%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS069+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 13:01:03 EDT 2022
% Result : Unsatisfiable 1.86s 2.07s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 11 unt; 0 nHn; 20 RR)
% Number of literals : 31 ( 4 equ; 12 neg)
% Maximal clause size : 3 ( 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 : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
( ~ cUnsatisfiable(A)
| rf1(A,dollar_f1(A)) ),
file('KRS069+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ cUnsatisfiable(A)
| cp1(dollar_f1(A)) ),
file('KRS069+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| rf2(A,dollar_f2(A)) ),
file('KRS069+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| ~ cp1(dollar_f2(A)) ),
file('KRS069+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ cUnsatisfiable(A)
| rf3(A,dollar_f3(A)) ),
file('KRS069+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ rf1(A,B)
| ~ rf1(A,C)
| B = C ),
file('KRS069+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ rf2(A,B)
| ~ rf2(A,C)
| B = C ),
file('KRS069+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ rf3(A,B)
| rf1(A,B) ),
file('KRS069+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ rf3(A,B)
| rf2(A,B) ),
file('KRS069+1.p',unknown),
[] ).
cnf(34,axiom,
cUnsatisfiable(i2003_11_14_17_18_2750),
file('KRS069+1.p',unknown),
[] ).
cnf(36,plain,
rf3(i2003_11_14_17_18_2750,dollar_f3(i2003_11_14_17_18_2750)),
inference(hyper,[status(thm)],[34,20]),
[iquote('hyper,34,20')] ).
cnf(37,plain,
rf2(i2003_11_14_17_18_2750,dollar_f2(i2003_11_14_17_18_2750)),
inference(hyper,[status(thm)],[34,18]),
[iquote('hyper,34,18')] ).
cnf(38,plain,
cp1(dollar_f1(i2003_11_14_17_18_2750)),
inference(hyper,[status(thm)],[34,17]),
[iquote('hyper,34,17')] ).
cnf(39,plain,
rf1(i2003_11_14_17_18_2750,dollar_f1(i2003_11_14_17_18_2750)),
inference(hyper,[status(thm)],[34,16]),
[iquote('hyper,34,16')] ).
cnf(55,plain,
rf2(i2003_11_14_17_18_2750,dollar_f3(i2003_11_14_17_18_2750)),
inference(hyper,[status(thm)],[36,27]),
[iquote('hyper,36,27')] ).
cnf(56,plain,
rf1(i2003_11_14_17_18_2750,dollar_f3(i2003_11_14_17_18_2750)),
inference(hyper,[status(thm)],[36,26]),
[iquote('hyper,36,26')] ).
cnf(85,plain,
dollar_f3(i2003_11_14_17_18_2750) = dollar_f2(i2003_11_14_17_18_2750),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[55,24,37])]),
[iquote('hyper,55,24,37,flip.1')] ).
cnf(92,plain,
rf1(i2003_11_14_17_18_2750,dollar_f2(i2003_11_14_17_18_2750)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),85]),
[iquote('back_demod,56,demod,85')] ).
cnf(104,plain,
dollar_f2(i2003_11_14_17_18_2750) = dollar_f1(i2003_11_14_17_18_2750),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[92,23,39])]),
[iquote('hyper,92,23,39,flip.1')] ).
cnf(141,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[104,19]),34,38]),
[iquote('para_from,104.1.1,19.2.1,unit_del,34,38')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS069+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.12 % 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 03:32:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.86/2.07 ----- Otter 3.3f, August 2004 -----
% 1.86/2.07 The process was started by sandbox on n020.cluster.edu,
% 1.86/2.07 Wed Jul 27 03:32:53 2022
% 1.86/2.07 The command was "./otter". The process ID is 1427.
% 1.86/2.07
% 1.86/2.07 set(prolog_style_variables).
% 1.86/2.07 set(auto).
% 1.86/2.07 dependent: set(auto1).
% 1.86/2.07 dependent: set(process_input).
% 1.86/2.07 dependent: clear(print_kept).
% 1.86/2.07 dependent: clear(print_new_demod).
% 1.86/2.07 dependent: clear(print_back_demod).
