TSTP Solution File: KRS106+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS106+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:01:09 EDT 2022
% Result : Unsatisfiable 1.78s 2.01s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 25 RR)
% Number of literals : 38 ( 4 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| rf3(A,dollar_f1(A)) ),
file('KRS106+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ cUnsatisfiable(A)
| rf1(A,dollar_f2(A)) ),
file('KRS106+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ cUnsatisfiable(A)
| cp1(dollar_f2(A)) ),
file('KRS106+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ cUnsatisfiable(A)
| rf2(A,dollar_f3(A)) ),
file('KRS106+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ cUnsatisfiable(A)
| cp1xcomp(dollar_f3(A)) ),
file('KRS106+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ cp1(A)
| ~ ra_Px1(A,B) ),
file('KRS106+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ cp1xcomp(A)
| ra_Px1(A,dollar_f5(A)) ),
file('KRS106+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ rf1(A,B)
| ~ rf1(A,C)
| B = C ),
file('KRS106+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ rf2(A,B)
| ~ rf2(A,C)
| B = C ),
file('KRS106+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ rf3(A,B)
| rf1(A,B) ),
file('KRS106+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ rf3(A,B)
| rf2(A,B) ),
file('KRS106+1.p',unknown),
[] ).
cnf(41,axiom,
cUnsatisfiable(i2003_11_14_17_20_57644),
file('KRS106+1.p',unknown),
[] ).
cnf(42,plain,
cp1xcomp(dollar_f3(i2003_11_14_17_20_57644)),
inference(hyper,[status(thm)],[41,24]),
[iquote('hyper,41,24')] ).
cnf(43,plain,
rf2(i2003_11_14_17_20_57644,dollar_f3(i2003_11_14_17_20_57644)),
inference(hyper,[status(thm)],[41,23]),
[iquote('hyper,41,23')] ).
cnf(44,plain,
cp1(dollar_f2(i2003_11_14_17_20_57644)),
inference(hyper,[status(thm)],[41,22]),
[iquote('hyper,41,22')] ).
cnf(45,plain,
rf1(i2003_11_14_17_20_57644,dollar_f2(i2003_11_14_17_20_57644)),
inference(hyper,[status(thm)],[41,21]),
[iquote('hyper,41,21')] ).
cnf(47,plain,
rf3(i2003_11_14_17_20_57644,dollar_f1(i2003_11_14_17_20_57644)),
inference(hyper,[status(thm)],[41,19]),
[iquote('hyper,41,19')] ).
cnf(51,plain,
ra_Px1(dollar_f3(i2003_11_14_17_20_57644),dollar_f5(dollar_f3(i2003_11_14_17_20_57644))),
inference(hyper,[status(thm)],[42,27]),
[iquote('hyper,42,27')] ).
cnf(88,plain,
rf2(i2003_11_14_17_20_57644,dollar_f1(i2003_11_14_17_20_57644)),
inference(hyper,[status(thm)],[47,33]),
[iquote('hyper,47,33')] ).
cnf(89,plain,
rf1(i2003_11_14_17_20_57644,dollar_f1(i2003_11_14_17_20_57644)),
inference(hyper,[status(thm)],[47,32]),
[iquote('hyper,47,32')] ).
cnf(103,plain,
dollar_f3(i2003_11_14_17_20_57644) = dollar_f1(i2003_11_14_17_20_57644),
inference(hyper,[status(thm)],[88,30,43]),
[iquote('hyper,88,30,43')] ).
cnf(113,plain,
ra_Px1(dollar_f1(i2003_11_14_17_20_57644),dollar_f5(dollar_f1(i2003_11_14_17_20_57644))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[51]),103,103]),
[iquote('back_demod,51,demod,103,103')] ).
cnf(122,plain,
dollar_f2(i2003_11_14_17_20_57644) = dollar_f1(i2003_11_14_17_20_57644),
inference(hyper,[status(thm)],[89,29,45]),
[iquote('hyper,89,29,45')] ).
cnf(132,plain,
cp1(dollar_f1(i2003_11_14_17_20_57644)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),122]),
[iquote('back_demod,44,demod,122')] ).
cnf(148,plain,
$false,
inference(hyper,[status(thm)],[113,26,132]),
[iquote('hyper,113,26,132')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KRS106+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 03:31:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.78/2.00 ----- Otter 3.3f, August 2004 -----
% 1.78/2.00 The process was started by sandbox2 on n014.cluster.edu,
% 1.78/2.00 Wed Jul 27 03:31:09 2022
% 1.78/2.00 The command was "./otter". The process ID is 23050.
% 1.78/2.00
% 1.78/2.00 set(prolog_style_variables).
% 1.78/2.00 set(auto).
% 1.78/2.00 dependent: set(auto1).
% 1.78/2.00 dependent: set(process_input).
