TSTP Solution File: NUN059+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 13:10:26 EDT 2022
% Result : Theorem 1.73s 1.98s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 17 unt; 0 nHn; 5 RR)
% Number of literals : 31 ( 10 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 32 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r1(A)
| A = dollar_c1 ),
file('NUN059+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ r4(A,A,B)
| C != B
| ~ r4(D,D,E)
| ~ r4(F,F,G)
| ~ r3(G,E,C) ),
file('NUN059+2.p',unknown),
[] ).
cnf(13,plain,
( ~ r4(A,A,B)
| C != B
| ~ r4(D,D,E)
| ~ r3(E,B,C) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.1.3')] ).
cnf(16,plain,
( ~ r4(A,A,B)
| C != B
| ~ r3(B,B,C) ),
inference(factor,[status(thm)],[13]),
[iquote('factor,13.1.3')] ).
cnf(17,axiom,
A = A,
file('NUN059+2.p',unknown),
[] ).
cnf(32,axiom,
r1(dollar_f12(A)),
file('NUN059+2.p',unknown),
[] ).
cnf(33,axiom,
r3(A,dollar_f12(A),dollar_f13(A)),
file('NUN059+2.p',unknown),
[] ).
cnf(35,axiom,
dollar_f13(A) = A,
file('NUN059+2.p',unknown),
[] ).
cnf(36,axiom,
r1(dollar_f14(A)),
file('NUN059+2.p',unknown),
[] ).
cnf(37,axiom,
r4(A,dollar_f14(A),dollar_f16(A)),
file('NUN059+2.p',unknown),
[] ).
cnf(38,axiom,
r1(dollar_f15(A)),
file('NUN059+2.p',unknown),
[] ).
cnf(40,axiom,
dollar_f16(A) = dollar_f15(A),
file('NUN059+2.p',unknown),
[] ).
cnf(49,plain,
r3(A,dollar_f12(A),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[33]),35]),
[iquote('back_demod,33,demod,35')] ).
cnf(50,plain,
r4(A,dollar_f14(A),dollar_f15(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),40]),
[iquote('back_demod,37,demod,40')] ).
cnf(60,plain,
dollar_f12(A) = dollar_c1,
inference(hyper,[status(thm)],[32,1]),
[iquote('hyper,32,1')] ).
cnf(61,plain,
r3(A,dollar_c1,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),60]),
[iquote('back_demod,49,demod,60')] ).
cnf(63,plain,
dollar_f14(A) = dollar_c1,
inference(hyper,[status(thm)],[36,1]),
[iquote('hyper,36,1')] ).
cnf(64,plain,
r4(A,dollar_c1,dollar_f15(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[50]),63]),
[iquote('back_demod,50,demod,63')] ).
cnf(66,plain,
dollar_f15(A) = dollar_c1,
inference(hyper,[status(thm)],[38,1]),
[iquote('hyper,38,1')] ).
cnf(67,plain,
r4(A,dollar_c1,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[64]),66]),
[iquote('back_demod,64,demod,66')] ).
cnf(98,plain,
$false,
inference(hyper,[status(thm)],[67,16,17,61]),
[iquote('hyper,67,16,17,61')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.11/0.12 % Command : otter-tptp-script %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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 02:23:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.97 ----- Otter 3.3f, August 2004 -----
% 1.73/1.97 The process was started by sandbox2 on n007.cluster.edu,
% 1.73/1.97 Wed Jul 27 02:23:31 2022
% 1.73/1.97 The command was "./otter". The process ID is 19547.
% 1.73/1.97
% 1.73/1.97 set(prolog_style_variables).
% 1.73/1.97 set(auto).
% 1.73/1.97 dependent: set(auto1).
% 1.73/1.97 dependent: set(process_input).
% 1.73/1.97 dependent: clear(print_kept).
% 1.73/1.97 dependent: clear(print_new_demod).
% 1.73/1.97 dependent: clear(print_back_demod).
% 1.73/1.97 dependent: clear(print_back_sub).
% 1.73/1.97 dependent: set(control_memory).
% 1.73/1.97 dependent: assign(max_mem, 12000).
% 1.73/1.97 dependent: assign(pick_given_ratio, 4).
% 1.73/1.97 dependent: assign(stats_level, 1).
% 1.73/1.97 dependent: assign(max_seconds, 10800).
% 1.73/1.97 clear(print_given).
% 1.73/1.97
% 1.73/1.97 formula_list(usable).
% 1.73/1.97 all A (A=A).
% 1.73/1.97 exists Y24 all X19 (-r1(X19)&X19!=Y24|r1(X19)&X19=Y24).
