TSTP Solution File: KRS115+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS115+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:01:11 EDT 2022
% Result : Unsatisfiable 1.75s 1.96s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 28 ( 16 unt; 0 nHn; 27 RR)
% Number of literals : 44 ( 4 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 20 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| rf2(A,dollar_f1(A)) ),
file('KRS115+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ cUnsatisfiable(A)
| cp2(dollar_f1(A)) ),
file('KRS115+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ cUnsatisfiable(A)
| rf1(A,dollar_f2(A)) ),
file('KRS115+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ cUnsatisfiable(A)
| cp1(dollar_f2(A)) ),
file('KRS115+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f3(A)) ),
file('KRS115+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ cp1(A)
| cp2xcomp(A) ),
file('KRS115+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ cp2(A)
| ~ ra_Px1(A,B) ),
file('KRS115+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ cp2xcomp(A)
| ra_Px1(A,dollar_f5(A)) ),
file('KRS115+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ cowlThing(A)
| ~ rf1(A,B)
| ~ rf1(A,C)
| B = C ),
file('KRS115+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ cowlThing(A)
| ~ rf2(A,B)
| ~ rf2(A,C)
| B = C ),
file('KRS115+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ rr(A,B)
| rf2(A,B) ),
file('KRS115+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ rr(A,B)
| rf1(A,B) ),
file('KRS115+1.p',unknown),
[] ).
cnf(37,axiom,
cowlThing(A),
file('KRS115+1.p',unknown),
[] ).
cnf(40,axiom,
cUnsatisfiable(i2003_11_14_17_21_30578),
file('KRS115+1.p',unknown),
[] ).
cnf(41,plain,
rr(i2003_11_14_17_21_30578,dollar_f3(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[40,23]),
[iquote('hyper,40,23')] ).
cnf(42,plain,
cp1(dollar_f2(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[40,22]),
[iquote('hyper,40,22')] ).
cnf(43,plain,
rf1(i2003_11_14_17_21_30578,dollar_f2(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[40,21]),
[iquote('hyper,40,21')] ).
cnf(44,plain,
cp2(dollar_f1(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[40,20]),
[iquote('hyper,40,20')] ).
cnf(45,plain,
rf2(i2003_11_14_17_21_30578,dollar_f1(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[40,19]),
[iquote('hyper,40,19')] ).
cnf(48,plain,
cp2xcomp(dollar_f2(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[42,26]),
[iquote('hyper,42,26')] ).
cnf(57,plain,
ra_Px1(dollar_f2(i2003_11_14_17_21_30578),dollar_f5(dollar_f2(i2003_11_14_17_21_30578))),
inference(hyper,[status(thm)],[48,28]),
[iquote('hyper,48,28')] ).
cnf(62,plain,
rf1(i2003_11_14_17_21_30578,dollar_f3(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[41,33]),
[iquote('hyper,41,33')] ).
cnf(63,plain,
rf2(i2003_11_14_17_21_30578,dollar_f3(i2003_11_14_17_21_30578)),
inference(hyper,[status(thm)],[41,32]),
[iquote('hyper,41,32')] ).
cnf(85,plain,
dollar_f3(i2003_11_14_17_21_30578) = dollar_f2(i2003_11_14_17_21_30578),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[62,30,37,43])]),
[iquote('hyper,62,30,37,43,flip.1')] ).
cnf(90,plain,
rf2(i2003_11_14_17_21_30578,dollar_f2(i2003_11_14_17_21_30578)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),85]),
[iquote('back_demod,63,demod,85')] ).
cnf(93,plain,
dollar_f2(i2003_11_14_17_21_30578) = dollar_f1(i2003_11_14_17_21_30578),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[90,31,37,45])]),
[iquote('hyper,90,31,37,45,flip.1')] ).
cnf(107,plain,
ra_Px1(dollar_f1(i2003_11_14_17_21_30578),dollar_f5(dollar_f1(i2003_11_14_17_21_30578))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),93,93]),
[iquote('back_demod,57,demod,93,93')] ).
cnf(131,plain,
$false,
inference(hyper,[status(thm)],[107,27,44]),
[iquote('hyper,107,27,44')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS115+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 03:31:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox2 on n003.cluster.edu,
% 1.75/1.96 Wed Jul 27 03:31:11 2022
% 1.75/1.96 The command was "./otter". The process ID is 7212.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 formula_list(usable).
