%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUN080+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:10:32 EDT 2022
% Result : Theorem 1.82s 2.01s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 12 ( 9 unt; 0 nHn; 4 RR)
% Number of literals : 19 ( 0 equ; 8 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 21 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( r2(A,B)
| ~ id(B,dollar_f1(A)) ),
file('NUN080+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ id(A,B)
| ~ r1(B)
| r1(A) ),
file('NUN080+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ id(A,B)
| ~ r3(C,D,A)
| ~ r2(E,D)
| ~ r1(F)
| ~ r2(F,E) ),
file('NUN080+1.p',unknown),
[] ).
cnf(42,axiom,
id(A,A),
file('NUN080+1.p',unknown),
[] ).
cnf(43,axiom,
id(dollar_f5(A,B),dollar_f7(A,B)),
file('NUN080+1.p',unknown),
[] ).
cnf(44,axiom,
r2(A,dollar_f4(B,A)),
file('NUN080+1.p',unknown),
[] ).
cnf(45,axiom,
r3(A,dollar_f4(A,B),dollar_f5(A,B)),
file('NUN080+1.p',unknown),
[] ).
cnf(53,axiom,
id(dollar_f13(A),A),
file('NUN080+1.p',unknown),
[] ).
cnf(56,axiom,
r1(dollar_f14(A)),
file('NUN080+1.p',unknown),
[] ).
cnf(66,plain,
r2(A,dollar_f1(A)),
inference(hyper,[status(thm)],[42,4]),
[iquote('hyper,42,4')] ).
cnf(74,plain,
r1(dollar_f13(dollar_f14(A))),
inference(hyper,[status(thm)],[53,12,56]),
[iquote('hyper,53,12,56')] ).
cnf(123,plain,
$false,
inference(hyper,[status(thm)],[45,21,43,44,74,66]),
[iquote('hyper,45,21,43,44,74,66')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN080+1 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 02:46:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.82/2.00 ----- Otter 3.3f, August 2004 -----
% 1.82/2.00 The process was started by sandbox on n029.cluster.edu,
% 1.82/2.00 Wed Jul 27 02:46:59 2022
% 1.82/2.00 The command was "./otter". The process ID is 5673.
% 1.82/2.00
% 1.82/2.00 set(prolog_style_variables).
% 1.82/2.00 set(auto).
% 1.82/2.00 dependent: set(auto1).
% 1.82/2.00 dependent: set(process_input).
% 1.82/2.00 dependent: clear(print_kept).
% 1.82/2.00 dependent: clear(print_new_demod).
% 1.82/2.00 dependent: clear(print_back_demod).
% 1.82/2.00 dependent: clear(print_back_sub).
% 1.82/2.00 dependent: set(control_memory).
% 1.82/2.00 dependent: assign(max_mem, 12000).
% 1.82/2.00 dependent: assign(pick_given_ratio, 4).
% 1.82/2.00 dependent: assign(stats_level, 1).
% 1.82/2.00 dependent: assign(max_seconds, 10800).
% 1.82/2.00 clear(print_given).
% 1.82/2.00
% 1.82/2.00 formula_list(usable).
% 1.82/2.00 exists Y24 all X19 (id(X19,Y24)&r1(X19)| -r1(X19)& -id(X19,Y24)).
% 1.82/2.00 all X11 exists Y21 all X12 (id(X12,Y21)&r2(X11,X12)| -r2(X11,X12)& -id(X12,Y21)).
% 1.82/2.00 all X13 X14 exists Y22 all X15 (id(X15,Y22)&r3(X13,X14,X15)| -r3(X13,X14,X15)& -id(X15,Y22)).
% 1.82/2.00 all X16 X17 exists Y23 all X18 (id(X18,Y23)&r4(X16,X17,X18)| -r4(X16,X17,X18)& -id(X18,Y23)).
% 1.82/2.00 all X20 id(X20,X20).
% 1.82/2.00 all X21 X22 (-id(X21,X22)|id(X22,X21)).
% 1.82/2.00 all X23 X24 X25 (-id(X23,X24)|id(X23,X25)| -id(X24,X25)).
% 1.82/2.00 all X26 X27 (-id(X26,X27)| -r1(X26)& -r1(X27)|r1(X26)&r1(X27)).
% 1.82/2.00 all X28 X29 X30 X31 (-id(X28,X30)| -id(X29,X31)| -r2(X28,X29)& -r2(X30,X31)|r2(X28,X29)&r2(X30,X31)).
% 1.82/2.00 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)).