% 1.73/1.97 all X11 exists Y21 all X12 (-r2(X11,X12)&X12!=Y21|r2(X11,X12)&X12=Y21).
% 1.73/1.97 all X13 X14 exists Y22 all X15 (-r3(X13,X14,X15)&X15!=Y22|r3(X13,X14,X15)&X15=Y22).
% 1.73/1.97 all X16 X17 exists Y23 all X18 (-r4(X16,X17,X18)&X18!=Y23|r4(X16,X17,X18)&X18=Y23).
% 1.73/1.97 all X1 X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15)&r3(X1,Y15,Y5)))&Y5=Y4))& (exists Y7 (r2(Y7,Y4)&r3(X1,X8,Y7)))).
% 1.73/1.97 all X2 X9 exists Y2 ((exists Y3 ((exists Y14 (r2(X9,Y14)&r4(X2,Y14,Y3)))&Y3=Y2))& (exists Y6 (r3(Y6,X2,Y2)&r4(X2,X9,Y6)))).
% 1.73/1.97 all X3 X10 ((all Y12 ((all Y13 (-r2(X3,Y13)|Y13!=Y12))| -r2(X10,Y12)))|X3=X10).
% 1.73/1.97 all X4 exists Y9 ((exists Y16 (r1(Y16)&r3(X4,Y16,Y9)))&Y9=X4).
% 1.73/1.97 all X5 exists Y8 ((exists Y17 (r1(Y17)&r4(X5,Y17,Y8)))& (exists Y18 (r1(Y18)&Y8=Y18))).
% 1.73/1.97 all X6 ((exists Y19 (r1(Y19)&X6=Y19))| (exists Y1 Y11 (r2(Y1,Y11)&X6=Y11))).
% 1.73/1.97 all X7 Y10 ((all Y20 (-r1(Y20)|Y20!=Y10))| -r2(X7,Y10)).
% 1.73/1.97 -(exists Y1 Y3 Y2 Y4 ((exists Y5 (r4(Y2,Y2,Y5)&Y4=Y5))& (exists Y6 (r4(Y3,Y3,Y6)& (exists Y7 (r4(Y1,Y1,Y7)&r3(Y7,Y6,Y4))))))).
% 1.73/1.97 end_of_list.
% 1.73/1.97
% 1.73/1.97 -------> usable clausifies to:
% 1.73/1.97
% 1.73/1.97 list(usable).
% 1.73/1.97 0 [] A=A.
% 1.73/1.97 0 [] -r1(X19)|X19=$c1.
% 1.73/1.97 0 [] X19!=$c1|r1(X19).
% 1.73/1.97 0 [] -r2(X11,X12)|X12=$f1(X11).
% 1.73/1.97 0 [] X12!=$f1(X11)|r2(X11,X12).
% 1.73/1.97 0 [] -r3(X13,X14,X15)|X15=$f2(X13,X14).
% 1.73/1.97 0 [] X15!=$f2(X13,X14)|r3(X13,X14,X15).
% 1.73/1.97 0 [] -r4(X16,X17,X18)|X18=$f3(X16,X17).
% 1.73/1.97 0 [] X18!=$f3(X16,X17)|r4(X16,X17,X18).
% 1.73/1.97 0 [] r2(X8,$f4(X1,X8)).
% 1.73/1.97 0 [] r3(X1,$f4(X1,X8),$f5(X1,X8)).
% 1.73/1.97 0 [] $f5(X1,X8)=$f7(X1,X8).
% 1.73/1.97 0 [] r2($f6(X1,X8),$f7(X1,X8)).
% 1.73/1.97 0 [] r3(X1,X8,$f6(X1,X8)).
% 1.73/1.97 0 [] r2(X9,$f8(X2,X9)).
% 1.73/1.97 0 [] r4(X2,$f8(X2,X9),$f9(X2,X9)).
% 1.73/1.97 0 [] $f9(X2,X9)=$f11(X2,X9).
% 1.73/1.97 0 [] r3($f10(X2,X9),X2,$f11(X2,X9)).
% 1.73/1.97 0 [] r4(X2,X9,$f10(X2,X9)).
% 1.73/1.97 0 [] -r2(X3,Y13)|Y13!=Y12| -r2(X10,Y12)|X3=X10.
% 1.73/1.97 0 [] r1($f12(X4)).
% 1.73/1.97 0 [] r3(X4,$f12(X4),$f13(X4)).
% 1.73/1.97 0 [] $f13(X4)=X4.
% 1.73/1.97 0 [] r1($f14(X5)).
% 1.73/1.97 0 [] r4(X5,$f14(X5),$f16(X5)).
