%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:01:13 EDT 2022
% Result : Theorem 1.62s 1.82s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 31 ( 8 unt; 17 nHn; 28 RR)
% Number of literals : 86 ( 0 equ; 35 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 13 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ cowlNothing(A),
file('KRS131+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ xsd_string(A)
| ~ xsd_integer(A) ),
file('KRS131+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ cA(A)
| rq(A,dollar_f1(A)) ),
file('KRS131+1.p',unknown),
[] ).
cnf(5,axiom,
( cA(A)
| ~ rq(A,B)
| ~ cowlThing(B) ),
file('KRS131+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ cNothing(A)
| ~ rp(A,B) ),
file('KRS131+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ cNothing(A)
| rp(A,dollar_f2(A)) ),
file('KRS131+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ cnotA(A)
| ~ rq(A,B)
| cNothing(B) ),
file('KRS131+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ cowlThing(dollar_c1)
| cowlNothing(dollar_c1)
| xsd_string(dollar_c2)
| ~ xsd_integer(dollar_c2)
| cnotA(dollar_c3)
| ~ cA(dollar_c3) ),
file('KRS131+1.p',unknown),
[] ).
cnf(11,plain,
( ~ cowlThing(dollar_c1)
| xsd_string(dollar_c2)
| ~ xsd_integer(dollar_c2)
| cnotA(dollar_c3)
| ~ cA(dollar_c3) ),
inference(unit_del,[status(thm)],[inference(copy,[status(thm)],[10]),1]),
[iquote('copy,10,unit_del,1')] ).
cnf(12,axiom,
( ~ cowlThing(dollar_c1)
| cowlNothing(dollar_c1)
| xsd_string(dollar_c2)
| ~ xsd_integer(dollar_c2)
| ~ cnotA(dollar_c3)
| cA(dollar_c3) ),
file('KRS131+1.p',unknown),
[] ).
cnf(13,plain,
( ~ cowlThing(dollar_c1)
| xsd_string(dollar_c2)
| ~ xsd_integer(dollar_c2)
| ~ cnotA(dollar_c3)
| cA(dollar_c3) ),
inference(unit_del,[status(thm)],[inference(copy,[status(thm)],[12]),1]),
[iquote('copy,12,unit_del,1')] ).
cnf(14,axiom,
( ~ cowlThing(dollar_c1)
| cowlNothing(dollar_c1)
| ~ xsd_string(dollar_c2)
| xsd_integer(dollar_c2)
| cnotA(dollar_c3)
| ~ cA(dollar_c3) ),
file('KRS131+1.p',unknown),
[] ).
cnf(15,plain,
( ~ cowlThing(dollar_c1)
| ~ xsd_string(dollar_c2)
| xsd_integer(dollar_c2)
| cnotA(dollar_c3)
| ~ cA(dollar_c3) ),
inference(unit_del,[status(thm)],[inference(copy,[status(thm)],[14]),1]),
[iquote('copy,14,unit_del,1')] ).
cnf(16,axiom,
( ~ cowlThing(dollar_c1)
| cowlNothing(dollar_c1)
| ~ xsd_string(dollar_c2)
| xsd_integer(dollar_c2)
| ~ cnotA(dollar_c3)
| cA(dollar_c3) ),
file('KRS131+1.p',unknown),
[] ).
cnf(17,plain,
( ~ cowlThing(dollar_c1)
| ~ xsd_string(dollar_c2)
| xsd_integer(dollar_c2)
| ~ cnotA(dollar_c3)
| cA(dollar_c3) ),
inference(unit_del,[status(thm)],[inference(copy,[status(thm)],[16]),1]),
[iquote('copy,16,unit_del,1')] ).
cnf(18,axiom,
cowlThing(A),
file('KRS131+1.p',unknown),
[] ).
cnf(19,axiom,
( xsd_string(A)
| xsd_integer(A) ),
file('KRS131+1.p',unknown),
[] ).
