TSTP Solution File: KRS077+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:01:05 EDT 2022
% Result : Unsatisfiable 1.95s 2.16s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 16 RR)
% Number of literals : 26 ( 2 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
( ~ cUnsatisfiable(A)
| ~ rr(A,B)
| ~ rr(A,C)
| B = C ),
file('KRS077+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f1(A)) ),
file('KRS077+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvS(dollar_f1(A),B)
| cp(B) ),
file('KRS077+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| ~ cp(A) ),
file('KRS077+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| rs(A,dollar_f2(A)) ),
file('KRS077+1.p',unknown),
[] ).
cnf(28,axiom,
( rinvS(A,B)
| ~ rs(B,A) ),
file('KRS077+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ rs(A,B)
| rr(A,B) ),
file('KRS077+1.p',unknown),
[] ).
cnf(37,axiom,
cUnsatisfiable(i2003_11_14_17_19_09372),
file('KRS077+1.p',unknown),
[] ).
cnf(39,plain,
rs(i2003_11_14_17_19_09372,dollar_f2(i2003_11_14_17_19_09372)),
inference(hyper,[status(thm)],[37,19]),
[iquote('hyper,37,19')] ).
cnf(40,plain,
rr(i2003_11_14_17_19_09372,dollar_f1(i2003_11_14_17_19_09372)),
inference(hyper,[status(thm)],[37,16]),
[iquote('hyper,37,16')] ).
cnf(44,plain,
rr(i2003_11_14_17_19_09372,dollar_f2(i2003_11_14_17_19_09372)),
inference(hyper,[status(thm)],[39,29]),
[iquote('hyper,39,29')] ).
cnf(45,plain,
rinvS(dollar_f2(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(hyper,[status(thm)],[39,28]),
[iquote('hyper,39,28')] ).
cnf(53,plain,
dollar_f2(i2003_11_14_17_19_09372) = dollar_f1(i2003_11_14_17_19_09372),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[44,15,37,40])]),
[iquote('hyper,44,15,37,40,flip.1')] ).
cnf(56,plain,
rinvS(dollar_f1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[45]),53]),
[iquote('back_demod,45,demod,53')] ).
cnf(61,plain,
cp(i2003_11_14_17_19_09372),
inference(hyper,[status(thm)],[56,17,37]),
[iquote('hyper,56,17,37')] ).
cnf(66,plain,
$false,
inference(hyper,[status(thm)],[61,18,37]),
[iquote('hyper,61,18,37')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 03:49:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.16 ----- Otter 3.3f, August 2004 -----
% 1.95/2.16 The process was started by sandbox2 on n023.cluster.edu,
% 1.95/2.16 Wed Jul 27 03:49:48 2022
% 1.95/2.16 The command was "./otter". The process ID is 10930.
% 1.95/2.16
% 1.95/2.16 set(prolog_style_variables).
% 1.95/2.16 set(auto).
% 1.95/2.16 dependent: set(auto1).
% 1.95/2.16 dependent: set(process_input).
% 1.95/2.16 dependent: clear(print_kept).
% 1.95/2.16 dependent: clear(print_new_demod).
% 1.95/2.16 dependent: clear(print_back_demod).
% 1.95/2.16 dependent: clear(print_back_sub).
% 1.95/2.16 dependent: set(control_memory).
% 1.95/2.16 dependent: assign(max_mem, 12000).
% 1.95/2.16 dependent: assign(pick_given_ratio, 4).
% 1.95/2.16 dependent: assign(stats_level, 1).
% 1.95/2.16 dependent: assign(max_seconds, 10800).
% 1.95/2.16 clear(print_given).
% 1.95/2.16
% 1.95/2.16 formula_list(usable).
% 1.95/2.16 all A (A=A).
% 1.95/2.16 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.95/2.16 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.95/2.16 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.95/2.16 all A B (A=B&cp(A)->cp(B)).
% 1.95/2.16 all A B C (A=B&rinvS(A,C)->rinvS(B,C)).
% 1.95/2.16 all A B C (A=B&rinvS(C,A)->rinvS(C,B)).