% 1.75/1.96 all A (A=A).
% 1.75/1.96 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.75/1.96 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.75/1.96 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.75/1.96 all A B (A=B&cp1(A)->cp1(B)).
% 1.75/1.96 all A B (A=B&cp2(A)->cp2(B)).
% 1.75/1.96 all A B (A=B&cp2xcomp(A)->cp2xcomp(B)).
% 1.75/1.96 all A B C (A=B&ra_Px1(A,C)->ra_Px1(B,C)).
% 1.75/1.96 all A B C (A=B&ra_Px1(C,A)->ra_Px1(C,B)).
% 1.75/1.96 all A B C (A=B&rf1(A,C)->rf1(B,C)).
% 1.75/1.96 all A B C (A=B&rf1(C,A)->rf1(C,B)).
% 1.75/1.96 all A B C (A=B&rf2(A,C)->rf2(B,C)).
% 1.75/1.96 all A B C (A=B&rf2(C,A)->rf2(C,B)).
% 1.75/1.96 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.75/1.96 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.75/1.96 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.75/1.96 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.75/1.96 all X (cowlThing(X)& -cowlNothing(X)).
% 1.75/1.96 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.75/1.96 all X (cUnsatisfiable(X)<-> (exists Y (rf2(X,Y)&cp2(Y)))& (exists Y (rf1(X,Y)&cp1(Y)))& (exists Y (rr(X,Y)&cowlThing(Y)))).
% 1.75/1.96 all X (cp1(X)->cp2xcomp(X)).
% 1.75/1.96 all X (cp2(X)<-> -(exists Y ra_Px1(X,Y))).
% 1.75/1.96 all X (cp2xcomp(X)<-> (exists Y0 ra_Px1(X,Y0))).
% 1.75/1.96 all X (cowlThing(X)-> (all Y0 Y1 (rf1(X,Y0)&rf1(X,Y1)->Y0=Y1))).
% 1.75/1.96 all X (cowlThing(X)-> (all Y0 Y1 (rf2(X,Y0)&rf2(X,Y1)->Y0=Y1))).
% 1.75/1.96 cUnsatisfiable(i2003_11_14_17_21_30578).
% 1.75/1.96 all X Y (rr(X,Y)->rf2(X,Y)).
% 1.75/1.96 all X Y (rr(X,Y)->rf1(X,Y)).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 -------> usable clausifies to:
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] A=A.
% 1.75/1.96 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.75/1.96 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.75/1.96 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.75/1.96 0 [] A!=B| -cp1(A)|cp1(B).
% 1.75/1.96 0 [] A!=B| -cp2(A)|cp2(B).
% 1.75/1.96 0 [] A!=B| -cp2xcomp(A)|cp2xcomp(B).
% 1.75/1.96 0 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.75/1.96 0 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.75/1.96 0 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.75/1.96 0 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.75/1.96 0 [] A!=B| -rf2(A,C)|rf2(B,C).
% 1.75/1.96 0 [] A!=B| -rf2(C,A)|rf2(C,B).
% 1.75/1.96 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.75/1.96 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.75/1.96 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.75/1.96 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.75/1.96 0 [] cowlThing(X).
% 1.75/1.96 0 [] -cowlNothing(X).
% 1.75/1.96 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.75/1.96 0 [] xsd_string(X)|xsd_integer(X).
% 1.75/1.96 0 [] -cUnsatisfiable(X)|rf2(X,$f1(X)).
% 1.75/1.96 0 [] -cUnsatisfiable(X)|cp2($f1(X)).
% 1.75/1.96 0 [] -cUnsatisfiable(X)|rf1(X,$f2(X)).
% 1.75/1.96 0 [] -cUnsatisfiable(X)|cp1($f2(X)).
% 1.75/1.96 0 [] -cUnsatisfiable(X)|rr(X,$f3(X)).
% 1.75/1.96 0 [] -cUnsatisfiable(X)|cowlThing($f3(X)).
% 1.75/1.96 0 [] cUnsatisfiable(X)| -rf2(X,Y)| -cp2(Y)| -rf1(X,X1)| -cp1(X1)| -rr(X,X2)| -cowlThing(X2).
% 1.75/1.96 0 [] -cp1(X)|cp2xcomp(X).