% 1.78/2.00 dependent: clear(print_kept).
% 1.78/2.00 dependent: clear(print_new_demod).
% 1.78/2.00 dependent: clear(print_back_demod).
% 1.78/2.00 dependent: clear(print_back_sub).
% 1.78/2.00 dependent: set(control_memory).
% 1.78/2.00 dependent: assign(max_mem, 12000).
% 1.78/2.00 dependent: assign(pick_given_ratio, 4).
% 1.78/2.00 dependent: assign(stats_level, 1).
% 1.78/2.00 dependent: assign(max_seconds, 10800).
% 1.78/2.00 clear(print_given).
% 1.78/2.00
% 1.78/2.00 formula_list(usable).
% 1.78/2.00 all A (A=A).
% 1.78/2.00 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.78/2.00 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.78/2.00 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.78/2.00 all A B (A=B&cp1(A)->cp1(B)).
% 1.78/2.00 all A B (A=B&cp1xcomp(A)->cp1xcomp(B)).
% 1.78/2.00 all A B (A=B&cp2(A)->cp2(B)).
% 1.78/2.00 all A B C (A=B&ra_Px1(A,C)->ra_Px1(B,C)).
% 1.78/2.00 all A B C (A=B&ra_Px1(C,A)->ra_Px1(C,B)).
% 1.78/2.00 all A B C (A=B&rf1(A,C)->rf1(B,C)).
% 1.78/2.00 all A B C (A=B&rf1(C,A)->rf1(C,B)).
% 1.78/2.00 all A B C (A=B&rf2(A,C)->rf2(B,C)).
% 1.78/2.00 all A B C (A=B&rf2(C,A)->rf2(C,B)).
% 1.78/2.00 all A B C (A=B&rf3(A,C)->rf3(B,C)).
% 1.78/2.00 all A B C (A=B&rf3(C,A)->rf3(C,B)).
% 1.78/2.00 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.78/2.00 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.78/2.00 all X (cowlThing(X)& -cowlNothing(X)).
% 1.78/2.00 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.78/2.00 all X (cUnsatisfiable(X)<-> (exists Y (rf3(X,Y)&cp2(Y)))& (exists Y (rf1(X,Y)&cp1(Y)))& (exists Y (rf2(X,Y)&cp1xcomp(Y)))).
% 1.78/2.00 all X (cp1(X)<-> -(exists Y ra_Px1(X,Y))).
% 1.78/2.00 all X (cp1xcomp(X)<-> (exists Y0 ra_Px1(X,Y0))).
% 1.78/2.00 all X Y Z (rf1(X,Y)&rf1(X,Z)->Y=Z).
% 1.78/2.00 all X Y Z (rf2(X,Y)&rf2(X,Z)->Y=Z).
% 1.78/2.00 all X Y Z (rf3(X,Y)&rf3(X,Z)->Y=Z).
% 1.78/2.00 cUnsatisfiable(i2003_11_14_17_20_57644).
% 1.78/2.00 all X Y (rf3(X,Y)->rf1(X,Y)).
% 1.78/2.00 all X Y (rf3(X,Y)->rf2(X,Y)).
% 1.78/2.00 end_of_list.
% 1.78/2.00
% 1.78/2.00 -------> usable clausifies to:
% 1.78/2.00
% 1.78/2.00 list(usable).
% 1.78/2.00 0 [] A=A.
% 1.78/2.00 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.78/2.00 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.78/2.00 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.78/2.00 0 [] A!=B| -cp1(A)|cp1(B).
% 1.78/2.00 0 [] A!=B| -cp1xcomp(A)|cp1xcomp(B).
% 1.78/2.00 0 [] A!=B| -cp2(A)|cp2(B).
% 1.78/2.00 0 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.78/2.00 0 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.78/2.00 0 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.78/2.00 0 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.78/2.00 0 [] A!=B| -rf2(A,C)|rf2(B,C).
% 1.78/2.00 0 [] A!=B| -rf2(C,A)|rf2(C,B).
% 1.78/2.00 0 [] A!=B| -rf3(A,C)|rf3(B,C).
% 1.78/2.00 0 [] A!=B| -rf3(C,A)|rf3(C,B).
% 1.78/2.00 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.78/2.00 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.78/2.00 0 [] cowlThing(X).
% 1.78/2.00 0 [] -cowlNothing(X).
% 1.78/2.00 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.78/2.00 0 [] xsd_string(X)|xsd_integer(X).
% 1.78/2.00 0 [] -cUnsatisfiable(X)|rf3(X,$f1(X)).
% 1.78/2.00 0 [] -cUnsatisfiable(X)|cp2($f1(X)).
% 1.78/2.00 0 [] -cUnsatisfiable(X)|rf1(X,$f2(X)).
% 1.78/2.00 0 [] -cUnsatisfiable(X)|cp1($f2(X)).
