TSTP Solution File: KRS127+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS127+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:01:13 EDT 2022
% Result : Unsatisfiable 1.99s 2.17s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 18 RR)
% Number of literals : 28 ( 2 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 11 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f1(A)) ),
file('KRS127+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ cUnsatisfiable(A)
| cc(dollar_f1(A)) ),
file('KRS127+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f2(A)) ),
file('KRS127+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| cd(dollar_f2(A)) ),
file('KRS127+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| ~ rr(A,B)
| ~ rr(A,C)
| B = C ),
file('KRS127+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ cc(A)
| cdxcomp(A) ),
file('KRS127+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ cd(A)
| ~ ra_Px1(A,B) ),
file('KRS127+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ cdxcomp(A)
| ra_Px1(A,dollar_f6(A)) ),
file('KRS127+1.p',unknown),
[] ).
cnf(35,axiom,
cUnsatisfiable(i2003_11_14_17_22_27794),
file('KRS127+1.p',unknown),
[] ).
cnf(36,plain,
cd(dollar_f2(i2003_11_14_17_22_27794)),
inference(hyper,[status(thm)],[35,18]),
[iquote('hyper,35,18')] ).
cnf(37,plain,
rr(i2003_11_14_17_22_27794,dollar_f2(i2003_11_14_17_22_27794)),
inference(hyper,[status(thm)],[35,17]),
[iquote('hyper,35,17')] ).
cnf(38,plain,
cc(dollar_f1(i2003_11_14_17_22_27794)),
inference(hyper,[status(thm)],[35,16]),
[iquote('hyper,35,16')] ).
cnf(39,plain,
rr(i2003_11_14_17_22_27794,dollar_f1(i2003_11_14_17_22_27794)),
inference(hyper,[status(thm)],[35,15]),
[iquote('hyper,35,15')] ).
cnf(43,plain,
cdxcomp(dollar_f1(i2003_11_14_17_22_27794)),
inference(hyper,[status(thm)],[38,23]),
[iquote('hyper,38,23')] ).
cnf(46,plain,
ra_Px1(dollar_f1(i2003_11_14_17_22_27794),dollar_f6(dollar_f1(i2003_11_14_17_22_27794))),
inference(hyper,[status(thm)],[43,25]),
[iquote('hyper,43,25')] ).
cnf(53,plain,
dollar_f2(i2003_11_14_17_22_27794) = dollar_f1(i2003_11_14_17_22_27794),
inference(hyper,[status(thm)],[39,19,35,37]),
[iquote('hyper,39,19,35,37')] ).
cnf(57,plain,
cd(dollar_f1(i2003_11_14_17_22_27794)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[36]),53]),
[iquote('back_demod,36,demod,53')] ).
cnf(62,plain,
$false,
inference(hyper,[status(thm)],[46,24,57]),
[iquote('hyper,46,24,57')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS127+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 03:28:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.17 ----- Otter 3.3f, August 2004 -----
% 1.99/2.17 The process was started by sandbox2 on n020.cluster.edu,
% 1.99/2.17 Wed Jul 27 03:28:08 2022
% 1.99/2.17 The command was "./otter". The process ID is 31067.
% 1.99/2.17
% 1.99/2.17 set(prolog_style_variables).
% 1.99/2.17 set(auto).
% 1.99/2.17 dependent: set(auto1).
% 1.99/2.17 dependent: set(process_input).
% 1.99/2.17 dependent: clear(print_kept).
% 1.99/2.17 dependent: clear(print_new_demod).
% 1.99/2.17 dependent: clear(print_back_demod).
% 1.99/2.17 dependent: clear(print_back_sub).
% 1.99/2.17 dependent: set(control_memory).
% 1.99/2.17 dependent: assign(max_mem, 12000).
% 1.99/2.17 dependent: assign(pick_given_ratio, 4).
% 1.99/2.17 dependent: assign(stats_level, 1).
