TSTP Solution File: KRS082+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 1.72s 1.93s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 10 unt; 0 nHn; 19 RR)
% Number of literals : 34 ( 0 equ; 16 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ cUnsatisfiable(A)
| rs(A,dollar_f5(A)) ),
file('KRS082+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ cUnsatisfiable(A)
| rp(dollar_f5(A),dollar_f1(A)) ),
file('KRS082+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ cUnsatisfiable(A)
| ~ rp(dollar_f5(A),B)
| rr(B,dollar_f2(A,B)) ),
file('KRS082+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ cUnsatisfiable(A)
| ~ rp(dollar_f5(A),B)
| ~ rr(B,C)
| cc(C) ),
file('KRS082+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ cUnsatisfiable(A)
| ca(A) ),
file('KRS082+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ cc(A)
| ~ rinvR(A,B)
| ~ rinvP(B,C)
| ~ rinvS(C,D)
| ~ ca(D) ),
file('KRS082+1.p',unknown),
[] ).
cnf(17,axiom,
( rinvP(A,B)
| ~ rp(B,A) ),
file('KRS082+1.p',unknown),
[] ).
cnf(19,axiom,
( rinvR(A,B)
| ~ rr(B,A) ),
file('KRS082+1.p',unknown),
[] ).
cnf(21,axiom,
( rinvS(A,B)
| ~ rs(B,A) ),
file('KRS082+1.p',unknown),
[] ).
cnf(29,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752),
file('KRS082+1.p',unknown),
[] ).
cnf(30,plain,
ca(i2003_11_14_17_19_28752),
inference(hyper,[status(thm)],[29,14]),
[iquote('hyper,29,14')] ).
cnf(32,plain,
rp(dollar_f5(i2003_11_14_17_19_28752),dollar_f1(i2003_11_14_17_19_28752)),
inference(hyper,[status(thm)],[29,4]),
[iquote('hyper,29,4')] ).
cnf(33,plain,
rs(i2003_11_14_17_19_28752,dollar_f5(i2003_11_14_17_19_28752)),
inference(hyper,[status(thm)],[29,3]),
[iquote('hyper,29,3')] ).
cnf(34,plain,
rinvS(dollar_f5(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752),
inference(hyper,[status(thm)],[33,21]),
[iquote('hyper,33,21')] ).
cnf(37,plain,
rinvP(dollar_f1(i2003_11_14_17_19_28752),dollar_f5(i2003_11_14_17_19_28752)),
inference(hyper,[status(thm)],[32,17]),
[iquote('hyper,32,17')] ).
cnf(39,plain,
rr(dollar_f1(i2003_11_14_17_19_28752),dollar_f2(i2003_11_14_17_19_28752,dollar_f1(i2003_11_14_17_19_28752))),
inference(hyper,[status(thm)],[32,7,29]),
[iquote('hyper,32,7,29')] ).
cnf(42,plain,
rinvR(dollar_f2(i2003_11_14_17_19_28752,dollar_f1(i2003_11_14_17_19_28752)),dollar_f1(i2003_11_14_17_19_28752)),
inference(hyper,[status(thm)],[39,19]),
[iquote('hyper,39,19')] ).
cnf(43,plain,
cc(dollar_f2(i2003_11_14_17_19_28752,dollar_f1(i2003_11_14_17_19_28752))),
inference(hyper,[status(thm)],[39,11,29,32]),
[iquote('hyper,39,11,29,32')] ).
cnf(47,plain,
$false,
inference(hyper,[status(thm)],[42,15,43,37,34,30]),
[iquote('hyper,42,15,43,37,34,30')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 03:47:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.93 ----- Otter 3.3f, August 2004 -----
% 1.72/1.93 The process was started by sandbox on n027.cluster.edu,
% 1.72/1.93 Wed Jul 27 03:47:36 2022
% 1.72/1.93 The command was "./otter". The process ID is 7667.
