TSTP Solution File: SET921+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:14:32 EDT 2022
% Result : Theorem 1.74s 1.93s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 6 unt; 4 nHn; 13 RR)
% Number of literals : 33 ( 12 equ; 14 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET921+1.p',unknown),
[] ).
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SET921+1.p',unknown),
[] ).
cnf(5,axiom,
( A != set_difference(B,C)
| ~ in(D,A)
| in(D,B) ),
file('SET921+1.p',unknown),
[] ).
cnf(6,axiom,
( A != set_difference(B,C)
| ~ in(D,A)
| ~ in(D,C) ),
file('SET921+1.p',unknown),
[] ).
cnf(7,axiom,
( A != set_difference(B,C)
| in(D,A)
| ~ in(D,B)
| in(D,C) ),
file('SET921+1.p',unknown),
[] ).
cnf(11,axiom,
( in(dollar_c5,set_difference(dollar_c4,singleton(dollar_c3)))
| dollar_c5 != dollar_c3 ),
file('SET921+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(dollar_c5,set_difference(dollar_c4,singleton(dollar_c3)))
| ~ in(dollar_c5,dollar_c4)
| dollar_c5 = dollar_c3 ),
file('SET921+1.p',unknown),
[] ).
cnf(17,axiom,
A = A,
file('SET921+1.p',unknown),
[] ).
cnf(21,axiom,
( in(dollar_c5,set_difference(dollar_c4,singleton(dollar_c3)))
| in(dollar_c5,dollar_c4) ),
file('SET921+1.p',unknown),
[] ).
cnf(23,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[17,3,17]),
[iquote('hyper,17,3,17')] ).
cnf(36,plain,
in(dollar_c5,dollar_c4),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[21,5,17])]),
[iquote('hyper,21,5,17,factor_simp')] ).
cnf(40,plain,
( in(dollar_c5,set_difference(dollar_c4,A))
| in(dollar_c5,A) ),
inference(hyper,[status(thm)],[36,7,17]),
[iquote('hyper,36,7,17')] ).
cnf(100,plain,
( in(dollar_c5,singleton(dollar_c3))
| dollar_c5 = dollar_c3 ),
inference(hyper,[status(thm)],[40,12,36]),
[iquote('hyper,40,12,36')] ).
cnf(177,plain,
dollar_c5 = dollar_c3,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[100,2,17])]),
[iquote('hyper,100,2,17,factor_simp')] ).
cnf(269,plain,
in(dollar_c3,set_difference(dollar_c4,singleton(dollar_c3))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),177,177]),17]),
[iquote('back_demod,11,demod,177,177,unit_del,17')] ).
cnf(355,plain,
$false,
inference(hyper,[status(thm)],[269,6,17,23]),
[iquote('hyper,269,6,17,23')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 11:00:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.93 ----- Otter 3.3f, August 2004 -----
% 1.74/1.93 The process was started by sandbox on n027.cluster.edu,
% 1.74/1.93 Wed Jul 27 11:00:22 2022
% 1.74/1.93 The command was "./otter". The process ID is 7059.
% 1.74/1.93
% 1.74/1.93 set(prolog_style_variables).
% 1.74/1.93 set(auto).
% 1.74/1.93 dependent: set(auto1).
% 1.74/1.93 dependent: set(process_input).
% 1.74/1.93 dependent: clear(print_kept).
% 1.74/1.93 dependent: clear(print_new_demod).
% 1.74/1.93 dependent: clear(print_back_demod).
% 1.74/1.93 dependent: clear(print_back_sub).
% 1.74/1.93 dependent: set(control_memory).
% 1.74/1.93 dependent: assign(max_mem, 12000).
% 1.74/1.93 dependent: assign(pick_given_ratio, 4).
% 1.74/1.93 dependent: assign(stats_level, 1).
% 1.74/1.93 dependent: assign(max_seconds, 10800).
% 1.74/1.93 clear(print_given).
% 1.74/1.93
% 1.74/1.93 formula_list(usable).
% 1.74/1.93 all A (A=A).
% 1.74/1.93 all A B (in(A,B)-> -in(B,A)).
% 1.74/1.93 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.74/1.93 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.74/1.93 exists A empty(A).
% 1.74/1.93 exists A (-empty(A)).
% 1.74/1.93 -(all A B C (in(A,set_difference(B,singleton(C)))<->in(A,B)&A!=C)).
% 1.74/1.93 end_of_list.
% 1.74/1.93
% 1.74/1.93 -------> usable clausifies to:
% 1.74/1.93
% 1.74/1.93 list(usable).
% 1.74/1.93 0 [] A=A.
% 1.74/1.93 0 [] -in(A,B)| -in(B,A).
% 1.74/1.93 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.74/1.93 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.74/1.93 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.74/1.93 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.74/1.93 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.74/1.93 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.74/1.93 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.74/1.93 0 [] C=set_difference(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A).
% 1.74/1.93 0 [] C=set_difference(A,B)|in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 1.74/1.93 0 [] C=set_difference(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 1.74/1.93 0 [] empty($c1).