% 1.78/2.00 0 [] -cUnsatisfiable(X)|rf2(X,$f3(X)).
% 1.78/2.00 0 [] -cUnsatisfiable(X)|cp1xcomp($f3(X)).
% 1.78/2.00 0 [] cUnsatisfiable(X)| -rf3(X,Y)| -cp2(Y)| -rf1(X,X1)| -cp1(X1)| -rf2(X,X2)| -cp1xcomp(X2).
% 1.78/2.00 0 [] -cp1(X)| -ra_Px1(X,Y).
% 1.78/2.00 0 [] cp1(X)|ra_Px1(X,$f4(X)).
% 1.78/2.00 0 [] -cp1xcomp(X)|ra_Px1(X,$f5(X)).
% 1.78/2.00 0 [] cp1xcomp(X)| -ra_Px1(X,Y0).
% 1.78/2.00 0 [] -rf1(X,Y)| -rf1(X,Z)|Y=Z.
% 1.78/2.00 0 [] -rf2(X,Y)| -rf2(X,Z)|Y=Z.
% 1.78/2.00 0 [] -rf3(X,Y)| -rf3(X,Z)|Y=Z.
% 1.78/2.00 0 [] cUnsatisfiable(i2003_11_14_17_20_57644).
% 1.78/2.00 0 [] -rf3(X,Y)|rf1(X,Y).
% 1.78/2.00 0 [] -rf3(X,Y)|rf2(X,Y).
% 1.78/2.00 end_of_list.
% 1.78/2.00
% 1.78/2.00 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.78/2.00
% 1.78/2.00 This ia a non-Horn set with equality. The strategy will be
% 1.78/2.00 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.78/2.00 deletion, with positive clauses in sos and nonpositive
% 1.78/2.00 clauses in usable.
% 1.78/2.00
% 1.78/2.00 dependent: set(knuth_bendix).
% 1.78/2.00 dependent: set(anl_eq).
% 1.78/2.00 dependent: set(para_from).
% 1.78/2.00 dependent: set(para_into).
% 1.78/2.00 dependent: clear(para_from_right).
% 1.78/2.00 dependent: clear(para_into_right).
% 1.78/2.00 dependent: set(para_from_vars).
% 1.78/2.00 dependent: set(eq_units_both_ways).
% 1.78/2.00 dependent: set(dynamic_demod_all).
% 1.78/2.00 dependent: set(dynamic_demod).
% 1.78/2.00 dependent: set(order_eq).
% 1.78/2.00 dependent: set(back_demod).
% 1.78/2.00 dependent: set(lrpo).
% 1.78/2.00 dependent: set(hyper_res).
% 1.78/2.00 dependent: set(unit_deletion).
% 1.78/2.00 dependent: set(factor).
% 1.78/2.00
% 1.78/2.00 ------------> process usable:
% 1.78/2.00 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.78/2.00 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.78/2.01 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.78/2.01 ** KEPT (pick-wt=7): 4 [] A!=B| -cp1(A)|cp1(B).
% 1.78/2.01 ** KEPT (pick-wt=7): 5 [] A!=B| -cp1xcomp(A)|cp1xcomp(B).
% 1.78/2.01 ** KEPT (pick-wt=7): 6 [] A!=B| -cp2(A)|cp2(B).
% 1.78/2.01 ** KEPT (pick-wt=9): 7 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.78/2.01 ** KEPT (pick-wt=9): 8 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.78/2.01 ** KEPT (pick-wt=9): 9 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.78/2.01 ** KEPT (pick-wt=9): 10 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.78/2.01 ** KEPT (pick-wt=9): 11 [] A!=B| -rf2(A,C)|rf2(B,C).
% 1.78/2.01 ** KEPT (pick-wt=9): 12 [] A!=B| -rf2(C,A)|rf2(C,B).
% 1.78/2.01 ** KEPT (pick-wt=9): 13 [] A!=B| -rf3(A,C)|rf3(B,C).
% 1.78/2.01 ** KEPT (pick-wt=9): 14 [] A!=B| -rf3(C,A)|rf3(C,B).
% 1.78/2.01 ** KEPT (pick-wt=7): 15 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.78/2.01 ** KEPT (pick-wt=7): 16 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.78/2.01 ** KEPT (pick-wt=2): 17 [] -cowlNothing(A).
% 1.78/2.01 ** KEPT (pick-wt=4): 18 [] -xsd_string(A)| -xsd_integer(A).
% 1.78/2.01 ** KEPT (pick-wt=6): 19 [] -cUnsatisfiable(A)|rf3(A,$f1(A)).
% 1.78/2.01 ** KEPT (pick-wt=5): 20 [] -cUnsatisfiable(A)|cp2($f1(A)).