% 1.72/1.93
% 1.72/1.93 set(prolog_style_variables).
% 1.72/1.93 set(auto).
% 1.72/1.93 dependent: set(auto1).
% 1.72/1.93 dependent: set(process_input).
% 1.72/1.93 dependent: clear(print_kept).
% 1.72/1.93 dependent: clear(print_new_demod).
% 1.72/1.93 dependent: clear(print_back_demod).
% 1.72/1.93 dependent: clear(print_back_sub).
% 1.72/1.93 dependent: set(control_memory).
% 1.72/1.93 dependent: assign(max_mem, 12000).
% 1.72/1.93 dependent: assign(pick_given_ratio, 4).
% 1.72/1.93 dependent: assign(stats_level, 1).
% 1.72/1.93 dependent: assign(max_seconds, 10800).
% 1.72/1.93 clear(print_given).
% 1.72/1.93
% 1.72/1.93 formula_list(usable).
% 1.72/1.93 all X (cowlThing(X)& -cowlNothing(X)).
% 1.72/1.93 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.72/1.93 all X (cUnsatisfiable(X)-> (exists Y (rs(X,Y)& (exists Z (rp(Y,Z)&cowlThing(Z)))& (all Z (rr(Y,Z)->cc(Z)))& (all Z (rp(Y,Z)-> (exists W (rr(Z,W)&cowlThing(W)))))& (all Z (rp(Y,Z)-> (exists W (rp(Z,W)&cowlThing(W)))))& (all Z (rp(Y,Z)-> (all W (rr(Z,W)->cc(W)))))& (exists Z (rr(Y,Z)&cowlThing(Z)))))).
% 1.72/1.93 all X (cUnsatisfiable(X)->ca(X)).
% 1.72/1.93 all X (cc(X)<-> (all Y (rinvR(X,Y)-> (all Z (rinvP(Y,Z)-> (all W (rinvS(Z,W)-> -ca(W)))))))).
% 1.72/1.93 all X Y (rinvP(X,Y)<->rp(Y,X)).
% 1.72/1.93 all X Y (rinvR(X,Y)<->rr(Y,X)).
% 1.72/1.93 all X Y (rinvS(X,Y)<->rs(Y,X)).
% 1.72/1.93 all X Y Z (rp(X,Y)&rp(Y,Z)->rp(X,Z)).
% 1.72/1.93 cUnsatisfiable(i2003_11_14_17_19_28752).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 -------> usable clausifies to:
% 1.72/1.93
% 1.72/1.93 list(usable).
% 1.72/1.93 0 [] cowlThing(X).
% 1.72/1.93 0 [] -cowlNothing(X).
% 1.72/1.93 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.72/1.93 0 [] xsd_string(X)|xsd_integer(X).
% 1.72/1.93 0 [] -cUnsatisfiable(X)|rs(X,$f5(X)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)|rp($f5(X),$f1(X)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)|cowlThing($f1(X)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)| -rr($f5(X),Z)|cc(Z).
% 1.72/1.93 0 [] -cUnsatisfiable(X)| -rp($f5(X),X1)|rr(X1,$f2(X,X1)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)| -rp($f5(X),X1)|cowlThing($f2(X,X1)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)| -rp($f5(X),X2)|rp(X2,$f3(X,X2)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)| -rp($f5(X),X2)|cowlThing($f3(X,X2)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)| -rp($f5(X),X3)| -rr(X3,W)|cc(W).
% 1.72/1.93 0 [] -cUnsatisfiable(X)|rr($f5(X),$f4(X)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)|cowlThing($f4(X)).
% 1.72/1.93 0 [] -cUnsatisfiable(X)|ca(X).
% 1.72/1.93 0 [] -cc(X)| -rinvR(X,Y)| -rinvP(Y,Z)| -rinvS(Z,W)| -ca(W).
% 1.72/1.93 0 [] cc(X)|rinvR(X,$f8(X)).