% 1.95/2.16 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.95/2.16 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.95/2.16 all A B C (A=B&rs(A,C)->rs(B,C)).
% 1.95/2.16 all A B C (A=B&rs(C,A)->rs(C,B)).
% 1.95/2.16 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.95/2.16 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.95/2.16 all X (cowlThing(X)& -cowlNothing(X)).
% 1.95/2.16 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.95/2.16 all X (cUnsatisfiable(X)<-> (all Y0 Y1 (rr(X,Y0)&rr(X,Y1)->Y0=Y1))& (exists Y (rr(X,Y)& (all Z (rinvS(Y,Z)->cp(Z)))))& -cp(X)& (exists Y (rs(X,Y)&cp(Y)))).
% 1.95/2.16 all X Y (rinvS(X,Y)<->rs(Y,X)).
% 1.95/2.16 cUnsatisfiable(i2003_11_14_17_19_09372).
% 1.95/2.16 all X Y (rs(X,Y)->rr(X,Y)).
% 1.95/2.16 end_of_list.
% 1.95/2.16
% 1.95/2.16 -------> usable clausifies to:
% 1.95/2.16
% 1.95/2.16 list(usable).
% 1.95/2.16 0 [] A=A.
% 1.95/2.16 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.95/2.16 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.95/2.16 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.95/2.16 0 [] A!=B| -cp(A)|cp(B).
% 1.95/2.16 0 [] A!=B| -rinvS(A,C)|rinvS(B,C).
% 1.95/2.16 0 [] A!=B| -rinvS(C,A)|rinvS(C,B).
% 1.95/2.16 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.95/2.16 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.95/2.16 0 [] A!=B| -rs(A,C)|rs(B,C).
% 1.95/2.16 0 [] A!=B| -rs(C,A)|rs(C,B).
% 1.95/2.16 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.95/2.16 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.95/2.16 0 [] cowlThing(X).
% 1.95/2.16 0 [] -cowlNothing(X).
% 1.95/2.16 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.95/2.16 0 [] xsd_string(X)|xsd_integer(X).
% 1.95/2.16 0 [] -cUnsatisfiable(X)| -rr(X,Y0)| -rr(X,Y1)|Y0=Y1.
% 1.95/2.16 0 [] -cUnsatisfiable(X)|rr(X,$f1(X)).
% 1.95/2.16 0 [] -cUnsatisfiable(X)| -rinvS($f1(X),Z)|cp(Z).
% 1.95/2.16 0 [] -cUnsatisfiable(X)| -cp(X).
% 1.95/2.16 0 [] -cUnsatisfiable(X)|rs(X,$f2(X)).
% 1.95/2.16 0 [] -cUnsatisfiable(X)|cp($f2(X)).
% 1.95/2.16 0 [] cUnsatisfiable(X)|rr(X,$f4(X))| -rr(X,Y)|rinvS(Y,$f5(X,Y))|cp(X)| -rs(X,X1)| -cp(X1).
% 1.95/2.16 0 [] cUnsatisfiable(X)|rr(X,$f4(X))| -rr(X,Y)| -cp($f5(X,Y))|cp(X)| -rs(X,X1)| -cp(X1).
% 1.95/2.16 0 [] cUnsatisfiable(X)|rr(X,$f3(X))| -rr(X,Y)|rinvS(Y,$f5(X,Y))|cp(X)| -rs(X,X1)| -cp(X1).
% 1.95/2.16 0 [] cUnsatisfiable(X)|rr(X,$f3(X))| -rr(X,Y)| -cp($f5(X,Y))|cp(X)| -rs(X,X1)| -cp(X1).
% 1.95/2.16 0 [] cUnsatisfiable(X)|$f4(X)!=$f3(X)| -rr(X,Y)|rinvS(Y,$f5(X,Y))|cp(X)| -rs(X,X1)| -cp(X1).
% 1.95/2.16 0 [] cUnsatisfiable(X)|$f4(X)!=$f3(X)| -rr(X,Y)| -cp($f5(X,Y))|cp(X)| -rs(X,X1)| -cp(X1).
% 1.95/2.16 0 [] -rinvS(X,Y)|rs(Y,X).