% 1.86/2.07 dependent: clear(print_back_sub).
% 1.86/2.07 dependent: set(control_memory).
% 1.86/2.07 dependent: assign(max_mem, 12000).
% 1.86/2.07 dependent: assign(pick_given_ratio, 4).
% 1.86/2.07 dependent: assign(stats_level, 1).
% 1.86/2.07 dependent: assign(max_seconds, 10800).
% 1.86/2.07 clear(print_given).
% 1.86/2.07
% 1.86/2.07 formula_list(usable).
% 1.86/2.07 all A (A=A).
% 1.86/2.07 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.86/2.07 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.86/2.07 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.86/2.07 all A B (A=B&cp1(A)->cp1(B)).
% 1.86/2.07 all A B (A=B&cp2(A)->cp2(B)).
% 1.86/2.07 all A B C (A=B&rf1(A,C)->rf1(B,C)).
% 1.86/2.07 all A B C (A=B&rf1(C,A)->rf1(C,B)).
% 1.86/2.07 all A B C (A=B&rf2(A,C)->rf2(B,C)).
% 1.86/2.07 all A B C (A=B&rf2(C,A)->rf2(C,B)).
% 1.86/2.07 all A B C (A=B&rf3(A,C)->rf3(B,C)).
% 1.86/2.07 all A B C (A=B&rf3(C,A)->rf3(C,B)).
% 1.86/2.07 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.86/2.07 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.86/2.07 all X (cowlThing(X)& -cowlNothing(X)).
% 1.86/2.07 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.86/2.07 all X (cUnsatisfiable(X)<-> (exists Y (rf1(X,Y)&cp1(Y)))& (exists Y (rf2(X,Y)& -cp1(Y)))& (exists Y (rf3(X,Y)&cp2(Y)))).
% 1.86/2.07 all X Y Z (rf1(X,Y)&rf1(X,Z)->Y=Z).
% 1.86/2.07 all X Y Z (rf2(X,Y)&rf2(X,Z)->Y=Z).
% 1.86/2.07 all X Y Z (rf3(X,Y)&rf3(X,Z)->Y=Z).
% 1.86/2.07 cUnsatisfiable(i2003_11_14_17_18_2750).
% 1.86/2.07 all X Y (rf3(X,Y)->rf1(X,Y)).
% 1.86/2.07 all X Y (rf3(X,Y)->rf2(X,Y)).
% 1.86/2.07 end_of_list.
% 1.86/2.07
% 1.86/2.07 -------> usable clausifies to:
% 1.86/2.07
% 1.86/2.07 list(usable).
% 1.86/2.07 0 [] A=A.
% 1.86/2.07 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.86/2.07 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.86/2.07 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.86/2.07 0 [] A!=B| -cp1(A)|cp1(B).
% 1.86/2.07 0 [] A!=B| -cp2(A)|cp2(B).
% 1.86/2.07 0 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.86/2.07 0 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.86/2.07 0 [] A!=B| -rf2(A,C)|rf2(B,C).
% 1.86/2.07 0 [] A!=B| -rf2(C,A)|rf2(C,B).
% 1.86/2.07 0 [] A!=B| -rf3(A,C)|rf3(B,C).
% 1.86/2.07 0 [] A!=B| -rf3(C,A)|rf3(C,B).
% 1.86/2.07 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.86/2.07 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.86/2.07 0 [] cowlThing(X).
% 1.86/2.07 0 [] -cowlNothing(X).
% 1.86/2.07 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.86/2.07 0 [] xsd_string(X)|xsd_integer(X).
% 1.86/2.07 0 [] -cUnsatisfiable(X)|rf1(X,$f1(X)).
% 1.86/2.07 0 [] -cUnsatisfiable(X)|cp1($f1(X)).
% 1.86/2.07 0 [] -cUnsatisfiable(X)|rf2(X,$f2(X)).
% 1.86/2.07 0 [] -cUnsatisfiable(X)| -cp1($f2(X)).
% 1.86/2.07 0 [] -cUnsatisfiable(X)|rf3(X,$f3(X)).
% 1.86/2.07 0 [] -cUnsatisfiable(X)|cp2($f3(X)).
