TSTP Solution File: SET930+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 4.16s 4.40s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 38 ( 22 unt; 10 nHn; 25 RR)
% Number of literals : 61 ( 33 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ in(A,B)
| ~ in(B,A) ),
file('SET930+1.p',unknown),
[] ).
cnf(4,axiom,
( set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C)
| ~ in(B,C) ),
file('SET930+1.p',unknown),
[] ).
cnf(5,axiom,
( set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C)
| A != B ),
file('SET930+1.p',unknown),
[] ).
cnf(8,axiom,
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
| ~ in(B,C) ),
file('SET930+1.p',unknown),
[] ).
cnf(10,axiom,
( set_difference(unordered_pair(A,B),C) != empty_set
| in(B,C) ),
file('SET930+1.p',unknown),
[] ).
cnf(11,axiom,
( set_difference(unordered_pair(A,B),C) = empty_set
| ~ in(A,C)
| ~ in(B,C) ),
file('SET930+1.p',unknown),
[] ).
cnf(12,axiom,
set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) != empty_set,
file('SET930+1.p',unknown),
[] ).
cnf(13,axiom,
set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) != singleton(dollar_c5),
file('SET930+1.p',unknown),
[] ).
cnf(14,plain,
singleton(dollar_c5) != set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(15,axiom,
set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) != singleton(dollar_c4),
file('SET930+1.p',unknown),
[] ).
cnf(16,plain,
singleton(dollar_c4) != set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(17,axiom,
set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) != unordered_pair(dollar_c5,dollar_c4),
file('SET930+1.p',unknown),
[] ).
cnf(18,plain,
~ in(A,A),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(19,plain,
( set_difference(unordered_pair(A,A),B) = empty_set
| ~ in(A,B) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.2.3')] ).
cnf(20,axiom,
A = A,
file('SET930+1.p',unknown),
[] ).
cnf(21,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SET930+1.p',unknown),
[] ).
cnf(24,axiom,
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(A,C)
| in(B,C) ),
file('SET930+1.p',unknown),
[] ).
cnf(25,plain,
( set_difference(unordered_pair(A,A),B) = unordered_pair(A,A)
| in(A,B) ),
inference(factor,[status(thm)],[24]),
[iquote('factor,24.2.3')] ).
cnf(26,plain,
( set_difference(unordered_pair(A,A),B) = singleton(A)
| in(A,B) ),
inference(hyper,[status(thm)],[20,5]),
[iquote('hyper,20,5')] ).
cnf(32,plain,
set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3) != empty_set,
inference(para_from,[status(thm),theory(equality)],[21,12]),
[iquote('para_from,21.1.1,12.1.1.1')] ).
cnf(43,plain,
( ~ in(dollar_c4,dollar_c3)
| ~ in(dollar_c5,dollar_c3) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[32,11]),20]),
[iquote('para_into,32.1.1,11.1.1,unit_del,20')] ).
cnf(53,plain,
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(B,C)
| set_difference(unordered_pair(D,C),A) = unordered_pair(D,C)
| in(D,A) ),
inference(hyper,[status(thm)],[24,1,24]),
[iquote('hyper,24,1,24')] ).
cnf(65,plain,
set_difference(unordered_pair(A,A),A) = unordered_pair(A,A),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[53]),18,18]),
[iquote('factor,53.1.3,unit_del,18,18')] ).
cnf(82,plain,
( in(dollar_c5,dollar_c3)
| in(dollar_c4,dollar_c3) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[24,17]),20]),
[iquote('para_from,24.1.1,17.1.1,unit_del,20')] ).
cnf(114,plain,
( in(dollar_c5,dollar_c3)
| singleton(A) = set_difference(unordered_pair(A,dollar_c4),dollar_c3)
| in(A,dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[82,4])]),
[iquote('hyper,82,4,flip.2')] ).
cnf(126,plain,
in(dollar_c5,dollar_c3),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[114]),14]),
[iquote('factor,114.1.3,unit_del,14')] ).