% 1.99/2.17 dependent: assign(max_seconds, 10800).
% 1.99/2.17 clear(print_given).
% 1.99/2.17
% 1.99/2.17 formula_list(usable).
% 1.99/2.17 all A (A=A).
% 1.99/2.17 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.99/2.17 all A B (A=B&cc(A)->cc(B)).
% 1.99/2.17 all A B (A=B&cd(A)->cd(B)).
% 1.99/2.17 all A B (A=B&cdxcomp(A)->cdxcomp(B)).
% 1.99/2.17 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.99/2.17 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.99/2.17 all A B C (A=B&ra_Px1(A,C)->ra_Px1(B,C)).
% 1.99/2.17 all A B C (A=B&ra_Px1(C,A)->ra_Px1(C,B)).
% 1.99/2.17 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.99/2.17 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.99/2.17 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.99/2.17 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.99/2.17 all X (cowlThing(X)& -cowlNothing(X)).
% 1.99/2.17 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.99/2.17 all X (cUnsatisfiable(X)<-> (exists Y (rr(X,Y)&cc(Y)))& (exists Y (rr(X,Y)&cd(Y)))& (all Y0 Y1 (rr(X,Y0)&rr(X,Y1)->Y0=Y1))).
% 1.99/2.17 all X (cc(X)->cdxcomp(X)).
% 1.99/2.17 all X (cd(X)<-> -(exists Y ra_Px1(X,Y))).
% 1.99/2.17 all X (cdxcomp(X)<-> (exists Y0 ra_Px1(X,Y0))).
% 1.99/2.17 cUnsatisfiable(i2003_11_14_17_22_27794).
% 1.99/2.17 end_of_list.
% 1.99/2.17
% 1.99/2.17 -------> usable clausifies to:
% 1.99/2.17
% 1.99/2.17 list(usable).
% 1.99/2.17 0 [] A=A.
% 1.99/2.17 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.99/2.17 0 [] A!=B| -cc(A)|cc(B).
% 1.99/2.17 0 [] A!=B| -cd(A)|cd(B).
% 1.99/2.17 0 [] A!=B| -cdxcomp(A)|cdxcomp(B).
% 1.99/2.17 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.99/2.17 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.99/2.17 0 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.99/2.17 0 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.99/2.17 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.99/2.17 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.99/2.17 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.99/2.17 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.99/2.17 0 [] cowlThing(X).
% 1.99/2.17 0 [] -cowlNothing(X).
% 1.99/2.17 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.99/2.17 0 [] xsd_string(X)|xsd_integer(X).
% 1.99/2.17 0 [] -cUnsatisfiable(X)|rr(X,$f1(X)).
% 1.99/2.17 0 [] -cUnsatisfiable(X)|cc($f1(X)).
% 1.99/2.17 0 [] -cUnsatisfiable(X)|rr(X,$f2(X)).
% 1.99/2.17 0 [] -cUnsatisfiable(X)|cd($f2(X)).
% 1.99/2.17 0 [] -cUnsatisfiable(X)| -rr(X,Y0)| -rr(X,Y1)|Y0=Y1.
% 1.99/2.17 0 [] cUnsatisfiable(X)| -rr(X,Y)| -cc(Y)| -rr(X,X1)| -cd(X1)|rr(X,$f4(X)).
% 1.99/2.17 0 [] cUnsatisfiable(X)| -rr(X,Y)| -cc(Y)| -rr(X,X1)| -cd(X1)|rr(X,$f3(X)).
% 1.99/2.17 0 [] cUnsatisfiable(X)| -rr(X,Y)| -cc(Y)| -rr(X,X1)| -cd(X1)|$f4(X)!=$f3(X).
% 1.99/2.17 0 [] -cc(X)|cdxcomp(X).
% 1.99/2.17 0 [] -cd(X)| -ra_Px1(X,Y).
