TSTP Solution File: KRS124+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS124+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:01:12 EDT 2022
% Result : Unsatisfiable 1.74s 1.90s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 8 unt; 0 nHn; 15 RR)
% Number of literals : 23 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 9 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f1(A)) ),
file('KRS124+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ cUnsatisfiable(A)
| ~ rr(A,B)
| ca_Ax3(B) ),
file('KRS124+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ cc(A)
| cdxcomp(A) ),
file('KRS124+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ cd(A)
| ~ ra_Px1(A,B) ),
file('KRS124+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ cdxcomp(A)
| ra_Px1(A,dollar_f4(A)) ),
file('KRS124+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ ca_Ax3(A)
| cd(A) ),
file('KRS124+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ ca_Ax3(A)
| cc(A) ),
file('KRS124+1.p',unknown),
[] ).
cnf(26,axiom,
cUnsatisfiable(i2003_11_14_17_22_10903),
file('KRS124+1.p',unknown),
[] ).
cnf(27,plain,
rr(i2003_11_14_17_22_10903,dollar_f1(i2003_11_14_17_22_10903)),
inference(hyper,[status(thm)],[26,3]),
[iquote('hyper,26,3')] ).
cnf(28,plain,
ca_Ax3(dollar_f1(i2003_11_14_17_22_10903)),
inference(hyper,[status(thm)],[27,5,26]),
[iquote('hyper,27,5,26')] ).
cnf(29,plain,
cc(dollar_f1(i2003_11_14_17_22_10903)),
inference(hyper,[status(thm)],[28,20]),
[iquote('hyper,28,20')] ).
cnf(30,plain,
cd(dollar_f1(i2003_11_14_17_22_10903)),
inference(hyper,[status(thm)],[28,19]),
[iquote('hyper,28,19')] ).
cnf(31,plain,
cdxcomp(dollar_f1(i2003_11_14_17_22_10903)),
inference(hyper,[status(thm)],[29,8]),
[iquote('hyper,29,8')] ).
cnf(32,plain,
ra_Px1(dollar_f1(i2003_11_14_17_22_10903),dollar_f4(dollar_f1(i2003_11_14_17_22_10903))),
inference(hyper,[status(thm)],[31,12]),
[iquote('hyper,31,12')] ).
cnf(33,plain,
$false,
inference(hyper,[status(thm)],[32,11,30]),
[iquote('hyper,32,11,30')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS124+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 03:28:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.90 ----- Otter 3.3f, August 2004 -----
% 1.74/1.90 The process was started by sandbox on n024.cluster.edu,
% 1.74/1.90 Wed Jul 27 03:28:10 2022
% 1.74/1.90 The command was "./otter". The process ID is 6449.
% 1.74/1.90
% 1.74/1.90 set(prolog_style_variables).
% 1.74/1.90 set(auto).
% 1.74/1.90 dependent: set(auto1).
% 1.74/1.90 dependent: set(process_input).
% 1.74/1.90 dependent: clear(print_kept).
% 1.74/1.90 dependent: clear(print_new_demod).
% 1.74/1.90 dependent: clear(print_back_demod).
% 1.74/1.90 dependent: clear(print_back_sub).
% 1.74/1.90 dependent: set(control_memory).
% 1.74/1.90 dependent: assign(max_mem, 12000).
% 1.74/1.90 dependent: assign(pick_given_ratio, 4).
% 1.74/1.90 dependent: assign(stats_level, 1).
% 1.74/1.90 dependent: assign(max_seconds, 10800).
% 1.74/1.90 clear(print_given).
% 1.74/1.90
% 1.74/1.90 formula_list(usable).
% 1.74/1.90 all X (cowlThing(X)& -cowlNothing(X)).
% 1.74/1.90 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.74/1.90 all X (cUnsatisfiable(X)<-> (exists Y (rr(X,Y)&cowlThing(Y)))& (all Y (rr(X,Y)->ca_Ax3(Y)))).
% 1.74/1.90 all X (cc(X)->cdxcomp(X)).
% 1.74/1.90 all X (cc1(X)->cd1(X)).
% 1.74/1.90 all X (cc1(X)->cd1xcomp(X)).
% 1.74/1.90 all X (cd(X)<-> -(exists Y ra_Px1(X,Y))).
% 1.74/1.90 all X (cdxcomp(X)<-> (exists Y0 ra_Px1(X,Y0))).
% 1.74/1.90 all X (cd1(X)<-> (exists Y0 ra_Px2(X,Y0))).