cnf(130,plain,
set_difference(unordered_pair(dollar_c5,dollar_c5),dollar_c3) = empty_set,
inference(hyper,[status(thm)],[126,19]),
[iquote('hyper,126,19')] ).
cnf(135,plain,
( singleton(A) = set_difference(unordered_pair(A,dollar_c5),dollar_c3)
| in(A,dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[126,4])]),
[iquote('hyper,126,4,flip.1')] ).
cnf(147,plain,
unordered_pair(dollar_c5,dollar_c5) != empty_set,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[130,8]),126])]),
[iquote('para_from,129.1.1,8.1.1,unit_del,126,flip.1')] ).
cnf(149,plain,
set_difference(unordered_pair(dollar_c4,dollar_c4),dollar_c3) = unordered_pair(dollar_c4,dollar_c4),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,43,25]),130]),147]),
[iquote('hyper,25,43,25,demod,130,unit_del,147')] ).
cnf(178,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[26,18]),65])]),
[iquote('hyper,26,18,demod,65,flip.1')] ).
cnf(183,plain,
set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) != unordered_pair(dollar_c4,dollar_c4),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),178])]),
[iquote('back_demod,16,demod,178,flip.1')] ).
cnf(200,plain,
( unordered_pair(A,A) = set_difference(unordered_pair(A,dollar_c5),dollar_c3)
| in(A,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[135]),178]),
[iquote('back_demod,135,demod,178')] ).
cnf(240,plain,
unordered_pair(A,A) != empty_set,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[65,10]),18]),
[iquote('para_from,64.1.1,10.1.1,unit_del,18')] ).
cnf(242,plain,
~ in(dollar_c4,dollar_c3),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[149,19]),240]),
[iquote('para_into,149.1.1,19.1.1,unit_del,240')] ).
cnf(244,plain,
set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3) != unordered_pair(dollar_c4,dollar_c4),
inference(para_into,[status(thm),theory(equality)],[183,21]),
[iquote('para_into,183.1.1.1,21.1.1')] ).
cnf(1264,plain,
set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3) = unordered_pair(dollar_c4,dollar_c4),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[200,242])]),
[iquote('hyper,200,242,flip.1')] ).
cnf(1266,plain,
$false,
inference(binary,[status(thm)],[1264,244]),
[iquote('binary,1264.1,244.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 10:49:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.92/2.13 ----- Otter 3.3f, August 2004 -----
% 1.92/2.13 The process was started by sandbox on n023.cluster.edu,
% 1.92/2.13 Wed Jul 27 10:49:48 2022
% 1.92/2.13 The command was "./otter". The process ID is 26695.
% 1.92/2.13
% 1.92/2.13 set(prolog_style_variables).
% 1.92/2.13 set(auto).
% 1.92/2.13 dependent: set(auto1).
% 1.92/2.13 dependent: set(process_input).
% 1.92/2.13 dependent: clear(print_kept).
% 1.92/2.13 dependent: clear(print_new_demod).
% 1.92/2.13 dependent: clear(print_back_demod).
% 1.92/2.13 dependent: clear(print_back_sub).
% 1.92/2.13 dependent: set(control_memory).
% 1.92/2.13 dependent: assign(max_mem, 12000).
% 1.92/2.13 dependent: assign(pick_given_ratio, 4).
% 1.92/2.13 dependent: assign(stats_level, 1).
% 1.92/2.13 dependent: assign(max_seconds, 10800).
% 1.92/2.13 clear(print_given).
% 1.92/2.13
% 1.92/2.13 formula_list(usable).
% 1.92/2.13 all A (A=A).
% 1.92/2.13 all A B (in(A,B)-> -in(B,A)).
% 1.92/2.13 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.92/2.13 empty(empty_set).
% 1.92/2.13 all A B C (set_difference(unordered_pair(A,B),C)=singleton(A)<-> -in(A,C)& (in(B,C)|A=B)).
% 1.92/2.13 exists A empty(A).
% 1.92/2.13 exists A (-empty(A)).
% 1.92/2.13 all A B C (set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)<-> -in(A,C)& -in(B,C)).
