TSTP Solution File: SET882+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET882+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 13:14:27 EDT 2022
% Result : Theorem 1.97s 2.14s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 11 unt; 6 nHn; 14 RR)
% Number of literals : 45 ( 28 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ in(A,B)
| ~ in(B,A) ),
file('SET882+1.p',unknown),
[] ).
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET882+1.p',unknown),
[] ).
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SET882+1.p',unknown),
[] ).
cnf(5,axiom,
( set_difference(unordered_pair(A,B),C) != singleton(A)
| ~ in(A,C) ),
file('SET882+1.p',unknown),
[] ).
cnf(7,axiom,
( set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C)
| ~ in(B,C) ),
file('SET882+1.p',unknown),
[] ).
cnf(8,axiom,
( set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C)
| A != B ),
file('SET882+1.p',unknown),
[] ).
cnf(10,axiom,
dollar_c4 != dollar_c3,
file('SET882+1.p',unknown),
[] ).
cnf(11,axiom,
set_difference(unordered_pair(dollar_c4,dollar_c3),singleton(dollar_c3)) != singleton(dollar_c4),
file('SET882+1.p',unknown),
[] ).
cnf(12,plain,
singleton(dollar_c4) != set_difference(unordered_pair(dollar_c4,dollar_c3),singleton(dollar_c3)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(13,plain,
~ in(A,A),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(14,axiom,
A = A,
file('SET882+1.p',unknown),
[] ).
cnf(18,plain,
( set_difference(unordered_pair(A,A),B) = singleton(A)
| in(A,B) ),
inference(hyper,[status(thm)],[14,8]),
[iquote('hyper,14,8')] ).
cnf(19,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[14,3,14]),
[iquote('hyper,14,3,14')] ).
cnf(96,plain,
singleton(A) = set_difference(unordered_pair(A,A),A),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,13])]),
[iquote('hyper,18,13,flip.1')] ).
cnf(97,plain,
( set_difference(unordered_pair(A,A),B) = set_difference(unordered_pair(A,A),A)
| set_difference(unordered_pair(C,A),B) = set_difference(unordered_pair(C,C),C)
| in(C,B) ),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,7]),96,96]),
[iquote('hyper,18,7,demod,96,96')] ).
cnf(98,plain,
( set_difference(unordered_pair(A,A),set_difference(unordered_pair(B,B),B)) = set_difference(unordered_pair(A,A),A)
| A = B ),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,2,14]),96,96]),
[iquote('hyper,18,2,14,demod,96,96')] ).
cnf(181,plain,
in(A,set_difference(unordered_pair(A,A),A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),96]),
[iquote('back_demod,19,demod,96')] ).
cnf(184,plain,
set_difference(unordered_pair(dollar_c4,dollar_c4),dollar_c4) != set_difference(unordered_pair(dollar_c4,dollar_c3),set_difference(unordered_pair(dollar_c3,dollar_c3),dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),96,96]),
[iquote('back_demod,12,demod,96,96')] ).
cnf(188,plain,
( set_difference(unordered_pair(A,B),C) != set_difference(unordered_pair(A,A),A)
| ~ in(A,C) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),96]),
[iquote('back_demod,5,demod,96')] ).
cnf(191,plain,
( A != set_difference(unordered_pair(B,B),B)
| ~ in(C,A)
| C = B ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),96]),
[iquote('back_demod,2,demod,96')] ).
cnf(196,plain,
( A != dollar_c3
| B != set_difference(unordered_pair(A,A),A)
| ~ in(dollar_c4,B) ),
inference(para_from,[status(thm),theory(equality)],[191,10]),
[iquote('para_from,191.3.1,10.1.1')] ).
cnf(258,plain,
( set_difference(unordered_pair(A,A),set_difference(unordered_pair(dollar_c3,dollar_c3),dollar_c3)) = set_difference(unordered_pair(A,A),A)
| set_difference(unordered_pair(B,B),set_difference(unordered_pair(A,A),A)) = set_difference(unordered_pair(B,B),B)
| set_difference(unordered_pair(dollar_c4,B),set_difference(unordered_pair(A,A),A)) = set_difference(unordered_pair(dollar_c4,dollar_c4),dollar_c4) ),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[98,196,96,97]),96,96]),
[iquote('hyper,98,196,95,97,demod,96,96')] ).