cnf(20,axiom,
( cnotA(A)
| rq(A,dollar_f3(A)) ),
file('KRS131+1.p',unknown),
[] ).
cnf(21,plain,
( rq(dollar_c3,dollar_f3(dollar_c3))
| xsd_integer(dollar_c2)
| cA(dollar_c3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[20,17,18,19])]),
[iquote('hyper,20,17,18,19,factor_simp')] ).
cnf(22,plain,
( rq(dollar_c3,dollar_f3(dollar_c3))
| cA(dollar_c3)
| xsd_string(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[21,13,18,20])])]),
[iquote('hyper,21,13,18,20,factor_simp,factor_simp')] ).
cnf(23,plain,
( rq(dollar_c3,dollar_f3(dollar_c3))
| cA(dollar_c3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,2,21])])]),
[iquote('hyper,22,2,21,factor_simp,factor_simp')] ).
cnf(24,plain,
( rq(dollar_c3,dollar_f3(dollar_c3))
| rq(dollar_c3,dollar_f1(dollar_c3)) ),
inference(hyper,[status(thm)],[23,3]),
[iquote('hyper,23,3')] ).
cnf(25,plain,
( rq(dollar_c3,dollar_f1(dollar_c3))
| cA(dollar_c3) ),
inference(hyper,[status(thm)],[24,5,18]),
[iquote('hyper,24,5,18')] ).
cnf(28,plain,
rq(dollar_c3,dollar_f1(dollar_c3)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[25,3])]),
[iquote('hyper,25,3,factor_simp')] ).
cnf(29,plain,
cA(dollar_c3),
inference(hyper,[status(thm)],[28,5,18]),
[iquote('hyper,28,5,18')] ).
cnf(30,plain,
( xsd_integer(dollar_c2)
| cnotA(dollar_c3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[29,15,18,19])]),
[iquote('hyper,29,15,18,19,factor_simp')] ).
cnf(32,plain,
( cnotA(dollar_c3)
| xsd_string(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[30,11,18,29])]),
[iquote('hyper,30,11,18,29,factor_simp')] ).
cnf(33,plain,
cnotA(dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[32,2,30])]),
[iquote('hyper,32,2,30,factor_simp')] ).
cnf(34,plain,
cNothing(dollar_f1(dollar_c3)),
inference(hyper,[status(thm)],[33,8,28]),
[iquote('hyper,33,8,28')] ).
cnf(35,plain,
rp(dollar_f1(dollar_c3),dollar_f2(dollar_f1(dollar_c3))),
inference(hyper,[status(thm)],[34,7]),
[iquote('hyper,34,7')] ).
cnf(36,plain,
$false,
inference(hyper,[status(thm)],[35,6,34]),
[iquote('hyper,35,6,34')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 03:28:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.62/1.82 ----- Otter 3.3f, August 2004 -----
% 1.62/1.82 The process was started by sandbox on n003.cluster.edu,
% 1.62/1.82 Wed Jul 27 03:28:11 2022
% 1.62/1.82 The command was "./otter". The process ID is 2773.
% 1.62/1.82
% 1.62/1.82 set(prolog_style_variables).
% 1.62/1.82 set(auto).
% 1.62/1.82 dependent: set(auto1).
% 1.62/1.82 dependent: set(process_input).
% 1.62/1.82 dependent: clear(print_kept).
% 1.62/1.82 dependent: clear(print_new_demod).
% 1.62/1.82 dependent: clear(print_back_demod).
% 1.62/1.82 dependent: clear(print_back_sub).
% 1.62/1.82 dependent: set(control_memory).
% 1.62/1.82 dependent: assign(max_mem, 12000).
% 1.62/1.82 dependent: assign(pick_given_ratio, 4).
% 1.62/1.82 dependent: assign(stats_level, 1).
% 1.62/1.82 dependent: assign(max_seconds, 10800).
