TSTP Solution File: KRS101+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS101+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.65s 1.90s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 7 unt; 2 nHn; 15 RR)
% Number of literals : 28 ( 4 equ; 13 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(14,axiom,
( ~ cUnsatisfiable(A)
| ~ rr(A,B)
| cd(B) ),
file('KRS101+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ cUnsatisfiable(A)
| ~ rr(A,B)
| ~ rs(B,C)
| ~ rs(B,D)
| C = D
| cc(B) ),
file('KRS101+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f3(A)) ),
file('KRS101+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ cUnsatisfiable(A)
| rs(dollar_f3(A),dollar_f2(A)) ),
file('KRS101+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| rs(dollar_f3(A),dollar_f1(A)) ),
file('KRS101+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| dollar_f2(A) != dollar_f1(A) ),
file('KRS101+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ cc(A)
| ~ cd(A) ),
file('KRS101+1.p',unknown),
[] ).
cnf(45,axiom,
cUnsatisfiable(i2003_11_14_17_20_36582),
file('KRS101+1.p',unknown),
[] ).
cnf(46,plain,
rs(dollar_f3(i2003_11_14_17_20_36582),dollar_f1(i2003_11_14_17_20_36582)),
inference(hyper,[status(thm)],[45,18]),
[iquote('hyper,45,18')] ).
cnf(47,plain,
rs(dollar_f3(i2003_11_14_17_20_36582),dollar_f2(i2003_11_14_17_20_36582)),
inference(hyper,[status(thm)],[45,17]),
[iquote('hyper,45,17')] ).
cnf(48,plain,
rr(i2003_11_14_17_20_36582,dollar_f3(i2003_11_14_17_20_36582)),
inference(hyper,[status(thm)],[45,16]),
[iquote('hyper,45,16')] ).
cnf(70,plain,
cd(dollar_f3(i2003_11_14_17_20_36582)),
inference(hyper,[status(thm)],[48,14,45]),
[iquote('hyper,48,14,45')] ).
cnf(170,plain,
( dollar_f2(i2003_11_14_17_20_36582) = dollar_f1(i2003_11_14_17_20_36582)
| cc(dollar_f3(i2003_11_14_17_20_36582)) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[47,15,45,48,46])]),
[iquote('hyper,47,15,45,48,46,flip.1')] ).
cnf(215,plain,
dollar_f2(i2003_11_14_17_20_36582) = dollar_f1(i2003_11_14_17_20_36582),
inference(hyper,[status(thm)],[170,30,70]),
[iquote('hyper,170,30,70')] ).
cnf(217,plain,
$false,
inference(hyper,[status(thm)],[215,19,45]),
[iquote('hyper,215,19,45')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS101+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 03:37:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.65/1.87 ----- Otter 3.3f, August 2004 -----
% 1.65/1.87 The process was started by sandbox on n018.cluster.edu,
% 1.65/1.87 Wed Jul 27 03:37:01 2022
% 1.65/1.87 The command was "./otter". The process ID is 21050.
% 1.65/1.87
% 1.65/1.87 set(prolog_style_variables).
% 1.65/1.87 set(auto).
% 1.65/1.87 dependent: set(auto1).
% 1.65/1.87 dependent: set(process_input).
% 1.65/1.87 dependent: clear(print_kept).
% 1.65/1.87 dependent: clear(print_new_demod).
% 1.65/1.87 dependent: clear(print_back_demod).
% 1.65/1.87 dependent: clear(print_back_sub).
% 1.65/1.87 dependent: set(control_memory).
% 1.65/1.87 dependent: assign(max_mem, 12000).
% 1.65/1.87 dependent: assign(pick_given_ratio, 4).
% 1.65/1.87 dependent: assign(stats_level, 1).
% 1.65/1.87 dependent: assign(max_seconds, 10800).
% 1.65/1.87 clear(print_given).
% 1.65/1.87
% 1.65/1.87 formula_list(usable).
% 1.65/1.87 all A (A=A).