% 1.72/1.93 0 [] cc(X)|rinvP($f8(X),$f7(X)).
% 1.72/1.93 0 [] cc(X)|rinvS($f7(X),$f6(X)).
% 1.72/1.93 0 [] cc(X)|ca($f6(X)).
% 1.72/1.93 0 [] -rinvP(X,Y)|rp(Y,X).
% 1.72/1.93 0 [] rinvP(X,Y)| -rp(Y,X).
% 1.72/1.93 0 [] -rinvR(X,Y)|rr(Y,X).
% 1.72/1.93 0 [] rinvR(X,Y)| -rr(Y,X).
% 1.72/1.93 0 [] -rinvS(X,Y)|rs(Y,X).
% 1.72/1.93 0 [] rinvS(X,Y)| -rs(Y,X).
% 1.72/1.93 0 [] -rp(X,Y)| -rp(Y,Z)|rp(X,Z).
% 1.72/1.93 0 [] cUnsatisfiable(i2003_11_14_17_19_28752).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.72/1.93
% 1.72/1.93 This is a non-Horn set without equality. The strategy will
% 1.72/1.93 be ordered hyper_res, unit deletion, and factoring, with
% 1.72/1.93 satellites in sos and with nuclei in usable.
% 1.72/1.93
% 1.72/1.93 dependent: set(hyper_res).
% 1.72/1.93 dependent: set(factor).
% 1.72/1.93 dependent: set(unit_deletion).
% 1.72/1.93
% 1.72/1.93 ------------> process usable:
% 1.72/1.93 ** KEPT (pick-wt=2): 1 [] -cowlNothing(A).
% 1.72/1.93 ** KEPT (pick-wt=4): 2 [] -xsd_string(A)| -xsd_integer(A).
% 1.72/1.93 ** KEPT (pick-wt=6): 3 [] -cUnsatisfiable(A)|rs(A,$f5(A)).
% 1.72/1.93 ** KEPT (pick-wt=7): 4 [] -cUnsatisfiable(A)|rp($f5(A),$f1(A)).
% 1.72/1.93 ** KEPT (pick-wt=5): 5 [] -cUnsatisfiable(A)|cowlThing($f1(A)).
% 1.72/1.93 ** KEPT (pick-wt=8): 6 [] -cUnsatisfiable(A)| -rr($f5(A),B)|cc(B).
% 1.72/1.93 ** KEPT (pick-wt=11): 7 [] -cUnsatisfiable(A)| -rp($f5(A),B)|rr(B,$f2(A,B)).
% 1.72/1.93 ** KEPT (pick-wt=10): 8 [] -cUnsatisfiable(A)| -rp($f5(A),B)|cowlThing($f2(A,B)).
% 1.72/1.93 ** KEPT (pick-wt=11): 9 [] -cUnsatisfiable(A)| -rp($f5(A),B)|rp(B,$f3(A,B)).
% 1.72/1.93 ** KEPT (pick-wt=10): 10 [] -cUnsatisfiable(A)| -rp($f5(A),B)|cowlThing($f3(A,B)).
% 1.72/1.93 ** KEPT (pick-wt=11): 11 [] -cUnsatisfiable(A)| -rp($f5(A),B)| -rr(B,C)|cc(C).
% 1.72/1.93 ** KEPT (pick-wt=7): 12 [] -cUnsatisfiable(A)|rr($f5(A),$f4(A)).
% 1.72/1.93 ** KEPT (pick-wt=5): 13 [] -cUnsatisfiable(A)|cowlThing($f4(A)).
% 1.72/1.93 ** KEPT (pick-wt=4): 14 [] -cUnsatisfiable(A)|ca(A).
% 1.72/1.93 ** KEPT (pick-wt=13): 15 [] -cc(A)| -rinvR(A,B)| -rinvP(B,C)| -rinvS(C,D)| -ca(D).
