TSTP Solution File: KRS073+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS073+1 : TPTP v8.1.0. Released v3.1.0.
% 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 13:01:04 EDT 2022
% Result : Unsatisfiable 1.65s 1.85s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 30 ( 2 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(21,axiom,
( ~ cUnsatisfiable(A)
| rf(A,dollar_f2(A)) ),
file('KRS073+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvS(dollar_f2(A),B)
| cp(B) ),
file('KRS073+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvF(dollar_f2(A),B)
| rs(B,dollar_f1(A,B)) ),
file('KRS073+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ cUnsatisfiable(A)
| ~ cp(A) ),
file('KRS073+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ rf(A,B)
| ~ rf(A,C)
| B = C ),
file('KRS073+1.p',unknown),
[] ).
cnf(33,axiom,
( rinvF(A,B)
| ~ rf(B,A) ),
file('KRS073+1.p',unknown),
[] ).
cnf(37,axiom,
( rinvS(A,B)
| ~ rs(B,A) ),
file('KRS073+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ rs(A,B)
| rf(A,B) ),
file('KRS073+1.p',unknown),
[] ).
cnf(48,axiom,
cUnsatisfiable(i2003_11_14_17_18_54369),
file('KRS073+1.p',unknown),
[] ).
cnf(49,plain,
rf(i2003_11_14_17_18_54369,dollar_f2(i2003_11_14_17_18_54369)),
inference(hyper,[status(thm)],[48,21]),
[iquote('hyper,48,21')] ).
cnf(53,plain,
rinvF(dollar_f2(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(hyper,[status(thm)],[49,33]),
[iquote('hyper,49,33')] ).
cnf(67,plain,
rs(i2003_11_14_17_18_54369,dollar_f1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)),
inference(hyper,[status(thm)],[53,23,48]),
[iquote('hyper,53,23,48')] ).
cnf(86,plain,
rf(i2003_11_14_17_18_54369,dollar_f1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)),
inference(hyper,[status(thm)],[67,40]),
[iquote('hyper,67,40')] ).
cnf(88,plain,
rinvS(dollar_f1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(hyper,[status(thm)],[67,37]),
[iquote('hyper,67,37')] ).
cnf(102,plain,
dollar_f2(i2003_11_14_17_18_54369) = dollar_f1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369),
inference(hyper,[status(thm)],[86,30,49]),
[iquote('hyper,86,30,49')] ).
cnf(176,plain,
( ~ rinvS(dollar_f1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369),A)
| cp(A) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[102,22]),48]),
[iquote('para_from,102.1.1,22.2.1,unit_del,48')] ).
cnf(177,plain,
cp(i2003_11_14_17_18_54369),
inference(hyper,[status(thm)],[176,88]),
[iquote('hyper,176,88')] ).
cnf(187,plain,
$false,
inference(hyper,[status(thm)],[177,25,48]),
[iquote('hyper,177,25,48')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS073+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 03:30:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.85 ----- Otter 3.3f, August 2004 -----
% 1.65/1.85 The process was started by sandbox on n024.cluster.edu,
% 1.65/1.85 Wed Jul 27 03:30:10 2022
% 1.65/1.85 The command was "./otter". The process ID is 9966.
% 1.65/1.85
% 1.65/1.85 set(prolog_style_variables).
% 1.65/1.85 set(auto).
% 1.65/1.85 dependent: set(auto1).
% 1.65/1.85 dependent: set(process_input).
% 1.65/1.85 dependent: clear(print_kept).
% 1.65/1.85 dependent: clear(print_new_demod).
% 1.65/1.85 dependent: clear(print_back_demod).
% 1.65/1.85 dependent: clear(print_back_sub).
% 1.65/1.85 dependent: set(control_memory).
% 1.65/1.85 dependent: assign(max_mem, 12000).
% 1.65/1.85 dependent: assign(pick_given_ratio, 4).
% 1.65/1.85 dependent: assign(stats_level, 1).
% 1.65/1.85 dependent: assign(max_seconds, 10800).
