TSTP Solution File: SET928+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 1.72s 1.94s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 10 unt; 9 nHn; 27 RR)
% Number of literals : 64 ( 12 equ; 30 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ in(A,B)
| ~ in(B,A) ),
file('SET928+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
file('SET928+1.p',unknown),
[] ).
cnf(5,axiom,
( set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = unordered_pair(dollar_c5,dollar_c4)
| ~ in(dollar_c5,dollar_c3) ),
file('SET928+1.p',unknown),
[] ).
cnf(6,axiom,
( set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = unordered_pair(dollar_c5,dollar_c4)
| ~ in(dollar_c4,dollar_c3) ),
file('SET928+1.p',unknown),
[] ).
cnf(7,axiom,
( set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) != unordered_pair(dollar_c5,dollar_c4)
| in(dollar_c5,dollar_c3)
| in(dollar_c4,dollar_c3) ),
file('SET928+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
file('SET928+1.p',unknown),
[] ).
cnf(9,axiom,
( disjoint(A,B)
| set_difference(A,B) != A ),
file('SET928+1.p',unknown),
[] ).
cnf(10,plain,
~ in(A,A),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(11,axiom,
A = A,
file('SET928+1.p',unknown),
[] ).
cnf(12,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SET928+1.p',unknown),
[] ).
cnf(14,axiom,
( in(A,B)
| in(C,B)
| disjoint(unordered_pair(A,C),B) ),
file('SET928+1.p',unknown),
[] ).
cnf(15,plain,
( in(A,B)
| disjoint(unordered_pair(A,A),B) ),
inference(factor,[status(thm)],[14]),
[iquote('factor,14.1.2')] ).
cnf(17,plain,
( unordered_pair(dollar_c5,dollar_c4) = set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3)
| ~ in(dollar_c4,dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[12,6])]),
[iquote('para_from,12.1.1,6.1.1.1,flip.1')] ).
cnf(18,plain,
( unordered_pair(dollar_c5,dollar_c4) = set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3)
| ~ in(dollar_c5,dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[12,5])]),
[iquote('para_from,12.1.1,5.1.1.1,flip.1')] ).
cnf(19,plain,
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(B,C) ),
inference(para_from,[status(thm),theory(equality)],[12,4]),
[iquote('para_from,12.1.1,4.1.1')] ).
cnf(21,plain,
( disjoint(unordered_pair(dollar_c4,dollar_c4),dollar_c3)
| set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = unordered_pair(dollar_c5,dollar_c4) ),
inference(hyper,[status(thm)],[15,6]),
[iquote('hyper,15,6')] ).
cnf(27,plain,
( in(A,B)
| disjoint(unordered_pair(B,A),B) ),
inference(hyper,[status(thm)],[14,10]),
[iquote('hyper,14,10')] ).
cnf(29,plain,
( in(A,dollar_c3)
| disjoint(unordered_pair(dollar_c5,A),dollar_c3)
| set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = unordered_pair(dollar_c5,dollar_c4) ),
inference(hyper,[status(thm)],[14,5]),
[iquote('hyper,14,5')] ).
cnf(79,plain,
( ~ disjoint(set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3),A)
| ~ in(dollar_c4,A)
| ~ in(dollar_c4,dollar_c3) ),
inference(para_from,[status(thm),theory(equality)],[17,19]),
[iquote('para_from,17.1.1,19.1.1')] ).
cnf(81,plain,
( ~ disjoint(set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3),dollar_c3)
| ~ in(dollar_c4,dollar_c3) ),
inference(factor,[status(thm)],[79]),
[iquote('factor,79.2.3')] ).
cnf(118,plain,
( ~ disjoint(set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3),A)
| ~ in(dollar_c5,A)
| ~ in(dollar_c5,dollar_c3) ),
inference(para_from,[status(thm),theory(equality)],[18,4]),
[iquote('para_from,18.1.1,4.1.1')] ).
cnf(119,plain,
( ~ disjoint(set_difference(unordered_pair(dollar_c4,dollar_c5),dollar_c3),dollar_c3)
| ~ in(dollar_c5,dollar_c3) ),
inference(factor,[status(thm)],[118]),
[iquote('factor,118.2.3')] ).
cnf(154,plain,
( ~ disjoint(set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3),dollar_c3)
| ~ in(dollar_c4,dollar_c3) ),
inference(para_into,[status(thm),theory(equality)],[81,12]),
[iquote('para_into,81.1.1.1,12.1.1')] ).
cnf(172,plain,
( disjoint(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| disjoint(unordered_pair(dollar_c4,dollar_c4),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[21,9]),11]),
[iquote('para_from,21.2.1,9.2.1,unit_del,11')] ).
cnf(271,plain,
( ~ disjoint(set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3),dollar_c3)
| ~ in(dollar_c5,dollar_c3) ),
inference(para_into,[status(thm),theory(equality)],[119,12]),
[iquote('para_into,119.1.1.1,12.1.1')] ).
