%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS078+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:01:05 EDT 2022
% Result : Unsatisfiable 1.76s 1.92s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 8 unt; 0 nHn; 16 RR)
% Number of literals : 27 ( 2 equ; 12 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 : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
( ~ cUnsatisfiable(A)
| rr(A,dollar_f2(A)) ),
file('KRS078+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ cUnsatisfiable(A)
| rinvR(dollar_f2(A),dollar_f1(A)) ),
file('KRS078+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| ~ rs(dollar_f1(A),B)
| cp(B) ),
file('KRS078+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvR(dollar_f2(A),B)
| ~ rinvR(dollar_f2(A),C)
| B = C ),
file('KRS078+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ cUnsatisfiable(A)
| rs(A,dollar_f3(A)) ),
file('KRS078+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ cUnsatisfiable(A)
| ~ cp(dollar_f3(A)) ),
file('KRS078+1.p',unknown),
[] ).
cnf(30,axiom,
( rinvR(A,B)
| ~ rr(B,A) ),
file('KRS078+1.p',unknown),
[] ).
cnf(35,axiom,
cUnsatisfiable(i2003_11_14_17_19_13721),
file('KRS078+1.p',unknown),
[] ).
cnf(36,plain,
rs(i2003_11_14_17_19_13721,dollar_f3(i2003_11_14_17_19_13721)),
inference(hyper,[status(thm)],[35,20]),
[iquote('hyper,35,20')] ).
cnf(37,plain,
rinvR(dollar_f2(i2003_11_14_17_19_13721),dollar_f1(i2003_11_14_17_19_13721)),
inference(hyper,[status(thm)],[35,17]),
[iquote('hyper,35,17')] ).
cnf(38,plain,
rr(i2003_11_14_17_19_13721,dollar_f2(i2003_11_14_17_19_13721)),
inference(hyper,[status(thm)],[35,16]),
[iquote('hyper,35,16')] ).
cnf(48,plain,
rinvR(dollar_f2(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721),
inference(hyper,[status(thm)],[38,30]),
[iquote('hyper,38,30')] ).
cnf(52,plain,
dollar_f1(i2003_11_14_17_19_13721) = i2003_11_14_17_19_13721,
inference(hyper,[status(thm)],[48,19,35,37]),
[iquote('hyper,48,19,35,37')] ).
cnf(58,plain,
( ~ rs(i2003_11_14_17_19_13721,A)
| cp(A) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[52,18]),35]),
[iquote('para_from,52.1.1,18.2.1,unit_del,35')] ).
cnf(59,plain,
cp(dollar_f3(i2003_11_14_17_19_13721)),
inference(hyper,[status(thm)],[58,36]),
[iquote('hyper,58,36')] ).
cnf(69,plain,
$false,
inference(hyper,[status(thm)],[59,22,35]),
[iquote('hyper,59,22,35')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS078+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 03:32:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.76/1.92 ----- Otter 3.3f, August 2004 -----
% 1.76/1.92 The process was started by sandbox2 on n019.cluster.edu,
% 1.76/1.92 Wed Jul 27 03:32:52 2022
% 1.76/1.92 The command was "./otter". The process ID is 9654.
% 1.76/1.92
% 1.76/1.92 set(prolog_style_variables).
% 1.76/1.92 set(auto).
% 1.76/1.92 dependent: set(auto1).
% 1.76/1.92 dependent: set(process_input).
% 1.76/1.92 dependent: clear(print_kept).
% 1.76/1.92 dependent: clear(print_new_demod).
% 1.76/1.92 dependent: clear(print_back_demod).
% 1.76/1.92 dependent: clear(print_back_sub).
% 1.76/1.92 dependent: set(control_memory).
% 1.76/1.92 dependent: assign(max_mem, 12000).
% 1.76/1.92 dependent: assign(pick_given_ratio, 4).
% 1.76/1.92 dependent: assign(stats_level, 1).
% 1.76/1.92 dependent: assign(max_seconds, 10800).
% 1.76/1.92 clear(print_given).
% 1.76/1.92
% 1.76/1.92 formula_list(usable).
% 1.76/1.92 all A (A=A).
% 1.76/1.92 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.76/1.92 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.76/1.92 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.76/1.92 all A B (A=B&cp(A)->cp(B)).
% 1.76/1.92 all A B (A=B&cq(A)->cq(B)).