% 1.74/1.90 all X (cd1xcomp(X)<-> -(exists Y ra_Px2(X,Y))).
% 1.74/1.90 all X (ce3(X)->cc(X)).
% 1.74/1.90 all X (cf(X)->cd(X)).
% 1.74/1.90 all X (ca_Ax3(X)<->cd(X)&cc(X)).
% 1.74/1.90 cUnsatisfiable(i2003_11_14_17_22_10903).
% 1.74/1.90 end_of_list.
% 1.74/1.90
% 1.74/1.90 -------> usable clausifies to:
% 1.74/1.90
% 1.74/1.90 list(usable).
% 1.74/1.90 0 [] cowlThing(X).
% 1.74/1.90 0 [] -cowlNothing(X).
% 1.74/1.90 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.74/1.90 0 [] xsd_string(X)|xsd_integer(X).
% 1.74/1.90 0 [] -cUnsatisfiable(X)|rr(X,$f1(X)).
% 1.74/1.90 0 [] -cUnsatisfiable(X)|cowlThing($f1(X)).
% 1.74/1.90 0 [] -cUnsatisfiable(X)| -rr(X,Y)|ca_Ax3(Y).
% 1.74/1.90 0 [] cUnsatisfiable(X)| -rr(X,X1)| -cowlThing(X1)|rr(X,$f2(X)).
% 1.74/1.90 0 [] cUnsatisfiable(X)| -rr(X,X1)| -cowlThing(X1)| -ca_Ax3($f2(X)).
% 1.74/1.90 0 [] -cc(X)|cdxcomp(X).
% 1.74/1.90 0 [] -cc1(X)|cd1(X).
% 1.74/1.90 0 [] -cc1(X)|cd1xcomp(X).
% 1.74/1.90 0 [] -cd(X)| -ra_Px1(X,Y).
% 1.74/1.90 0 [] cd(X)|ra_Px1(X,$f3(X)).
% 1.74/1.90 0 [] -cdxcomp(X)|ra_Px1(X,$f4(X)).
% 1.74/1.90 0 [] cdxcomp(X)| -ra_Px1(X,Y0).
% 1.74/1.90 0 [] -cd1(X)|ra_Px2(X,$f5(X)).
% 1.74/1.90 0 [] cd1(X)| -ra_Px2(X,Y0).
% 1.74/1.90 0 [] -cd1xcomp(X)| -ra_Px2(X,Y).
% 1.74/1.90 0 [] cd1xcomp(X)|ra_Px2(X,$f6(X)).
% 1.74/1.90 0 [] -ce3(X)|cc(X).
% 1.74/1.90 0 [] -cf(X)|cd(X).
% 1.74/1.90 0 [] -ca_Ax3(X)|cd(X).
% 1.74/1.90 0 [] -ca_Ax3(X)|cc(X).
% 1.74/1.90 0 [] ca_Ax3(X)| -cd(X)| -cc(X).
% 1.74/1.90 0 [] cUnsatisfiable(i2003_11_14_17_22_10903).
% 1.74/1.90 end_of_list.
% 1.74/1.90
% 1.74/1.90 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.74/1.90
% 1.74/1.90 This is a non-Horn set without equality. The strategy will
% 1.74/1.90 be ordered hyper_res, unit deletion, and factoring, with
% 1.74/1.90 satellites in sos and with nuclei in usable.
% 1.74/1.90
% 1.74/1.90 dependent: set(hyper_res).
% 1.74/1.90 dependent: set(factor).
% 1.74/1.90 dependent: set(unit_deletion).
% 1.74/1.90
% 1.74/1.90 ------------> process usable:
% 1.74/1.90 ** KEPT (pick-wt=2): 1 [] -cowlNothing(A).
% 1.74/1.90 ** KEPT (pick-wt=4): 2 [] -xsd_string(A)| -xsd_integer(A).
% 1.74/1.90 ** KEPT (pick-wt=6): 3 [] -cUnsatisfiable(A)|rr(A,$f1(A)).
% 1.74/1.90 ** KEPT (pick-wt=5): 4 [] -cUnsatisfiable(A)|cowlThing($f1(A)).
% 1.74/1.90 ** KEPT (pick-wt=7): 5 [] -cUnsatisfiable(A)| -rr(A,B)|ca_Ax3(B).
% 1.74/1.90 ** KEPT (pick-wt=11): 6 [] cUnsatisfiable(A)| -rr(A,B)| -cowlThing(B)|rr(A,$f2(A)).