% 1.62/1.82 clear(print_given).
% 1.62/1.82
% 1.62/1.82 formula_list(usable).
% 1.62/1.82 all X (cowlThing(X)& -cowlNothing(X)).
% 1.62/1.82 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.62/1.82 all X (cA(X)<-> (exists Y (rq(X,Y)&cowlThing(Y)))).
% 1.62/1.82 all X (cNothing(X)-> -(exists Y rp(X,Y))).
% 1.62/1.82 all X (cNothing(X)-> (exists Y0 rp(X,Y0))).
% 1.62/1.82 all X (cnotA(X)<-> (all Y (rq(X,Y)->cNothing(Y)))).
% 1.62/1.82 -((all X (cowlThing(X)& -cowlNothing(X)))& (all X (xsd_string(X)<-> -xsd_integer(X)))& (all X (cnotA(X)<-> -cA(X)))).
% 1.62/1.82 end_of_list.
% 1.62/1.82
% 1.62/1.82 -------> usable clausifies to:
% 1.62/1.82
% 1.62/1.82 list(usable).
% 1.62/1.82 0 [] cowlThing(X).
% 1.62/1.82 0 [] -cowlNothing(X).
% 1.62/1.82 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.62/1.82 0 [] xsd_string(X)|xsd_integer(X).
% 1.62/1.82 0 [] -cA(X)|rq(X,$f1(X)).
% 1.62/1.82 0 [] -cA(X)|cowlThing($f1(X)).
% 1.62/1.82 0 [] cA(X)| -rq(X,Y)| -cowlThing(Y).
% 1.62/1.82 0 [] -cNothing(X)| -rp(X,Y).
% 1.62/1.82 0 [] -cNothing(X)|rp(X,$f2(X)).
% 1.62/1.82 0 [] -cnotA(X)| -rq(X,Y)|cNothing(Y).
% 1.62/1.82 0 [] cnotA(X)|rq(X,$f3(X)).
% 1.62/1.82 0 [] cnotA(X)| -cNothing($f3(X)).
% 1.62/1.82 0 [] -cowlThing($c1)|cowlNothing($c1)|xsd_string($c2)| -xsd_integer($c2)|cnotA($c3)| -cA($c3).
% 1.62/1.82 0 [] -cowlThing($c1)|cowlNothing($c1)|xsd_string($c2)| -xsd_integer($c2)| -cnotA($c3)|cA($c3).
% 1.62/1.82 0 [] -cowlThing($c1)|cowlNothing($c1)| -xsd_string($c2)|xsd_integer($c2)|cnotA($c3)| -cA($c3).
% 1.62/1.82 0 [] -cowlThing($c1)|cowlNothing($c1)| -xsd_string($c2)|xsd_integer($c2)| -cnotA($c3)|cA($c3).
% 1.62/1.82 end_of_list.
% 1.62/1.82
% 1.62/1.82 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.62/1.82
% 1.62/1.82 This is a non-Horn set without equality. The strategy will
% 1.62/1.82 be ordered hyper_res, unit deletion, and factoring, with
% 1.62/1.82 satellites in sos and with nuclei in usable.
% 1.62/1.82
% 1.62/1.82 dependent: set(hyper_res).
% 1.62/1.82 dependent: set(factor).
% 1.62/1.82 dependent: set(unit_deletion).
% 1.62/1.82
% 1.62/1.82 ------------> process usable:
% 1.62/1.82 ** KEPT (pick-wt=2): 1 [] -cowlNothing(A).
% 1.62/1.82 ** KEPT (pick-wt=4): 2 [] -xsd_string(A)| -xsd_integer(A).
% 1.62/1.82 ** KEPT (pick-wt=6): 3 [] -cA(A)|rq(A,$f1(A)).
% 1.62/1.82 ** KEPT (pick-wt=5): 4 [] -cA(A)|cowlThing($f1(A)).
