TSTP Solution File: KRS084+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS084+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 13:01:06 EDT 2022
% Result : Unsatisfiable 2.11s 2.28s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 24 ( 13 unt; 0 nHn; 24 RR)
% Number of literals : 38 ( 2 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| rinvF(A,dollar_f1(A)) ),
file('KRS084+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| cd(dollar_f1(A)) ),
file('KRS084+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvR(A,B)
| rinvF(B,dollar_f2(A,B)) ),
file('KRS084+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvR(A,B)
| cd(dollar_f2(A,B)) ),
file('KRS084+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ cd(A)
| rf(A,dollar_f4(A)) ),
file('KRS084+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ cd(A)
| ~ cc(dollar_f4(A)) ),
file('KRS084+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ cd(A)
| cc(A) ),
file('KRS084+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ rf(A,B)
| ~ rf(A,C)
| B = C ),
file('KRS084+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ rinvF(A,B)
| rf(B,A) ),
file('KRS084+1.p',unknown),
[] ).
cnf(33,axiom,
( rinvR(A,B)
| ~ rr(B,A) ),
file('KRS084+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ rf(A,B)
| rr(A,B) ),
file('KRS084+1.p',unknown),
[] ).
cnf(41,axiom,
cUnsatisfiable(i2003_11_14_17_19_35232),
file('KRS084+1.p',unknown),
[] ).
cnf(42,plain,
cd(dollar_f1(i2003_11_14_17_19_35232)),
inference(hyper,[status(thm)],[41,19]),
[iquote('hyper,41,19')] ).
cnf(43,plain,
rinvF(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232)),
inference(hyper,[status(thm)],[41,18]),
[iquote('hyper,41,18')] ).
cnf(45,plain,
cc(dollar_f1(i2003_11_14_17_19_35232)),
inference(hyper,[status(thm)],[42,27]),
[iquote('hyper,42,27')] ).
cnf(51,plain,
rf(dollar_f1(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(hyper,[status(thm)],[43,30]),
[iquote('hyper,43,30')] ).
cnf(55,plain,
rr(dollar_f1(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(hyper,[status(thm)],[51,35]),
[iquote('hyper,51,35')] ).
cnf(59,plain,
rinvR(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232)),
inference(hyper,[status(thm)],[55,33]),
[iquote('hyper,55,33')] ).
cnf(63,plain,
cd(dollar_f2(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232))),
inference(hyper,[status(thm)],[59,21,41]),
[iquote('hyper,59,21,41')] ).
cnf(64,plain,
rinvF(dollar_f1(i2003_11_14_17_19_35232),dollar_f2(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232))),
inference(hyper,[status(thm)],[59,20,41]),
[iquote('hyper,59,20,41')] ).
cnf(70,plain,
rf(dollar_f2(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232)),dollar_f4(dollar_f2(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232)))),
inference(hyper,[status(thm)],[63,25]),
[iquote('hyper,63,25')] ).
cnf(92,plain,
rf(dollar_f2(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232)),dollar_f1(i2003_11_14_17_19_35232)),
inference(hyper,[status(thm)],[64,30]),
[iquote('hyper,64,30')] ).
cnf(196,plain,
dollar_f4(dollar_f2(i2003_11_14_17_19_35232,dollar_f1(i2003_11_14_17_19_35232))) = dollar_f1(i2003_11_14_17_19_35232),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[70,29,92])]),
[iquote('hyper,70,29,92,flip.1')] ).
cnf(202,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[196,26]),63,45]),
[iquote('para_from,196.1.1,26.2.1,unit_del,63,45')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KRS084+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.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 03:27:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.11/2.27 ----- Otter 3.3f, August 2004 -----
% 2.11/2.27 The process was started by sandbox2 on n020.cluster.edu,
% 2.11/2.27 Wed Jul 27 03:27:23 2022
% 2.11/2.27 The command was "./otter". The process ID is 27411.
% 2.11/2.27
% 2.11/2.27 set(prolog_style_variables).
% 2.11/2.27 set(auto).
% 2.11/2.27 dependent: set(auto1).
% 2.11/2.27 dependent: set(process_input).
% 2.11/2.27 dependent: clear(print_kept).
% 2.11/2.27 dependent: clear(print_new_demod).
% 2.11/2.27 dependent: clear(print_back_demod).
% 2.11/2.27 dependent: clear(print_back_sub).
% 2.11/2.27 dependent: set(control_memory).
% 2.11/2.27 dependent: assign(max_mem, 12000).
% 2.11/2.27 dependent: assign(pick_given_ratio, 4).
% 2.11/2.27 dependent: assign(stats_level, 1).
% 2.11/2.27 dependent: assign(max_seconds, 10800).