% 1.82/2.00 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)).
% 1.82/2.00 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)))).
% 1.82/2.00 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)))).
% 1.82/2.00 all X3 X10 ((all Y12 ((all Y13 (-id(Y13,Y12)| -r2(X3,Y13)))| -r2(X10,Y12)))|id(X3,X10)).
% 1.82/2.00 all X4 exists Y9 (id(Y9,X4)& (exists Y16 (r1(Y16)&r3(X4,Y16,Y9)))).
% 1.82/2.00 all X5 exists Y8 ((exists Y17 (r1(Y17)&r4(X5,Y17,Y8)))& (exists Y18 (id(Y8,Y18)&r1(Y18)))).
% 1.82/2.00 all X6 ((exists Y19 (id(X6,Y19)&r1(Y19)))| (exists Y1 Y11 (id(X6,Y11)&r2(Y1,Y11)))).
% 1.82/2.00 all X7 Y10 ((all Y20 (-id(Y20,Y10)| -r1(Y20)))| -r2(X7,Y10)).
% 1.82/2.00 -(exists Y1 Y2 Y3 (id(Y3,Y2)& (exists Y4 (r3(Y1,Y4,Y3)& (exists Y5 (r2(Y5,Y4)& (exists Y6 (r1(Y6)&r2(Y6,Y5))))))))).
% 1.82/2.00 end_of_list.
% 1.82/2.00
% 1.82/2.00 -------> usable clausifies to:
% 1.82/2.00
% 1.82/2.00 list(usable).
% 1.82/2.00 0 [] id(X19,$c1)| -r1(X19).
% 1.82/2.00 0 [] r1(X19)| -id(X19,$c1).
% 1.82/2.00 0 [] id(X12,$f1(X11))| -r2(X11,X12).
% 1.82/2.00 0 [] r2(X11,X12)| -id(X12,$f1(X11)).
% 1.82/2.00 0 [] id(X15,$f2(X13,X14))| -r3(X13,X14,X15).
% 1.82/2.00 0 [] r3(X13,X14,X15)| -id(X15,$f2(X13,X14)).
% 1.82/2.00 0 [] id(X18,$f3(X16,X17))| -r4(X16,X17,X18).
% 1.82/2.00 0 [] r4(X16,X17,X18)| -id(X18,$f3(X16,X17)).
% 1.82/2.00 0 [] id(X20,X20).
% 1.82/2.00 0 [] -id(X21,X22)|id(X22,X21).
% 1.82/2.00 0 [] -id(X23,X24)|id(X23,X25)| -id(X24,X25).
% 1.82/2.00 0 [] -id(X26,X27)| -r1(X26)|r1(X27).
% 1.82/2.00 0 [] -id(X26,X27)| -r1(X27)|r1(X26).
% 1.82/2.00 0 [] -id(X28,X30)| -id(X29,X31)| -r2(X28,X29)|r2(X30,X31).
% 1.82/2.00 0 [] -id(X28,X30)| -id(X29,X31)| -r2(X30,X31)|r2(X28,X29).
% 1.82/2.00 0 [] -id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X32,X33,X34)|r3(X35,X36,X37).
% 1.82/2.00 0 [] -id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X35,X36,X37)|r3(X32,X33,X34).
% 1.82/2.00 0 [] -id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X38,X39,X40)|r4(X41,X42,X43).
% 1.82/2.00 0 [] -id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X41,X42,X43)|r4(X38,X39,X40).
% 1.82/2.00 0 [] id($f5(X1,X8),$f7(X1,X8)).
% 1.82/2.00 0 [] r2(X8,$f4(X1,X8)).
% 1.82/2.00 0 [] r3(X1,$f4(X1,X8),$f5(X1,X8)).
% 1.82/2.00 0 [] r2($f6(X1,X8),$f7(X1,X8)).
% 1.82/2.00 0 [] r3(X1,X8,$f6(X1,X8)).
% 1.82/2.00 0 [] id($f9(X2,X9),$f11(X2,X9)).
% 1.82/2.00 0 [] r2(X9,$f8(X2,X9)).
% 1.82/2.00 0 [] r4(X2,$f8(X2,X9),$f9(X2,X9)).
% 1.82/2.00 0 [] r3($f10(X2,X9),X2,$f11(X2,X9)).
% 1.82/2.00 0 [] r4(X2,X9,$f10(X2,X9)).
% 1.82/2.00 0 [] -id(Y13,Y12)| -r2(X3,Y13)| -r2(X10,Y12)|id(X3,X10).