% 1.65/1.85 clear(print_given).
% 1.65/1.85
% 1.65/1.85 formula_list(usable).
% 1.65/1.85 all A (A=A).
% 1.65/1.85 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.65/1.85 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.65/1.85 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.65/1.85 all A B (A=B&cp(A)->cp(B)).
% 1.65/1.85 all A B C (A=B&rf(A,C)->rf(B,C)).
% 1.65/1.85 all A B C (A=B&rf(C,A)->rf(C,B)).
% 1.65/1.85 all A B C (A=B&rf1(A,C)->rf1(B,C)).
% 1.65/1.85 all A B C (A=B&rf1(C,A)->rf1(C,B)).
% 1.65/1.85 all A B C (A=B&rinvF(A,C)->rinvF(B,C)).
% 1.65/1.85 all A B C (A=B&rinvF(C,A)->rinvF(C,B)).
% 1.65/1.85 all A B C (A=B&rinvF1(A,C)->rinvF1(B,C)).
% 1.65/1.85 all A B C (A=B&rinvF1(C,A)->rinvF1(C,B)).
% 1.65/1.85 all A B C (A=B&rinvS(A,C)->rinvS(B,C)).
% 1.65/1.85 all A B C (A=B&rinvS(C,A)->rinvS(C,B)).
% 1.65/1.85 all A B C (A=B&rs(A,C)->rs(B,C)).
% 1.65/1.85 all A B C (A=B&rs(C,A)->rs(C,B)).
% 1.65/1.85 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.65/1.85 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.65/1.85 all X (cowlThing(X)& -cowlNothing(X)).
% 1.65/1.85 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.65/1.85 all X (cUnsatisfiable(X)<-> (exists Y (rf(X,Y)& (all Z (rinvS(Y,Z)->cp(Z)))& (all Z (rinvF(Y,Z)-> (exists W (rs(Z,W)&cp(W)))))))& -cp(X)).
% 1.65/1.85 all X Y Z (rf(X,Y)&rf(X,Z)->Y=Z).
% 1.65/1.85 all X Y Z (rf1(X,Y)&rf1(X,Z)->Y=Z).
% 1.65/1.85 all X Y (rinvF(X,Y)<->rf(Y,X)).
% 1.65/1.85 all X Y (rinvF1(X,Y)<->rf1(Y,X)).
% 1.65/1.85 all X Y (rinvS(X,Y)<->rs(Y,X)).
% 1.65/1.85 all X Y Z (rs(X,Y)&rs(X,Z)->Y=Z).
% 1.65/1.85 cUnsatisfiable(i2003_11_14_17_18_54369).
% 1.65/1.85 all X Y (rs(X,Y)->rf1(X,Y)).
% 1.65/1.85 all X Y (rs(X,Y)->rf(X,Y)).
% 1.65/1.85 end_of_list.
% 1.65/1.85
% 1.65/1.85 -------> usable clausifies to:
% 1.65/1.85
% 1.65/1.85 list(usable).
% 1.65/1.85 0 [] A=A.
% 1.65/1.85 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.65/1.85 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.65/1.85 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.65/1.85 0 [] A!=B| -cp(A)|cp(B).
% 1.65/1.85 0 [] A!=B| -rf(A,C)|rf(B,C).
% 1.65/1.85 0 [] A!=B| -rf(C,A)|rf(C,B).
% 1.65/1.85 0 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.65/1.85 0 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.65/1.85 0 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 1.65/1.85 0 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 1.65/1.85 0 [] A!=B| -rinvF1(A,C)|rinvF1(B,C).
% 1.65/1.85 0 [] A!=B| -rinvF1(C,A)|rinvF1(C,B).
% 1.65/1.85 0 [] A!=B| -rinvS(A,C)|rinvS(B,C).
% 1.65/1.85 0 [] A!=B| -rinvS(C,A)|rinvS(C,B).
% 1.65/1.85 0 [] A!=B| -rs(A,C)|rs(B,C).