% 1.73/1.97 0 [] r1($f15(X5)).
% 1.73/1.97 0 [] $f16(X5)=$f15(X5).
% 1.73/1.97 0 [] r1($f17(X6))|r2($f19(X6),$f18(X6)).
% 1.73/1.97 0 [] r1($f17(X6))|X6=$f18(X6).
% 1.73/1.97 0 [] X6=$f17(X6)|r2($f19(X6),$f18(X6)).
% 1.73/1.97 0 [] X6=$f17(X6)|X6=$f18(X6).
% 1.73/1.97 0 [] -r1(Y20)|Y20!=Y10| -r2(X7,Y10).
% 1.73/1.97 0 [] -r4(Y2,Y2,Y5)|Y4!=Y5| -r4(Y3,Y3,Y6)| -r4(Y1,Y1,Y7)| -r3(Y7,Y6,Y4).
% 1.73/1.97 end_of_list.
% 1.73/1.97
% 1.73/1.97 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.73/1.97
% 1.73/1.97 This ia a non-Horn set with equality. The strategy will be
% 1.73/1.97 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.97 deletion, with positive clauses in sos and nonpositive
% 1.73/1.97 clauses in usable.
% 1.73/1.97
% 1.73/1.97 dependent: set(knuth_bendix).
% 1.73/1.97 dependent: set(anl_eq).
% 1.73/1.97 dependent: set(para_from).
% 1.73/1.97 dependent: set(para_into).
% 1.73/1.97 dependent: clear(para_from_right).
% 1.73/1.97 dependent: clear(para_into_right).
% 1.73/1.97 dependent: set(para_from_vars).
% 1.73/1.97 dependent: set(eq_units_both_ways).
% 1.73/1.97 dependent: set(dynamic_demod_all).
% 1.73/1.97 dependent: set(dynamic_demod).
% 1.73/1.97 dependent: set(order_eq).
% 1.73/1.97 dependent: set(back_demod).
% 1.73/1.97 dependent: set(lrpo).
% 1.73/1.97 dependent: set(hyper_res).
% 1.73/1.97 dependent: set(unit_deletion).
% 1.73/1.97 dependent: set(factor).
% 1.73/1.97
% 1.73/1.97 ------------> process usable:
% 1.73/1.97 ** KEPT (pick-wt=5): 1 [] -r1(A)|A=$c1.
% 1.73/1.97 ** KEPT (pick-wt=5): 2 [] A!=$c1|r1(A).
% 1.73/1.97 ** KEPT (pick-wt=7): 3 [] -r2(A,B)|B=$f1(A).
% 1.73/1.97 ** KEPT (pick-wt=7): 4 [] A!=$f1(B)|r2(B,A).
% 1.73/1.97 ** KEPT (pick-wt=9): 5 [] -r3(A,B,C)|C=$f2(A,B).
% 1.73/1.97 ** KEPT (pick-wt=9): 6 [] A!=$f2(B,C)|r3(B,C,A).
% 1.73/1.97 ** KEPT (pick-wt=9): 7 [] -r4(A,B,C)|C=$f3(A,B).
% 1.73/1.97 ** KEPT (pick-wt=9): 8 [] A!=$f3(B,C)|r4(B,C,A).
% 1.73/1.97 ** KEPT (pick-wt=12): 9 [] -r2(A,B)|B!=C| -r2(D,C)|A=D.
% 1.73/1.97 ** KEPT (pick-wt=8): 10 [] -r1(A)|A!=B| -r2(C,B).
% 1.73/1.97 ** KEPT (pick-wt=19): 11 [] -r4(A,A,B)|C!=B| -r4(D,D,E)| -r4(F,F,G)| -r3(G,E,C).
% 1.73/1.98
% 1.73/1.98 ------------> process sos:
% 1.73/1.98 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.73/1.98 ** KEPT (pick-wt=5): 18 [] r2(A,$f4(B,A)).
% 1.73/1.98 ** KEPT (pick-wt=8): 19 [] r3(A,$f4(A,B),$f5(A,B)).
% 1.73/1.98 ** KEPT (pick-wt=7): 21 [copy,20,flip.1] $f7(A,B)=$f5(A,B).
% 1.73/1.98 ---> New Demodulator: 22 [new_demod,21] $f7(A,B)=$f5(A,B).
% 1.73/1.98 ** KEPT (pick-wt=7): 24 [copy,23,demod,22] r2($f6(A,B),$f5(A,B)).
% 1.73/1.98 ** KEPT (pick-wt=6): 25 [] r3(A,B,$f6(A,B)).
% 1.73/1.98 ** KEPT (pick-wt=5): 26 [] r2(A,$f8(B,A)).
