TSTP Solution File: KRS072+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS072+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 13:01:04 EDT 2022
% Result : Unsatisfiable 1.81s 2.00s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 16 RR)
% Number of literals : 25 ( 2 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(17,axiom,
( ~ cUnsatisfiable(A)
| rinvR(A,dollar_f2(A)) ),
file('KRS072+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| ~ rr(dollar_f2(A),B)
| ~ rr(dollar_f2(A),C)
| B = C ),
file('KRS072+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| rr(dollar_f2(A),dollar_f1(A)) ),
file('KRS072+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ cUnsatisfiable(A)
| cp1(dollar_f1(A)) ),
file('KRS072+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ cUnsatisfiable(A)
| cp2(A) ),
file('KRS072+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ cp1(A)
| ~ cp2(A) ),
file('KRS072+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ rinvR(A,B)
| rr(B,A) ),
file('KRS072+1.p',unknown),
[] ).
cnf(41,axiom,
cUnsatisfiable(i2003_11_14_17_18_50190),
file('KRS072+1.p',unknown),
[] ).
cnf(42,plain,
cp2(i2003_11_14_17_18_50190),
inference(hyper,[status(thm)],[41,21]),
[iquote('hyper,41,21')] ).
cnf(43,plain,
cp1(dollar_f1(i2003_11_14_17_18_50190)),
inference(hyper,[status(thm)],[41,20]),
[iquote('hyper,41,20')] ).
cnf(44,plain,
rr(dollar_f2(i2003_11_14_17_18_50190),dollar_f1(i2003_11_14_17_18_50190)),
inference(hyper,[status(thm)],[41,19]),
[iquote('hyper,41,19')] ).
cnf(45,plain,
rinvR(i2003_11_14_17_18_50190,dollar_f2(i2003_11_14_17_18_50190)),
inference(hyper,[status(thm)],[41,17]),
[iquote('hyper,41,17')] ).
cnf(50,plain,
rr(dollar_f2(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190),
inference(hyper,[status(thm)],[45,35]),
[iquote('hyper,45,35')] ).
cnf(59,plain,
dollar_f1(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[44,18,41,50])]),
[iquote('hyper,44,18,41,50,flip.1')] ).
cnf(61,plain,
cp1(i2003_11_14_17_18_50190),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[43]),59]),
[iquote('back_demod,43,demod,59')] ).
cnf(62,plain,
$false,
inference(hyper,[status(thm)],[61,26,42]),
[iquote('hyper,61,26,42')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS072+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 03:46:51 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.81/1.99 ----- Otter 3.3f, August 2004 -----
% 1.81/1.99 The process was started by sandbox on n027.cluster.edu,
% 1.81/1.99 Wed Jul 27 03:46:51 2022
% 1.81/1.99 The command was "./otter". The process ID is 3823.
% 1.81/1.99
% 1.81/1.99 set(prolog_style_variables).
% 1.81/1.99 set(auto).
% 1.81/1.99 dependent: set(auto1).
% 1.81/1.99 dependent: set(process_input).
% 1.81/1.99 dependent: clear(print_kept).
% 1.81/1.99 dependent: clear(print_new_demod).
% 1.81/1.99 dependent: clear(print_back_demod).
% 1.81/1.99 dependent: clear(print_back_sub).
% 1.81/1.99 dependent: set(control_memory).
% 1.81/1.99 dependent: assign(max_mem, 12000).
% 1.81/1.99 dependent: assign(pick_given_ratio, 4).
% 1.81/1.99 dependent: assign(stats_level, 1).
% 1.81/1.99 dependent: assign(max_seconds, 10800).
% 1.81/1.99 clear(print_given).
% 1.81/1.99
% 1.81/1.99 formula_list(usable).
% 1.81/1.99 all A (A=A).
% 1.81/1.99 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.81/1.99 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.81/1.99 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.81/1.99 all A B (A=B&cp1(A)->cp1(B)).
% 1.81/1.99 all A B (A=B&cp2(A)->cp2(B)).