% 1.65/1.85 0 [] A!=B| -rs(C,A)|rs(C,B).
% 1.65/1.85 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.65/1.85 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.65/1.85 0 [] cowlThing(X).
% 1.65/1.85 0 [] -cowlNothing(X).
% 1.65/1.85 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.65/1.85 0 [] xsd_string(X)|xsd_integer(X).
% 1.65/1.85 0 [] -cUnsatisfiable(X)|rf(X,$f2(X)).
% 1.65/1.85 0 [] -cUnsatisfiable(X)| -rinvS($f2(X),Z)|cp(Z).
% 1.65/1.85 0 [] -cUnsatisfiable(X)| -rinvF($f2(X),X1)|rs(X1,$f1(X,X1)).
% 1.65/1.85 0 [] -cUnsatisfiable(X)| -rinvF($f2(X),X1)|cp($f1(X,X1)).
% 1.65/1.85 0 [] -cUnsatisfiable(X)| -cp(X).
% 1.65/1.85 0 [] cUnsatisfiable(X)| -rf(X,Y)|rinvS(Y,$f3(X,Y))|rinvF(Y,$f4(X,Y))|cp(X).
% 1.65/1.85 0 [] cUnsatisfiable(X)| -rf(X,Y)|rinvS(Y,$f3(X,Y))| -rs($f4(X,Y),W)| -cp(W)|cp(X).
% 1.65/1.85 0 [] cUnsatisfiable(X)| -rf(X,Y)| -cp($f3(X,Y))|rinvF(Y,$f4(X,Y))|cp(X).
% 1.65/1.85 0 [] cUnsatisfiable(X)| -rf(X,Y)| -cp($f3(X,Y))| -rs($f4(X,Y),W)| -cp(W)|cp(X).
% 1.65/1.85 0 [] -rf(X,Y)| -rf(X,Z)|Y=Z.
% 1.65/1.85 0 [] -rf1(X,Y)| -rf1(X,Z)|Y=Z.
% 1.65/1.85 0 [] -rinvF(X,Y)|rf(Y,X).
% 1.65/1.85 0 [] rinvF(X,Y)| -rf(Y,X).
% 1.65/1.85 0 [] -rinvF1(X,Y)|rf1(Y,X).
% 1.65/1.85 0 [] rinvF1(X,Y)| -rf1(Y,X).
% 1.65/1.85 0 [] -rinvS(X,Y)|rs(Y,X).
% 1.65/1.85 0 [] rinvS(X,Y)| -rs(Y,X).
% 1.65/1.85 0 [] -rs(X,Y)| -rs(X,Z)|Y=Z.
% 1.65/1.85 0 [] cUnsatisfiable(i2003_11_14_17_18_54369).
% 1.65/1.85 0 [] -rs(X,Y)|rf1(X,Y).
% 1.65/1.85 0 [] -rs(X,Y)|rf(X,Y).
% 1.65/1.85 end_of_list.
% 1.65/1.85
% 1.65/1.85 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.65/1.85
% 1.65/1.85 This ia a non-Horn set with equality. The strategy will be
% 1.65/1.85 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.65/1.85 deletion, with positive clauses in sos and nonpositive
% 1.65/1.85 clauses in usable.
% 1.65/1.85
% 1.65/1.85 dependent: set(knuth_bendix).
% 1.65/1.85 dependent: set(anl_eq).
% 1.65/1.85 dependent: set(para_from).
% 1.65/1.85 dependent: set(para_into).
% 1.65/1.85 dependent: clear(para_from_right).
% 1.65/1.85 dependent: clear(para_into_right).
% 1.65/1.85 dependent: set(para_from_vars).
% 1.65/1.85 dependent: set(eq_units_both_ways).
% 1.65/1.85 dependent: set(dynamic_demod_all).
% 1.65/1.85 dependent: set(dynamic_demod).
% 1.65/1.85 dependent: set(order_eq).
% 1.65/1.85 dependent: set(back_demod).
% 1.65/1.85 dependent: set(lrpo).