% 1.82/2.00 0 [] id($f13(X4),X4).
% 1.82/2.00 0 [] r1($f12(X4)).
% 1.82/2.00 0 [] r3(X4,$f12(X4),$f13(X4)).
% 1.82/2.00 0 [] r1($f14(X5)).
% 1.82/2.00 0 [] r4(X5,$f14(X5),$f16(X5)).
% 1.82/2.00 0 [] id($f16(X5),$f15(X5)).
% 1.82/2.00 0 [] r1($f15(X5)).
% 1.82/2.00 0 [] id(X6,$f17(X6))|id(X6,$f18(X6)).
% 1.82/2.00 0 [] id(X6,$f17(X6))|r2($f19(X6),$f18(X6)).
% 1.82/2.00 0 [] r1($f17(X6))|id(X6,$f18(X6)).
% 1.82/2.00 0 [] r1($f17(X6))|r2($f19(X6),$f18(X6)).
% 1.82/2.00 0 [] -id(Y20,Y10)| -r1(Y20)| -r2(X7,Y10).
% 1.82/2.00 0 [] -id(Y3,Y2)| -r3(Y1,Y4,Y3)| -r2(Y5,Y4)| -r1(Y6)| -r2(Y6,Y5).
% 1.82/2.01 end_of_list.
% 1.82/2.01
% 1.82/2.01 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.82/2.01
% 1.82/2.01 This is a non-Horn set without equality. The strategy will
% 1.82/2.01 be ordered hyper_res, unit deletion, and factoring, with
% 1.82/2.01 satellites in sos and with nuclei in usable.
% 1.82/2.01
% 1.82/2.01 dependent: set(hyper_res).
% 1.82/2.01 dependent: set(factor).
% 1.82/2.01 dependent: set(unit_deletion).
% 1.82/2.01
% 1.82/2.01 ------------> process usable:
% 1.82/2.01 ** KEPT (pick-wt=5): 1 [] id(A,$c1)| -r1(A).
% 1.82/2.01 ** KEPT (pick-wt=5): 2 [] r1(A)| -id(A,$c1).
% 1.82/2.01 ** KEPT (pick-wt=7): 3 [] id(A,$f1(B))| -r2(B,A).
% 1.82/2.01 ** KEPT (pick-wt=7): 4 [] r2(A,B)| -id(B,$f1(A)).
% 1.82/2.01 ** KEPT (pick-wt=9): 5 [] id(A,$f2(B,C))| -r3(B,C,A).
% 1.82/2.01 ** KEPT (pick-wt=9): 6 [] r3(A,B,C)| -id(C,$f2(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=9): 7 [] id(A,$f3(B,C))| -r4(B,C,A).
% 1.82/2.01 ** KEPT (pick-wt=9): 8 [] r4(A,B,C)| -id(C,$f3(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=6): 9 [] -id(A,B)|id(B,A).
% 1.82/2.01 ** KEPT (pick-wt=9): 10 [] -id(A,B)|id(A,C)| -id(B,C).
% 1.82/2.01 ** KEPT (pick-wt=7): 11 [] -id(A,B)| -r1(A)|r1(B).
% 1.82/2.01 ** KEPT (pick-wt=7): 12 [] -id(A,B)| -r1(B)|r1(A).
% 1.82/2.01 ** KEPT (pick-wt=12): 13 [] -id(A,B)| -id(C,D)| -r2(A,C)|r2(B,D).
% 1.82/2.01 ** KEPT (pick-wt=12): 14 [] -id(A,B)| -id(C,D)| -r2(B,D)|r2(A,C).
% 1.82/2.01 ** KEPT (pick-wt=17): 15 [] -id(A,B)| -id(C,D)| -id(E,F)| -r3(A,C,E)|r3(B,D,F).
% 1.82/2.01 ** KEPT (pick-wt=17): 16 [] -id(A,B)| -id(C,D)| -id(E,F)| -r3(B,D,F)|r3(A,C,E).
% 1.82/2.01 ** KEPT (pick-wt=17): 17 [] -id(A,B)| -id(C,D)| -id(E,F)| -r4(A,C,E)|r4(B,D,F).
% 1.82/2.01 ** KEPT (pick-wt=17): 18 [] -id(A,B)| -id(C,D)| -id(E,F)| -r4(B,D,F)|r4(A,C,E).
% 1.82/2.01 ** KEPT (pick-wt=12): 19 [] -id(A,B)| -r2(C,A)| -r2(D,B)|id(C,D).