% 1.75/1.96 0 [] -cp2(X)| -ra_Px1(X,Y).
% 1.75/1.96 0 [] cp2(X)|ra_Px1(X,$f4(X)).
% 1.75/1.96 0 [] -cp2xcomp(X)|ra_Px1(X,$f5(X)).
% 1.75/1.96 0 [] cp2xcomp(X)| -ra_Px1(X,Y0).
% 1.75/1.96 0 [] -cowlThing(X)| -rf1(X,Y0)| -rf1(X,Y1)|Y0=Y1.
% 1.75/1.96 0 [] -cowlThing(X)| -rf2(X,Y0)| -rf2(X,Y1)|Y0=Y1.
% 1.75/1.96 0 [] cUnsatisfiable(i2003_11_14_17_21_30578).
% 1.75/1.96 0 [] -rr(X,Y)|rf2(X,Y).
% 1.75/1.96 0 [] -rr(X,Y)|rf1(X,Y).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.75/1.96
% 1.75/1.96 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.96 deletion, with positive clauses in sos and nonpositive
% 1.75/1.96 clauses in usable.
% 1.75/1.96
% 1.75/1.96 dependent: set(knuth_bendix).
% 1.75/1.96 dependent: set(anl_eq).
% 1.75/1.96 dependent: set(para_from).
% 1.75/1.96 dependent: set(para_into).
% 1.75/1.96 dependent: clear(para_from_right).
% 1.75/1.96 dependent: clear(para_into_right).
% 1.75/1.96 dependent: set(para_from_vars).
% 1.75/1.96 dependent: set(eq_units_both_ways).
% 1.75/1.96 dependent: set(dynamic_demod_all).
% 1.75/1.96 dependent: set(dynamic_demod).
% 1.75/1.96 dependent: set(order_eq).
% 1.75/1.96 dependent: set(back_demod).
% 1.75/1.96 dependent: set(lrpo).
% 1.75/1.96 dependent: set(hyper_res).
% 1.75/1.96 dependent: set(unit_deletion).
% 1.75/1.96 dependent: set(factor).
% 1.75/1.96
% 1.75/1.96 ------------> process usable:
% 1.75/1.96 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.75/1.96 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.75/1.96 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.75/1.96 ** KEPT (pick-wt=7): 4 [] A!=B| -cp1(A)|cp1(B).
% 1.75/1.96 ** KEPT (pick-wt=7): 5 [] A!=B| -cp2(A)|cp2(B).
% 1.75/1.96 ** KEPT (pick-wt=7): 6 [] A!=B| -cp2xcomp(A)|cp2xcomp(B).
% 1.75/1.96 ** KEPT (pick-wt=9): 7 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.75/1.96 ** KEPT (pick-wt=9): 8 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.75/1.96 ** KEPT (pick-wt=9): 9 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.75/1.96 ** KEPT (pick-wt=9): 10 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.75/1.96 ** KEPT (pick-wt=9): 11 [] A!=B| -rf2(A,C)|rf2(B,C).
% 1.75/1.96 ** KEPT (pick-wt=9): 12 [] A!=B| -rf2(C,A)|rf2(C,B).
% 1.75/1.96 ** KEPT (pick-wt=9): 13 [] A!=B| -rr(A,C)|rr(B,C).
% 1.75/1.96 ** KEPT (pick-wt=9): 14 [] A!=B| -rr(C,A)|rr(C,B).
% 1.75/1.96 ** KEPT (pick-wt=7): 15 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.75/1.96 ** KEPT (pick-wt=7): 16 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.75/1.96 ** KEPT (pick-wt=2): 17 [] -cowlNothing(A).
% 1.75/1.96 ** KEPT (pick-wt=4): 18 [] -xsd_string(A)| -xsd_integer(A).
% 1.75/1.96 ** KEPT (pick-wt=6): 19 [] -cUnsatisfiable(A)|rf2(A,$f1(A)).
% 1.75/1.96 ** KEPT (pick-wt=5): 20 [] -cUnsatisfiable(A)|cp2($f1(A)).
% 1.75/1.96 ** KEPT (pick-wt=6): 21 [] -cUnsatisfiable(A)|rf1(A,$f2(A)).
% 1.75/1.96 ** KEPT (pick-wt=5): 22 [] -cUnsatisfiable(A)|cp1($f2(A)).