% 1.76/1.92 all A B C (A=B&rinvR(A,C)->rinvR(B,C)).
% 1.76/1.92 all A B C (A=B&rinvR(C,A)->rinvR(C,B)).
% 1.76/1.92 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.76/1.92 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.76/1.92 all A B C (A=B&rs(A,C)->rs(B,C)).
% 1.76/1.92 all A B C (A=B&rs(C,A)->rs(C,B)).
% 1.76/1.92 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.76/1.92 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.76/1.92 all X (cowlThing(X)& -cowlNothing(X)).
% 1.76/1.92 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.76/1.92 all X (cUnsatisfiable(X)<-> (exists Y (rr(X,Y)& (exists Z (rinvR(Y,Z)& (all W (rs(Z,W)->cp(W)))))& (all Z0 Z1 (rinvR(Y,Z0)&rinvR(Y,Z1)->Z0=Z1))))& (exists Y (rs(X,Y)& -cq(Y)& -cp(Y)))).
% 1.76/1.92 all X Y (rinvR(X,Y)<->rr(Y,X)).
% 1.76/1.92 cUnsatisfiable(i2003_11_14_17_19_13721).
% 1.76/1.92 end_of_list.
% 1.76/1.92
% 1.76/1.92 -------> usable clausifies to:
% 1.76/1.92
% 1.76/1.92 list(usable).
% 1.76/1.92 0 [] A=A.
% 1.76/1.92 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.76/1.92 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.76/1.92 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.76/1.92 0 [] A!=B| -cp(A)|cp(B).
% 1.76/1.92 0 [] A!=B| -cq(A)|cq(B).
% 1.76/1.92 0 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.76/1.92 0 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.76/1.92 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.76/1.92 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.76/1.92 0 [] A!=B| -rs(A,C)|rs(B,C).
% 1.76/1.92 0 [] A!=B| -rs(C,A)|rs(C,B).
% 1.76/1.92 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.76/1.92 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.76/1.92 0 [] cowlThing(X).
% 1.76/1.92 0 [] -cowlNothing(X).
% 1.76/1.92 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.76/1.92 0 [] xsd_string(X)|xsd_integer(X).
% 1.76/1.92 0 [] -cUnsatisfiable(X)|rr(X,$f2(X)).
% 1.76/1.92 0 [] -cUnsatisfiable(X)|rinvR($f2(X),$f1(X)).
% 1.76/1.92 0 [] -cUnsatisfiable(X)| -rs($f1(X),W)|cp(W).
% 1.76/1.92 0 [] -cUnsatisfiable(X)| -rinvR($f2(X),Z0)| -rinvR($f2(X),Z1)|Z0=Z1.
% 1.76/1.92 0 [] -cUnsatisfiable(X)|rs(X,$f3(X)).
% 1.76/1.92 0 [] -cUnsatisfiable(X)| -cq($f3(X)).
% 1.76/1.92 0 [] -cUnsatisfiable(X)| -cp($f3(X)).
% 1.76/1.92 0 [] cUnsatisfiable(X)| -rr(X,Y)| -rinvR(Y,Z)|rs(Z,$f4(X,Y,Z))|rinvR(Y,$f6(X,Y))| -rs(X,X1)|cq(X1)|cp(X1).
% 1.76/1.92 0 [] cUnsatisfiable(X)| -rr(X,Y)| -rinvR(Y,Z)|rs(Z,$f4(X,Y,Z))|rinvR(Y,$f5(X,Y))| -rs(X,X1)|cq(X1)|cp(X1).
% 1.76/1.92 0 [] cUnsatisfiable(X)| -rr(X,Y)| -rinvR(Y,Z)|rs(Z,$f4(X,Y,Z))|$f6(X,Y)!=$f5(X,Y)| -rs(X,X1)|cq(X1)|cp(X1).
% 1.76/1.92 0 [] cUnsatisfiable(X)| -rr(X,Y)| -rinvR(Y,Z)| -cp($f4(X,Y,Z))|rinvR(Y,$f6(X,Y))| -rs(X,X1)|cq(X1)|cp(X1).
% 1.76/1.92 0 [] cUnsatisfiable(X)| -rr(X,Y)| -rinvR(Y,Z)| -cp($f4(X,Y,Z))|rinvR(Y,$f5(X,Y))| -rs(X,X1)|cq(X1)|cp(X1).
