TSTP Solution File: SET890+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:14:28 EDT 2022
% Result : Theorem 2.94s 3.21s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 11 unt; 5 nHn; 14 RR)
% Number of literals : 44 ( 16 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ in(A,B)
| ~ in(B,A) ),
file('SET890+1.p',unknown),
[] ).
cnf(5,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET890+1.p',unknown),
[] ).
cnf(6,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SET890+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SET890+1.p',unknown),
[] ).
cnf(13,axiom,
( A = union(B)
| ~ in(dollar_f5(B,A),A)
| ~ in(dollar_f5(B,A),C)
| ~ in(C,B) ),
file('SET890+1.p',unknown),
[] ).
cnf(16,axiom,
union(singleton(dollar_c3)) != dollar_c3,
file('SET890+1.p',unknown),
[] ).
cnf(17,plain,
~ in(A,A),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(19,plain,
( A = union(B)
| ~ in(dollar_f5(B,A),A)
| ~ in(A,B) ),
inference(factor,[status(thm)],[13]),
[iquote('factor,13.2.3')] ).
cnf(20,axiom,
A = A,
file('SET890+1.p',unknown),
[] ).
cnf(22,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SET890+1.p',unknown),
[] ).
cnf(23,axiom,
( A = union(B)
| in(dollar_f5(B,A),A)
| in(dollar_f5(B,A),dollar_f4(B,A)) ),
file('SET890+1.p',unknown),
[] ).
cnf(24,axiom,
( A = union(B)
| in(dollar_f5(B,A),A)
| in(dollar_f4(B,A),B) ),
file('SET890+1.p',unknown),
[] ).
cnf(27,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[20,6,20]),
[iquote('hyper,20,6,20')] ).
cnf(139,plain,
( in(dollar_f2(singleton(A),B),singleton(A))
| in(A,B) ),
inference(hyper,[status(thm)],[22,8,27]),
[iquote('hyper,22,8,27')] ).
cnf(405,plain,
( union(singleton(A)) = A
| in(dollar_f4(singleton(A),A),singleton(A)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[24,19,27])]),
[iquote('hyper,24,19,27,factor_simp')] ).
cnf(648,plain,
in(dollar_f2(singleton(A),A),singleton(A)),
inference(hyper,[status(thm)],[139,17]),
[iquote('hyper,139,17')] ).
cnf(662,plain,
dollar_f2(singleton(A),A) = A,
inference(hyper,[status(thm)],[648,5,20]),
[iquote('hyper,648,5,20')] ).
cnf(666,plain,
( A = B
| C != singleton(A)
| ~ in(B,C) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[662,5]),662]),
[iquote('para_into,661.1.1,5.3.1,demod,662')] ).
cnf(854,plain,
in(dollar_f4(singleton(dollar_c3),dollar_c3),singleton(dollar_c3)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[405,16]),20]),
[iquote('para_from,405.1.1,16.1.1,unit_del,20')] ).
cnf(856,plain,
dollar_f4(singleton(dollar_c3),dollar_c3) = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[854,666,20])]),
[iquote('hyper,854,666,20,flip.1')] ).
cnf(861,plain,
in(dollar_f5(singleton(dollar_c3),dollar_c3),dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[854,19,23]),856,856,856,856,856]),16,16]),
[iquote('hyper,854,19,23,demod,856,856,856,856,856,unit_del,16,16')] ).
cnf(872,plain,
union(singleton(dollar_c3)) = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[861,19,27])]),
[iquote('hyper,861,19,27,flip.1')] ).
cnf(874,plain,
$false,
inference(binary,[status(thm)],[872,16]),
[iquote('binary,872.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:40:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.80/1.98 ----- Otter 3.3f, August 2004 -----
% 1.80/1.98 The process was started by sandbox2 on n007.cluster.edu,
% 1.80/1.98 Wed Jul 27 10:40:01 2022
% 1.80/1.98 The command was "./otter". The process ID is 14320.
% 1.80/1.98
% 1.80/1.98 set(prolog_style_variables).
% 1.80/1.98 set(auto).
% 1.80/1.98 dependent: set(auto1).
% 1.80/1.98 dependent: set(process_input).
% 1.80/1.98 dependent: clear(print_kept).
% 1.80/1.98 dependent: clear(print_new_demod).
% 1.80/1.98 dependent: clear(print_back_demod).