% 2.11/2.27 clear(print_given).
% 2.11/2.27
% 2.11/2.27 formula_list(usable).
% 2.11/2.27 all A (A=A).
% 2.11/2.27 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 2.11/2.27 all A B (A=B&cc(A)->cc(B)).
% 2.11/2.27 all A B (A=B&cd(A)->cd(B)).
% 2.11/2.27 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 2.11/2.27 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 2.11/2.27 all A B C (A=B&rf(A,C)->rf(B,C)).
% 2.11/2.27 all A B C (A=B&rf(C,A)->rf(C,B)).
% 2.11/2.27 all A B C (A=B&rinvF(A,C)->rinvF(B,C)).
% 2.11/2.27 all A B C (A=B&rinvF(C,A)->rinvF(C,B)).
% 2.11/2.27 all A B C (A=B&rinvR(A,C)->rinvR(B,C)).
% 2.11/2.27 all A B C (A=B&rinvR(C,A)->rinvR(C,B)).
% 2.11/2.27 all A B C (A=B&rr(A,C)->rr(B,C)).
% 2.11/2.27 all A B C (A=B&rr(C,A)->rr(C,B)).
% 2.11/2.27 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 2.11/2.27 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 2.11/2.27 all X (cowlThing(X)& -cowlNothing(X)).
% 2.11/2.27 all X (xsd_string(X)<-> -xsd_integer(X)).
% 2.11/2.27 all X (cUnsatisfiable(X)<-> (exists Y (rinvF(X,Y)&cd(Y)))& (all Y (rinvR(X,Y)-> (exists Z (rinvF(Y,Z)&cd(Z)))))& -cc(X)).
% 2.11/2.27 all X (cd(X)<-> (exists Y (rf(X,Y)& -cc(Y)))&cc(X)).
% 2.11/2.27 all X Y Z (rf(X,Y)&rf(X,Z)->Y=Z).
% 2.11/2.27 all X Y (rinvF(X,Y)<->rf(Y,X)).
% 2.11/2.27 all X Y (rinvR(X,Y)<->rr(Y,X)).
% 2.11/2.27 all X Y Z (rr(X,Y)&rr(Y,Z)->rr(X,Z)).
% 2.11/2.27 cUnsatisfiable(i2003_11_14_17_19_35232).
% 2.11/2.27 all X Y (rf(X,Y)->rr(X,Y)).
% 2.11/2.27 end_of_list.
% 2.11/2.27
% 2.11/2.27 -------> usable clausifies to:
% 2.11/2.27
% 2.11/2.27 list(usable).
% 2.11/2.27 0 [] A=A.
% 2.11/2.27 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 2.11/2.27 0 [] A!=B| -cc(A)|cc(B).
% 2.11/2.27 0 [] A!=B| -cd(A)|cd(B).
% 2.11/2.27 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 2.11/2.27 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 2.11/2.27 0 [] A!=B| -rf(A,C)|rf(B,C).
% 2.11/2.27 0 [] A!=B| -rf(C,A)|rf(C,B).
% 2.11/2.27 0 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 2.11/2.27 0 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 2.11/2.27 0 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 2.11/2.27 0 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 2.11/2.27 0 [] A!=B| -rr(A,C)|rr(B,C).
% 2.11/2.27 0 [] A!=B| -rr(C,A)|rr(C,B).
% 2.11/2.27 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 2.11/2.27 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 2.11/2.27 0 [] cowlThing(X).
% 2.11/2.27 0 [] -cowlNothing(X).
% 2.11/2.27 0 [] -xsd_string(X)| -xsd_integer(X).
% 2.11/2.27 0 [] xsd_string(X)|xsd_integer(X).
% 2.11/2.27 0 [] -cUnsatisfiable(X)|rinvF(X,$f1(X)).
% 2.11/2.27 0 [] -cUnsatisfiable(X)|cd($f1(X)).
% 2.11/2.27 0 [] -cUnsatisfiable(X)| -rinvR(X,Y)|rinvF(Y,$f2(X,Y)).
% 2.11/2.27 0 [] -cUnsatisfiable(X)| -rinvR(X,Y)|cd($f2(X,Y)).
% 2.11/2.27 0 [] -cUnsatisfiable(X)| -cc(X).
% 2.11/2.27 0 [] cUnsatisfiable(X)| -rinvF(X,X1)| -cd(X1)|rinvR(X,$f3(X))|cc(X).
% 2.11/2.27 0 [] cUnsatisfiable(X)| -rinvF(X,X1)| -cd(X1)| -rinvF($f3(X),Z)| -cd(Z)|cc(X).
% 2.11/2.27 0 [] -cd(X)|rf(X,$f4(X)).