cnf(276,plain,
set_difference(unordered_pair(dollar_c3,dollar_c3),set_difference(unordered_pair(dollar_c3,dollar_c3),dollar_c3)) = set_difference(unordered_pair(dollar_c3,dollar_c3),dollar_c3),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[258]),184]),
[iquote('factor,258.1.2,unit_del,184')] ).
cnf(697,plain,
$false,
inference(hyper,[status(thm)],[276,188,181]),
[iquote('hyper,276,188,181')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % 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 10:38:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.14 ----- Otter 3.3f, August 2004 -----
% 1.97/2.14 The process was started by sandbox2 on n007.cluster.edu,
% 1.97/2.14 Wed Jul 27 10:38:31 2022
% 1.97/2.14 The command was "./otter". The process ID is 8891.
% 1.97/2.14
% 1.97/2.14 set(prolog_style_variables).
% 1.97/2.14 set(auto).
% 1.97/2.14 dependent: set(auto1).
% 1.97/2.14 dependent: set(process_input).
% 1.97/2.14 dependent: clear(print_kept).
% 1.97/2.14 dependent: clear(print_new_demod).
% 1.97/2.14 dependent: clear(print_back_demod).
% 1.97/2.14 dependent: clear(print_back_sub).
% 1.97/2.14 dependent: set(control_memory).
% 1.97/2.14 dependent: assign(max_mem, 12000).
% 1.97/2.14 dependent: assign(pick_given_ratio, 4).
% 1.97/2.14 dependent: assign(stats_level, 1).
% 1.97/2.14 dependent: assign(max_seconds, 10800).
% 1.97/2.14 clear(print_given).
% 1.97/2.14
% 1.97/2.14 formula_list(usable).
% 1.97/2.14 all A (A=A).
% 1.97/2.14 all A B (in(A,B)-> -in(B,A)).
% 1.97/2.14 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.97/2.14 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.97/2.14 all A B C (set_difference(unordered_pair(A,B),C)=singleton(A)<-> -in(A,C)& (in(B,C)|A=B)).
% 1.97/2.14 exists A empty(A).
% 1.97/2.14 exists A (-empty(A)).
% 1.97/2.14 -(all A B (A!=B->set_difference(unordered_pair(A,B),singleton(B))=singleton(A))).
% 1.97/2.14 end_of_list.
% 1.97/2.14
% 1.97/2.14 -------> usable clausifies to:
% 1.97/2.14
% 1.97/2.14 list(usable).
% 1.97/2.14 0 [] A=A.
% 1.97/2.14 0 [] -in(A,B)| -in(B,A).
% 1.97/2.14 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.14 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.97/2.14 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.97/2.14 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.97/2.14 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.97/2.14 0 [] set_difference(unordered_pair(A,B),C)!=singleton(A)| -in(A,C).
% 1.97/2.14 0 [] set_difference(unordered_pair(A,B),C)!=singleton(A)|in(B,C)|A=B.
% 1.97/2.14 0 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)| -in(B,C).
% 1.97/2.14 0 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)|A!=B.
% 1.97/2.14 0 [] empty($c1).
% 1.97/2.14 0 [] -empty($c2).
% 1.97/2.14 0 [] $c4!=$c3.
% 1.97/2.14 0 [] set_difference(unordered_pair($c4,$c3),singleton($c3))!=singleton($c4).
% 1.97/2.14 end_of_list.
% 1.97/2.14
% 1.97/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.97/2.14
% 1.97/2.14 This ia a non-Horn set with equality. The strategy will be
% 1.97/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.14 deletion, with positive clauses in sos and nonpositive
% 1.97/2.14 clauses in usable.
% 1.97/2.14
% 1.97/2.14 dependent: set(knuth_bendix).