% 1.65/1.87 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.65/1.87 all A B (A=B&cc(A)->cc(B)).
% 1.65/1.87 all A B (A=B&cd(A)->cd(B)).
% 1.65/1.87 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.65/1.87 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.65/1.87 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.65/1.87 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.65/1.87 all A B C (A=B&rs(A,C)->rs(B,C)).
% 1.65/1.87 all A B C (A=B&rs(C,A)->rs(C,B)).
% 1.65/1.87 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.65/1.87 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.65/1.87 all X (cowlThing(X)& -cowlNothing(X)).
% 1.65/1.87 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.65/1.87 all X (cUnsatisfiable(X)<-> (all Y (rr(X,Y)->cd(Y)))& (all Y (rr(X,Y)-> -(exists Z0 Z1 (rs(Y,Z0)&rs(Y,Z1)&Z0!=Z1))|cc(Y)))& (exists Y (rr(X,Y)& -(all Z0 Z1 (rs(Y,Z0)&rs(Y,Z1)->Z0=Z1))))).
% 1.65/1.87 all X (cc(X)-> -cd(X)).
% 1.65/1.87 cUnsatisfiable(i2003_11_14_17_20_36582).
% 1.65/1.87 end_of_list.
% 1.65/1.87
% 1.65/1.87 -------> usable clausifies to:
% 1.65/1.87
% 1.65/1.87 list(usable).
% 1.65/1.87 0 [] A=A.
% 1.65/1.87 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.65/1.87 0 [] A!=B| -cc(A)|cc(B).
% 1.65/1.87 0 [] A!=B| -cd(A)|cd(B).
% 1.65/1.87 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.65/1.87 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.65/1.87 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.65/1.87 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.65/1.87 0 [] A!=B| -rs(A,C)|rs(B,C).
% 1.65/1.87 0 [] A!=B| -rs(C,A)|rs(C,B).
% 1.65/1.87 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.65/1.87 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.65/1.87 0 [] cowlThing(X).
% 1.65/1.87 0 [] -cowlNothing(X).
% 1.65/1.87 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.65/1.87 0 [] xsd_string(X)|xsd_integer(X).
% 1.65/1.87 0 [] -cUnsatisfiable(X)| -rr(X,Y)|cd(Y).
% 1.65/1.87 0 [] -cUnsatisfiable(X)| -rr(X,X1)| -rs(X1,Z0)| -rs(X1,Z1)|Z0=Z1|cc(X1).
% 1.65/1.87 0 [] -cUnsatisfiable(X)|rr(X,$f3(X)).
% 1.65/1.87 0 [] -cUnsatisfiable(X)|rs($f3(X),$f2(X)).
% 1.65/1.87 0 [] -cUnsatisfiable(X)|rs($f3(X),$f1(X)).
% 1.65/1.87 0 [] -cUnsatisfiable(X)|$f2(X)!=$f1(X).
% 1.65/1.87 0 [] cUnsatisfiable(X)|rr(X,$f4(X))|rr(X,$f7(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)|rr(X,$f4(X))|rs($f7(X),$f6(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)|rr(X,$f4(X))|rs($f7(X),$f5(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)|rr(X,$f4(X))|$f6(X)!=$f5(X)| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)|rr(X,$f4(X))| -cc($f7(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)| -cd($f4(X))|rr(X,$f7(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)| -cd($f4(X))|rs($f7(X),$f6(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)| -cd($f4(X))|rs($f7(X),$f5(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)| -cd($f4(X))|$f6(X)!=$f5(X)| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] cUnsatisfiable(X)| -cd($f4(X))| -cc($f7(X))| -rr(X,X2)| -rs(X2,X3)| -rs(X2,X4)|X3=X4.
% 1.65/1.87 0 [] -cc(X)| -cd(X).
% 1.65/1.87 0 [] cUnsatisfiable(i2003_11_14_17_20_36582).
% 1.65/1.87 end_of_list.