% 1.65/1.85 dependent: set(hyper_res).
% 1.65/1.85 dependent: set(unit_deletion).
% 1.65/1.85 dependent: set(factor).
% 1.65/1.85
% 1.65/1.85 ------------> process usable:
% 1.65/1.85 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.65/1.85 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.65/1.85 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.65/1.85 ** KEPT (pick-wt=7): 4 [] A!=B| -cp(A)|cp(B).
% 1.65/1.85 ** KEPT (pick-wt=9): 5 [] A!=B| -rf(A,C)|rf(B,C).
% 1.65/1.85 ** KEPT (pick-wt=9): 6 [] A!=B| -rf(C,A)|rf(C,B).
% 1.65/1.85 ** KEPT (pick-wt=9): 7 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.65/1.85 ** KEPT (pick-wt=9): 8 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.65/1.85 ** KEPT (pick-wt=9): 9 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 1.65/1.85 ** KEPT (pick-wt=9): 10 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 1.65/1.85 ** KEPT (pick-wt=9): 11 [] A!=B| -rinvF1(A,C)|rinvF1(B,C).
% 1.65/1.85 ** KEPT (pick-wt=9): 12 [] A!=B| -rinvF1(C,A)|rinvF1(C,B).
% 1.65/1.85 ** KEPT (pick-wt=9): 13 [] A!=B| -rinvS(A,C)|rinvS(B,C).
% 1.65/1.85 ** KEPT (pick-wt=9): 14 [] A!=B| -rinvS(C,A)|rinvS(C,B).
% 1.65/1.85 ** KEPT (pick-wt=9): 15 [] A!=B| -rs(A,C)|rs(B,C).
% 1.65/1.85 ** KEPT (pick-wt=9): 16 [] A!=B| -rs(C,A)|rs(C,B).
% 1.65/1.85 ** KEPT (pick-wt=7): 17 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.65/1.85 ** KEPT (pick-wt=7): 18 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.65/1.85 ** KEPT (pick-wt=2): 19 [] -cowlNothing(A).
% 1.65/1.85 ** KEPT (pick-wt=4): 20 [] -xsd_string(A)| -xsd_integer(A).
% 1.65/1.85 ** KEPT (pick-wt=6): 21 [] -cUnsatisfiable(A)|rf(A,$f2(A)).
% 1.65/1.85 ** KEPT (pick-wt=8): 22 [] -cUnsatisfiable(A)| -rinvS($f2(A),B)|cp(B).
% 1.65/1.85 ** KEPT (pick-wt=11): 23 [] -cUnsatisfiable(A)| -rinvF($f2(A),B)|rs(B,$f1(A,B)).
% 1.65/1.85 ** KEPT (pick-wt=10): 24 [] -cUnsatisfiable(A)| -rinvF($f2(A),B)|cp($f1(A,B)).
% 1.65/1.85 ** KEPT (pick-wt=4): 25 [] -cUnsatisfiable(A)| -cp(A).
% 1.65/1.85 ** KEPT (pick-wt=17): 26 [] cUnsatisfiable(A)| -rf(A,B)|rinvS(B,$f3(A,B))|rinvF(B,$f4(A,B))|cp(A).
% 1.65/1.85 ** KEPT (pick-wt=19): 27 [] cUnsatisfiable(A)| -rf(A,B)|rinvS(B,$f3(A,B))| -rs($f4(A,B),C)| -cp(C)|cp(A).
% 1.65/1.85 ** KEPT (pick-wt=16): 28 [] cUnsatisfiable(A)| -rf(A,B)| -cp($f3(A,B))|rinvF(B,$f4(A,B))|cp(A).
% 1.65/1.85 ** KEPT (pick-wt=18): 29 [] cUnsatisfiable(A)| -rf(A,B)| -cp($f3(A,B))| -rs($f4(A,B),C)| -cp(C)|cp(A).
% 1.65/1.85 ** KEPT (pick-wt=9): 30 [] -rf(A,B)| -rf(A,C)|B=C.
