TSTP Solution File: SET954+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:14:35 EDT 2022
% Result : Theorem 1.66s 1.84s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
file('SET954+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
file('SET954+1.p',unknown),
[] ).
cnf(5,axiom,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
file('SET954+1.p',unknown),
[] ).
cnf(7,axiom,
~ in(ordered_pair(dollar_c5,dollar_c6),cartesian_product2(dollar_c3,dollar_c4)),
file('SET954+1.p',unknown),
[] ).
cnf(14,axiom,
in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3)),
file('SET954+1.p',unknown),
[] ).
cnf(16,plain,
in(dollar_c5,dollar_c3),
inference(hyper,[status(thm)],[14,4]),
[iquote('hyper,14,4')] ).
cnf(17,plain,
in(dollar_c6,dollar_c4),
inference(hyper,[status(thm)],[14,3]),
[iquote('hyper,14,3')] ).
cnf(28,plain,
in(ordered_pair(dollar_c5,dollar_c6),cartesian_product2(dollar_c3,dollar_c4)),
inference(hyper,[status(thm)],[17,5,16]),
[iquote('hyper,17,5,16')] ).
cnf(29,plain,
$false,
inference(binary,[status(thm)],[28,7]),
[iquote('binary,28.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 10:21:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.66/1.84 ----- Otter 3.3f, August 2004 -----
% 1.66/1.84 The process was started by sandbox on n021.cluster.edu,
% 1.66/1.84 Wed Jul 27 10:21:23 2022
% 1.66/1.84 The command was "./otter". The process ID is 12576.
% 1.66/1.84
% 1.66/1.84 set(prolog_style_variables).
% 1.66/1.84 set(auto).
% 1.66/1.84 dependent: set(auto1).
% 1.66/1.84 dependent: set(process_input).
% 1.66/1.84 dependent: clear(print_kept).
% 1.66/1.84 dependent: clear(print_new_demod).
% 1.66/1.84 dependent: clear(print_back_demod).
% 1.66/1.84 dependent: clear(print_back_sub).
% 1.66/1.84 dependent: set(control_memory).
% 1.66/1.84 dependent: assign(max_mem, 12000).
% 1.66/1.84 dependent: assign(pick_given_ratio, 4).
% 1.66/1.84 dependent: assign(stats_level, 1).
% 1.66/1.84 dependent: assign(max_seconds, 10800).
% 1.66/1.84 clear(print_given).
% 1.66/1.84
% 1.66/1.84 formula_list(usable).
% 1.66/1.84 all A (A=A).
% 1.66/1.84 all A B (in(A,B)-> -in(B,A)).
% 1.66/1.84 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.66/1.84 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.66/1.84 all A B (-empty(ordered_pair(A,B))).
% 1.66/1.84 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 1.66/1.84 exists A empty(A).
% 1.66/1.84 exists A (-empty(A)).
% 1.66/1.84 -(all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))->in(ordered_pair(B,A),cartesian_product2(D,C)))).
% 1.66/1.84 end_of_list.
% 1.66/1.84
% 1.66/1.84 -------> usable clausifies to:
% 1.66/1.84
% 1.66/1.84 list(usable).
% 1.66/1.84 0 [] A=A.
% 1.66/1.84 0 [] -in(A,B)| -in(B,A).
% 1.66/1.84 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.66/1.84 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.66/1.84 0 [] -empty(ordered_pair(A,B)).
% 1.66/1.84 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.66/1.84 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.66/1.84 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.66/1.84 0 [] empty($c1).
% 1.66/1.84 0 [] -empty($c2).
% 1.66/1.84 0 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3)).
% 1.66/1.84 0 [] -in(ordered_pair($c5,$c6),cartesian_product2($c3,$c4)).
% 1.66/1.84 end_of_list.
% 1.66/1.84
% 1.66/1.84 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.66/1.84
% 1.66/1.84 This is a Horn set with equality. The strategy will be
% 1.66/1.84 Knuth-Bendix and hyper_res, with positive clauses in
% 1.66/1.84 sos and nonpositive clauses in usable.