% 1.62/1.82 ** KEPT (pick-wt=7): 5 [] cA(A)| -rq(A,B)| -cowlThing(B).
% 1.62/1.82 ** KEPT (pick-wt=5): 6 [] -cNothing(A)| -rp(A,B).
% 1.62/1.82 ** KEPT (pick-wt=6): 7 [] -cNothing(A)|rp(A,$f2(A)).
% 1.62/1.82 ** KEPT (pick-wt=7): 8 [] -cnotA(A)| -rq(A,B)|cNothing(B).
% 1.62/1.82 ** KEPT (pick-wt=5): 9 [] cnotA(A)| -cNothing($f3(A)).
% 1.62/1.82 ** KEPT (pick-wt=10): 11 [copy,10,unit_del,1] -cowlThing($c1)|xsd_string($c2)| -xsd_integer($c2)|cnotA($c3)| -cA($c3).
% 1.62/1.82 ** KEPT (pick-wt=10): 13 [copy,12,unit_del,1] -cowlThing($c1)|xsd_string($c2)| -xsd_integer($c2)| -cnotA($c3)|cA($c3).
% 1.62/1.82 ** KEPT (pick-wt=10): 15 [copy,14,unit_del,1] -cowlThing($c1)| -xsd_string($c2)|xsd_integer($c2)|cnotA($c3)| -cA($c3).
% 1.62/1.82 ** KEPT (pick-wt=10): 17 [copy,16,unit_del,1] -cowlThing($c1)| -xsd_string($c2)|xsd_integer($c2)| -cnotA($c3)|cA($c3).
% 1.62/1.82
% 1.62/1.82 ------------> process sos:
% 1.62/1.82 ** KEPT (pick-wt=2): 18 [] cowlThing(A).
% 1.62/1.82 ** KEPT (pick-wt=4): 19 [] xsd_string(A)|xsd_integer(A).
% 1.62/1.82 ** KEPT (pick-wt=6): 20 [] cnotA(A)|rq(A,$f3(A)).
% 1.62/1.82 18 back subsumes 4.
% 1.62/1.82
% 1.62/1.82 ======= end of input processing =======
% 1.62/1.82
% 1.62/1.82 =========== start of search ===========
% 1.62/1.82
% 1.62/1.82 -------- PROOF --------
% 1.62/1.82
% 1.62/1.82 -----> EMPTY CLAUSE at 0.00 sec ----> 36 [hyper,35,6,34] $F.
% 1.62/1.82
% 1.62/1.82 Length of proof is 16. Level of proof is 13.
% 1.62/1.82
% 1.62/1.82 ---------------- PROOF ----------------
% 1.62/1.82 % SZS status Theorem
% 1.62/1.82 % SZS output start Refutation
% See solution above
% 1.62/1.82 ------------ end of proof -------------
% 1.62/1.82
% 1.62/1.82
% 1.62/1.82 Search stopped by max_proofs option.
% 1.62/1.82
% 1.62/1.82
% 1.62/1.82 Search stopped by max_proofs option.
% 1.62/1.82
% 1.62/1.82 ============ end of search ============
% 1.62/1.82
% 1.62/1.82 -------------- statistics -------------
% 1.62/1.82 clauses given 16
% 1.62/1.82 clauses generated 24
% 1.62/1.82 clauses kept 31
% 1.62/1.82 clauses forward subsumed 8
% 1.62/1.82 clauses back subsumed 15
% 1.62/1.82 Kbytes malloced 976
% 1.62/1.82
% 1.62/1.82 ----------- times (seconds) -----------
% 1.62/1.82 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.62/1.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.62/1.82 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.62/1.82
% 1.62/1.82 That finishes the proof of the theorem.
% 1.62/1.82
% 1.62/1.82 Process 2773 finished Wed Jul 27 03:28:13 2022
% 1.62/1.82 Otter interrupted
% 1.62/1.82 PROOF FOUND
%------------------------------------------------------------------------------