% 1.76/1.92 0 [] cUnsatisfiable(X)| -rr(X,Y)| -rinvR(Y,Z)| -cp($f4(X,Y,Z))|$f6(X,Y)!=$f5(X,Y)| -rs(X,X1)|cq(X1)|cp(X1).
% 1.76/1.92 0 [] -rinvR(X,Y)|rr(Y,X).
% 1.76/1.92 0 [] rinvR(X,Y)| -rr(Y,X).
% 1.76/1.92 0 [] cUnsatisfiable(i2003_11_14_17_19_13721).
% 1.76/1.92 end_of_list.
% 1.76/1.92
% 1.76/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.76/1.92
% 1.76/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.76/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.76/1.92 deletion, with positive clauses in sos and nonpositive
% 1.76/1.92 clauses in usable.
% 1.76/1.92
% 1.76/1.92 dependent: set(knuth_bendix).
% 1.76/1.92 dependent: set(anl_eq).
% 1.76/1.92 dependent: set(para_from).
% 1.76/1.92 dependent: set(para_into).
% 1.76/1.92 dependent: clear(para_from_right).
% 1.76/1.92 dependent: clear(para_into_right).
% 1.76/1.92 dependent: set(para_from_vars).
% 1.76/1.92 dependent: set(eq_units_both_ways).
% 1.76/1.92 dependent: set(dynamic_demod_all).
% 1.76/1.92 dependent: set(dynamic_demod).
% 1.76/1.92 dependent: set(order_eq).
% 1.76/1.92 dependent: set(back_demod).
% 1.76/1.92 dependent: set(lrpo).
% 1.76/1.92 dependent: set(hyper_res).
% 1.76/1.92 dependent: set(unit_deletion).
% 1.76/1.92 dependent: set(factor).
% 1.76/1.92
% 1.76/1.92 ------------> process usable:
% 1.76/1.92 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.76/1.92 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.76/1.92 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.76/1.92 ** KEPT (pick-wt=7): 4 [] A!=B| -cp(A)|cp(B).
% 1.76/1.92 ** KEPT (pick-wt=7): 5 [] A!=B| -cq(A)|cq(B).
% 1.76/1.92 ** KEPT (pick-wt=9): 6 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.76/1.92 ** KEPT (pick-wt=9): 7 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.76/1.92 ** KEPT (pick-wt=9): 8 [] A!=B| -rr(A,C)|rr(B,C).
% 1.76/1.92 ** KEPT (pick-wt=9): 9 [] A!=B| -rr(C,A)|rr(C,B).
% 1.76/1.92 ** KEPT (pick-wt=9): 10 [] A!=B| -rs(A,C)|rs(B,C).
% 1.76/1.92 ** KEPT (pick-wt=9): 11 [] A!=B| -rs(C,A)|rs(C,B).
% 1.76/1.92 ** KEPT (pick-wt=7): 12 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.76/1.92 ** KEPT (pick-wt=7): 13 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.76/1.92 ** KEPT (pick-wt=2): 14 [] -cowlNothing(A).
% 1.76/1.92 ** KEPT (pick-wt=4): 15 [] -xsd_string(A)| -xsd_integer(A).
% 1.76/1.92 ** KEPT (pick-wt=6): 16 [] -cUnsatisfiable(A)|rr(A,$f2(A)).
% 1.76/1.92 ** KEPT (pick-wt=7): 17 [] -cUnsatisfiable(A)|rinvR($f2(A),$f1(A)).
% 1.76/1.92 ** KEPT (pick-wt=8): 18 [] -cUnsatisfiable(A)| -rs($f1(A),B)|cp(B).
% 1.76/1.92 ** KEPT (pick-wt=13): 19 [] -cUnsatisfiable(A)| -rinvR($f2(A),B)| -rinvR($f2(A),C)|B=C.
% 1.76/1.92 ** KEPT (pick-wt=6): 20 [] -cUnsatisfiable(A)|rs(A,$f3(A)).
% 1.76/1.92 ** KEPT (pick-wt=5): 21 [] -cUnsatisfiable(A)| -cq($f3(A)).
% 1.76/1.92 ** KEPT (pick-wt=5): 22 [] -cUnsatisfiable(A)| -cp($f3(A)).
% 1.76/1.92 ** KEPT (pick-wt=26): 23 [] cUnsatisfiable(A)| -rr(A,B)| -rinvR(B,C)|rs(C,$f4(A,B,C))|rinvR(B,$f6(A,B))| -rs(A,D)|cq(D)|cp(D).
