TSTP Solution File: KRS095+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS095+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:01:08 EDT 2022
% Result : Unsatisfiable 1.89s 2.10s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 3 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(12,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f2(A)) ),
file('KRS095+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f1(A)) ),
file('KRS095+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ cUnsatisfiable(A)
| dollar_f2(A) != dollar_f1(A) ),
file('KRS095+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ cUnsatisfiable(A)
| ~ rr(A,B)
| ~ rr(A,C)
| B = C ),
file('KRS095+1.p',unknown),
[] ).
cnf(27,axiom,
cUnsatisfiable(i2003_11_14_17_20_14253),
file('KRS095+1.p',unknown),
[] ).
cnf(28,plain,
rr(i2003_11_14_17_20_14253,dollar_f1(i2003_11_14_17_20_14253)),
inference(hyper,[status(thm)],[27,13]),
[iquote('hyper,27,13')] ).
cnf(29,plain,
rr(i2003_11_14_17_20_14253,dollar_f2(i2003_11_14_17_20_14253)),
inference(hyper,[status(thm)],[27,12]),
[iquote('hyper,27,12')] ).
cnf(49,plain,
dollar_f2(i2003_11_14_17_20_14253) = dollar_f1(i2003_11_14_17_20_14253),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[29,15,27,28])]),
[iquote('hyper,29,15,27,28,flip.1')] ).
cnf(51,plain,
$false,
inference(hyper,[status(thm)],[49,14,27]),
[iquote('hyper,49,14,27')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS095+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 03:35:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.10 ----- Otter 3.3f, August 2004 -----
% 1.89/2.10 The process was started by sandbox on n015.cluster.edu,
% 1.89/2.10 Wed Jul 27 03:35:41 2022
% 1.89/2.10 The command was "./otter". The process ID is 17588.
% 1.89/2.10
% 1.89/2.10 set(prolog_style_variables).
% 1.89/2.10 set(auto).
% 1.89/2.10 dependent: set(auto1).
% 1.89/2.10 dependent: set(process_input).
% 1.89/2.10 dependent: clear(print_kept).
% 1.89/2.10 dependent: clear(print_new_demod).
% 1.89/2.10 dependent: clear(print_back_demod).
% 1.89/2.10 dependent: clear(print_back_sub).
% 1.89/2.10 dependent: set(control_memory).
% 1.89/2.10 dependent: assign(max_mem, 12000).
% 1.89/2.10 dependent: assign(pick_given_ratio, 4).
% 1.89/2.10 dependent: assign(stats_level, 1).
% 1.89/2.10 dependent: assign(max_seconds, 10800).
% 1.89/2.10 clear(print_given).
% 1.89/2.10
% 1.89/2.10 formula_list(usable).
% 1.89/2.10 all A (A=A).
% 1.89/2.10 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.89/2.10 all A B (A=B&cc(A)->cc(B)).
% 1.89/2.10 all A B (A=B&cd(A)->cd(B)).
% 1.89/2.10 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.89/2.10 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.89/2.10 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.89/2.10 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.89/2.10 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.89/2.10 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.89/2.10 all X (cowlThing(X)& -cowlNothing(X)).
% 1.89/2.10 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.89/2.10 all X (cUnsatisfiable(X)<-> (exists Y0 Y1 (rr(X,Y0)&rr(X,Y1)&Y0!=Y1))& (all Y0 Y1 (rr(X,Y0)&rr(X,Y1)->Y0=Y1))).
% 1.89/2.10 all X (cc(X)-> -cd(X)).
% 1.89/2.10 cUnsatisfiable(i2003_11_14_17_20_14253).
% 1.89/2.10 end_of_list.
% 1.89/2.10
% 1.89/2.10 -------> usable clausifies to:
% 1.89/2.10
% 1.89/2.10 list(usable).
% 1.89/2.10 0 [] A=A.
% 1.89/2.10 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.89/2.10 0 [] A!=B| -cc(A)|cc(B).
% 1.89/2.10 0 [] A!=B| -cd(A)|cd(B).
% 1.89/2.10 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.89/2.10 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.89/2.10 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.89/2.10 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.89/2.10 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.89/2.10 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.89/2.10 0 [] cowlThing(X).
% 1.89/2.10 0 [] -cowlNothing(X).
% 1.89/2.10 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.89/2.10 0 [] xsd_string(X)|xsd_integer(X).
% 1.89/2.10 0 [] -cUnsatisfiable(X)|rr(X,$f2(X)).
% 1.89/2.10 0 [] -cUnsatisfiable(X)|rr(X,$f1(X)).
% 1.89/2.10 0 [] -cUnsatisfiable(X)|$f2(X)!=$f1(X).
% 1.89/2.10 0 [] -cUnsatisfiable(X)| -rr(X,Y0)| -rr(X,Y1)|Y0=Y1.
% 1.89/2.10 0 [] cUnsatisfiable(X)| -rr(X,X1)| -rr(X,X2)|X1=X2|rr(X,$f4(X)).
% 1.89/2.10 0 [] cUnsatisfiable(X)| -rr(X,X1)| -rr(X,X2)|X1=X2|rr(X,$f3(X)).
% 1.89/2.10 0 [] cUnsatisfiable(X)| -rr(X,X1)| -rr(X,X2)|X1=X2|$f4(X)!=$f3(X).
% 1.89/2.10 0 [] -cc(X)| -cd(X).
% 1.89/2.10 0 [] cUnsatisfiable(i2003_11_14_17_20_14253).
% 1.89/2.10 end_of_list.
% 1.89/2.10
% 1.89/2.10 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.89/2.10
% 1.89/2.10 This ia a non-Horn set with equality. The strategy will be
% 1.89/2.10 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.89/2.10 deletion, with positive clauses in sos and nonpositive
% 1.89/2.10 clauses in usable.
