT (pick-wt=17): 18 [] -id(A,B)| -id(C,D)| -id(E,F)| -r4(B,D,F)|r4(A,C,E).
% 1.78/1.95 ** KEPT (pick-wt=12): 19 [] -id(A,B)| -r2(C,A)| -r2(D,B)|id(C,D).
% 1.78/1.95 ** KEPT (pick-wt=8): 20 [] -id(A,B)| -r1(A)| -r2(C,B).
% 1.78/1.95
% 1.78/1.95 ------------> process sos:
% 1.78/1.95 ** KEPT (pick-wt=3): 40 [] id(A,A).
% 1.78/1.95 ** KEPT (pick-wt=7): 41 [] id($f5(A,B),$f7(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=5): 42 [] r2(A,$f4(B,A)).
% 1.78/1.95 ** KEPT (pick-wt=8): 43 [] r3(A,$f4(A,B),$f5(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=7): 44 [] r2($f6(A,B),$f7(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=6): 45 [] r3(A,B,$f6(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=7): 46 [] id($f9(A,B),$f11(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=5): 47 [] r2(A,$f8(B,A)).
% 1.78/1.95 ** KEPT (pick-wt=8): 48 [] r4(A,$f8(A,B),$f9(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=8): 49 [] r3($f10(A,B),A,$f11(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=6): 50 [] r4(A,B,$f10(A,B)).
% 1.78/1.95 ** KEPT (pick-wt=4): 51 [] id($f13(A),A).
% 1.78/1.95 ** KEPT (pick-wt=3): 52 [] r1($f12(A)).
% 1.78/1.95 ** KEPT (pick-wt=6): 53 [] r3(A,$f12(A),$f13(A)).
% 1.78/1.95 ** KEPT (pick-wt=3): 54 [] r1($f14(A)).
% 1.78/1.95 ** KEPT (pick-wt=6): 55 [] r4(A,$f14(A),$f16(A)).
% 1.78/1.95 ** KEPT (pick-wt=5): 56 [] id($f16(A),$f15(A)).
% 1.78/1.95 ** KEPT (pick-wt=3): 57 [] r1($f15(A)).
% 1.78/1.95 ** KEPT (pick-wt=8): 58 [] id(A,$f17(A))|id(A,$f18(A)).
% 1.78/1.95 ** KEPT (pick-wt=9): 59 [] id(A,$f17(A))|r2($f19(A),$f18(A)).
% 1.78/1.95 ** KEPT (pick-wt=7): 60 [] r1($f17(A))|id(A,$f18(A)).
% 1.78/1.95 ** KEPT (pick-wt=8): 61 [] r1($f17(A))|r2($f19(A),$f18(A)).
% 1.78/1.95 ** KEPT (pick-wt=3): 62 [] id($c2,$c4).
% 1.78/1.95 ** KEPT (pick-wt=2): 63 [] r1($c2).
% 1.78/1.95 ** KEPT (pick-wt=2): 64 [] r1($c3).
% 1.78/1.95 ** KEPT (pick-wt=3): 65 [] r2($c3,$c4).
% 1.78/1.95 40 back subsumes 35.
% 1.78/1.95
% 1.78/1.95 ======= end of input processing =======
% 1.78/1.95
% 1.78/1.95 =========== start of search ===========
% 1.78/1.95
% 1.78/1.95 -------- PROOF --------
% 1.78/1.95
% 1.78/1.95 -----> EMPTY CLAUSE at 0.01 sec ----> 84 [hyper,65,20,62,63] $F.
% 1.78/1.95
% 1.78/1.95 Length of proof is 0. Level of proof is 0.
% 1.78/1.95
% 1.78/1.95 ---------------- PROOF ----------------
% 1.78/1.95 % SZS status Theorem
% 1.78/1.95 % SZS output start Refutation
% See solution above
% 1.78/1.96 ------------ end of proof -------------
% 1.78/1.96
% 1.78/1.96
% 1.78/1.96 Search stopped by max_proofs option.
% 1.78/1.96
% 1.78/1.96
% 1.78/1.96 Search stopped by max_proofs option.
% 1.78/1.96
% 1.78/1.96 ============ end of search ============
% 1.78/1.96
% 1.78/1.96 -------------- statistics -------------
% 1.78/1.96 clauses given 12
% 1.78/1.96 clauses generated 74
% 1.78/1.96 clauses kept 83
% 1.78/1.96 clauses forward subsumed 35
% 1.78/1.96 clauses back subsumed 1
% 1.78/1.96 Kbytes malloced 976
% 1.78/1.96
% 1.78/1.96 ----------- times (seconds) -----------
% 1.78/1.96 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.78/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.78/1.96 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.78/1.96
% 1.78/1.96 That finishes the proof of the theorem.
% 1.78/1.96
% 1.78/1.96 Process 9483 finished Wed Jul 27 02:32:07 2022
% 1.78/1.96 Otter interrupted
% 1.78/1.96 PROOF FOUND
%------------------------------------------------------------------------------