% 1.80/1.98 dependent: clear(print_back_sub).
% 1.80/1.98 dependent: set(control_memory).
% 1.80/1.98 dependent: assign(max_mem, 12000).
% 1.80/1.98 dependent: assign(pick_given_ratio, 4).
% 1.80/1.98 dependent: assign(stats_level, 1).
% 1.80/1.98 dependent: assign(max_seconds, 10800).
% 1.80/1.98 clear(print_given).
% 1.80/1.98
% 1.80/1.98 formula_list(usable).
% 1.80/1.98 all A (A=A).
% 1.80/1.98 all A B (in(A,B)-> -in(B,A)).
% 1.80/1.98 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.80/1.98 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.80/1.98 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.80/1.98 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 1.80/1.98 all A B (in(A,B)->subset(A,union(B))).
% 1.80/1.98 exists A empty(A).
% 1.80/1.98 exists A (-empty(A)).
% 1.80/1.98 all A B subset(A,A).
% 1.80/1.98 -(all A (union(singleton(A))=A)).
% 1.80/1.98 end_of_list.
% 1.80/1.98
% 1.80/1.98 -------> usable clausifies to:
% 1.80/1.98
% 1.80/1.98 list(usable).
% 1.80/1.98 0 [] A=A.
% 1.80/1.98 0 [] -in(A,B)| -in(B,A).
% 1.80/1.98 0 [] A!=B|subset(A,B).
% 1.80/1.98 0 [] A!=B|subset(B,A).
% 1.80/1.98 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.80/1.98 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.80/1.98 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.80/1.98 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.80/1.98 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.80/1.98 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.80/1.98 0 [] subset(A,B)|in($f2(A,B),A).
% 1.80/1.98 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.80/1.98 0 [] B!=union(A)| -in(C,B)|in(C,$f3(A,B,C)).
% 1.80/1.98 0 [] B!=union(A)| -in(C,B)|in($f3(A,B,C),A).
% 1.80/1.98 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 1.80/1.98 0 [] B=union(A)|in($f5(A,B),B)|in($f5(A,B),$f4(A,B)).
% 1.80/1.98 0 [] B=union(A)|in($f5(A,B),B)|in($f4(A,B),A).
% 1.80/1.98 0 [] B=union(A)| -in($f5(A,B),B)| -in($f5(A,B),X1)| -in(X1,A).
% 1.80/1.98 0 [] -in(A,B)|subset(A,union(B)).
% 1.80/1.98 0 [] empty($c1).
% 1.80/1.98 0 [] -empty($c2).
% 1.80/1.98 0 [] subset(A,A).
% 1.80/1.98 0 [] union(singleton($c3))!=$c3.
% 1.80/1.98 end_of_list.
% 1.80/1.98
% 1.80/1.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.80/1.98
% 1.80/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.80/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.80/1.98 deletion, with positive clauses in sos and nonpositive
% 1.80/1.98 clauses in usable.
% 1.80/1.98
% 1.80/1.98 dependent: set(knuth_bendix).
% 1.80/1.98 dependent: set(anl_eq).
% 1.80/1.98 dependent: set(para_from).
% 1.80/1.98 dependent: set(para_into).
% 1.80/1.98 dependent: clear(para_from_right).
% 1.80/1.98 dependent: clear(para_into_right).
% 1.80/1.98 dependent: set(para_from_vars).
% 1.80/1.98 dependent: set(eq_units_both_ways).
% 1.80/1.98 dependent: set(dynamic_demod_all).
% 1.80/1.98 dependent: set(dynamic_demod).
% 1.80/1.98 dependent: set(order_eq).
% 1.80/1.98 dependent: set(back_demod).
% 1.80/1.98 dependent: set(lrpo).
% 1.80/1.98 dependent: set(hyper_res).
% 1.80/1.98 dependent: set(unit_deletion).
% 1.80/1.98 dependent: set(factor).
% 1.80/1.98
% 1.80/1.98 ------------> process usable:
% 1.80/1.98 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.80/1.98 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.80/1.98 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.80/1.98 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.80/1.98 ** KEPT (pick-wt=10): 5 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.80/1.98 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.80/1.98 ** KEPT (pick-wt=14): 7 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.80/1.98 ** KEPT (pick-wt=9): 8 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.80/1.98 ** KEPT (pick-wt=8): 9 [] subset(A,B)| -in($f2(A,B),B).