% 1.74/1.90 ** KEPT (pick-wt=10): 7 [] cUnsatisfiable(A)| -rr(A,B)| -cowlThing(B)| -ca_Ax3($f2(A)).
% 1.74/1.90 ** KEPT (pick-wt=4): 8 [] -cc(A)|cdxcomp(A).
% 1.74/1.90 ** KEPT (pick-wt=4): 9 [] -cc1(A)|cd1(A).
% 1.74/1.90 ** KEPT (pick-wt=4): 10 [] -cc1(A)|cd1xcomp(A).
% 1.74/1.90 ** KEPT (pick-wt=5): 11 [] -cd(A)| -ra_Px1(A,B).
% 1.74/1.90 ** KEPT (pick-wt=6): 12 [] -cdxcomp(A)|ra_Px1(A,$f4(A)).
% 1.74/1.90 ** KEPT (pick-wt=5): 13 [] cdxcomp(A)| -ra_Px1(A,B).
% 1.74/1.90 ** KEPT (pick-wt=6): 14 [] -cd1(A)|ra_Px2(A,$f5(A)).
% 1.74/1.90 ** KEPT (pick-wt=5): 15 [] cd1(A)| -ra_Px2(A,B).
% 1.74/1.90 ** KEPT (pick-wt=5): 16 [] -cd1xcomp(A)| -ra_Px2(A,B).
% 1.74/1.90 ** KEPT (pick-wt=4): 17 [] -ce3(A)|cc(A).
% 1.74/1.90 ** KEPT (pick-wt=4): 18 [] -cf(A)|cd(A).
% 1.74/1.90 ** KEPT (pick-wt=4): 19 [] -ca_Ax3(A)|cd(A).
% 1.74/1.90 ** KEPT (pick-wt=4): 20 [] -ca_Ax3(A)|cc(A).
% 1.74/1.90 ** KEPT (pick-wt=6): 21 [] ca_Ax3(A)| -cd(A)| -cc(A).
% 1.74/1.90
% 1.74/1.90 ------------> process sos:
% 1.74/1.90 ** KEPT (pick-wt=2): 22 [] cowlThing(A).
% 1.74/1.90 ** KEPT (pick-wt=4): 23 [] xsd_string(A)|xsd_integer(A).
% 1.74/1.90 ** KEPT (pick-wt=6): 24 [] cd(A)|ra_Px1(A,$f3(A)).
% 1.74/1.90 ** KEPT (pick-wt=6): 25 [] cd1xcomp(A)|ra_Px2(A,$f6(A)).
% 1.74/1.90 ** KEPT (pick-wt=2): 26 [] cUnsatisfiable(i2003_11_14_17_22_10903).
% 1.74/1.90 22 back subsumes 4.
% 1.74/1.90
% 1.74/1.90 ======= end of input processing =======
% 1.74/1.90
% 1.74/1.90 =========== start of search ===========
% 1.74/1.90
% 1.74/1.90 -------- PROOF --------
% 1.74/1.90
% 1.74/1.90 -----> EMPTY CLAUSE at 0.00 sec ----> 33 [hyper,32,11,30] $F.
% 1.74/1.90
% 1.74/1.90 Length of proof is 6. Level of proof is 5.
% 1.74/1.90
% 1.74/1.90 ---------------- PROOF ----------------
% 1.74/1.90 % SZS status Theorem
% 1.74/1.90 % SZS output start Refutation
% See solution above
% 1.74/1.90 ------------ end of proof -------------
% 1.74/1.90
% 1.74/1.90
% 1.74/1.90 Search stopped by max_proofs option.
% 1.74/1.90
% 1.74/1.90
% 1.74/1.90 Search stopped by max_proofs option.
% 1.74/1.90
% 1.74/1.90 ============ end of search ============
% 1.74/1.90
% 1.74/1.90 -------------- statistics -------------
% 1.74/1.90 clauses given 11
% 1.74/1.90 clauses generated 11
% 1.74/1.90 clauses kept 32
% 1.74/1.90 clauses forward subsumed 4
% 1.74/1.90 clauses back subsumed 1
% 1.74/1.90 Kbytes malloced 976
% 1.74/1.90
% 1.74/1.90 ----------- times (seconds) -----------
% 1.74/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.90
% 1.74/1.90 That finishes the proof of the theorem.
% 1.74/1.90
% 1.74/1.90 Process 6449 finished Wed Jul 27 03:28:11 2022
% 1.74/1.90 Otter interrupted
% 1.74/1.90 PROOF FOUND
%------------------------------------------------------------------------------