% 1.65/1.87
% 1.65/1.87 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.65/1.87
% 1.65/1.87 This ia a non-Horn set with equality. The strategy will be
% 1.65/1.87 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.65/1.87 deletion, with positive clauses in sos and nonpositive
% 1.65/1.87 clauses in usable.
% 1.65/1.87
% 1.65/1.87 dependent: set(knuth_bendix).
% 1.65/1.87 dependent: set(anl_eq).
% 1.65/1.87 dependent: set(para_from).
% 1.65/1.87 dependent: set(para_into).
% 1.65/1.87 dependent: clear(para_from_right).
% 1.65/1.87 dependent: clear(para_into_right).
% 1.65/1.87 dependent: set(para_from_vars).
% 1.65/1.87 dependent: set(eq_units_both_ways).
% 1.65/1.87 dependent: set(dynamic_demod_all).
% 1.65/1.87 dependent: set(dynamic_demod).
% 1.65/1.87 dependent: set(order_eq).
% 1.65/1.87 dependent: set(back_demod).
% 1.65/1.87 dependent: set(lrpo).
% 1.65/1.87 dependent: set(hyper_res).
% 1.65/1.87 dependent: set(unit_deletion).
% 1.65/1.87 dependent: set(factor).
% 1.65/1.87
% 1.65/1.87 ------------> process usable:
% 1.65/1.87 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.65/1.90 ** KEPT (pick-wt=7): 2 [] A!=B| -cc(A)|cc(B).
% 1.65/1.90 ** KEPT (pick-wt=7): 3 [] A!=B| -cd(A)|cd(B).
% 1.65/1.90 ** KEPT (pick-wt=7): 4 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.65/1.90 ** KEPT (pick-wt=7): 5 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.65/1.90 ** KEPT (pick-wt=9): 6 [] A!=B| -rr(A,C)|rr(B,C).
% 1.65/1.90 ** KEPT (pick-wt=9): 7 [] A!=B| -rr(C,A)|rr(C,B).
% 1.65/1.90 ** KEPT (pick-wt=9): 8 [] A!=B| -rs(A,C)|rs(B,C).
% 1.65/1.90 ** KEPT (pick-wt=9): 9 [] A!=B| -rs(C,A)|rs(C,B).
% 1.65/1.90 ** KEPT (pick-wt=7): 10 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.65/1.90 ** KEPT (pick-wt=7): 11 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.65/1.90 ** KEPT (pick-wt=2): 12 [] -cowlNothing(A).
% 1.65/1.90 ** KEPT (pick-wt=4): 13 [] -xsd_string(A)| -xsd_integer(A).
% 1.65/1.90 ** KEPT (pick-wt=7): 14 [] -cUnsatisfiable(A)| -rr(A,B)|cd(B).
% 1.65/1.90 ** KEPT (pick-wt=16): 15 [] -cUnsatisfiable(A)| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D|cc(B).
% 1.65/1.90 ** KEPT (pick-wt=6): 16 [] -cUnsatisfiable(A)|rr(A,$f3(A)).
% 1.65/1.90 ** KEPT (pick-wt=7): 17 [] -cUnsatisfiable(A)|rs($f3(A),$f2(A)).
% 1.65/1.90 ** KEPT (pick-wt=7): 18 [] -cUnsatisfiable(A)|rs($f3(A),$f1(A)).
% 1.65/1.90 ** KEPT (pick-wt=7): 19 [] -cUnsatisfiable(A)|$f2(A)!=$f1(A).