% 2.11/2.27 0 [] -cd(X)| -cc($f4(X)).
% 2.11/2.27 0 [] -cd(X)|cc(X).
% 2.11/2.27 0 [] cd(X)| -rf(X,Y)|cc(Y)| -cc(X).
% 2.11/2.27 0 [] -rf(X,Y)| -rf(X,Z)|Y=Z.
% 2.11/2.27 0 [] -rinvF(X,Y)|rf(Y,X).
% 2.11/2.27 0 [] rinvF(X,Y)| -rf(Y,X).
% 2.11/2.27 0 [] -rinvR(X,Y)|rr(Y,X).
% 2.11/2.27 0 [] rinvR(X,Y)| -rr(Y,X).
% 2.11/2.27 0 [] -rr(X,Y)| -rr(Y,Z)|rr(X,Z).
% 2.11/2.27 0 [] cUnsatisfiable(i2003_11_14_17_19_35232).
% 2.11/2.27 0 [] -rf(X,Y)|rr(X,Y).
% 2.11/2.27 end_of_list.
% 2.11/2.27
% 2.11/2.27 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 2.11/2.27
% 2.11/2.27 This ia a non-Horn set with equality. The strategy will be
% 2.11/2.27 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.11/2.27 deletion, with positive clauses in sos and nonpositive
% 2.11/2.27 clauses in usable.
% 2.11/2.27
% 2.11/2.27 dependent: set(knuth_bendix).
% 2.11/2.27 dependent: set(anl_eq).
% 2.11/2.27 dependent: set(para_from).
% 2.11/2.27 dependent: set(para_into).
% 2.11/2.27 dependent: clear(para_from_right).
% 2.11/2.27 dependent: clear(para_into_right).
% 2.11/2.27 dependent: set(para_from_vars).
% 2.11/2.27 dependent: set(eq_units_both_ways).
% 2.11/2.27 dependent: set(dynamic_demod_all).
% 2.11/2.27 dependent: set(dynamic_demod).
% 2.11/2.27 dependent: set(order_eq).
% 2.11/2.27 dependent: set(back_demod).
% 2.11/2.27 dependent: set(lrpo).
% 2.11/2.27 dependent: set(hyper_res).
% 2.11/2.27 dependent: set(unit_deletion).
% 2.11/2.27 dependent: set(factor).
% 2.11/2.27
% 2.11/2.27 ------------> process usable:
% 2.11/2.27 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 2.11/2.27 ** KEPT (pick-wt=7): 2 [] A!=B| -cc(A)|cc(B).
% 2.11/2.27 ** KEPT (pick-wt=7): 3 [] A!=B| -cd(A)|cd(B).
% 2.11/2.28 ** KEPT (pick-wt=7): 4 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 2.11/2.28 ** KEPT (pick-wt=7): 5 [] A!=B| -cowlThing(A)|cowlThing(B).
% 2.11/2.28 ** KEPT (pick-wt=9): 6 [] A!=B| -rf(A,C)|rf(B,C).
% 2.11/2.28 ** KEPT (pick-wt=9): 7 [] A!=B| -rf(C,A)|rf(C,B).
% 2.11/2.28 ** KEPT (pick-wt=9): 8 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 2.11/2.28 ** KEPT (pick-wt=9): 9 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 2.11/2.28 ** KEPT (pick-wt=9): 10 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 2.11/2.28 ** KEPT (pick-wt=9): 11 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 2.11/2.28 ** KEPT (pick-wt=9): 12 [] A!=B| -rr(A,C)|rr(B,C).
% 2.11/2.28 ** KEPT (pick-wt=9): 13 [] A!=B| -rr(C,A)|rr(C,B).
% 2.11/2.28 ** KEPT (pick-wt=7): 14 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 2.11/2.28 ** KEPT (pick-wt=7): 15 [] A!=B| -xsd_string(A)|xsd_string(B).
% 2.11/2.28 ** KEPT (pick-wt=2): 16 [] -cowlNothing(A).
% 2.11/2.28 ** KEPT (pick-wt=4): 17 [] -xsd_string(A)| -xsd_integer(A).
% 2.11/2.28 ** KEPT (pick-wt=6): 18 [] -cUnsatisfiable(A)|rinvF(A,$f1(A)).
% 2.11/2.28 ** KEPT (pick-wt=5): 19 [] -cUnsatisfiable(A)|cd($f1(A)).
% 2.11/2.28 ** KEPT (pick-wt=10): 20 [] -cUnsatisfiable(A)| -rinvR(A,B)|rinvF(B,$f2(A,B)).
% 2.11/2.28 ** KEPT (pick-wt=9): 21 [] -cUnsatisfiable(A)| -rinvR(A,B)|cd($f2(A,B)).