% 1.92/2.13 all A B C (set_difference(unordered_pair(A,B),C)=empty_set<->in(A,C)&in(B,C)).
% 1.92/2.13 -(all A B C (-(set_difference(unordered_pair(A,B),C)!=empty_set&set_difference(unordered_pair(A,B),C)!=singleton(A)&set_difference(unordered_pair(A,B),C)!=singleton(B)&set_difference(unordered_pair(A,B),C)!=unordered_pair(A,B)))).
% 1.92/2.13 end_of_list.
% 1.92/2.13
% 1.92/2.13 -------> usable clausifies to:
% 1.92/2.13
% 1.92/2.13 list(usable).
% 1.92/2.13 0 [] A=A.
% 1.92/2.13 0 [] -in(A,B)| -in(B,A).
% 1.92/2.13 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.92/2.13 0 [] empty(empty_set).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)!=singleton(A)| -in(A,C).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)!=singleton(A)|in(B,C)|A=B.
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)| -in(B,C).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)|A!=B.
% 1.92/2.13 0 [] empty($c1).
% 1.92/2.13 0 [] -empty($c2).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)!=unordered_pair(A,B)| -in(A,C).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)!=unordered_pair(A,B)| -in(B,C).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|in(A,C)|in(B,C).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)!=empty_set|in(A,C).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)!=empty_set|in(B,C).
% 1.92/2.13 0 [] set_difference(unordered_pair(A,B),C)=empty_set| -in(A,C)| -in(B,C).
% 1.92/2.13 0 [] set_difference(unordered_pair($c5,$c4),$c3)!=empty_set.
% 1.92/2.13 0 [] set_difference(unordered_pair($c5,$c4),$c3)!=singleton($c5).
% 1.92/2.13 0 [] set_difference(unordered_pair($c5,$c4),$c3)!=singleton($c4).
% 1.92/2.13 0 [] set_difference(unordered_pair($c5,$c4),$c3)!=unordered_pair($c5,$c4).
% 1.92/2.13 end_of_list.
% 1.92/2.13
% 1.92/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.92/2.13
% 1.92/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.92/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.92/2.13 deletion, with positive clauses in sos and nonpositive
% 1.92/2.13 clauses in usable.
% 1.92/2.13
% 1.92/2.13 dependent: set(knuth_bendix).
% 1.92/2.13 dependent: set(anl_eq).
% 1.92/2.13 dependent: set(para_from).
% 1.92/2.13 dependent: set(para_into).
% 1.92/2.13 dependent: clear(para_from_right).
% 1.92/2.13 dependent: clear(para_into_right).
% 1.92/2.13 dependent: set(para_from_vars).
% 1.92/2.13 dependent: set(eq_units_both_ways).
% 1.92/2.13 dependent: set(dynamic_demod_all).
% 1.92/2.13 dependent: set(dynamic_demod).
% 1.92/2.13 dependent: set(order_eq).
% 1.92/2.13 dependent: set(back_demod).
% 1.92/2.13 dependent: set(lrpo).
% 1.92/2.13 dependent: set(hyper_res).
% 1.92/2.13 dependent: set(unit_deletion).
% 1.92/2.13 dependent: set(factor).
% 1.92/2.13
% 1.92/2.13 ------------> process usable:
% 1.92/2.13 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.92/2.13 ** KEPT (pick-wt=11): 2 [] set_difference(unordered_pair(A,B),C)!=singleton(A)| -in(A,C).
% 1.92/2.13 ** KEPT (pick-wt=14): 3 [] set_difference(unordered_pair(A,B),C)!=singleton(A)|in(B,C)|A=B.
% 1.92/2.13 ** KEPT (pick-wt=14): 4 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)| -in(B,C).
% 1.92/2.13 ** KEPT (pick-wt=14): 5 [] set_difference(unordered_pair(A,B),C)=singleton(A)|in(A,C)|A!=B.
% 1.92/2.13 ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.92/2.13 ** KEPT (pick-wt=12): 7 [] set_difference(unordered_pair(A,B),C)!=unordered_pair(A,B)| -in(A,C).
