TSTP Solution File: SET941+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET941+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:14:34 EDT 2022
% Result : Theorem 1.63s 1.81s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 9 unt; 1 nHn; 13 RR)
% Number of literals : 24 ( 3 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SET941+1.p',unknown),
[] ).
cnf(3,axiom,
( subset(A,B)
| ~ in(dollar_f1(A,B),B) ),
file('SET941+1.p',unknown),
[] ).
cnf(4,axiom,
( A != union(B)
| ~ in(C,A)
| in(C,dollar_f2(B,A,C)) ),
file('SET941+1.p',unknown),
[] ).
cnf(5,axiom,
( A != union(B)
| ~ in(C,A)
| in(dollar_f2(B,A,C),B) ),
file('SET941+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(A,dollar_c4)
| subset(A,dollar_c3) ),
file('SET941+1.p',unknown),
[] ).
cnf(10,axiom,
~ subset(union(dollar_c4),dollar_c3),
file('SET941+1.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('SET941+1.p',unknown),
[] ).
cnf(14,axiom,
( subset(A,B)
| in(dollar_f1(A,B),A) ),
file('SET941+1.p',unknown),
[] ).
cnf(21,plain,
in(dollar_f1(union(dollar_c4),dollar_c3),union(dollar_c4)),
inference(hyper,[status(thm)],[14,10]),
[iquote('hyper,14,10')] ).
cnf(24,plain,
in(dollar_f2(dollar_c4,union(dollar_c4),dollar_f1(union(dollar_c4),dollar_c3)),dollar_c4),
inference(hyper,[status(thm)],[21,5,13]),
[iquote('hyper,21,5,13')] ).
cnf(25,plain,
in(dollar_f1(union(dollar_c4),dollar_c3),dollar_f2(dollar_c4,union(dollar_c4),dollar_f1(union(dollar_c4),dollar_c3))),
inference(hyper,[status(thm)],[21,4,13]),
[iquote('hyper,21,4,13')] ).
cnf(87,plain,
subset(dollar_f2(dollar_c4,union(dollar_c4),dollar_f1(union(dollar_c4),dollar_c3)),dollar_c3),
inference(hyper,[status(thm)],[24,9]),
[iquote('hyper,24,9')] ).
cnf(167,plain,
in(dollar_f1(union(dollar_c4),dollar_c3),dollar_c3),
inference(hyper,[status(thm)],[25,2,87]),
[iquote('hyper,25,2,87')] ).
cnf(315,plain,
subset(union(dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[167,3]),
[iquote('hyper,167,3')] ).
cnf(316,plain,
$false,
inference(binary,[status(thm)],[315,10]),
[iquote('binary,315.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET941+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 10:27:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.62/1.81 ----- Otter 3.3f, August 2004 -----
% 1.62/1.81 The process was started by sandbox2 on n005.cluster.edu,
% 1.62/1.81 Wed Jul 27 10:27:05 2022
% 1.62/1.81 The command was "./otter". The process ID is 5989.
% 1.62/1.81
% 1.62/1.81 set(prolog_style_variables).
% 1.62/1.81 set(auto).
% 1.62/1.81 dependent: set(auto1).
% 1.62/1.81 dependent: set(process_input).
% 1.62/1.81 dependent: clear(print_kept).
% 1.62/1.81 dependent: clear(print_new_demod).
% 1.62/1.81 dependent: clear(print_back_demod).
% 1.62/1.81 dependent: clear(print_back_sub).
% 1.62/1.81 dependent: set(control_memory).
% 1.62/1.81 dependent: assign(max_mem, 12000).
% 1.62/1.81 dependent: assign(pick_given_ratio, 4).
% 1.62/1.81 dependent: assign(stats_level, 1).
% 1.62/1.81 dependent: assign(max_seconds, 10800).
% 1.62/1.81 clear(print_given).
% 1.62/1.81
% 1.62/1.81 formula_list(usable).
% 1.62/1.81 all A (A=A).
% 1.62/1.81 all A B (in(A,B)-> -in(B,A)).
% 1.62/1.81 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.62/1.81 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 1.62/1.81 exists A empty(A).
% 1.62/1.81 exists A (-empty(A)).
% 1.62/1.81 all A B subset(A,A).
% 1.62/1.81 -(all A B ((all C (in(C,A)->subset(C,B)))->subset(union(A),B))).
% 1.62/1.81 end_of_list.
% 1.62/1.81
% 1.62/1.81 -------> usable clausifies to:
% 1.62/1.81
% 1.62/1.81 list(usable).
% 1.62/1.81 0 [] A=A.
% 1.62/1.81 0 [] -in(A,B)| -in(B,A).
% 1.62/1.81 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.62/1.81 0 [] subset(A,B)|in($f1(A,B),A).
% 1.62/1.81 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.62/1.81 0 [] B!=union(A)| -in(C,B)|in(C,$f2(A,B,C)).
% 1.62/1.81 0 [] B!=union(A)| -in(C,B)|in($f2(A,B,C),A).
% 1.62/1.81 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 1.62/1.81 0 [] B=union(A)|in($f4(A,B),B)|in($f4(A,B),$f3(A,B)).
% 1.62/1.81 0 [] B=union(A)|in($f4(A,B),B)|in($f3(A,B),A).
% 1.62/1.81 0 [] B=union(A)| -in($f4(A,B),B)| -in($f4(A,B),X1)| -in(X1,A).