% 1.72/1.93 ** KEPT (pick-wt=6): 16 [] -rinvP(A,B)|rp(B,A).
% 1.72/1.93 ** KEPT (pick-wt=6): 17 [] rinvP(A,B)| -rp(B,A).
% 1.72/1.93 ** KEPT (pick-wt=6): 18 [] -rinvR(A,B)|rr(B,A).
% 1.72/1.93 ** KEPT (pick-wt=6): 19 [] rinvR(A,B)| -rr(B,A).
% 1.72/1.93 ** KEPT (pick-wt=6): 20 [] -rinvS(A,B)|rs(B,A).
% 1.72/1.93 ** KEPT (pick-wt=6): 21 [] rinvS(A,B)| -rs(B,A).
% 1.72/1.93 ** KEPT (pick-wt=9): 22 [] -rp(A,B)| -rp(B,C)|rp(A,C).
% 1.72/1.93
% 1.72/1.93 ------------> process sos:
% 1.72/1.93 ** KEPT (pick-wt=2): 23 [] cowlThing(A).
% 1.72/1.93 ** KEPT (pick-wt=4): 24 [] xsd_string(A)|xsd_integer(A).
% 1.72/1.93 ** KEPT (pick-wt=6): 25 [] cc(A)|rinvR(A,$f8(A)).
% 1.72/1.93 ** KEPT (pick-wt=7): 26 [] cc(A)|rinvP($f8(A),$f7(A)).
% 1.72/1.93 ** KEPT (pick-wt=7): 27 [] cc(A)|rinvS($f7(A),$f6(A)).
% 1.72/1.93 ** KEPT (pick-wt=5): 28 [] cc(A)|ca($f6(A)).
% 1.72/1.93 ** KEPT (pick-wt=2): 29 [] cUnsatisfiable(i2003_11_14_17_19_28752).
% 1.72/1.93 23 back subsumes 13.
% 1.72/1.93 23 back subsumes 10.
% 1.72/1.93 23 back subsumes 8.
% 1.72/1.93 23 back subsumes 5.
% 1.72/1.93
% 1.72/1.93 ======= end of input processing =======
% 1.72/1.93
% 1.72/1.93 =========== start of search ===========
% 1.72/1.93
% 1.72/1.93 -------- PROOF --------
% 1.72/1.93
% 1.72/1.93 -----> EMPTY CLAUSE at 0.00 sec ----> 47 [hyper,42,15,43,37,34,30] $F.
% 1.72/1.93
% 1.72/1.93 Length of proof is 8. Level of proof is 3.
% 1.72/1.93
% 1.72/1.93 ---------------- PROOF ----------------
% 1.72/1.93 % SZS status Theorem
% 1.72/1.93 % SZS output start Refutation
% See solution above
% 1.72/1.93 ------------ end of proof -------------
% 1.72/1.93
% 1.72/1.93
% 1.72/1.93 Search stopped by max_proofs option.
% 1.72/1.93
% 1.72/1.93
% 1.72/1.93 Search stopped by max_proofs option.
% 1.72/1.93
% 1.72/1.93 ============ end of search ============
% 1.72/1.93
% 1.72/1.93 -------------- statistics -------------
% 1.72/1.93 clauses given 21
% 1.72/1.93 clauses generated 24
% 1.72/1.93 clauses kept 46
% 1.72/1.93 clauses forward subsumed 5
% 1.72/1.93 clauses back subsumed 4
% 1.72/1.93 Kbytes malloced 976
% 1.72/1.93
% 1.72/1.93 ----------- times (seconds) -----------
% 1.72/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.93 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.93
% 1.72/1.93 That finishes the proof of the theorem.
% 1.72/1.93
% 1.72/1.93 Process 7667 finished Wed Jul 27 03:47:38 2022
% 1.72/1.93 Otter interrupted
% 1.72/1.93 PROOF FOUND
%------------------------------------------------------------------------------