% 1.81/1.99 all A B (A=B&cp3(A)->cp3(B)).
% 1.81/1.99 all A B (A=B&cp4(A)->cp4(B)).
% 1.81/1.99 all A B (A=B&cp5(A)->cp5(B)).
% 1.81/1.99 all A B C (A=B&rinvR(A,C)->rinvR(B,C)).
% 1.81/1.99 all A B C (A=B&rinvR(C,A)->rinvR(C,B)).
% 1.81/1.99 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.81/1.99 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.81/1.99 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.81/1.99 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.81/1.99 all X (cowlThing(X)& -cowlNothing(X)).
% 1.81/1.99 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.81/1.99 all X (cUnsatisfiable(X)<-> (exists Y (rinvR(X,Y)& (all Z0 Z1 (rr(Y,Z0)&rr(Y,Z1)->Z0=Z1))& (exists Z (rr(Y,Z)&cp1(Z)))))&cp2(X)).
% 1.81/1.99 all X (cp1(X)-> -(cp3(X)|cp2(X)|cp4(X)|cp5(X))).
% 1.81/1.99 all X (cp2(X)-> -(cp3(X)|cp4(X)|cp5(X))).
% 1.81/1.99 all X (cp3(X)-> -(cp4(X)|cp5(X))).
% 1.81/1.99 all X (cp4(X)-> -cp5(X)).
% 1.81/1.99 all X Y (rinvR(X,Y)<->rr(Y,X)).
% 1.81/1.99 cUnsatisfiable(i2003_11_14_17_18_50190).
% 1.81/1.99 end_of_list.
% 1.81/1.99
% 1.81/1.99 -------> usable clausifies to:
% 1.81/1.99
% 1.81/1.99 list(usable).
% 1.81/1.99 0 [] A=A.
% 1.81/1.99 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.81/1.99 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.81/1.99 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.81/1.99 0 [] A!=B| -cp1(A)|cp1(B).
% 1.81/1.99 0 [] A!=B| -cp2(A)|cp2(B).
% 1.81/1.99 0 [] A!=B| -cp3(A)|cp3(B).
% 1.81/1.99 0 [] A!=B| -cp4(A)|cp4(B).
% 1.81/1.99 0 [] A!=B| -cp5(A)|cp5(B).
% 1.81/1.99 0 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.81/1.99 0 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.81/1.99 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.81/1.99 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.81/1.99 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.81/1.99 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.81/1.99 0 [] cowlThing(X).
% 1.81/1.99 0 [] -cowlNothing(X).
% 1.81/1.99 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.81/1.99 0 [] xsd_string(X)|xsd_integer(X).
% 1.81/1.99 0 [] -cUnsatisfiable(X)|rinvR(X,$f2(X)).
% 1.81/1.99 0 [] -cUnsatisfiable(X)| -rr($f2(X),Z0)| -rr($f2(X),Z1)|Z0=Z1.
% 1.81/1.99 0 [] -cUnsatisfiable(X)|rr($f2(X),$f1(X)).
% 1.81/1.99 0 [] -cUnsatisfiable(X)|cp1($f1(X)).
% 1.81/1.99 0 [] -cUnsatisfiable(X)|cp2(X).
% 1.81/1.99 0 [] cUnsatisfiable(X)| -rinvR(X,Y)|rr(Y,$f4(X,Y))| -rr(Y,Z)| -cp1(Z)| -cp2(X).
% 1.81/1.99 0 [] cUnsatisfiable(X)| -rinvR(X,Y)|rr(Y,$f3(X,Y))| -rr(Y,Z)| -cp1(Z)| -cp2(X).
% 1.81/1.99 0 [] cUnsatisfiable(X)| -rinvR(X,Y)|$f4(X,Y)!=$f3(X,Y)| -rr(Y,Z)| -cp1(Z)| -cp2(X).
% 1.81/1.99 0 [] -cp1(X)| -cp3(X).
% 1.81/1.99 0 [] -cp1(X)| -cp2(X).
% 1.81/1.99 0 [] -cp1(X)| -cp4(X).