% 1.76/1.92 ** KEPT (pick-wt=26): 24 [] cUnsatisfiable(A)| -rr(A,B)| -rinvR(B,C)|rs(C,$f4(A,B,C))|rinvR(B,$f5(A,B))| -rs(A,D)|cq(D)|cp(D).
% 1.76/1.92 ** KEPT (pick-wt=28): 25 [] cUnsatisfiable(A)| -rr(A,B)| -rinvR(B,C)|rs(C,$f4(A,B,C))|$f6(A,B)!=$f5(A,B)| -rs(A,D)|cq(D)|cp(D).
% 1.76/1.92 ** KEPT (pick-wt=25): 26 [] cUnsatisfiable(A)| -rr(A,B)| -rinvR(B,C)| -cp($f4(A,B,C))|rinvR(B,$f6(A,B))| -rs(A,D)|cq(D)|cp(D).
% 1.76/1.92 ** KEPT (pick-wt=25): 27 [] cUnsatisfiable(A)| -rr(A,B)| -rinvR(B,C)| -cp($f4(A,B,C))|rinvR(B,$f5(A,B))| -rs(A,D)|cq(D)|cp(D).
% 1.76/1.92 ** KEPT (pick-wt=27): 28 [] cUnsatisfiable(A)| -rr(A,B)| -rinvR(B,C)| -cp($f4(A,B,C))|$f6(A,B)!=$f5(A,B)| -rs(A,D)|cq(D)|cp(D).
% 1.76/1.92 ** KEPT (pick-wt=6): 29 [] -rinvR(A,B)|rr(B,A).
% 1.76/1.92 ** KEPT (pick-wt=6): 30 [] rinvR(A,B)| -rr(B,A).
% 1.76/1.92 14 back subsumes 2.
% 1.76/1.92
% 1.76/1.92 ------------> process sos:
% 1.76/1.92 ** KEPT (pick-wt=3): 32 [] A=A.
% 1.76/1.92 ** KEPT (pick-wt=2): 33 [] cowlThing(A).
% 1.76/1.92 ** KEPT (pick-wt=4): 34 [] xsd_string(A)|xsd_integer(A).
% 1.76/1.92 ** KEPT (pick-wt=2): 35 [] cUnsatisfiable(i2003_11_14_17_19_13721).
% 1.76/1.92 Following clause subsumed by 32 during input processing: 0 [copy,32,flip.1] A=A.
% 1.76/1.92 32 back subsumes 31.
% 1.76/1.92 33 back subsumes 3.
% 1.76/1.92
% 1.76/1.92 ======= end of input processing =======
% 1.76/1.92
% 1.76/1.92 =========== start of search ===========
% 1.76/1.92
% 1.76/1.92 -------- PROOF --------
% 1.76/1.92
% 1.76/1.92 -----> EMPTY CLAUSE at 0.00 sec ----> 69 [hyper,59,22,35] $F.
% 1.76/1.92
% 1.76/1.92 Length of proof is 7. Level of proof is 5.
% 1.76/1.92
% 1.76/1.92 ---------------- PROOF ----------------
% 1.76/1.92 % SZS status Theorem
% 1.76/1.92 % SZS output start Refutation
% See solution above
% 1.76/1.92 ------------ end of proof -------------
% 1.76/1.92
% 1.76/1.92
% 1.76/1.92 Search stopped by max_proofs option.
% 1.76/1.92
% 1.76/1.92
% 1.76/1.92 Search stopped by max_proofs option.
% 1.76/1.92
% 1.76/1.92 ============ end of search ============
% 1.76/1.92
% 1.76/1.92 -------------- statistics -------------
% 1.76/1.92 clauses given 12
% 1.76/1.92 clauses generated 100
% 1.76/1.92 clauses kept 67
% 1.76/1.92 clauses forward subsumed 72
% 1.76/1.92 clauses back subsumed 3
% 1.76/1.92 Kbytes malloced 976
% 1.76/1.92
% 1.76/1.92 ----------- times (seconds) -----------
% 1.76/1.92 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.76/1.92
% 1.76/1.92 That finishes the proof of the theorem.
% 1.76/1.92
% 1.76/1.92 Process 9654 finished Wed Jul 27 03:32:53 2022
% 1.76/1.92 Otter interrupted
% 1.76/1.92 PROOF FOUND
%------------------------------------------------------------------------------