% 1.95/2.16 0 [] rinvS(X,Y)| -rs(Y,X).
% 1.95/2.16 0 [] cUnsatisfiable(i2003_11_14_17_19_09372).
% 1.95/2.16 0 [] -rs(X,Y)|rr(X,Y).
% 1.95/2.16 end_of_list.
% 1.95/2.16
% 1.95/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.95/2.16
% 1.95/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.95/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.95/2.16 deletion, with positive clauses in sos and nonpositive
% 1.95/2.16 clauses in usable.
% 1.95/2.16
% 1.95/2.16 dependent: set(knuth_bendix).
% 1.95/2.16 dependent: set(anl_eq).
% 1.95/2.16 dependent: set(para_from).
% 1.95/2.16 dependent: set(para_into).
% 1.95/2.16 dependent: clear(para_from_right).
% 1.95/2.16 dependent: clear(para_into_right).
% 1.95/2.16 dependent: set(para_from_vars).
% 1.95/2.16 dependent: set(eq_units_both_ways).
% 1.95/2.16 dependent: set(dynamic_demod_all).
% 1.95/2.16 dependent: set(dynamic_demod).
% 1.95/2.16 dependent: set(order_eq).
% 1.95/2.16 dependent: set(back_demod).
% 1.95/2.16 dependent: set(lrpo).
% 1.95/2.16 dependent: set(hyper_res).
% 1.95/2.16 dependent: set(unit_deletion).
% 1.95/2.16 dependent: set(factor).
% 1.95/2.16
% 1.95/2.16 ------------> process usable:
% 1.95/2.16 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.95/2.16 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.95/2.16 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.95/2.16 ** KEPT (pick-wt=7): 4 [] A!=B| -cp(A)|cp(B).
% 1.95/2.16 ** KEPT (pick-wt=9): 5 [] A!=B| -rinvS(A,C)|rinvS(B,C).
% 1.95/2.16 ** KEPT (pick-wt=9): 6 [] A!=B| -rinvS(C,A)|rinvS(C,B).
% 1.95/2.16 ** KEPT (pick-wt=9): 7 [] A!=B| -rr(A,C)|rr(B,C).
% 1.95/2.16 ** KEPT (pick-wt=9): 8 [] A!=B| -rr(C,A)|rr(C,B).
% 1.95/2.16 ** KEPT (pick-wt=9): 9 [] A!=B| -rs(A,C)|rs(B,C).
% 1.95/2.16 ** KEPT (pick-wt=9): 10 [] A!=B| -rs(C,A)|rs(C,B).
% 1.95/2.16 ** KEPT (pick-wt=7): 11 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.95/2.16 ** KEPT (pick-wt=7): 12 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.95/2.16 ** KEPT (pick-wt=2): 13 [] -cowlNothing(A).
% 1.95/2.16 ** KEPT (pick-wt=4): 14 [] -xsd_string(A)| -xsd_integer(A).
% 1.95/2.16 ** KEPT (pick-wt=11): 15 [] -cUnsatisfiable(A)| -rr(A,B)| -rr(A,C)|B=C.
% 1.95/2.16 ** KEPT (pick-wt=6): 16 [] -cUnsatisfiable(A)|rr(A,$f1(A)).
% 1.95/2.16 ** KEPT (pick-wt=8): 17 [] -cUnsatisfiable(A)| -rinvS($f1(A),B)|cp(B).
% 1.95/2.16 ** KEPT (pick-wt=4): 18 [] -cUnsatisfiable(A)| -cp(A).
% 1.95/2.16 ** KEPT (pick-wt=6): 19 [] -cUnsatisfiable(A)|rs(A,$f2(A)).
% 1.95/2.16 ** KEPT (pick-wt=5): 20 [] -cUnsatisfiable(A)|cp($f2(A)).
% 1.95/2.16 ** KEPT (pick-wt=21): 21 [] cUnsatisfiable(A)|rr(A,$f4(A))| -rr(A,B)|rinvS(B,$f5(A,B))|cp(A)| -rs(A,C)| -cp(C).