% 1.78/2.01 ** KEPT (pick-wt=6): 21 [] -cUnsatisfiable(A)|rf1(A,$f2(A)).
% 1.78/2.01 ** KEPT (pick-wt=5): 22 [] -cUnsatisfiable(A)|cp1($f2(A)).
% 1.78/2.01 ** KEPT (pick-wt=6): 23 [] -cUnsatisfiable(A)|rf2(A,$f3(A)).
% 1.78/2.01 ** KEPT (pick-wt=5): 24 [] -cUnsatisfiable(A)|cp1xcomp($f3(A)).
% 1.78/2.01 ** KEPT (pick-wt=17): 25 [] cUnsatisfiable(A)| -rf3(A,B)| -cp2(B)| -rf1(A,C)| -cp1(C)| -rf2(A,D)| -cp1xcomp(D).
% 1.78/2.01 ** KEPT (pick-wt=5): 26 [] -cp1(A)| -ra_Px1(A,B).
% 1.78/2.01 ** KEPT (pick-wt=6): 27 [] -cp1xcomp(A)|ra_Px1(A,$f5(A)).
% 1.78/2.01 ** KEPT (pick-wt=5): 28 [] cp1xcomp(A)| -ra_Px1(A,B).
% 1.78/2.01 ** KEPT (pick-wt=9): 29 [] -rf1(A,B)| -rf1(A,C)|B=C.
% 1.78/2.01 ** KEPT (pick-wt=9): 30 [] -rf2(A,B)| -rf2(A,C)|B=C.
% 1.78/2.01 ** KEPT (pick-wt=9): 31 [] -rf3(A,B)| -rf3(A,C)|B=C.
% 1.78/2.01 ** KEPT (pick-wt=6): 32 [] -rf3(A,B)|rf1(A,B).
% 1.78/2.01 ** KEPT (pick-wt=6): 33 [] -rf3(A,B)|rf2(A,B).
% 1.78/2.01 17 back subsumes 2.
% 1.78/2.01
% 1.78/2.01 ------------> process sos:
% 1.78/2.01 ** KEPT (pick-wt=3): 37 [] A=A.
% 1.78/2.01 ** KEPT (pick-wt=2): 38 [] cowlThing(A).
% 1.78/2.01 ** KEPT (pick-wt=4): 39 [] xsd_string(A)|xsd_integer(A).
% 1.78/2.01 ** KEPT (pick-wt=6): 40 [] cp1(A)|ra_Px1(A,$f4(A)).
% 1.78/2.01 ** KEPT (pick-wt=2): 41 [] cUnsatisfiable(i2003_11_14_17_20_57644).
% 1.78/2.01 Following clause subsumed by 37 during input processing: 0 [copy,37,flip.1] A=A.
% 1.78/2.01 37 back subsumes 36.
% 1.78/2.01 37 back subsumes 35.
% 1.78/2.01 37 back subsumes 34.
% 1.78/2.01 38 back subsumes 3.
% 1.78/2.01
% 1.78/2.01 ======= end of input processing =======
% 1.78/2.01
% 1.78/2.01 =========== start of search ===========
% 1.78/2.01
% 1.78/2.01 -------- PROOF --------
% 1.78/2.01
% 1.78/2.01 -----> EMPTY CLAUSE at 0.01 sec ----> 148 [hyper,113,26,132] $F.
% 1.78/2.01
% 1.78/2.01 Length of proof is 12. Level of proof is 4.
% 1.78/2.01
% 1.78/2.01 ---------------- PROOF ----------------
% 1.78/2.01 % SZS status Theorem
% 1.78/2.01 % SZS output start Refutation
% See solution above
% 1.78/2.01 ------------ end of proof -------------
% 1.78/2.01
% 1.78/2.01
% 1.78/2.01 Search stopped by max_proofs option.
% 1.78/2.01
% 1.78/2.01
% 1.78/2.01 Search stopped by max_proofs option.
% 1.78/2.01
% 1.78/2.01 ============ end of search ============
% 1.78/2.01
% 1.78/2.01 -------------- statistics -------------
% 1.78/2.01 clauses given 19
% 1.78/2.01 clauses generated 258
% 1.78/2.01 clauses kept 145
% 1.78/2.01 clauses forward subsumed 174
% 1.78/2.01 clauses back subsumed 5
% 1.78/2.01 Kbytes malloced 976
% 1.78/2.01
% 1.78/2.01 ----------- times (seconds) -----------
% 1.78/2.01 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.78/2.01 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.78/2.01 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.78/2.01
% 1.78/2.01 That finishes the proof of the theorem.
% 1.78/2.01
% 1.78/2.01 Process 23050 finished Wed Jul 27 03:31:11 2022
% 1.78/2.01 Otter interrupted
% 1.78/2.01 PROOF FOUND
%------------------------------------------------------------------------------