% 1.97/2.14 dependent: set(anl_eq).
% 1.97/2.14 dependent: set(para_from).
% 1.97/2.14 dependent: set(para_into).
% 1.97/2.14 dependent: clear(para_from_right).
% 1.97/2.14 dependent: clear(para_into_right).
% 1.97/2.14 dependent: set(para_from_vars).
% 1.97/2.14 dependent: set(eq_units_both_ways).
% 1.97/2.14 dependent: set(dynamic_demod_all).
% 1.97/2.14 dependent: set(dynamic_demod).
% 1.97/2.14 dependent: set(order_eq).
% 1.97/2.14 dependent: set(back_demod).
% 1.97/2.14 dependent: set(lrpo).
% 1.97/2.14 dependent: set(hyper_res).
% 1.97/2.14 dependent: set(unit_deletion).
% 1.97/2.14 dependent: set(factor).
% 1.97/2.14
% 1.97/2.14 ------------> process usable:
% 1.97/2.14 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.97/2.14 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.97/2.14 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.97/2.14 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.97/2.14 ** KEPT (pick-wt=11): 5 [] set_difference(unordered_pair(A,B),C)!=singleton(A)| -in(A,C).
% 1.97/2.14 ** KEPT (pick-wt=14): 6 [] set_difference(unordered_pair(A,B),C)!=singleton(A)|in(B,C)|A=B.
% 1.97/2.14 ** KEPT (pick-wt=14): 7 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)| -in(B,C).
% 1.97/2.14 ** KEPT (pick-wt=14): 8 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)|A!=B.
% 1.97/2.14 ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.97/2.14 ** KEPT (pick-wt=3): 10 [] $c4!=$c3.
% 1.97/2.14 ** KEPT (pick-wt=9): 12 [copy,11,flip.1] singleton($c4)!=set_difference(unordered_pair($c4,$c3),singleton($c3)).
% 1.97/2.14
% 1.97/2.14 ------------> process sos:
% 1.97/2.14 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.97/2.14 ** KEPT (pick-wt=7): 15 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.14 ** KEPT (pick-wt=14): 16 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.97/2.14 ** KEPT (pick-wt=2): 17 [] empty($c1).
% 1.97/2.14 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.97/2.14 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.14
% 1.97/2.14 ======= end of input processing =======
% 1.97/2.14
% 1.97/2.14 =========== start of search ===========
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Resetting weight limit to 17.
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Resetting weight limit to 17.
% 1.97/2.14
% 1.97/2.14 sos_size=513
% 1.97/2.14
% 1.97/2.14 -------- PROOF --------
% 1.97/2.14
% 1.97/2.14 -----> EMPTY CLAUSE at 0.22 sec ----> 697 [hyper,276,188,181] $F.
% 1.97/2.14
% 1.97/2.14 Length of proof is 14. Level of proof is 6.
% 1.97/2.14
% 1.97/2.14 ---------------- PROOF ----------------
% 1.97/2.14 % SZS status Theorem
% 1.97/2.14 % SZS output start Refutation
% See solution above
% 1.97/2.14 ------------ end of proof -------------
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14 ============ end of search ============
% 1.97/2.14
% 1.97/2.14 -------------- statistics -------------
% 1.97/2.14 clauses given 74
% 1.97/2.14 clauses generated 4947
% 1.97/2.14 clauses kept 684
% 1.97/2.14 clauses forward subsumed 797
% 1.97/2.14 clauses back subsumed 8
% 1.97/2.14 Kbytes malloced 4882
% 1.97/2.14
% 1.97/2.14 ----------- times (seconds) -----------
% 1.97/2.14 user CPU time 0.22 (0 hr, 0 min, 0 sec)
% 1.97/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.14
% 1.97/2.14 That finishes the proof of the theorem.
% 1.97/2.14
% 1.97/2.14 Process 8891 finished Wed Jul 27 10:38:33 2022
% 1.97/2.14 Otter interrupted
% 1.97/2.14 PROOF FOUND
%------------------------------------------------------------------------------