% 1.73/1.98 ** KEPT (pick-wt=8): 27 [] r4(A,$f8(A,B),$f9(A,B)).
% 1.73/1.98 ** KEPT (pick-wt=7): 28 [] $f9(A,B)=$f11(A,B).
% 1.73/1.98 ---> New Demodulator: 29 [new_demod,28] $f9(A,B)=$f11(A,B).
% 1.73/1.98 ** KEPT (pick-wt=8): 30 [] r3($f10(A,B),A,$f11(A,B)).
% 1.73/1.98 ** KEPT (pick-wt=6): 31 [] r4(A,B,$f10(A,B)).
% 1.73/1.98 ** KEPT (pick-wt=3): 32 [] r1($f12(A)).
% 1.73/1.98 ** KEPT (pick-wt=6): 33 [] r3(A,$f12(A),$f13(A)).
% 1.73/1.98 ** KEPT (pick-wt=4): 34 [] $f13(A)=A.
% 1.73/1.98 ---> New Demodulator: 35 [new_demod,34] $f13(A)=A.
% 1.73/1.98 ** KEPT (pick-wt=3): 36 [] r1($f14(A)).
% 1.73/1.98 ** KEPT (pick-wt=6): 37 [] r4(A,$f14(A),$f16(A)).
% 1.73/1.98 ** KEPT (pick-wt=3): 38 [] r1($f15(A)).
% 1.73/1.98 ** KEPT (pick-wt=5): 39 [] $f16(A)=$f15(A).
% 1.73/1.98 ---> New Demodulator: 40 [new_demod,39] $f16(A)=$f15(A).
% 1.73/1.98 ** KEPT (pick-wt=8): 41 [] r1($f17(A))|r2($f19(A),$f18(A)).
% 1.73/1.98 ** KEPT (pick-wt=7): 43 [copy,42,flip.2] r1($f17(A))|$f18(A)=A.
% 1.73/1.98 ** KEPT (pick-wt=9): 45 [copy,44,flip.1] $f17(A)=A|r2($f19(A),$f18(A)).
% 1.73/1.98 ** KEPT (pick-wt=8): 47 [copy,46,flip.1,flip.2] $f17(A)=A|$f18(A)=A.
% 1.73/1.98 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.73/1.98 17 back subsumes 12.
% 1.73/1.98 >>>> Starting back demodulation with 22.
% 1.73/1.98 >>>> Starting back demodulation with 29.
% 1.73/1.98 >> back demodulating 27 with 29.
% 1.73/1.98 >>>> Starting back demodulation with 35.
% 1.73/1.98 >> back demodulating 33 with 35.
% 1.73/1.98 >>>> Starting back demodulation with 40.
% 1.73/1.98 >> back demodulating 37 with 40.
% 1.73/1.98
% 1.73/1.98 ======= end of input processing =======
% 1.73/1.98
% 1.73/1.98 =========== start of search ===========
% 1.73/1.98
% 1.73/1.98 -------- PROOF --------
% 1.73/1.98
% 1.73/1.98 -----> EMPTY CLAUSE at 0.01 sec ----> 98 [hyper,67,16,17,61] $F.
% 1.73/1.98
% 1.73/1.98 Length of proof is 10. Level of proof is 3.
% 1.73/1.98
% 1.73/1.98 ---------------- PROOF ----------------
% 1.73/1.98 % SZS status Theorem
% 1.73/1.98 % SZS output start Refutation
% See solution above
% 1.73/1.98 ------------ end of proof -------------
% 1.73/1.98
% 1.73/1.98
% 1.73/1.98 Search stopped by max_proofs option.
% 1.73/1.98
% 1.73/1.98
% 1.73/1.98 Search stopped by max_proofs option.
% 1.73/1.98
% 1.73/1.98 ============ end of search ============
% 1.73/1.98
% 1.73/1.98 -------------- statistics -------------
% 1.73/1.98 clauses given 14
% 1.73/1.98 clauses generated 84
% 1.73/1.98 clauses kept 81
% 1.73/1.98 clauses forward subsumed 51
% 1.73/1.98 clauses back subsumed 1
% 1.73/1.98 Kbytes malloced 976
% 1.73/1.98
% 1.73/1.98 ----------- times (seconds) -----------
% 1.73/1.98 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.73/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.73/1.98
% 1.73/1.98 That finishes the proof of the theorem.
% 1.73/1.98
% 1.73/1.98 Process 19547 finished Wed Jul 27 02:23:32 2022
% 1.73/1.98 Otter interrupted
% 1.73/1.98 PROOF FOUND
%------------------------------------------------------------------------------