TSTP Solution File: COM012+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 12:48:21 EDT 2022
% Result : Theorem 1.87s 2.04s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 17 ( 12 unt; 4 nHn; 17 RR)
% Number of literals : 27 ( 4 equ; 8 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ aElement0(A)
| ~ aRewritingSystem0(B)
| ~ aElement0(C)
| ~ aElement0(D)
| ~ sdtmndtplgtdt0(A,B,C)
| ~ sdtmndtplgtdt0(C,B,D)
| sdtmndtplgtdt0(A,B,D) ),
file('COM012+3.p',unknown),
[] ).
cnf(15,axiom,
~ sdtmndtplgtdt0(xx,xR,xz),
file('COM012+3.p',unknown),
[] ).
cnf(16,axiom,
~ sdtmndtasgtdt0(xx,xR,xz),
file('COM012+3.p',unknown),
[] ).
cnf(27,axiom,
aElement0(xx),
file('COM012+3.p',unknown),
[] ).
cnf(28,axiom,
aRewritingSystem0(xR),
file('COM012+3.p',unknown),
[] ).
cnf(29,axiom,
aElement0(xy),
file('COM012+3.p',unknown),
[] ).
cnf(30,axiom,
aElement0(xz),
file('COM012+3.p',unknown),
[] ).
cnf(37,axiom,
( xx = xy
| sdtmndtplgtdt0(xx,xR,xy) ),
file('COM012+3.p',unknown),
[] ).
cnf(38,plain,
( xy = xx
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[37])]),
[iquote('copy,37,flip.1')] ).
cnf(39,axiom,
sdtmndtasgtdt0(xx,xR,xy),
file('COM012+3.p',unknown),
[] ).
cnf(46,axiom,
( xy = xz
| sdtmndtplgtdt0(xy,xR,xz) ),
file('COM012+3.p',unknown),
[] ).
cnf(47,plain,
( xz = xy
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[46])]),
[iquote('copy,46,flip.1')] ).
cnf(48,axiom,
sdtmndtasgtdt0(xy,xR,xz),
file('COM012+3.p',unknown),
[] ).
cnf(95,plain,
sdtmndtplgtdt0(xx,xR,xy),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[38,48]),16]),
[iquote('para_from,38.1.1,48.1.1,unit_del,16')] ).
cnf(117,plain,
sdtmndtplgtdt0(xy,xR,xz),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[47,16]),39]),
[iquote('para_from,47.1.1,16.1.3,unit_del,39')] ).
cnf(118,plain,
sdtmndtplgtdt0(xx,xR,xz),
inference(hyper,[status(thm)],[117,7,27,28,29,30,95]),
[iquote('hyper,117,7,27,28,29,30,95')] ).
cnf(119,plain,
$false,
inference(binary,[status(thm)],[118,15]),
[iquote('binary,118.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 06:39:10 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.87/2.04 ----- Otter 3.3f, August 2004 -----
% 1.87/2.04 The process was started by sandbox on n024.cluster.edu,
% 1.87/2.04 Wed Jul 27 06:39:10 2022
% 1.87/2.04 The command was "./otter". The process ID is 14435.
% 1.87/2.04
% 1.87/2.04 set(prolog_style_variables).
% 1.87/2.04 set(auto).
% 1.87/2.04 dependent: set(auto1).
% 1.87/2.04 dependent: set(process_input).
% 1.87/2.04 dependent: clear(print_kept).
% 1.87/2.04 dependent: clear(print_new_demod).
% 1.87/2.04 dependent: clear(print_back_demod).
% 1.87/2.04 dependent: clear(print_back_sub).
% 1.87/2.04 dependent: set(control_memory).
% 1.87/2.04 dependent: assign(max_mem, 12000).
% 1.87/2.04 dependent: assign(pick_given_ratio, 4).
% 1.87/2.04 dependent: assign(stats_level, 1).
% 1.87/2.04 dependent: assign(max_seconds, 10800).
% 1.87/2.04 clear(print_given).
% 1.87/2.04
% 1.87/2.04 formula_list(usable).
% 1.87/2.04 all A (A=A).
% 1.87/2.04 all W0 (aElement0(W0)->$T).
% 1.87/2.04 all W0 (aRewritingSystem0(W0)->$T).
% 1.87/2.04 all W0 W1 (aElement0(W0)&aRewritingSystem0(W1)-> (all W2 (aReductOfIn0(W2,W0,W1)->aElement0(W2)))).