cnf(334,plain,
disjoint(unordered_pair(dollar_c4,dollar_c4),dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[172,19,15])]),
[iquote('hyper,172,19,15,factor_simp')] ).
cnf(351,plain,
( disjoint(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| in(A,dollar_c3)
| disjoint(unordered_pair(dollar_c5,A),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[29,9]),11]),
[iquote('para_from,29.3.1,9.2.1,unit_del,11')] ).
cnf(352,plain,
( disjoint(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| in(dollar_c4,dollar_c3) ),
inference(factor,[status(thm)],[351]),
[iquote('factor,351.1.3')] ).
cnf(354,plain,
disjoint(unordered_pair(dollar_c3,dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[334,19,27]),
[iquote('hyper,334,19,27')] ).
cnf(512,plain,
disjoint(unordered_pair(dollar_c5,dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[352,19,354]),
[iquote('hyper,352,19,354')] ).
cnf(514,plain,
set_difference(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = unordered_pair(dollar_c5,dollar_c4),
inference(hyper,[status(thm)],[512,8]),
[iquote('hyper,512,8')] ).
cnf(524,plain,
~ in(dollar_c5,dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[271]),514]),512]),
[iquote('back_demod,271,demod,514,unit_del,512')] ).
cnf(525,plain,
~ in(dollar_c4,dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[154]),514]),512]),
[iquote('back_demod,154,demod,514,unit_del,512')] ).
cnf(526,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),514]),11,524,525]),
[iquote('back_demod,7,demod,514,unit_del,11,524,525')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 10:44:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.94 ----- Otter 3.3f, August 2004 -----
% 1.72/1.94 The process was started by sandbox2 on n012.cluster.edu,
% 1.72/1.94 Wed Jul 27 10:44:20 2022
% 1.72/1.94 The command was "./otter". The process ID is 26629.
% 1.72/1.94
% 1.72/1.94 set(prolog_style_variables).
% 1.72/1.94 set(auto).
% 1.72/1.94 dependent: set(auto1).
% 1.72/1.94 dependent: set(process_input).
% 1.72/1.94 dependent: clear(print_kept).
% 1.72/1.94 dependent: clear(print_new_demod).
% 1.72/1.94 dependent: clear(print_back_demod).
% 1.72/1.94 dependent: clear(print_back_sub).
% 1.72/1.94 dependent: set(control_memory).
% 1.72/1.94 dependent: assign(max_mem, 12000).
% 1.72/1.94 dependent: assign(pick_given_ratio, 4).
% 1.72/1.94 dependent: assign(stats_level, 1).
% 1.72/1.94 dependent: assign(max_seconds, 10800).
% 1.72/1.94 clear(print_given).
% 1.72/1.94
% 1.72/1.94 formula_list(usable).
% 1.72/1.94 all A (A=A).
% 1.72/1.94 all A B (in(A,B)-> -in(B,A)).
% 1.72/1.94 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.72/1.94 exists A empty(A).
% 1.72/1.94 exists A (-empty(A)).
% 1.72/1.94 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.72/1.94 all A B C (-(disjoint(unordered_pair(A,B),C)&in(A,C))).
% 1.72/1.94 all A B C (-(-in(A,B)& -in(C,B)& -disjoint(unordered_pair(A,C),B))).
% 1.72/1.94 -(all A B C (set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)<-> -in(A,C)& -in(B,C))).
% 1.72/1.94 all A B (disjoint(A,B)<->set_difference(A,B)=A).
% 1.72/1.94 end_of_list.
% 1.72/1.94
% 1.72/1.94 -------> usable clausifies to:
% 1.72/1.94
% 1.72/1.94 list(usable).
% 1.72/1.94 0 [] A=A.
% 1.72/1.94 0 [] -in(A,B)| -in(B,A).
% 1.72/1.94 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.94 0 [] empty($c1).
% 1.72/1.94 0 [] -empty($c2).
% 1.72/1.94 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.72/1.94 0 [] -disjoint(unordered_pair(A,B),C)| -in(A,C).
% 1.72/1.94 0 [] in(A,B)|in(C,B)|disjoint(unordered_pair(A,C),B).
% 1.72/1.94 0 [] set_difference(unordered_pair($c5,$c4),$c3)=unordered_pair($c5,$c4)| -in($c5,$c3).
% 1.72/1.94 0 [] set_difference(unordered_pair($c5,$c4),$c3)=unordered_pair($c5,$c4)| -in($c4,$c3).
% 1.72/1.94 0 [] set_difference(unordered_pair($c5,$c4),$c3)!=unordered_pair($c5,$c4)|in($c5,$c3)|in($c4,$c3).
% 1.72/1.94 0 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.72/1.94 0 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.72/1.94 end_of_list.