% 1.81/1.99 0 [] -cp1(X)| -cp5(X).
% 1.81/1.99 0 [] -cp2(X)| -cp3(X).
% 1.81/1.99 0 [] -cp2(X)| -cp4(X).
% 1.81/1.99 0 [] -cp2(X)| -cp5(X).
% 1.81/1.99 0 [] -cp3(X)| -cp4(X).
% 1.81/1.99 0 [] -cp3(X)| -cp5(X).
% 1.81/1.99 0 [] -cp4(X)| -cp5(X).
% 1.81/1.99 0 [] -rinvR(X,Y)|rr(Y,X).
% 1.81/1.99 0 [] rinvR(X,Y)| -rr(Y,X).
% 1.81/1.99 0 [] cUnsatisfiable(i2003_11_14_17_18_50190).
% 1.81/1.99 end_of_list.
% 1.81/1.99
% 1.81/1.99 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.81/1.99
% 1.81/1.99 This ia a non-Horn set with equality. The strategy will be
% 1.81/1.99 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.81/1.99 deletion, with positive clauses in sos and nonpositive
% 1.81/1.99 clauses in usable.
% 1.81/1.99
% 1.81/1.99 dependent: set(knuth_bendix).
% 1.81/1.99 dependent: set(anl_eq).
% 1.81/1.99 dependent: set(para_from).
% 1.81/1.99 dependent: set(para_into).
% 1.81/1.99 dependent: clear(para_from_right).
% 1.81/1.99 dependent: clear(para_into_right).
% 1.81/1.99 dependent: set(para_from_vars).
% 1.81/1.99 dependent: set(eq_units_both_ways).
% 1.81/1.99 dependent: set(dynamic_demod_all).
% 1.81/1.99 dependent: set(dynamic_demod).
% 1.81/1.99 dependent: set(order_eq).
% 1.81/1.99 dependent: set(back_demod).
% 1.81/1.99 dependent: set(lrpo).
% 1.81/1.99 dependent: set(hyper_res).
% 1.81/1.99 dependent: set(unit_deletion).
% 1.81/1.99 dependent: set(factor).
% 1.81/1.99
% 1.81/1.99 ------------> process usable:
% 1.81/1.99 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 4 [] A!=B| -cp1(A)|cp1(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 5 [] A!=B| -cp2(A)|cp2(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 6 [] A!=B| -cp3(A)|cp3(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 7 [] A!=B| -cp4(A)|cp4(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 8 [] A!=B| -cp5(A)|cp5(B).
% 1.81/1.99 ** KEPT (pick-wt=9): 9 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.81/1.99 ** KEPT (pick-wt=9): 10 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.81/1.99 ** KEPT (pick-wt=9): 11 [] A!=B| -rr(A,C)|rr(B,C).
% 1.81/1.99 ** KEPT (pick-wt=9): 12 [] A!=B| -rr(C,A)|rr(C,B).
% 1.81/1.99 ** KEPT (pick-wt=7): 13 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.81/1.99 ** KEPT (pick-wt=7): 14 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.81/1.99 ** KEPT (pick-wt=2): 15 [] -cowlNothing(A).
% 1.81/1.99 ** KEPT (pick-wt=4): 16 [] -xsd_string(A)| -xsd_integer(A).
% 1.81/1.99 ** KEPT (pick-wt=6): 17 [] -cUnsatisfiable(A)|rinvR(A,$f2(A)).
% 1.81/1.99 ** KEPT (pick-wt=13): 18 [] -cUnsatisfiable(A)| -rr($f2(A),B)| -rr($f2(A),C)|B=C.
% 1.81/1.99 ** KEPT (pick-wt=7): 19 [] -cUnsatisfiable(A)|rr($f2(A),$f1(A)).
% 1.81/1.99 ** KEPT (pick-wt=5): 20 [] -cUnsatisfiable(A)|cp1($f1(A)).
% 1.81/1.99 ** KEPT (pick-wt=4): 21 [] -cUnsatisfiable(A)|cp2(A).