% 1.62/1.81 0 [] empty($c1).
% 1.62/1.81 0 [] -empty($c2).
% 1.62/1.81 0 [] subset(A,A).
% 1.62/1.81 0 [] -in(C,$c4)|subset(C,$c3).
% 1.62/1.81 0 [] -subset(union($c4),$c3).
% 1.62/1.81 end_of_list.
% 1.62/1.81
% 1.62/1.81 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.62/1.81
% 1.62/1.81 This ia a non-Horn set with equality. The strategy will be
% 1.62/1.81 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.62/1.81 deletion, with positive clauses in sos and nonpositive
% 1.62/1.81 clauses in usable.
% 1.62/1.81
% 1.62/1.81 dependent: set(knuth_bendix).
% 1.62/1.81 dependent: set(anl_eq).
% 1.62/1.81 dependent: set(para_from).
% 1.62/1.81 dependent: set(para_into).
% 1.62/1.81 dependent: clear(para_from_right).
% 1.62/1.81 dependent: clear(para_into_right).
% 1.62/1.81 dependent: set(para_from_vars).
% 1.62/1.81 dependent: set(eq_units_both_ways).
% 1.62/1.81 dependent: set(dynamic_demod_all).
% 1.62/1.81 dependent: set(dynamic_demod).
% 1.62/1.81 dependent: set(order_eq).
% 1.62/1.81 dependent: set(back_demod).
% 1.62/1.81 dependent: set(lrpo).
% 1.62/1.81 dependent: set(hyper_res).
% 1.62/1.81 dependent: set(unit_deletion).
% 1.62/1.81 dependent: set(factor).
% 1.62/1.81
% 1.62/1.81 ------------> process usable:
% 1.62/1.81 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.62/1.81 ** KEPT (pick-wt=9): 2 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.62/1.81 ** KEPT (pick-wt=8): 3 [] subset(A,B)| -in($f1(A,B),B).
% 1.62/1.81 ** KEPT (pick-wt=13): 4 [] A!=union(B)| -in(C,A)|in(C,$f2(B,A,C)).
% 1.62/1.81 ** KEPT (pick-wt=13): 5 [] A!=union(B)| -in(C,A)|in($f2(B,A,C),B).
% 1.62/1.81 ** KEPT (pick-wt=13): 6 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 1.62/1.81 ** KEPT (pick-wt=17): 7 [] A=union(B)| -in($f4(B,A),A)| -in($f4(B,A),C)| -in(C,B).
% 1.62/1.81 ** KEPT (pick-wt=2): 8 [] -empty($c2).
% 1.62/1.81 ** KEPT (pick-wt=6): 9 [] -in(A,$c4)|subset(A,$c3).
% 1.62/1.81 ** KEPT (pick-wt=4): 10 [] -subset(union($c4),$c3).
% 1.62/1.81
% 1.62/1.81 ------------> process sos:
% 1.62/1.81 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.62/1.81 ** KEPT (pick-wt=8): 14 [] subset(A,B)|in($f1(A,B),A).
% 1.63/1.81 ** KEPT (pick-wt=16): 15 [] A=union(B)|in($f4(B,A),A)|in($f4(B,A),$f3(B,A)).
% 1.63/1.81 ** KEPT (pick-wt=14): 16 [] A=union(B)|in($f4(B,A),A)|in($f3(B,A),B).
% 1.63/1.81 ** KEPT (pick-wt=2): 17 [] empty($c1).
% 1.63/1.81 ** KEPT (pick-wt=3): 18 [] subset(A,A).
% 1.63/1.81 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.63/1.81
% 1.63/1.81 ======= end of input processing =======
% 1.63/1.81
% 1.63/1.81 =========== start of search ===========
% 1.63/1.81
% 1.63/1.81 -------- PROOF --------
% 1.63/1.81
% 1.63/1.81 ----> UNIT CONFLICT at 0.01 sec ----> 316 [binary,315.1,10.1] $F.
% 1.63/1.81
% 1.63/1.81 Length of proof is 6. Level of proof is 5.
% 1.63/1.81
% 1.63/1.81 ---------------- PROOF ----------------
% 1.63/1.81 % SZS status Theorem
% 1.63/1.81 % SZS output start Refutation
% See solution above
% 1.63/1.81 ------------ end of proof -------------
% 1.63/1.81
% 1.63/1.81
% 1.63/1.81 Search stopped by max_proofs option.
% 1.63/1.81
% 1.63/1.81
% 1.63/1.81 Search stopped by max_proofs option.
% 1.63/1.81
% 1.63/1.81 ============ end of search ============
% 1.63/1.81
% 1.63/1.81 -------------- statistics -------------
% 1.63/1.81 clauses given 12
% 1.63/1.81 clauses generated 490
% 1.63/1.81 clauses kept 315
% 1.63/1.81 clauses forward subsumed 192
% 1.63/1.81 clauses back subsumed 0
% 1.63/1.81 Kbytes malloced 1953
% 1.63/1.81
% 1.63/1.81 ----------- times (seconds) -----------
% 1.63/1.81 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.63/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.81 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.63/1.81
% 1.63/1.81 That finishes the proof of the theorem.
% 1.63/1.81
% 1.63/1.81 Process 5989 finished Wed Jul 27 10:27:07 2022
% 1.63/1.81 Otter interrupted
% 1.63/1.81 PROOF FOUND
%------------------------------------------------------------------------------