% 1.87/2.04 all W0 W1 (aElement0(W0)&aElement0(W1)-> (iLess0(W0,W1)->$T)).
% 1.87/2.04 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W0,W1,W2)->$T)).
% 1.87/2.04 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W0,W1,W2)<->aReductOfIn0(W2,W0,W1)| (exists W3 (aElement0(W3)&aReductOfIn0(W3,W0,W1)&sdtmndtplgtdt0(W3,W1,W2))))).
% 1.87/2.04 all W0 W1 W2 W3 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)&aElement0(W3)-> (sdtmndtplgtdt0(W0,W1,W2)&sdtmndtplgtdt0(W2,W1,W3)->sdtmndtplgtdt0(W0,W1,W3))).
% 1.87/2.04 all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtasgtdt0(W0,W1,W2)<->W0=W2|sdtmndtplgtdt0(W0,W1,W2))).
% 1.87/2.04 aElement0(xx).
% 1.87/2.04 aRewritingSystem0(xR).
% 1.87/2.04 aElement0(xy).
% 1.87/2.04 aElement0(xz).
% 1.87/2.04 -((xx=xy| (aReductOfIn0(xy,xx,xR)| (exists W0 (aElement0(W0)&aReductOfIn0(W0,xx,xR)&sdtmndtplgtdt0(W0,xR,xy))))&sdtmndtplgtdt0(xx,xR,xy))&sdtmndtasgtdt0(xx,xR,xy)& (xy=xz| (aReductOfIn0(xz,xy,xR)| (exists W0 (aElement0(W0)&aReductOfIn0(W0,xy,xR)&sdtmndtplgtdt0(W0,xR,xz))))&sdtmndtplgtdt0(xy,xR,xz))&sdtmndtasgtdt0(xy,xR,xz)->xx=xz|aReductOfIn0(xz,xx,xR)| (exists W0 (aElement0(W0)&aReductOfIn0(W0,xx,xR)&sdtmndtplgtdt0(W0,xR,xz)))|sdtmndtplgtdt0(xx,xR,xz)|sdtmndtasgtdt0(xx,xR,xz)).
% 1.87/2.04 end_of_list.
% 1.87/2.04
% 1.87/2.04 -------> usable clausifies to:
% 1.87/2.04
% 1.87/2.04 list(usable).
% 1.87/2.04 0 [] A=A.
% 1.87/2.04 0 [] -aElement0(W0)|$T.
% 1.87/2.04 0 [] -aRewritingSystem0(W0)|$T.
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aReductOfIn0(W2,W0,W1)|aElement0(W2).
% 1.87/2.04 0 [] -aElement0(W0)| -aElement0(W1)| -iLess0(W0,W1)|$T.
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|$T.
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aElement0($f1(W0,W1,W2)).
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aReductOfIn0($f1(W0,W1,W2),W0,W1).
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|sdtmndtplgtdt0($f1(W0,W1,W2),W1,W2).
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aReductOfIn0(W2,W0,W1).
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aElement0(W3)| -aReductOfIn0(W3,W0,W1)| -sdtmndtplgtdt0(W3,W1,W2).
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtplgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W2,W1,W3)|sdtmndtplgtdt0(W0,W1,W3).
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,W1,W2)|W0=W2|sdtmndtplgtdt0(W0,W1,W2).
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)|W0!=W2.
% 1.87/2.04 0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W0,W1,W2).
% 1.87/2.04 0 [] aElement0(xx).
% 1.87/2.04 0 [] aRewritingSystem0(xR).
% 1.87/2.04 0 [] aElement0(xy).
% 1.87/2.04 0 [] aElement0(xz).
% 1.87/2.04 0 [] xx=xy|aReductOfIn0(xy,xx,xR)|aElement0($c1).
% 1.87/2.04 0 [] xx=xy|aReductOfIn0(xy,xx,xR)|aReductOfIn0($c1,xx,xR).
% 1.87/2.04 0 [] xx=xy|aReductOfIn0(xy,xx,xR)|sdtmndtplgtdt0($c1,xR,xy).
% 1.87/2.04 0 [] xx=xy|sdtmndtplgtdt0(xx,xR,xy).
% 1.87/2.04 0 [] sdtmndtasgtdt0(xx,xR,xy).
% 1.87/2.04 0 [] xy=xz|aReductOfIn0(xz,xy,xR)|aElement0($c2).
% 1.87/2.04 0 [] xy=xz|aReductOfIn0(xz,xy,xR)|aReductOfIn0($c2,xy,xR).