% 1.72/1.94
% 1.72/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.72/1.94
% 1.72/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.94 deletion, with positive clauses in sos and nonpositive
% 1.72/1.94 clauses in usable.
% 1.72/1.94
% 1.72/1.94 dependent: set(knuth_bendix).
% 1.72/1.94 dependent: set(anl_eq).
% 1.72/1.94 dependent: set(para_from).
% 1.72/1.94 dependent: set(para_into).
% 1.72/1.94 dependent: clear(para_from_right).
% 1.72/1.94 dependent: clear(para_into_right).
% 1.72/1.94 dependent: set(para_from_vars).
% 1.72/1.94 dependent: set(eq_units_both_ways).
% 1.72/1.94 dependent: set(dynamic_demod_all).
% 1.72/1.94 dependent: set(dynamic_demod).
% 1.72/1.94 dependent: set(order_eq).
% 1.72/1.94 dependent: set(back_demod).
% 1.72/1.94 dependent: set(lrpo).
% 1.72/1.94 dependent: set(hyper_res).
% 1.72/1.94 dependent: set(unit_deletion).
% 1.72/1.94 dependent: set(factor).
% 1.72/1.94
% 1.72/1.94 ------------> process usable:
% 1.72/1.94 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.72/1.94 ** KEPT (pick-wt=2): 2 [] -empty($c2).
% 1.72/1.94 ** KEPT (pick-wt=6): 3 [] -disjoint(A,B)|disjoint(B,A).
% 1.72/1.94 ** KEPT (pick-wt=8): 4 [] -disjoint(unordered_pair(A,B),C)| -in(A,C).
% 1.72/1.94 ** KEPT (pick-wt=12): 5 [] set_difference(unordered_pair($c5,$c4),$c3)=unordered_pair($c5,$c4)| -in($c5,$c3).
% 1.72/1.94 ** KEPT (pick-wt=12): 6 [] set_difference(unordered_pair($c5,$c4),$c3)=unordered_pair($c5,$c4)| -in($c4,$c3).
% 1.72/1.94 ** KEPT (pick-wt=15): 7 [] set_difference(unordered_pair($c5,$c4),$c3)!=unordered_pair($c5,$c4)|in($c5,$c3)|in($c4,$c3).
% 1.72/1.94 ** KEPT (pick-wt=8): 8 [] -disjoint(A,B)|set_difference(A,B)=A.
% 1.72/1.94 ** KEPT (pick-wt=8): 9 [] disjoint(A,B)|set_difference(A,B)!=A.
% 1.72/1.94
% 1.72/1.94 ------------> process sos:
% 1.72/1.94 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.72/1.94 ** KEPT (pick-wt=7): 12 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.94 ** KEPT (pick-wt=2): 13 [] empty($c1).
% 1.72/1.94 ** KEPT (pick-wt=11): 14 [] in(A,B)|in(C,B)|disjoint(unordered_pair(A,C),B).
% 1.72/1.94 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.72/1.94 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.94
% 1.72/1.94 ======= end of input processing =======
% 1.72/1.94
% 1.72/1.94 =========== start of search ===========
% 1.72/1.94
% 1.72/1.94 -------- PROOF --------
% 1.72/1.94
% 1.72/1.94 -----> EMPTY CLAUSE at 0.05 sec ----> 526 [back_demod,7,demod,514,unit_del,11,524,525] $F.
% 1.72/1.94
% 1.72/1.94 Length of proof is 23. Level of proof is 8.
% 1.72/1.94
% 1.72/1.94 ---------------- PROOF ----------------
% 1.72/1.94 % SZS status Theorem
% 1.72/1.94 % SZS output start Refutation
% See solution above
% 1.72/1.94 ------------ end of proof -------------
% 1.72/1.94
% 1.72/1.94
% 1.72/1.94 Search stopped by max_proofs option.
% 1.72/1.94
% 1.72/1.94
% 1.72/1.94 Search stopped by max_proofs option.
% 1.72/1.94
% 1.72/1.94 ============ end of search ============
% 1.72/1.94
% 1.72/1.94 -------------- statistics -------------
% 1.72/1.94 clauses given 54
% 1.72/1.94 clauses generated 1638
% 1.72/1.94 clauses kept 516
% 1.72/1.94 clauses forward subsumed 1164
% 1.72/1.94 clauses back subsumed 27
% 1.72/1.94 Kbytes malloced 1953
% 1.72/1.94
% 1.72/1.94 ----------- times (seconds) -----------
% 1.72/1.94 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.72/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.94
% 1.72/1.94 That finishes the proof of the theorem.
% 1.72/1.94
% 1.72/1.94 Process 26629 finished Wed Jul 27 10:44:22 2022
% 1.72/1.94 Otter interrupted
% 1.72/1.94 PROOF FOUND
%------------------------------------------------------------------------------