% 1.86/2.07 0 [] cUnsatisfiable(X)| -rf1(X,Y)| -cp1(Y)| -rf2(X,X1)|cp1(X1)| -rf3(X,X2)| -cp2(X2).
% 1.86/2.07 0 [] -rf1(X,Y)| -rf1(X,Z)|Y=Z.
% 1.86/2.07 0 [] -rf2(X,Y)| -rf2(X,Z)|Y=Z.
% 1.86/2.07 0 [] -rf3(X,Y)| -rf3(X,Z)|Y=Z.
% 1.86/2.07 0 [] cUnsatisfiable(i2003_11_14_17_18_2750).
% 1.86/2.07 0 [] -rf3(X,Y)|rf1(X,Y).
% 1.86/2.07 0 [] -rf3(X,Y)|rf2(X,Y).
% 1.86/2.07 end_of_list.
% 1.86/2.07
% 1.86/2.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.86/2.07
% 1.86/2.07 This ia a non-Horn set with equality. The strategy will be
% 1.86/2.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.86/2.07 deletion, with positive clauses in sos and nonpositive
% 1.86/2.07 clauses in usable.
% 1.86/2.07
% 1.86/2.07 dependent: set(knuth_bendix).
% 1.86/2.07 dependent: set(anl_eq).
% 1.86/2.07 dependent: set(para_from).
% 1.86/2.07 dependent: set(para_into).
% 1.86/2.07 dependent: clear(para_from_right).
% 1.86/2.07 dependent: clear(para_into_right).
% 1.86/2.07 dependent: set(para_from_vars).
% 1.86/2.07 dependent: set(eq_units_both_ways).
% 1.86/2.07 dependent: set(dynamic_demod_all).
% 1.86/2.07 dependent: set(dynamic_demod).
% 1.86/2.07 dependent: set(order_eq).
% 1.86/2.07 dependent: set(back_demod).
% 1.86/2.07 dependent: set(lrpo).
% 1.86/2.07 dependent: set(hyper_res).
% 1.86/2.07 dependent: set(unit_deletion).
% 1.86/2.07 dependent: set(factor).
% 1.86/2.07
% 1.86/2.07 ------------> process usable:
% 1.86/2.07 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.86/2.07 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.86/2.07 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.86/2.07 ** KEPT (pick-wt=7): 4 [] A!=B| -cp1(A)|cp1(B).
% 1.86/2.07 ** KEPT (pick-wt=7): 5 [] A!=B| -cp2(A)|cp2(B).
% 1.86/2.07 ** KEPT (pick-wt=9): 6 [] A!=B| -rf1(A,C)|rf1(B,C).
% 1.86/2.07 ** KEPT (pick-wt=9): 7 [] A!=B| -rf1(C,A)|rf1(C,B).
% 1.86/2.07 ** KEPT (pick-wt=9): 8 [] A!=B| -rf2(A,C)|rf2(B,C).
% 1.86/2.07 ** KEPT (pick-wt=9): 9 [] A!=B| -rf2(C,A)|rf2(C,B).
% 1.86/2.07 ** KEPT (pick-wt=9): 10 [] A!=B| -rf3(A,C)|rf3(B,C).
% 1.86/2.07 ** KEPT (pick-wt=9): 11 [] A!=B| -rf3(C,A)|rf3(C,B).
% 1.86/2.07 ** KEPT (pick-wt=7): 12 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.86/2.07 ** KEPT (pick-wt=7): 13 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.86/2.07 ** KEPT (pick-wt=2): 14 [] -cowlNothing(A).
% 1.86/2.07 ** KEPT (pick-wt=4): 15 [] -xsd_string(A)| -xsd_integer(A).
% 1.86/2.07 ** KEPT (pick-wt=6): 16 [] -cUnsatisfiable(A)|rf1(A,$f1(A)).
% 1.86/2.07 ** KEPT (pick-wt=5): 17 [] -cUnsatisfiable(A)|cp1($f1(A)).
% 1.86/2.07 ** KEPT (pick-wt=6): 18 [] -cUnsatisfiable(A)|rf2(A,$f2(A)).