% 1.95/2.16 ** KEPT (pick-wt=20): 22 [] cUnsatisfiable(A)|rr(A,$f4(A))| -rr(A,B)| -cp($f5(A,B))|cp(A)| -rs(A,C)| -cp(C).
% 1.95/2.16 ** KEPT (pick-wt=21): 23 [] cUnsatisfiable(A)|rr(A,$f3(A))| -rr(A,B)|rinvS(B,$f5(A,B))|cp(A)| -rs(A,C)| -cp(C).
% 1.95/2.16 ** KEPT (pick-wt=20): 24 [] cUnsatisfiable(A)|rr(A,$f3(A))| -rr(A,B)| -cp($f5(A,B))|cp(A)| -rs(A,C)| -cp(C).
% 1.95/2.16 ** KEPT (pick-wt=22): 25 [] cUnsatisfiable(A)|$f4(A)!=$f3(A)| -rr(A,B)|rinvS(B,$f5(A,B))|cp(A)| -rs(A,C)| -cp(C).
% 1.95/2.16 ** KEPT (pick-wt=21): 26 [] cUnsatisfiable(A)|$f4(A)!=$f3(A)| -rr(A,B)| -cp($f5(A,B))|cp(A)| -rs(A,C)| -cp(C).
% 1.95/2.16 ** KEPT (pick-wt=6): 27 [] -rinvS(A,B)|rs(B,A).
% 1.95/2.16 ** KEPT (pick-wt=6): 28 [] rinvS(A,B)| -rs(B,A).
% 1.95/2.16 ** KEPT (pick-wt=6): 29 [] -rs(A,B)|rr(A,B).
% 1.95/2.16 13 back subsumes 2.
% 1.95/2.16
% 1.95/2.16 ------------> process sos:
% 1.95/2.16 ** KEPT (pick-wt=3): 34 [] A=A.
% 1.95/2.16 ** KEPT (pick-wt=2): 35 [] cowlThing(A).
% 1.95/2.16 ** KEPT (pick-wt=4): 36 [] xsd_string(A)|xsd_integer(A).
% 1.95/2.16 ** KEPT (pick-wt=2): 37 [] cUnsatisfiable(i2003_11_14_17_19_09372).
% 1.95/2.16 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] A=A.
% 1.95/2.16 34 back subsumes 30.
% 1.95/2.16 35 back subsumes 3.
% 1.95/2.16
% 1.95/2.16 ======= end of input processing =======
% 1.95/2.16
% 1.95/2.16 =========== start of search ===========
% 1.95/2.16
% 1.95/2.16 -------- PROOF --------
% 1.95/2.16
% 1.95/2.16 -----> EMPTY CLAUSE at 0.00 sec ----> 66 [hyper,61,18,37] $F.
% 1.95/2.16
% 1.95/2.16 Length of proof is 7. Level of proof is 5.
% 1.95/2.16
% 1.95/2.16 ---------------- PROOF ----------------
% 1.95/2.16 % SZS status Theorem
% 1.95/2.16 % SZS output start Refutation
% See solution above
% 1.95/2.16 ------------ end of proof -------------
% 1.95/2.16
% 1.95/2.16
% 1.95/2.16 Search stopped by max_proofs option.
% 1.95/2.16
% 1.95/2.16
% 1.95/2.16 Search stopped by max_proofs option.
% 1.95/2.16
% 1.95/2.16 ============ end of search ============
% 1.95/2.16
% 1.95/2.16 -------------- statistics -------------
% 1.95/2.16 clauses given 12
% 1.95/2.16 clauses generated 72
% 1.95/2.16 clauses kept 64
% 1.95/2.16 clauses forward subsumed 48
% 1.95/2.16 clauses back subsumed 3
% 1.95/2.16 Kbytes malloced 976
% 1.95/2.16
% 1.95/2.16 ----------- times (seconds) -----------
% 1.95/2.16 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.16
% 1.95/2.16 That finishes the proof of the theorem.
% 1.95/2.16
% 1.95/2.16 Process 10930 finished Wed Jul 27 03:49:50 2022
% 1.95/2.16 Otter interrupted
% 1.95/2.16 PROOF FOUND
%------------------------------------------------------------------------------