% 1.81/1.99 ** KEPT (pick-wt=17): 22 [] cUnsatisfiable(A)| -rinvR(A,B)|rr(B,$f4(A,B))| -rr(B,C)| -cp1(C)| -cp2(A).
% 1.81/2.00 ** KEPT (pick-wt=17): 23 [] cUnsatisfiable(A)| -rinvR(A,B)|rr(B,$f3(A,B))| -rr(B,C)| -cp1(C)| -cp2(A).
% 1.81/2.00 ** KEPT (pick-wt=19): 24 [] cUnsatisfiable(A)| -rinvR(A,B)|$f4(A,B)!=$f3(A,B)| -rr(B,C)| -cp1(C)| -cp2(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 25 [] -cp1(A)| -cp3(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 26 [] -cp1(A)| -cp2(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 27 [] -cp1(A)| -cp4(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 28 [] -cp1(A)| -cp5(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 29 [] -cp2(A)| -cp3(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 30 [] -cp2(A)| -cp4(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 31 [] -cp2(A)| -cp5(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 32 [] -cp3(A)| -cp4(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 33 [] -cp3(A)| -cp5(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 34 [] -cp4(A)| -cp5(A).
% 1.81/2.00 ** KEPT (pick-wt=6): 35 [] -rinvR(A,B)|rr(B,A).
% 1.81/2.00 ** KEPT (pick-wt=6): 36 [] rinvR(A,B)| -rr(B,A).
% 1.81/2.00 15 back subsumes 2.
% 1.81/2.00
% 1.81/2.00 ------------> process sos:
% 1.81/2.00 ** KEPT (pick-wt=3): 38 [] A=A.
% 1.81/2.00 ** KEPT (pick-wt=2): 39 [] cowlThing(A).
% 1.81/2.00 ** KEPT (pick-wt=4): 40 [] xsd_string(A)|xsd_integer(A).
% 1.81/2.00 ** KEPT (pick-wt=2): 41 [] cUnsatisfiable(i2003_11_14_17_18_50190).
% 1.81/2.00 Following clause subsumed by 38 during input processing: 0 [copy,38,flip.1] A=A.
% 1.81/2.00 38 back subsumes 37.
% 1.81/2.00 39 back subsumes 3.
% 1.81/2.00
% 1.81/2.00 ======= end of input processing =======
% 1.81/2.00
% 1.81/2.00 =========== start of search ===========
% 1.81/2.00
% 1.81/2.00 -------- PROOF --------
% 1.81/2.00
% 1.81/2.00 -----> EMPTY CLAUSE at 0.00 sec ----> 62 [hyper,61,26,42] $F.
% 1.81/2.00
% 1.81/2.00 Length of proof is 7. Level of proof is 4.
% 1.81/2.00
% 1.81/2.00 ---------------- PROOF ----------------
% 1.81/2.00 % SZS status Theorem
% 1.81/2.00 % SZS output start Refutation
% See solution above
% 1.81/2.00 ------------ end of proof -------------
% 1.81/2.00
% 1.81/2.00
% 1.81/2.00 Search stopped by max_proofs option.
% 1.81/2.00
% 1.81/2.00
% 1.81/2.00 Search stopped by max_proofs option.
% 1.81/2.00
% 1.81/2.00 ============ end of search ============
% 1.81/2.00
% 1.81/2.00 -------------- statistics -------------
% 1.81/2.00 clauses given 10
% 1.81/2.00 clauses generated 48
% 1.81/2.00 clauses kept 60
% 1.81/2.00 clauses forward subsumed 32
% 1.81/2.00 clauses back subsumed 3
% 1.81/2.00 Kbytes malloced 976
% 1.81/2.00
% 1.81/2.00 ----------- times (seconds) -----------
% 1.81/2.00 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.81/2.00
% 1.81/2.00 That finishes the proof of the theorem.
% 1.81/2.00
% 1.81/2.00 Process 3823 finished Wed Jul 27 03:46:53 2022
% 1.81/2.00 Otter interrupted
% 1.81/2.00 PROOF FOUND
%------------------------------------------------------------------------------