%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET932+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:14:33 EDT 2022
% Result : Theorem 1.75s 1.90s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 9 unt; 1 nHn; 12 RR)
% Number of literals : 22 ( 3 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != powerset(B)
| ~ in(C,A)
| subset(C,B) ),
file('SET932+1.p',unknown),
[] ).
cnf(3,axiom,
( A != powerset(B)
| in(C,A)
| ~ subset(C,B) ),
file('SET932+1.p',unknown),
[] ).
cnf(6,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SET932+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SET932+1.p',unknown),
[] ).
cnf(9,axiom,
~ subset(powerset(dollar_c4),powerset(dollar_c3)),
file('SET932+1.p',unknown),
[] ).
cnf(11,axiom,
A = A,
file('SET932+1.p',unknown),
[] ).
cnf(13,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SET932+1.p',unknown),
[] ).
cnf(16,axiom,
subset(dollar_c4,dollar_c3),
file('SET932+1.p',unknown),
[] ).
cnf(48,plain,
in(dollar_f2(powerset(dollar_c4),powerset(dollar_c3)),powerset(dollar_c4)),
inference(hyper,[status(thm)],[13,9]),
[iquote('hyper,13,9')] ).
cnf(60,plain,
subset(dollar_f2(powerset(dollar_c4),powerset(dollar_c3)),dollar_c4),
inference(hyper,[status(thm)],[48,2,11]),
[iquote('hyper,48,2,11')] ).
cnf(77,plain,
subset(dollar_f2(powerset(dollar_c4),powerset(dollar_c3)),dollar_c3),
inference(hyper,[status(thm)],[60,8,16]),
[iquote('hyper,60,8,16')] ).
cnf(106,plain,
in(dollar_f2(powerset(dollar_c4),powerset(dollar_c3)),powerset(dollar_c3)),
inference(hyper,[status(thm)],[77,3,11]),
[iquote('hyper,77,3,11')] ).
cnf(145,plain,
subset(powerset(dollar_c4),powerset(dollar_c3)),
inference(hyper,[status(thm)],[106,6]),
[iquote('hyper,106,6')] ).
cnf(146,plain,
$false,
inference(binary,[status(thm)],[145,9]),
[iquote('binary,145.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET932+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n008.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 10:55:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.75/1.90 ----- Otter 3.3f, August 2004 -----
% 1.75/1.90 The process was started by sandbox on n008.cluster.edu,
% 1.75/1.90 Wed Jul 27 10:55:53 2022
% 1.75/1.90 The command was "./otter". The process ID is 18220.
% 1.75/1.90
% 1.75/1.90 set(prolog_style_variables).
% 1.75/1.90 set(auto).
% 1.75/1.90 dependent: set(auto1).
% 1.75/1.90 dependent: set(process_input).
% 1.75/1.90 dependent: clear(print_kept).
% 1.75/1.90 dependent: clear(print_new_demod).
% 1.75/1.90 dependent: clear(print_back_demod).
% 1.75/1.90 dependent: clear(print_back_sub).
% 1.75/1.90 dependent: set(control_memory).
% 1.75/1.90 dependent: assign(max_mem, 12000).
% 1.75/1.90 dependent: assign(pick_given_ratio, 4).
% 1.75/1.90 dependent: assign(stats_level, 1).
% 1.75/1.90 dependent: assign(max_seconds, 10800).
% 1.75/1.90 clear(print_given).
% 1.75/1.90
% 1.75/1.90 formula_list(usable).
% 1.75/1.90 all A (A=A).
% 1.75/1.90 all A B (in(A,B)-> -in(B,A)).
% 1.75/1.90 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.75/1.90 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.75/1.90 exists A empty(A).
% 1.75/1.90 exists A (-empty(A)).
% 1.75/1.90 all A B subset(A,A).
% 1.75/1.90 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.75/1.90 -(all A B (subset(A,B)->subset(powerset(A),powerset(B)))).
% 1.75/1.90 end_of_list.
% 1.75/1.90
% 1.75/1.90 -------> usable clausifies to:
% 1.75/1.90
% 1.75/1.90 list(usable).
% 1.75/1.90 0 [] A=A.
% 1.75/1.90 0 [] -in(A,B)| -in(B,A).
% 1.75/1.90 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.75/1.90 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.75/1.90 0 [] B=powerset(A)|in($f1(A,B),B)|subset($f1(A,B),A).
% 1.75/1.90 0 [] B=powerset(A)| -in($f1(A,B),B)| -subset($f1(A,B),A).
% 1.75/1.90 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.75/1.90 0 [] subset(A,B)|in($f2(A,B),A).
% 1.75/1.90 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.75/1.90 0 [] empty($c1).