% 1.75/1.96 ** KEPT (pick-wt=6): 23 [] -cUnsatisfiable(A)|rr(A,$f3(A)).
% 1.75/1.96 ** KEPT (pick-wt=5): 24 [] -cUnsatisfiable(A)|cowlThing($f3(A)).
% 1.75/1.96 ** KEPT (pick-wt=17): 25 [] cUnsatisfiable(A)| -rf2(A,B)| -cp2(B)| -rf1(A,C)| -cp1(C)| -rr(A,D)| -cowlThing(D).
% 1.75/1.96 ** KEPT (pick-wt=4): 26 [] -cp1(A)|cp2xcomp(A).
% 1.75/1.96 ** KEPT (pick-wt=5): 27 [] -cp2(A)| -ra_Px1(A,B).
% 1.75/1.96 ** KEPT (pick-wt=6): 28 [] -cp2xcomp(A)|ra_Px1(A,$f5(A)).
% 1.75/1.96 ** KEPT (pick-wt=5): 29 [] cp2xcomp(A)| -ra_Px1(A,B).
% 1.75/1.96 ** KEPT (pick-wt=11): 30 [] -cowlThing(A)| -rf1(A,B)| -rf1(A,C)|B=C.
% 1.75/1.96 ** KEPT (pick-wt=11): 31 [] -cowlThing(A)| -rf2(A,B)| -rf2(A,C)|B=C.
% 1.75/1.96 ** KEPT (pick-wt=6): 32 [] -rr(A,B)|rf2(A,B).
% 1.75/1.96 ** KEPT (pick-wt=6): 33 [] -rr(A,B)|rf1(A,B).
% 1.75/1.96 17 back subsumes 2.
% 1.75/1.96
% 1.75/1.96 ------------> process sos:
% 1.75/1.96 ** KEPT (pick-wt=3): 36 [] A=A.
% 1.75/1.96 ** KEPT (pick-wt=2): 37 [] cowlThing(A).
% 1.75/1.96 ** KEPT (pick-wt=4): 38 [] xsd_string(A)|xsd_integer(A).
% 1.75/1.96 ** KEPT (pick-wt=6): 39 [] cp2(A)|ra_Px1(A,$f4(A)).
% 1.75/1.96 ** KEPT (pick-wt=2): 40 [] cUnsatisfiable(i2003_11_14_17_21_30578).
% 1.75/1.96 Following clause subsumed by 36 during input processing: 0 [copy,36,flip.1] A=A.
% 1.75/1.96 36 back subsumes 35.
% 1.75/1.96 36 back subsumes 34.
% 1.75/1.96 37 back subsumes 24.
% 1.75/1.96 37 back subsumes 3.
% 1.75/1.96
% 1.75/1.96 ======= end of input processing =======
% 1.75/1.96
% 1.75/1.96 =========== start of search ===========
% 1.75/1.96
% 1.75/1.96 -------- PROOF --------
% 1.75/1.96
% 1.75/1.96 -----> EMPTY CLAUSE at 0.00 sec ----> 131 [hyper,107,27,44] $F.
% 1.75/1.96
% 1.75/1.96 Length of proof is 13. Level of proof is 6.
% 1.75/1.96
% 1.75/1.96 ---------------- PROOF ----------------
% 1.75/1.96 % SZS status Theorem
% 1.75/1.96 % SZS output start Refutation
% See solution above
% 1.75/1.96 ------------ end of proof -------------
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96 ============ end of search ============
% 1.75/1.96
% 1.75/1.96 -------------- statistics -------------
% 1.75/1.96 clauses given 22
% 1.75/1.96 clauses generated 214
% 1.75/1.96 clauses kept 127
% 1.75/1.96 clauses forward subsumed 151
% 1.75/1.96 clauses back subsumed 5
% 1.75/1.96 Kbytes malloced 976
% 1.75/1.96
% 1.75/1.96 ----------- times (seconds) -----------
% 1.75/1.96 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.96 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.96
% 1.75/1.96 That finishes the proof of the theorem.
% 1.75/1.96
% 1.75/1.96 Process 7212 finished Wed Jul 27 03:31:13 2022
% 1.75/1.97 Otter interrupted
% 1.75/1.97 PROOF FOUND
%------------------------------------------------------------------------------