% 1.87/2.04 0 [] xy=xz|aReductOfIn0(xz,xy,xR)|sdtmndtplgtdt0($c2,xR,xz).
% 1.87/2.04 0 [] xy=xz|sdtmndtplgtdt0(xy,xR,xz).
% 1.87/2.04 0 [] sdtmndtasgtdt0(xy,xR,xz).
% 1.87/2.04 0 [] xx!=xz.
% 1.87/2.04 0 [] -aReductOfIn0(xz,xx,xR).
% 1.87/2.04 0 [] -aElement0(W0)| -aReductOfIn0(W0,xx,xR)| -sdtmndtplgtdt0(W0,xR,xz).
% 1.87/2.04 0 [] -sdtmndtplgtdt0(xx,xR,xz).
% 1.87/2.04 0 [] -sdtmndtasgtdt0(xx,xR,xz).
% 1.87/2.04 end_of_list.
% 1.87/2.04
% 1.87/2.04 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.87/2.04
% 1.87/2.04 This ia a non-Horn set with equality. The strategy will be
% 1.87/2.04 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.87/2.04 deletion, with positive clauses in sos and nonpositive
% 1.87/2.04 clauses in usable.
% 1.87/2.04
% 1.87/2.04 dependent: set(knuth_bendix).
% 1.87/2.04 dependent: set(anl_eq).
% 1.87/2.04 dependent: set(para_from).
% 1.87/2.04 dependent: set(para_into).
% 1.87/2.04 dependent: clear(para_from_right).
% 1.87/2.04 dependent: clear(para_into_right).
% 1.87/2.04 dependent: set(para_from_vars).
% 1.87/2.04 dependent: set(eq_units_both_ways).
% 1.87/2.04 dependent: set(dynamic_demod_all).
% 1.87/2.04 dependent: set(dynamic_demod).
% 1.87/2.04 dependent: set(order_eq).
% 1.87/2.04 dependent: set(back_demod).
% 1.87/2.04 dependent: set(lrpo).
% 1.87/2.04 dependent: set(hyper_res).
% 1.87/2.04 dependent: set(unit_deletion).
% 1.87/2.04 dependent: set(factor).
% 1.87/2.04
% 1.87/2.04 ------------> process usable:
% 1.87/2.04 ** KEPT (pick-wt=10): 1 [] -aElement0(A)| -aRewritingSystem0(B)| -aReductOfIn0(C,A,B)|aElement0(C).
% 1.87/2.04 ** KEPT (pick-wt=19): 2 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aElement0($f1(A,B,C)).
% 1.87/2.04 ** KEPT (pick-wt=21): 3 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aReductOfIn0($f1(A,B,C),A,B).
% 1.87/2.04 ** KEPT (pick-wt=21): 4 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|sdtmndtplgtdt0($f1(A,B,C),B,C).
% 1.87/2.04 ** KEPT (pick-wt=14): 5 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtplgtdt0(A,B,C)| -aReductOfIn0(C,A,B).
% 1.87/2.04 ** KEPT (pick-wt=20): 6 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtplgtdt0(A,B,C)| -aElement0(D)| -aReductOfIn0(D,A,B)| -sdtmndtplgtdt0(D,B,C).
% 1.87/2.04 ** KEPT (pick-wt=20): 7 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtplgtdt0(A,B,C)| -sdtmndtplgtdt0(C,B,D)|sdtmndtplgtdt0(A,B,D).
% 1.87/2.04 ** KEPT (pick-wt=17): 8 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,B,C)|A=C|sdtmndtplgtdt0(A,B,C).
% 1.87/2.04 ** KEPT (pick-wt=13): 9 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)|A!=C.
% 1.87/2.04 ** KEPT (pick-wt=14): 10 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)| -sdtmndtplgtdt0(A,B,C).
% 1.87/2.04 ** KEPT (pick-wt=3): 12 [copy,11,flip.1] xz!=xx.
% 1.87/2.04 ** KEPT (pick-wt=4): 13 [] -aReductOfIn0(xz,xx,xR).
% 1.87/2.04 ** KEPT (pick-wt=10): 14 [] -aElement0(A)| -aReductOfIn0(A,xx,xR)| -sdtmndtplgtdt0(A,xR,xz).
% 1.87/2.04 ** KEPT (pick-wt=4): 15 [] -sdtmndtplgtdt0(xx,xR,xz).