% 1.89/2.10
% 1.89/2.10 dependent: set(knuth_bendix).
% 1.89/2.10 dependent: set(anl_eq).
% 1.89/2.10 dependent: set(para_from).
% 1.89/2.10 dependent: set(para_into).
% 1.89/2.10 dependent: clear(para_from_right).
% 1.89/2.10 dependent: clear(para_into_right).
% 1.89/2.10 dependent: set(para_from_vars).
% 1.89/2.10 dependent: set(eq_units_both_ways).
% 1.89/2.10 dependent: set(dynamic_demod_all).
% 1.89/2.10 dependent: set(dynamic_demod).
% 1.89/2.10 dependent: set(order_eq).
% 1.89/2.10 dependent: set(back_demod).
% 1.89/2.10 dependent: set(lrpo).
% 1.89/2.10 dependent: set(hyper_res).
% 1.89/2.10 dependent: set(unit_deletion).
% 1.89/2.10 dependent: set(factor).
% 1.89/2.10
% 1.89/2.10 ------------> process usable:
% 1.89/2.10 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 2 [] A!=B| -cc(A)|cc(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 3 [] A!=B| -cd(A)|cd(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 4 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 5 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.89/2.10 ** KEPT (pick-wt=9): 6 [] A!=B| -rr(A,C)|rr(B,C).
% 1.89/2.10 ** KEPT (pick-wt=9): 7 [] A!=B| -rr(C,A)|rr(C,B).
% 1.89/2.10 ** KEPT (pick-wt=7): 8 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.89/2.10 ** KEPT (pick-wt=7): 9 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.89/2.10 ** KEPT (pick-wt=2): 10 [] -cowlNothing(A).
% 1.89/2.10 ** KEPT (pick-wt=4): 11 [] -xsd_string(A)| -xsd_integer(A).
% 1.89/2.10 ** KEPT (pick-wt=6): 12 [] -cUnsatisfiable(A)|rr(A,$f2(A)).
% 1.89/2.10 ** KEPT (pick-wt=6): 13 [] -cUnsatisfiable(A)|rr(A,$f1(A)).
% 1.89/2.10 ** KEPT (pick-wt=7): 14 [] -cUnsatisfiable(A)|$f2(A)!=$f1(A).
% 1.89/2.10 ** KEPT (pick-wt=11): 15 [] -cUnsatisfiable(A)| -rr(A,B)| -rr(A,C)|B=C.
% 1.89/2.10 ** KEPT (pick-wt=15): 16 [] cUnsatisfiable(A)| -rr(A,B)| -rr(A,C)|B=C|rr(A,$f4(A)).
% 1.89/2.10 ** KEPT (pick-wt=15): 17 [] cUnsatisfiable(A)| -rr(A,B)| -rr(A,C)|B=C|rr(A,$f3(A)).
% 1.89/2.10 ** KEPT (pick-wt=16): 18 [] cUnsatisfiable(A)| -rr(A,B)| -rr(A,C)|B=C|$f4(A)!=$f3(A).
% 1.89/2.10 ** KEPT (pick-wt=4): 19 [] -cc(A)| -cd(A).
% 1.89/2.10 10 back subsumes 4.
% 1.89/2.10
% 1.89/2.10 ------------> process sos:
% 1.89/2.10 ** KEPT (pick-wt=3): 24 [] A=A.
% 1.89/2.10 ** KEPT (pick-wt=2): 25 [] cowlThing(A).
% 1.89/2.10 ** KEPT (pick-wt=4): 26 [] xsd_string(A)|xsd_integer(A).
% 1.89/2.10 ** KEPT (pick-wt=2): 27 [] cUnsatisfiable(i2003_11_14_17_20_14253).
% 1.89/2.10 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] A=A.
% 1.89/2.10 24 back subsumes 23.
% 1.89/2.10 24 back subsumes 22.
% 1.89/2.10 24 back subsumes 21.
% 1.89/2.10 24 back subsumes 20.
% 1.89/2.10 25 back subsumes 5.
% 1.89/2.10
% 1.89/2.10 ======= end of input processing =======
% 1.89/2.10
% 1.89/2.10 =========== start of search ===========
% 1.89/2.10
% 1.89/2.10 -------- PROOF --------
% 1.89/2.10
% 1.89/2.10 -----> EMPTY CLAUSE at 0.00 sec ----> 51 [hyper,49,14,27] $F.
% 1.89/2.10
% 1.89/2.10 Length of proof is 3. Level of proof is 2.
% 1.89/2.10
% 1.89/2.10 ---------------- PROOF ----------------
% 1.89/2.10 % SZS status Theorem
% 1.89/2.10 % SZS output start Refutation
% See solution above
% 1.89/2.10 ------------ end of proof -------------
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Search stopped by max_proofs option.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Search stopped by max_proofs option.
% 1.89/2.10
% 1.89/2.10 ============ end of search ============
% 1.89/2.10
% 1.89/2.10 -------------- statistics -------------
% 1.89/2.10 clauses given 7
% 1.89/2.10 clauses generated 71
% 1.89/2.10 clauses kept 49
% 1.89/2.10 clauses forward subsumed 44
% 1.89/2.10 clauses back subsumed 6
% 1.89/2.10 Kbytes malloced 976
% 1.89/2.10
% 1.89/2.10 ----------- times (seconds) -----------
% 1.89/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.89/2.10
% 1.89/2.10 That finishes the proof of the theorem.
% 1.89/2.10
% 1.89/2.10 Process 17588 finished Wed Jul 27 03:35:43 2022
% 1.89/2.10 Otter interrupted
% 1.89/2.10 PROOF FOUND
%------------------------------------------------------------------------------