% 1.92/2.13 ** KEPT (pick-wt=12): 8 [] set_difference(unordered_pair(A,B),C)!=unordered_pair(A,B)| -in(B,C).
% 1.92/2.13 ** KEPT (pick-wt=10): 9 [] set_difference(unordered_pair(A,B),C)!=empty_set|in(A,C).
% 1.92/2.13 ** KEPT (pick-wt=10): 10 [] set_difference(unordered_pair(A,B),C)!=empty_set|in(B,C).
% 4.16/4.40 ** KEPT (pick-wt=13): 11 [] set_difference(unordered_pair(A,B),C)=empty_set| -in(A,C)| -in(B,C).
% 4.16/4.40 ** KEPT (pick-wt=7): 12 [] set_difference(unordered_pair($c5,$c4),$c3)!=empty_set.
% 4.16/4.40 ** KEPT (pick-wt=8): 14 [copy,13,flip.1] singleton($c5)!=set_difference(unordered_pair($c5,$c4),$c3).
% 4.16/4.40 ** KEPT (pick-wt=8): 16 [copy,15,flip.1] singleton($c4)!=set_difference(unordered_pair($c5,$c4),$c3).
% 4.16/4.40 ** KEPT (pick-wt=9): 17 [] set_difference(unordered_pair($c5,$c4),$c3)!=unordered_pair($c5,$c4).
% 4.16/4.40
% 4.16/4.40 ------------> process sos:
% 4.16/4.40 ** KEPT (pick-wt=3): 20 [] A=A.
% 4.16/4.40 ** KEPT (pick-wt=7): 21 [] unordered_pair(A,B)=unordered_pair(B,A).
% 4.16/4.40 ** KEPT (pick-wt=2): 22 [] empty(empty_set).
% 4.16/4.40 ** KEPT (pick-wt=2): 23 [] empty($c1).
% 4.16/4.40 ** KEPT (pick-wt=15): 24 [] set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|in(A,C)|in(B,C).
% 4.16/4.40 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 4.16/4.40 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 4.16/4.40
% 4.16/4.40 ======= end of input processing =======
% 4.16/4.40
% 4.16/4.40 =========== start of search ===========
% 4.16/4.40
% 4.16/4.40 -------- PROOF --------
% 4.16/4.40
% 4.16/4.40 ----> UNIT CONFLICT at 2.27 sec ----> 1266 [binary,1264.1,244.1] $F.
% 4.16/4.40
% 4.16/4.40 Length of proof is 24. Level of proof is 8.
% 4.16/4.40
% 4.16/4.40 ---------------- PROOF ----------------
% 4.16/4.40 % SZS status Theorem
% 4.16/4.40 % SZS output start Refutation
% See solution above
% 4.16/4.40 ------------ end of proof -------------
% 4.16/4.40
% 4.16/4.40
% 4.16/4.40 Search stopped by max_proofs option.
% 4.16/4.40
% 4.16/4.40
% 4.16/4.40 Search stopped by max_proofs option.
% 4.16/4.40
% 4.16/4.40 ============ end of search ============
% 4.16/4.40
% 4.16/4.40 -------------- statistics -------------
% 4.16/4.40 clauses given 74
% 4.16/4.40 clauses generated 8012
% 4.16/4.40 clauses kept 1249
% 4.16/4.40 clauses forward subsumed 6723
% 4.16/4.40 clauses back subsumed 51
% 4.16/4.40 Kbytes malloced 2929
% 4.16/4.40
% 4.16/4.40 ----------- times (seconds) -----------
% 4.16/4.40 user CPU time 2.27 (0 hr, 0 min, 2 sec)
% 4.16/4.40 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 4.16/4.40 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.16/4.40
% 4.16/4.40 That finishes the proof of the theorem.
% 4.16/4.40
% 4.16/4.40 Process 26695 finished Wed Jul 27 10:49:52 2022
% 4.16/4.40 Otter interrupted
% 4.16/4.40 PROOF FOUND
%------------------------------------------------------------------------------