% 1.82/2.01 ** KEPT (pick-wt=8): 20 [] -id(A,B)| -r1(A)| -r2(C,B).
% 1.82/2.01 ** KEPT (pick-wt=15): 21 [] -id(A,B)| -r3(C,D,A)| -r2(E,D)| -r1(F)| -r2(F,E).
% 1.82/2.01
% 1.82/2.01 ------------> process sos:
% 1.82/2.01 ** KEPT (pick-wt=3): 42 [] id(A,A).
% 1.82/2.01 ** KEPT (pick-wt=7): 43 [] id($f5(A,B),$f7(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=5): 44 [] r2(A,$f4(B,A)).
% 1.82/2.01 ** KEPT (pick-wt=8): 45 [] r3(A,$f4(A,B),$f5(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=7): 46 [] r2($f6(A,B),$f7(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=6): 47 [] r3(A,B,$f6(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=7): 48 [] id($f9(A,B),$f11(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=5): 49 [] r2(A,$f8(B,A)).
% 1.82/2.01 ** KEPT (pick-wt=8): 50 [] r4(A,$f8(A,B),$f9(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=8): 51 [] r3($f10(A,B),A,$f11(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=6): 52 [] r4(A,B,$f10(A,B)).
% 1.82/2.01 ** KEPT (pick-wt=4): 53 [] id($f13(A),A).
% 1.82/2.01 ** KEPT (pick-wt=3): 54 [] r1($f12(A)).
% 1.82/2.01 ** KEPT (pick-wt=6): 55 [] r3(A,$f12(A),$f13(A)).
% 1.82/2.01 ** KEPT (pick-wt=3): 56 [] r1($f14(A)).
% 1.82/2.01 ** KEPT (pick-wt=6): 57 [] r4(A,$f14(A),$f16(A)).
% 1.82/2.01 ** KEPT (pick-wt=5): 58 [] id($f16(A),$f15(A)).
% 1.82/2.01 ** KEPT (pick-wt=3): 59 [] r1($f15(A)).
% 1.82/2.01 ** KEPT (pick-wt=8): 60 [] id(A,$f17(A))|id(A,$f18(A)).
% 1.82/2.01 ** KEPT (pick-wt=9): 61 [] id(A,$f17(A))|r2($f19(A),$f18(A)).
% 1.82/2.01 ** KEPT (pick-wt=7): 62 [] r1($f17(A))|id(A,$f18(A)).
% 1.82/2.01 ** KEPT (pick-wt=8): 63 [] r1($f17(A))|r2($f19(A),$f18(A)).
% 1.82/2.01 42 back subsumes 36.
% 1.82/2.01
% 1.82/2.01 ======= end of input processing =======
% 1.82/2.01
% 1.82/2.01 =========== start of search ===========
% 1.82/2.01
% 1.82/2.01 -------- PROOF --------
% 1.82/2.01
% 1.82/2.01 -----> EMPTY CLAUSE at 0.01 sec ----> 123 [hyper,45,21,43,44,74,66] $F.
% 1.82/2.01
% 1.82/2.01 Length of proof is 2. Level of proof is 1.
% 1.82/2.01
% 1.82/2.01 ---------------- PROOF ----------------
% 1.82/2.01 % SZS status Theorem
% 1.82/2.01 % SZS output start Refutation
% See solution above
% 1.82/2.01 ------------ end of proof -------------
% 1.82/2.01
% 1.82/2.01
% 1.82/2.01 Search stopped by max_proofs option.
% 1.82/2.01
% 1.82/2.01
% 1.82/2.01 Search stopped by max_proofs option.
% 1.82/2.01
% 1.82/2.01 ============ end of search ============
% 1.82/2.01
% 1.82/2.01 -------------- statistics -------------
% 1.82/2.01 clauses given 16
% 1.82/2.01 clauses generated 144
% 1.82/2.01 clauses kept 122
% 1.82/2.01 clauses forward subsumed 63
% 1.82/2.01 clauses back subsumed 1
% 1.82/2.01 Kbytes malloced 976
% 1.82/2.01
% 1.82/2.01 ----------- times (seconds) -----------
% 1.82/2.01 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.82/2.01 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.01 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.01
% 1.82/2.01 That finishes the proof of the theorem.
% 1.82/2.01
% 1.82/2.01 Process 5673 finished Wed Jul 27 02:47:01 2022
% 1.82/2.01 Otter interrupted
% 1.82/2.01 PROOF FOUND
%------------------------------------------------------------------------------