% 1.87/2.04 ** KEPT (pick-wt=4): 16 [] -sdtmndtasgtdt0(xx,xR,xz).
% 1.87/2.04
% 1.87/2.04 ------------> process sos:
% 1.87/2.04 ** KEPT (pick-wt=3): 26 [] A=A.
% 1.87/2.04 ** KEPT (pick-wt=2): 27 [] aElement0(xx).
% 1.87/2.04 ** KEPT (pick-wt=2): 28 [] aRewritingSystem0(xR).
% 1.87/2.04 ** KEPT (pick-wt=2): 29 [] aElement0(xy).
% 1.87/2.04 ** KEPT (pick-wt=2): 30 [] aElement0(xz).
% 1.87/2.04 ** KEPT (pick-wt=9): 32 [copy,31,flip.1] xy=xx|aReductOfIn0(xy,xx,xR)|aElement0($c1).
% 1.87/2.04 ** KEPT (pick-wt=11): 34 [copy,33,flip.1] xy=xx|aReductOfIn0(xy,xx,xR)|aReductOfIn0($c1,xx,xR).
% 1.87/2.04 ** KEPT (pick-wt=11): 36 [copy,35,flip.1] xy=xx|aReductOfIn0(xy,xx,xR)|sdtmndtplgtdt0($c1,xR,xy).
% 1.87/2.04 ** KEPT (pick-wt=7): 38 [copy,37,flip.1] xy=xx|sdtmndtplgtdt0(xx,xR,xy).
% 1.87/2.04 ** KEPT (pick-wt=4): 39 [] sdtmndtasgtdt0(xx,xR,xy).
% 1.87/2.04 ** KEPT (pick-wt=9): 41 [copy,40,flip.1] xz=xy|aReductOfIn0(xz,xy,xR)|aElement0($c2).
% 1.87/2.04 ** KEPT (pick-wt=11): 43 [copy,42,flip.1] xz=xy|aReductOfIn0(xz,xy,xR)|aReductOfIn0($c2,xy,xR).
% 1.87/2.04 ** KEPT (pick-wt=11): 45 [copy,44,flip.1] xz=xy|aReductOfIn0(xz,xy,xR)|sdtmndtplgtdt0($c2,xR,xz).
% 1.87/2.04 ** KEPT (pick-wt=7): 47 [copy,46,flip.1] xz=xy|sdtmndtplgtdt0(xy,xR,xz).
% 1.87/2.04 ** KEPT (pick-wt=4): 48 [] sdtmndtasgtdt0(xy,xR,xz).
% 1.87/2.04 Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] A=A.
% 1.87/2.04 26 back subsumes 23.
% 1.87/2.04
% 1.87/2.04 ======= end of input processing =======
% 1.87/2.04
% 1.87/2.04 =========== start of search ===========
% 1.87/2.04
% 1.87/2.04 -------- PROOF --------
% 1.87/2.04
% 1.87/2.04 ----> UNIT CONFLICT at 0.01 sec ----> 119 [binary,118.1,15.1] $F.
% 1.87/2.04
% 1.87/2.04 Length of proof is 5. Level of proof is 3.
% 1.87/2.04
% 1.87/2.04 ---------------- PROOF ----------------
% 1.87/2.04 % SZS status Theorem
% 1.87/2.04 % SZS output start Refutation
% See solution above
% 1.87/2.04 ------------ end of proof -------------
% 1.87/2.04
% 1.87/2.04
% 1.87/2.04 Search stopped by max_proofs option.
% 1.87/2.04
% 1.87/2.04
% 1.87/2.04 Search stopped by max_proofs option.
% 1.87/2.04
% 1.87/2.04 ============ end of search ============
% 1.87/2.04
% 1.87/2.04 -------------- statistics -------------
% 1.87/2.04 clauses given 18
% 1.87/2.04 clauses generated 170
% 1.87/2.04 clauses kept 109
% 1.87/2.04 clauses forward subsumed 80
% 1.87/2.04 clauses back subsumed 24
% 1.87/2.04 Kbytes malloced 976
% 1.87/2.04
% 1.87/2.04 ----------- times (seconds) -----------
% 1.87/2.04 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.87/2.04 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.04 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.87/2.04
% 1.87/2.04 That finishes the proof of the theorem.
% 1.87/2.04
% 1.87/2.04 Process 14435 finished Wed Jul 27 06:39:12 2022
% 1.87/2.04 Otter interrupted
% 1.87/2.04 PROOF FOUND
%------------------------------------------------------------------------------