% 1.65/1.85 ** KEPT (pick-wt=9): 31 [] -rf1(A,B)| -rf1(A,C)|B=C.
% 1.65/1.85 ** KEPT (pick-wt=6): 32 [] -rinvF(A,B)|rf(B,A).
% 1.65/1.85 ** KEPT (pick-wt=6): 33 [] rinvF(A,B)| -rf(B,A).
% 1.65/1.85 ** KEPT (pick-wt=6): 34 [] -rinvF1(A,B)|rf1(B,A).
% 1.65/1.85 ** KEPT (pick-wt=6): 35 [] rinvF1(A,B)| -rf1(B,A).
% 1.65/1.85 ** KEPT (pick-wt=6): 36 [] -rinvS(A,B)|rs(B,A).
% 1.65/1.85 ** KEPT (pick-wt=6): 37 [] rinvS(A,B)| -rs(B,A).
% 1.65/1.85 ** KEPT (pick-wt=9): 38 [] -rs(A,B)| -rs(A,C)|B=C.
% 1.65/1.85 ** KEPT (pick-wt=6): 39 [] -rs(A,B)|rf1(A,B).
% 1.65/1.85 ** KEPT (pick-wt=6): 40 [] -rs(A,B)|rf(A,B).
% 1.65/1.85 19 back subsumes 2.
% 1.65/1.85
% 1.65/1.85 ------------> process sos:
% 1.65/1.85 ** KEPT (pick-wt=3): 45 [] A=A.
% 1.65/1.85 ** KEPT (pick-wt=2): 46 [] cowlThing(A).
% 1.65/1.85 ** KEPT (pick-wt=4): 47 [] xsd_string(A)|xsd_integer(A).
% 1.65/1.85 ** KEPT (pick-wt=2): 48 [] cUnsatisfiable(i2003_11_14_17_18_54369).
% 1.65/1.85 Following clause subsumed by 45 during input processing: 0 [copy,45,flip.1] A=A.
% 1.65/1.85 45 back subsumes 44.
% 1.65/1.85 45 back subsumes 43.
% 1.65/1.85 45 back subsumes 42.
% 1.65/1.85 46 back subsumes 3.
% 1.65/1.85
% 1.65/1.85 ======= end of input processing =======
% 1.65/1.85
% 1.65/1.85 =========== start of search ===========
% 1.65/1.85
% 1.65/1.85 -------- PROOF --------
% 1.65/1.85
% 1.65/1.85 -----> EMPTY CLAUSE at 0.01 sec ----> 187 [hyper,177,25,48] $F.
% 1.65/1.85
% 1.65/1.85 Length of proof is 8. Level of proof is 7.
% 1.65/1.85
% 1.65/1.85 ---------------- PROOF ----------------
% 1.65/1.85 % SZS status Theorem
% 1.65/1.85 % SZS output start Refutation
% See solution above
% 1.65/1.85 ------------ end of proof -------------
% 1.65/1.85
% 1.65/1.85
% 1.65/1.85 Search stopped by max_proofs option.
% 1.65/1.85
% 1.65/1.85
% 1.65/1.85 Search stopped by max_proofs option.
% 1.65/1.85
% 1.65/1.85 ============ end of search ============
% 1.65/1.85
% 1.65/1.85 -------------- statistics -------------
% 1.65/1.85 clauses given 19
% 1.65/1.85 clauses generated 327
% 1.65/1.85 clauses kept 185
% 1.65/1.85 clauses forward subsumed 200
% 1.65/1.85 clauses back subsumed 5
% 1.65/1.85 Kbytes malloced 976
% 1.65/1.85
% 1.65/1.85 ----------- times (seconds) -----------
% 1.65/1.85 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.85 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.85 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.85
% 1.65/1.85 That finishes the proof of the theorem.
% 1.65/1.85
% 1.65/1.85 Process 9966 finished Wed Jul 27 03:30:11 2022
% 1.65/1.85 Otter interrupted
% 1.65/1.85 PROOF FOUND
%------------------------------------------------------------------------------