% 2.11/2.28 ** KEPT (pick-wt=4): 22 [] -cUnsatisfiable(A)| -cc(A).
% 2.11/2.28 ** KEPT (pick-wt=13): 23 [] cUnsatisfiable(A)| -rinvF(A,B)| -cd(B)|rinvR(A,$f3(A))|cc(A).
% 2.11/2.28 ** KEPT (pick-wt=15): 24 [] cUnsatisfiable(A)| -rinvF(A,B)| -cd(B)| -rinvF($f3(A),C)| -cd(C)|cc(A).
% 2.11/2.28 ** KEPT (pick-wt=6): 25 [] -cd(A)|rf(A,$f4(A)).
% 2.11/2.28 ** KEPT (pick-wt=5): 26 [] -cd(A)| -cc($f4(A)).
% 2.11/2.28 ** KEPT (pick-wt=4): 27 [] -cd(A)|cc(A).
% 2.11/2.28 ** KEPT (pick-wt=9): 28 [] cd(A)| -rf(A,B)|cc(B)| -cc(A).
% 2.11/2.28 ** KEPT (pick-wt=9): 29 [] -rf(A,B)| -rf(A,C)|B=C.
% 2.11/2.28 ** KEPT (pick-wt=6): 30 [] -rinvF(A,B)|rf(B,A).
% 2.11/2.28 ** KEPT (pick-wt=6): 31 [] rinvF(A,B)| -rf(B,A).
% 2.11/2.28 ** KEPT (pick-wt=6): 32 [] -rinvR(A,B)|rr(B,A).
% 2.11/2.28 ** KEPT (pick-wt=6): 33 [] rinvR(A,B)| -rr(B,A).
% 2.11/2.28 ** KEPT (pick-wt=9): 34 [] -rr(A,B)| -rr(B,C)|rr(A,C).
% 2.11/2.28 ** KEPT (pick-wt=6): 35 [] -rf(A,B)|rr(A,B).
% 2.11/2.28 16 back subsumes 4.
% 2.11/2.28
% 2.11/2.28 ------------> process sos:
% 2.11/2.28 ** KEPT (pick-wt=3): 38 [] A=A.
% 2.11/2.28 ** KEPT (pick-wt=2): 39 [] cowlThing(A).
% 2.11/2.28 ** KEPT (pick-wt=4): 40 [] xsd_string(A)|xsd_integer(A).
% 2.11/2.28 ** KEPT (pick-wt=2): 41 [] cUnsatisfiable(i2003_11_14_17_19_35232).
% 2.11/2.28 Following clause subsumed by 38 during input processing: 0 [copy,38,flip.1] A=A.
% 2.11/2.28 38 back subsumes 37.
% 2.11/2.28 39 back subsumes 5.
% 2.11/2.28
% 2.11/2.28 ======= end of input processing =======
% 2.11/2.28
% 2.11/2.28 =========== start of search ===========
% 2.11/2.28
% 2.11/2.28 -------- PROOF --------
% 2.11/2.28
% 2.11/2.28 -----> EMPTY CLAUSE at 0.01 sec ----> 202 [para_from,196.1.1,26.2.1,unit_del,63,45] $F.
% 2.11/2.28
% 2.11/2.28 Length of proof is 11. Level of proof is 7.
% 2.11/2.28
% 2.11/2.28 ---------------- PROOF ----------------
% 2.11/2.28 % SZS status Theorem
% 2.11/2.28 % SZS output start Refutation
% See solution above
% 2.11/2.28 ------------ end of proof -------------
% 2.11/2.28
% 2.11/2.28
% 2.11/2.28 Search stopped by max_proofs option.
% 2.11/2.28
% 2.11/2.28
% 2.11/2.28 Search stopped by max_proofs option.
% 2.11/2.28
% 2.11/2.28 ============ end of search ============
% 2.11/2.28
% 2.11/2.28 -------------- statistics -------------
% 2.11/2.28 clauses given 44
% 2.11/2.28 clauses generated 525
% 2.11/2.28 clauses kept 199
% 2.11/2.28 clauses forward subsumed 377
% 2.11/2.28 clauses back subsumed 5
% 2.11/2.28 Kbytes malloced 976
% 2.11/2.28
% 2.11/2.28 ----------- times (seconds) -----------
% 2.11/2.28 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.11/2.28 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.11/2.28 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.11/2.28
% 2.11/2.28 That finishes the proof of the theorem.
% 2.11/2.28
% 2.11/2.28 Process 27411 finished Wed Jul 27 03:27:25 2022
% 2.11/2.28 Otter interrupted
% 2.11/2.28 PROOF FOUND
%------------------------------------------------------------------------------