% 1.74/1.93 0 [] -empty($c2).
% 1.74/1.93 0 [] in($c5,set_difference($c4,singleton($c3)))|in($c5,$c4).
% 1.74/1.93 0 [] in($c5,set_difference($c4,singleton($c3)))|$c5!=$c3.
% 1.74/1.93 0 [] -in($c5,set_difference($c4,singleton($c3)))| -in($c5,$c4)|$c5=$c3.
% 1.74/1.93 end_of_list.
% 1.74/1.93
% 1.74/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.74/1.93
% 1.74/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.93 deletion, with positive clauses in sos and nonpositive
% 1.74/1.93 clauses in usable.
% 1.74/1.93
% 1.74/1.93 dependent: set(knuth_bendix).
% 1.74/1.93 dependent: set(anl_eq).
% 1.74/1.93 dependent: set(para_from).
% 1.74/1.93 dependent: set(para_into).
% 1.74/1.93 dependent: clear(para_from_right).
% 1.74/1.93 dependent: clear(para_into_right).
% 1.74/1.93 dependent: set(para_from_vars).
% 1.74/1.93 dependent: set(eq_units_both_ways).
% 1.74/1.93 dependent: set(dynamic_demod_all).
% 1.74/1.93 dependent: set(dynamic_demod).
% 1.74/1.93 dependent: set(order_eq).
% 1.74/1.93 dependent: set(back_demod).
% 1.74/1.93 dependent: set(lrpo).
% 1.74/1.93 dependent: set(hyper_res).
% 1.74/1.93 dependent: set(unit_deletion).
% 1.74/1.93 dependent: set(factor).
% 1.74/1.93
% 1.74/1.93 ------------> process usable:
% 1.74/1.93 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.74/1.93 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.74/1.93 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.74/1.93 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.74/1.93 ** KEPT (pick-wt=11): 5 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.74/1.93 ** KEPT (pick-wt=11): 6 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.74/1.93 ** KEPT (pick-wt=14): 7 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.74/1.93 ** KEPT (pick-wt=17): 8 [] A=set_difference(B,C)|in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 1.74/1.93 ** KEPT (pick-wt=23): 9 [] A=set_difference(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 1.74/1.93 ** KEPT (pick-wt=2): 10 [] -empty($c2).
% 1.74/1.93 ** KEPT (pick-wt=9): 11 [] in($c5,set_difference($c4,singleton($c3)))|$c5!=$c3.
% 1.74/1.93 ** KEPT (pick-wt=12): 12 [] -in($c5,set_difference($c4,singleton($c3)))| -in($c5,$c4)|$c5=$c3.
% 1.74/1.93
% 1.74/1.93 ------------> process sos:
% 1.74/1.93 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.74/1.93 ** KEPT (pick-wt=14): 18 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.74/1.93 ** KEPT (pick-wt=17): 19 [] A=set_difference(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B).
% 1.74/1.93 ** KEPT (pick-wt=2): 20 [] empty($c1).
% 1.74/1.93 ** KEPT (pick-wt=9): 21 [] in($c5,set_difference($c4,singleton($c3)))|in($c5,$c4).
% 1.74/1.93 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.74/1.93
% 1.74/1.93 ======= end of input processing =======
% 1.74/1.93
% 1.74/1.93 =========== start of search ===========
% 1.74/1.93
% 1.74/1.93 -------- PROOF --------
% 1.74/1.93
% 1.74/1.93 -----> EMPTY CLAUSE at 0.02 sec ----> 355 [hyper,269,6,17,23] $F.
% 1.74/1.93
% 1.74/1.93 Length of proof is 6. Level of proof is 5.
% 1.74/1.93
% 1.74/1.93 ---------------- PROOF ----------------
% 1.74/1.93 % SZS status Theorem
% 1.74/1.93 % SZS output start Refutation
% See solution above
% 1.74/1.93 ------------ end of proof -------------
% 1.74/1.93
% 1.74/1.93
% 1.74/1.93 Search stopped by max_proofs option.
% 1.74/1.93
% 1.74/1.93
% 1.74/1.93 Search stopped by max_proofs option.
% 1.74/1.93
% 1.74/1.93 ============ end of search ============
% 1.74/1.93
% 1.74/1.93 -------------- statistics -------------
% 1.74/1.93 clauses given 14
% 1.74/1.93 clauses generated 357
% 1.74/1.93 clauses kept 353
% 1.74/1.93 clauses forward subsumed 125
% 1.74/1.93 clauses back subsumed 13
% 1.74/1.93 Kbytes malloced 1953
% 1.74/1.93
% 1.74/1.93 ----------- times (seconds) -----------
% 1.74/1.93 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.74/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.93
% 1.74/1.93 That finishes the proof of the theorem.
% 1.74/1.93
% 1.74/1.93 Process 7059 finished Wed Jul 27 11:00:23 2022
% 1.74/1.93 Otter interrupted
% 1.74/1.93 PROOF FOUND
%------------------------------------------------------------------------------