% 1.75/1.90 0 [] -empty($c2).
% 1.75/1.90 0 [] subset(A,A).
% 1.75/1.90 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.75/1.90 0 [] subset($c4,$c3).
% 1.75/1.90 0 [] -subset(powerset($c4),powerset($c3)).
% 1.75/1.90 end_of_list.
% 1.75/1.90
% 1.75/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.75/1.90
% 1.75/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.90 deletion, with positive clauses in sos and nonpositive
% 1.75/1.90 clauses in usable.
% 1.75/1.90
% 1.75/1.90 dependent: set(knuth_bendix).
% 1.75/1.90 dependent: set(anl_eq).
% 1.75/1.90 dependent: set(para_from).
% 1.75/1.90 dependent: set(para_into).
% 1.75/1.90 dependent: clear(para_from_right).
% 1.75/1.90 dependent: clear(para_into_right).
% 1.75/1.90 dependent: set(para_from_vars).
% 1.75/1.90 dependent: set(eq_units_both_ways).
% 1.75/1.90 dependent: set(dynamic_demod_all).
% 1.75/1.90 dependent: set(dynamic_demod).
% 1.75/1.90 dependent: set(order_eq).
% 1.75/1.90 dependent: set(back_demod).
% 1.75/1.90 dependent: set(lrpo).
% 1.75/1.90 dependent: set(hyper_res).
% 1.75/1.90 dependent: set(unit_deletion).
% 1.75/1.90 dependent: set(factor).
% 1.75/1.90
% 1.75/1.90 ------------> process usable:
% 1.75/1.90 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.75/1.90 ** KEPT (pick-wt=10): 2 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.75/1.90 ** KEPT (pick-wt=10): 3 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.75/1.90 ** KEPT (pick-wt=14): 4 [] A=powerset(B)| -in($f1(B,A),A)| -subset($f1(B,A),B).
% 1.75/1.90 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.75/1.90 ** KEPT (pick-wt=8): 6 [] subset(A,B)| -in($f2(A,B),B).
% 1.75/1.90 ** KEPT (pick-wt=2): 7 [] -empty($c2).
% 1.75/1.90 ** KEPT (pick-wt=9): 8 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.75/1.90 ** KEPT (pick-wt=5): 9 [] -subset(powerset($c4),powerset($c3)).
% 1.75/1.90
% 1.75/1.90 ------------> process sos:
% 1.75/1.90 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.75/1.90 ** KEPT (pick-wt=14): 12 [] A=powerset(B)|in($f1(B,A),A)|subset($f1(B,A),B).
% 1.75/1.90 ** KEPT (pick-wt=8): 13 [] subset(A,B)|in($f2(A,B),A).
% 1.75/1.90 ** KEPT (pick-wt=2): 14 [] empty($c1).
% 1.75/1.90 ** KEPT (pick-wt=3): 15 [] subset(A,A).
% 1.75/1.90 ** KEPT (pick-wt=3): 16 [] subset($c4,$c3).
% 1.75/1.90 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.75/1.90
% 1.75/1.90 ======= end of input processing =======
% 1.75/1.90
% 1.75/1.90 =========== start of search ===========
% 1.75/1.90
% 1.75/1.90 -------- PROOF --------
% 1.75/1.90
% 1.75/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 146 [binary,145.1,9.1] $F.
% 1.75/1.90
% 1.75/1.90 Length of proof is 5. Level of proof is 5.
% 1.75/1.90
% 1.75/1.90 ---------------- PROOF ----------------
% 1.75/1.90 % SZS status Theorem
% 1.75/1.90 % SZS output start Refutation
% See solution above
% 1.75/1.90 ------------ end of proof -------------
% 1.75/1.90
% 1.75/1.90
% 1.75/1.90 Search stopped by max_proofs option.
% 1.75/1.90
% 1.75/1.90
% 1.75/1.90 Search stopped by max_proofs option.
% 1.75/1.90
% 1.75/1.90 ============ end of search ============
% 1.75/1.90
% 1.75/1.90 -------------- statistics -------------
% 1.75/1.90 clauses given 15
% 1.75/1.90 clauses generated 178
% 1.75/1.90 clauses kept 145
% 1.75/1.90 clauses forward subsumed 48
% 1.75/1.90 clauses back subsumed 0
% 1.75/1.90 Kbytes malloced 976
% 1.75/1.90
% 1.75/1.90 ----------- times (seconds) -----------
% 1.75/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.90
% 1.75/1.90 That finishes the proof of the theorem.
% 1.75/1.90
% 1.75/1.90 Process 18220 finished Wed Jul 27 10:55:55 2022
% 1.75/1.90 Otter interrupted
% 1.75/1.90 PROOF FOUND
%------------------------------------------------------------------------------