% 1.99/2.17 0 [] cd(X)|ra_Px1(X,$f5(X)).
% 1.99/2.17 0 [] -cdxcomp(X)|ra_Px1(X,$f6(X)).
% 1.99/2.17 0 [] cdxcomp(X)| -ra_Px1(X,Y0).
% 1.99/2.17 0 [] cUnsatisfiable(i2003_11_14_17_22_27794).
% 1.99/2.17 end_of_list.
% 1.99/2.17
% 1.99/2.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.99/2.17
% 1.99/2.17 This ia a non-Horn set with equality. The strategy will be
% 1.99/2.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.99/2.17 deletion, with positive clauses in sos and nonpositive
% 1.99/2.17 clauses in usable.
% 1.99/2.17
% 1.99/2.17 dependent: set(knuth_bendix).
% 1.99/2.17 dependent: set(anl_eq).
% 1.99/2.17 dependent: set(para_from).
% 1.99/2.17 dependent: set(para_into).
% 1.99/2.17 dependent: clear(para_from_right).
% 1.99/2.17 dependent: clear(para_into_right).
% 1.99/2.17 dependent: set(para_from_vars).
% 1.99/2.17 dependent: set(eq_units_both_ways).
% 1.99/2.17 dependent: set(dynamic_demod_all).
% 1.99/2.17 dependent: set(dynamic_demod).
% 1.99/2.17 dependent: set(order_eq).
% 1.99/2.17 dependent: set(back_demod).
% 1.99/2.17 dependent: set(lrpo).
% 1.99/2.17 dependent: set(hyper_res).
% 1.99/2.17 dependent: set(unit_deletion).
% 1.99/2.17 dependent: set(factor).
% 1.99/2.17
% 1.99/2.17 ------------> process usable:
% 1.99/2.17 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.99/2.17 ** KEPT (pick-wt=7): 2 [] A!=B| -cc(A)|cc(B).
% 1.99/2.17 ** KEPT (pick-wt=7): 3 [] A!=B| -cd(A)|cd(B).
% 1.99/2.17 ** KEPT (pick-wt=7): 4 [] A!=B| -cdxcomp(A)|cdxcomp(B).
% 1.99/2.17 ** KEPT (pick-wt=7): 5 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.99/2.17 ** KEPT (pick-wt=7): 6 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.99/2.17 ** KEPT (pick-wt=9): 7 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.99/2.17 ** KEPT (pick-wt=9): 8 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.99/2.17 ** KEPT (pick-wt=9): 9 [] A!=B| -rr(A,C)|rr(B,C).
% 1.99/2.17 ** KEPT (pick-wt=9): 10 [] A!=B| -rr(C,A)|rr(C,B).
% 1.99/2.17 ** KEPT (pick-wt=7): 11 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.99/2.17 ** KEPT (pick-wt=7): 12 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.99/2.17 ** KEPT (pick-wt=2): 13 [] -cowlNothing(A).
% 1.99/2.17 ** KEPT (pick-wt=4): 14 [] -xsd_string(A)| -xsd_integer(A).
% 1.99/2.17 ** KEPT (pick-wt=6): 15 [] -cUnsatisfiable(A)|rr(A,$f1(A)).
% 1.99/2.17 ** KEPT (pick-wt=5): 16 [] -cUnsatisfiable(A)|cc($f1(A)).
% 1.99/2.17 ** KEPT (pick-wt=6): 17 [] -cUnsatisfiable(A)|rr(A,$f2(A)).
% 1.99/2.17 ** KEPT (pick-wt=5): 18 [] -cUnsatisfiable(A)|cd($f2(A)).
% 1.99/2.17 ** KEPT (pick-wt=11): 19 [] -cUnsatisfiable(A)| -rr(A,B)| -rr(A,C)|B=C.
% 1.99/2.17 ** KEPT (pick-wt=16): 20 [] cUnsatisfiable(A)| -rr(A,B)| -cc(B)| -rr(A,C)| -cd(C)|rr(A,$f4(A)).