% 1.80/1.98 ** KEPT (pick-wt=13): 10 [] A!=union(B)| -in(C,A)|in(C,$f3(B,A,C)).
% 1.80/1.98 ** KEPT (pick-wt=13): 11 [] A!=union(B)| -in(C,A)|in($f3(B,A,C),B).
% 1.80/1.98 ** KEPT (pick-wt=13): 12 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 1.80/1.98 ** KEPT (pick-wt=17): 13 [] A=union(B)| -in($f5(B,A),A)| -in($f5(B,A),C)| -in(C,B).
% 1.80/1.98 ** KEPT (pick-wt=7): 14 [] -in(A,B)|subset(A,union(B)).
% 1.80/1.98 ** KEPT (pick-wt=2): 15 [] -empty($c2).
% 1.80/1.98 ** KEPT (pick-wt=5): 16 [] union(singleton($c3))!=$c3.
% 1.80/1.98
% 1.80/1.98 ------------> process sos:
% 1.80/1.98 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.80/1.98 ** KEPT (pick-wt=14): 21 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.80/1.98 ** KEPT (pick-wt=8): 22 [] subset(A,B)|in($f2(A,B),A).
% 1.80/1.98 ** KEPT (pick-wt=16): 23 [] A=union(B)|in($f5(B,A),A)|in($f5(B,A),$f4(B,A)).
% 1.80/1.98 ** KEPT (pick-wt=14): 24 [] A=union(B)|in($f5(B,A),A)|in($f4(B,A),B).
% 1.80/1.98 ** KEPT (pick-wt=2): 25 [] empty($c1).
% 1.80/1.98 ** KEPT (pick-wt=3): 26 [] subset(A,A).
% 1.80/1.98 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 2.94/3.21 20 back subsumes 18.
% 2.94/3.21
% 2.94/3.21 ======= end of input processing =======
% 2.94/3.21
% 2.94/3.21 =========== start of search ===========
% 2.94/3.21
% 2.94/3.21
% 2.94/3.21 Resetting weight limit to 13.
% 2.94/3.21
% 2.94/3.21
% 2.94/3.21 Resetting weight limit to 13.
% 2.94/3.21
% 2.94/3.21 sos_size=605
% 2.94/3.21
% 2.94/3.21
% 2.94/3.21 Resetting weight limit to 12.
% 2.94/3.21
% 2.94/3.21
% 2.94/3.21 Resetting weight limit to 12.
% 2.94/3.21
% 2.94/3.21 sos_size=645
% 2.94/3.21
% 2.94/3.21 -------- PROOF --------
% 2.94/3.21
% 2.94/3.21 ----> UNIT CONFLICT at 1.22 sec ----> 874 [binary,872.1,16.1] $F.
% 2.94/3.21
% 2.94/3.21 Length of proof is 12. Level of proof is 8.
% 2.94/3.21
% 2.94/3.21 ---------------- PROOF ----------------
% 2.94/3.21 % SZS status Theorem
% 2.94/3.21 % SZS output start Refutation
% See solution above
% 3.04/3.21 ------------ end of proof -------------
% 3.04/3.21
% 3.04/3.21
% 3.04/3.21 Search stopped by max_proofs option.
% 3.04/3.21
% 3.04/3.21
% 3.04/3.21 Search stopped by max_proofs option.
% 3.04/3.21
% 3.04/3.21 ============ end of search ============
% 3.04/3.21
% 3.04/3.21 -------------- statistics -------------
% 3.04/3.21 clauses given 150
% 3.04/3.21 clauses generated 68751
% 3.04/3.21 clauses kept 851
% 3.04/3.21 clauses forward subsumed 2974
% 3.04/3.21 clauses back subsumed 7
% 3.04/3.21 Kbytes malloced 6835
% 3.04/3.21
% 3.04/3.21 ----------- times (seconds) -----------
% 3.04/3.21 user CPU time 1.22 (0 hr, 0 min, 1 sec)
% 3.04/3.21 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.04/3.21 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.04/3.21
% 3.04/3.21 That finishes the proof of the theorem.
% 3.04/3.21
% 3.04/3.21 Process 14320 finished Wed Jul 27 10:40:04 2022
% 3.04/3.21 Otter interrupted
% 3.04/3.21 PROOF FOUND
%------------------------------------------------------------------------------