% 1.66/1.84
% 1.66/1.84 dependent: set(knuth_bendix).
% 1.66/1.84 dependent: set(anl_eq).
% 1.66/1.84 dependent: set(para_from).
% 1.66/1.84 dependent: set(para_into).
% 1.66/1.84 dependent: clear(para_from_right).
% 1.66/1.84 dependent: clear(para_into_right).
% 1.66/1.84 dependent: set(para_from_vars).
% 1.66/1.84 dependent: set(eq_units_both_ways).
% 1.66/1.84 dependent: set(dynamic_demod_all).
% 1.66/1.84 dependent: set(dynamic_demod).
% 1.66/1.84 dependent: set(order_eq).
% 1.66/1.84 dependent: set(back_demod).
% 1.66/1.84 dependent: set(lrpo).
% 1.66/1.84 dependent: set(hyper_res).
% 1.66/1.84 dependent: clear(order_hyper).
% 1.66/1.84
% 1.66/1.84 ------------> process usable:
% 1.66/1.84 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.66/1.84 ** KEPT (pick-wt=4): 2 [] -empty(ordered_pair(A,B)).
% 1.66/1.84 ** KEPT (pick-wt=10): 3 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.66/1.84 ** KEPT (pick-wt=10): 4 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.66/1.84 ** KEPT (pick-wt=13): 5 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.66/1.84 ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.66/1.84 ** KEPT (pick-wt=7): 7 [] -in(ordered_pair($c5,$c6),cartesian_product2($c3,$c4)).
% 1.66/1.84
% 1.66/1.84 ------------> process sos:
% 1.66/1.84 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.66/1.84 ** KEPT (pick-wt=7): 9 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.66/1.84 ** KEPT (pick-wt=10): 11 [copy,10,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.66/1.84 ---> New Demodulator: 12 [new_demod,11] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.66/1.84 ** KEPT (pick-wt=2): 13 [] empty($c1).
% 1.66/1.84 ** KEPT (pick-wt=7): 14 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3)).
% 1.66/1.84 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.66/1.84 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.66/1.84 >>>> Starting back demodulation with 12.
% 1.66/1.84
% 1.66/1.84 ======= end of input processing =======
% 1.66/1.84
% 1.66/1.84 =========== start of search ===========
% 1.66/1.84
% 1.66/1.84 -------- PROOF --------
% 1.66/1.84
% 1.66/1.84 ----> UNIT CONFLICT at 0.00 sec ----> 29 [binary,28.1,7.1] $F.
% 1.66/1.84
% 1.66/1.84 Length of proof is 3. Level of proof is 2.
% 1.66/1.84
% 1.66/1.84 ---------------- PROOF ----------------
% 1.66/1.84 % SZS status Theorem
% 1.66/1.84 % SZS output start Refutation
% See solution above
% 1.66/1.84 ------------ end of proof -------------
% 1.66/1.84
% 1.66/1.84
% 1.66/1.84 Search stopped by max_proofs option.
% 1.66/1.84
% 1.66/1.84
% 1.66/1.84 Search stopped by max_proofs option.
% 1.66/1.84
% 1.66/1.84 ============ end of search ============
% 1.66/1.84
% 1.66/1.84 -------------- statistics -------------
% 1.66/1.84 clauses given 7
% 1.66/1.84 clauses generated 19
% 1.66/1.84 clauses kept 23
% 1.66/1.84 clauses forward subsumed 10
% 1.66/1.84 clauses back subsumed 0
% 1.66/1.84 Kbytes malloced 976
% 1.66/1.84
% 1.66/1.84 ----------- times (seconds) -----------
% 1.66/1.84 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.84 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.84 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.84
% 1.66/1.84 That finishes the proof of the theorem.
% 1.66/1.84
% 1.66/1.84 Process 12576 finished Wed Jul 27 10:21:24 2022
% 1.66/1.84 Otter interrupted
% 1.66/1.84 PROOF FOUND
%------------------------------------------------------------------------------