% 1.99/2.17 ** KEPT (pick-wt=16): 21 [] cUnsatisfiable(A)| -rr(A,B)| -cc(B)| -rr(A,C)| -cd(C)|rr(A,$f3(A)).
% 1.99/2.17 ** KEPT (pick-wt=17): 22 [] cUnsatisfiable(A)| -rr(A,B)| -cc(B)| -rr(A,C)| -cd(C)|$f4(A)!=$f3(A).
% 1.99/2.17 ** KEPT (pick-wt=4): 23 [] -cc(A)|cdxcomp(A).
% 1.99/2.17 ** KEPT (pick-wt=5): 24 [] -cd(A)| -ra_Px1(A,B).
% 1.99/2.17 ** KEPT (pick-wt=6): 25 [] -cdxcomp(A)|ra_Px1(A,$f6(A)).
% 1.99/2.17 ** KEPT (pick-wt=5): 26 [] cdxcomp(A)| -ra_Px1(A,B).
% 1.99/2.17 13 back subsumes 5.
% 1.99/2.17
% 1.99/2.17 ------------> process sos:
% 1.99/2.17 ** KEPT (pick-wt=3): 31 [] A=A.
% 1.99/2.17 ** KEPT (pick-wt=2): 32 [] cowlThing(A).
% 1.99/2.17 ** KEPT (pick-wt=4): 33 [] xsd_string(A)|xsd_integer(A).
% 1.99/2.17 ** KEPT (pick-wt=6): 34 [] cd(A)|ra_Px1(A,$f5(A)).
% 1.99/2.17 ** KEPT (pick-wt=2): 35 [] cUnsatisfiable(i2003_11_14_17_22_27794).
% 1.99/2.17 Following clause subsumed by 31 during input processing: 0 [copy,31,flip.1] A=A.
% 1.99/2.17 31 back subsumes 27.
% 1.99/2.17 32 back subsumes 6.
% 1.99/2.17
% 1.99/2.17 ======= end of input processing =======
% 1.99/2.17
% 1.99/2.17 =========== start of search ===========
% 1.99/2.17
% 1.99/2.17 -------- PROOF --------
% 1.99/2.17
% 1.99/2.17 -----> EMPTY CLAUSE at 0.00 sec ----> 62 [hyper,46,24,57] $F.
% 1.99/2.17
% 1.99/2.17 Length of proof is 8. Level of proof is 3.
% 1.99/2.17
% 1.99/2.17 ---------------- PROOF ----------------
% 1.99/2.17 % SZS status Theorem
% 1.99/2.17 % SZS output start Refutation
% See solution above
% 1.99/2.17 ------------ end of proof -------------
% 1.99/2.17
% 1.99/2.17
% 1.99/2.17 Search stopped by max_proofs option.
% 1.99/2.17
% 1.99/2.17
% 1.99/2.17 Search stopped by max_proofs option.
% 1.99/2.17
% 1.99/2.17 ============ end of search ============
% 1.99/2.17
% 1.99/2.17 -------------- statistics -------------
% 1.99/2.17 clauses given 13
% 1.99/2.17 clauses generated 80
% 1.99/2.17 clauses kept 60
% 1.99/2.17 clauses forward subsumed 56
% 1.99/2.17 clauses back subsumed 3
% 1.99/2.17 Kbytes malloced 976
% 1.99/2.17
% 1.99/2.17 ----------- times (seconds) -----------
% 1.99/2.17 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.17 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.17 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.99/2.17
% 1.99/2.17 That finishes the proof of the theorem.
% 1.99/2.17
% 1.99/2.17 Process 31067 finished Wed Jul 27 03:28:10 2022
% 1.99/2.17 Otter interrupted
% 1.99/2.18 PROOF FOUND
%------------------------------------------------------------------------------