% 1.65/1.90 ** KEPT (pick-wt=22): 20 [] cUnsatisfiable(A)|rr(A,$f4(A))|rr(A,$f7(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=23): 21 [] cUnsatisfiable(A)|rr(A,$f4(A))|rs($f7(A),$f6(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=23): 22 [] cUnsatisfiable(A)|rr(A,$f4(A))|rs($f7(A),$f5(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=23): 23 [] cUnsatisfiable(A)|rr(A,$f4(A))|$f6(A)!=$f5(A)| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=21): 24 [] cUnsatisfiable(A)|rr(A,$f4(A))| -cc($f7(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=21): 25 [] cUnsatisfiable(A)| -cd($f4(A))|rr(A,$f7(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=22): 26 [] cUnsatisfiable(A)| -cd($f4(A))|rs($f7(A),$f6(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=22): 27 [] cUnsatisfiable(A)| -cd($f4(A))|rs($f7(A),$f5(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=22): 28 [] cUnsatisfiable(A)| -cd($f4(A))|$f6(A)!=$f5(A)| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=20): 29 [] cUnsatisfiable(A)| -cd($f4(A))| -cc($f7(A))| -rr(A,B)| -rs(B,C)| -rs(B,D)|C=D.
% 1.65/1.90 ** KEPT (pick-wt=4): 30 [] -cc(A)| -cd(A).
% 1.65/1.90 12 back subsumes 4.
% 1.65/1.90
% 1.65/1.90 ------------> process sos:
% 1.65/1.90 ** KEPT (pick-wt=3): 42 [] A=A.
% 1.65/1.90 ** KEPT (pick-wt=2): 43 [] cowlThing(A).
% 1.65/1.90 ** KEPT (pick-wt=4): 44 [] xsd_string(A)|xsd_integer(A).
% 1.65/1.90 ** KEPT (pick-wt=2): 45 [] cUnsatisfiable(i2003_11_14_17_20_36582).
% 1.65/1.90 Following clause subsumed by 42 during input processing: 0 [copy,42,flip.1] A=A.
% 1.65/1.90 42 back subsumes 41.
% 1.65/1.90 42 back subsumes 40.
% 1.65/1.90 42 back subsumes 39.
% 1.65/1.90 42 back subsumes 38.
% 1.65/1.90 42 back subsumes 37.
% 1.65/1.90 42 back subsumes 36.
% 1.65/1.90 42 back subsumes 35.
% 1.65/1.90 42 back subsumes 34.
% 1.65/1.90 42 back subsumes 33.
% 1.65/1.90 42 back subsumes 32.
% 1.65/1.90 42 back subsumes 31.
% 1.65/1.90 43 back subsumes 5.
% 1.65/1.90
% 1.65/1.90 ======= end of input processing =======
% 1.65/1.90
% 1.65/1.90 =========== start of search ===========
% 1.65/1.90
% 1.65/1.90 -------- PROOF --------
% 1.65/1.90
% 1.65/1.90 -----> EMPTY CLAUSE at 0.03 sec ----> 217 [hyper,215,19,45] $F.
% 1.65/1.90
% 1.65/1.90 Length of proof is 6. Level of proof is 3.
% 1.65/1.90
% 1.65/1.90 ---------------- PROOF ----------------
% 1.65/1.90 % SZS status Theorem
% 1.65/1.90 % SZS output start Refutation
% See solution above
% 1.65/1.90 ------------ end of proof -------------
% 1.65/1.90
% 1.65/1.90
% 1.65/1.90 Search stopped by max_proofs option.
% 1.65/1.90
% 1.65/1.90
% 1.65/1.90 Search stopped by max_proofs option.
% 1.65/1.90
% 1.65/1.90 ============ end of search ============
% 1.65/1.90
% 1.65/1.90 -------------- statistics -------------
% 1.65/1.90 clauses given 10
% 1.65/1.90 clauses generated 386
% 1.65/1.90 clauses kept 215
% 1.65/1.90 clauses forward subsumed 240
% 1.65/1.90 clauses back subsumed 13
% 1.65/1.90 Kbytes malloced 976
% 1.65/1.90
% 1.65/1.90 ----------- times (seconds) -----------
% 1.65/1.90 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.65/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.90
% 1.65/1.90 That finishes the proof of the theorem.
% 1.65/1.90
% 1.65/1.90 Process 21050 finished Wed Jul 27 03:37:02 2022
% 1.65/1.90 Otter interrupted
% 1.65/1.90 PROOF FOUND
%------------------------------------------------------------------------------