% 1.86/2.07 ** KEPT (pick-wt=5): 19 [] -cUnsatisfiable(A)| -cp1($f2(A)).
% 1.86/2.07 ** KEPT (pick-wt=6): 20 [] -cUnsatisfiable(A)|rf3(A,$f3(A)).
% 1.86/2.07 ** KEPT (pick-wt=5): 21 [] -cUnsatisfiable(A)|cp2($f3(A)).
% 1.86/2.07 ** KEPT (pick-wt=17): 22 [] cUnsatisfiable(A)| -rf1(A,B)| -cp1(B)| -rf2(A,C)|cp1(C)| -rf3(A,D)| -cp2(D).
% 1.86/2.07 ** KEPT (pick-wt=9): 23 [] -rf1(A,B)| -rf1(A,C)|B=C.
% 1.86/2.07 ** KEPT (pick-wt=9): 24 [] -rf2(A,B)| -rf2(A,C)|B=C.
% 1.86/2.07 ** KEPT (pick-wt=9): 25 [] -rf3(A,B)| -rf3(A,C)|B=C.
% 1.86/2.07 ** KEPT (pick-wt=6): 26 [] -rf3(A,B)|rf1(A,B).
% 1.86/2.07 ** KEPT (pick-wt=6): 27 [] -rf3(A,B)|rf2(A,B).
% 1.86/2.07 14 back subsumes 2.
% 1.86/2.07
% 1.86/2.07 ------------> process sos:
% 1.86/2.07 ** KEPT (pick-wt=3): 31 [] A=A.
% 1.86/2.07 ** KEPT (pick-wt=2): 32 [] cowlThing(A).
% 1.86/2.07 ** KEPT (pick-wt=4): 33 [] xsd_string(A)|xsd_integer(A).
% 1.86/2.07 ** KEPT (pick-wt=2): 34 [] cUnsatisfiable(i2003_11_14_17_18_2750).
% 1.86/2.07 Following clause subsumed by 31 during input processing: 0 [copy,31,flip.1] A=A.
% 1.86/2.07 31 back subsumes 30.
% 1.86/2.07 31 back subsumes 29.
% 1.86/2.07 31 back subsumes 28.
% 1.86/2.07 32 back subsumes 3.
% 1.86/2.07
% 1.86/2.07 ======= end of input processing =======
% 1.86/2.07
% 1.86/2.07 =========== start of search ===========
% 1.86/2.07
% 1.86/2.07 -------- PROOF --------
% 1.86/2.07
% 1.86/2.07 -----> EMPTY CLAUSE at 0.01 sec ----> 141 [para_from,104.1.1,19.2.1,unit_del,34,38] $F.
% 1.86/2.07
% 1.86/2.07 Length of proof is 9. Level of proof is 5.
% 1.86/2.07
% 1.86/2.07 ---------------- PROOF ----------------
% 1.86/2.07 % SZS status Theorem
% 1.86/2.07 % SZS output start Refutation
% See solution above
% 1.86/2.07 ------------ end of proof -------------
% 1.86/2.07
% 1.86/2.07
% 1.86/2.07 Search stopped by max_proofs option.
% 1.86/2.07
% 1.86/2.07
% 1.86/2.07 Search stopped by max_proofs option.
% 1.86/2.07
% 1.86/2.07 ============ end of search ============
% 1.86/2.07
% 1.86/2.07 -------------- statistics -------------
% 1.86/2.07 clauses given 18
% 1.86/2.07 clauses generated 242
% 1.86/2.07 clauses kept 137
% 1.86/2.07 clauses forward subsumed 169
% 1.86/2.07 clauses back subsumed 5
% 1.86/2.07 Kbytes malloced 976
% 1.86/2.07
% 1.86/2.07 ----------- times (seconds) -----------
% 1.86/2.07 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.86/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.86/2.07
% 1.86/2.07 That finishes the proof of the theorem.
% 1.86/2.07
% 1.86/2.07 Process 1427 finished Wed Jul 27 03:32:55 2022
% 1.86/2.07 Otter interrupted
% 1.86/2.07 PROOF FOUND
%------------------------------------------------------------------------------