TSTP Solution File: SEU165+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:15:00 EDT 2022
% Result : Theorem 1.68s 1.88s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 4 unt; 2 nHn; 10 RR)
% Number of literals : 18 ( 0 equ; 7 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(4,axiom,
( ~ in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3))
| ~ in(dollar_c6,dollar_c4)
| ~ in(dollar_c5,dollar_c3) ),
file('SEU165+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
file('SEU165+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
file('SEU165+1.p',unknown),
[] ).
cnf(7,axiom,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
file('SEU165+1.p',unknown),
[] ).
cnf(16,axiom,
( in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3))
| in(dollar_c6,dollar_c4) ),
file('SEU165+1.p',unknown),
[] ).
cnf(17,axiom,
( in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3))
| in(dollar_c5,dollar_c3) ),
file('SEU165+1.p',unknown),
[] ).
cnf(26,plain,
in(dollar_c6,dollar_c4),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[16,5])]),
[iquote('hyper,16,5,factor_simp')] ).
cnf(29,plain,
in(dollar_c5,dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[17,6])]),
[iquote('hyper,17,6,factor_simp')] ).
cnf(33,plain,
in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3)),
inference(hyper,[status(thm)],[29,7,26]),
[iquote('hyper,29,7,26')] ).
cnf(64,plain,
$false,
inference(hyper,[status(thm)],[33,4,26,29]),
[iquote('hyper,33,4,26,29')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 08:00:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.88 ----- Otter 3.3f, August 2004 -----
% 1.68/1.88 The process was started by sandbox on n005.cluster.edu,
% 1.68/1.88 Wed Jul 27 08:00:05 2022
% 1.68/1.88 The command was "./otter". The process ID is 21739.
% 1.68/1.88
% 1.68/1.88 set(prolog_style_variables).
% 1.68/1.88 set(auto).
% 1.68/1.88 dependent: set(auto1).
% 1.68/1.88 dependent: set(process_input).
% 1.68/1.88 dependent: clear(print_kept).
% 1.68/1.88 dependent: clear(print_new_demod).
% 1.68/1.88 dependent: clear(print_back_demod).
% 1.68/1.88 dependent: clear(print_back_sub).
% 1.68/1.88 dependent: set(control_memory).
% 1.68/1.88 dependent: assign(max_mem, 12000).
% 1.68/1.88 dependent: assign(pick_given_ratio, 4).
% 1.68/1.88 dependent: assign(stats_level, 1).
% 1.68/1.88 dependent: assign(max_seconds, 10800).
% 1.68/1.88 clear(print_given).
% 1.68/1.88
% 1.68/1.88 formula_list(usable).
% 1.68/1.88 all A (A=A).
% 1.68/1.88 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.68/1.88 $T.
% 1.68/1.88 $T.
% 1.68/1.88 exists A empty(A).
% 1.68/1.88 exists A (-empty(A)).
% 1.68/1.88 all A B (in(A,B)-> -in(B,A)).
% 1.68/1.88 $T.
% 1.68/1.88 $T.
% 1.68/1.88 all A B (-empty(ordered_pair(A,B))).
% 1.68/1.88 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.68/1.88 -(all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D))).
% 1.68/1.88 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 1.68/1.88 end_of_list.
% 1.68/1.88
% 1.68/1.88 -------> usable clausifies to:
% 1.68/1.88
% 1.68/1.88 list(usable).
% 1.68/1.88 0 [] A=A.
% 1.68/1.88 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.68/1.88 0 [] $T.
% 1.68/1.88 0 [] $T.
% 1.68/1.88 0 [] empty($c1).
% 1.68/1.88 0 [] -empty($c2).
% 1.68/1.88 0 [] -in(A,B)| -in(B,A).
% 1.68/1.88 0 [] $T.
% 1.68/1.88 0 [] $T.
% 1.68/1.88 0 [] -empty(ordered_pair(A,B)).
% 1.68/1.88 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.68/1.88 0 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3))|in($c6,$c4).
% 1.68/1.88 0 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3))|in($c5,$c3).
% 1.68/1.88 0 [] -in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3))| -in($c6,$c4)| -in($c5,$c3).
% 1.68/1.88 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.68/1.88 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.68/1.88 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.68/1.88 end_of_list.
% 1.68/1.88
% 1.68/1.88 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.88
% 1.68/1.88 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.88 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.88 deletion, with positive clauses in sos and nonpositive
% 1.68/1.88 clauses in usable.
% 1.68/1.88
% 1.68/1.88 dependent: set(knuth_bendix).
% 1.68/1.88 dependent: set(anl_eq).
% 1.68/1.88 dependent: set(para_from).
% 1.68/1.88 dependent: set(para_into).
% 1.68/1.88 dependent: clear(para_from_right).
% 1.68/1.88 dependent: clear(para_into_right).
% 1.68/1.88 dependent: set(para_from_vars).
% 1.68/1.88 dependent: set(eq_units_both_ways).
% 1.68/1.88 dependent: set(dynamic_demod_all).
% 1.68/1.88 dependent: set(dynamic_demod).
% 1.68/1.88 dependent: set(order_eq).
% 1.68/1.88 dependent: set(back_demod).
% 1.68/1.88 dependent: set(lrpo).
% 1.68/1.88 dependent: set(hyper_res).
% 1.68/1.88 dependent: set(unit_deletion).
% 1.68/1.88 dependent: set(factor).
% 1.68/1.88
% 1.68/1.88 ------------> process usable:
% 1.68/1.88 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.68/1.88 ** KEPT (pick-wt=6): 2 [] -in(A,B)| -in(B,A).
% 1.68/1.88 ** KEPT (pick-wt=4): 3 [] -empty(ordered_pair(A,B)).
% 1.68/1.88 ** KEPT (pick-wt=13): 4 [] -in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3))| -in($c6,$c4)| -in($c5,$c3).
% 1.68/1.88 ** KEPT (pick-wt=10): 5 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.68/1.88 ** KEPT (pick-wt=10): 6 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.68/1.88 ** KEPT (pick-wt=13): 7 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.68/1.88
% 1.68/1.88 ------------> process sos:
% 1.68/1.88 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.68/1.88 ** KEPT (pick-wt=7): 11 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.68/1.88 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.68/1.88 ** KEPT (pick-wt=10): 14 [copy,13,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.68/1.88 ---> New Demodulator: 15 [new_demod,14] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.68/1.88 ** KEPT (pick-wt=10): 16 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3))|in($c6,$c4).
% 1.68/1.88 ** KEPT (pick-wt=10): 17 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3))|in($c5,$c3).
% 1.68/1.88 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.68/1.88 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.68/1.88 >>>> Starting back demodulation with 15.
% 1.68/1.88
% 1.68/1.88 ======= end of input processing =======
% 1.68/1.88
% 1.68/1.88 =========== start of search ===========
% 1.68/1.88
% 1.68/1.88 -------- PROOF --------
% 1.68/1.88
% 1.68/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 64 [hyper,33,4,26,29] $F.
% 1.68/1.88
% 1.68/1.88 Length of proof is 3. Level of proof is 2.
% 1.68/1.88
% 1.68/1.88 ---------------- PROOF ----------------
% 1.68/1.88 % SZS status Theorem
% 1.68/1.88 % SZS output start Refutation
% See solution above
% 1.68/1.88 ------------ end of proof -------------
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88 ============ end of search ============
% 1.68/1.88
% 1.68/1.88 -------------- statistics -------------
% 1.68/1.88 clauses given 12
% 1.68/1.88 clauses generated 86
% 1.68/1.88 clauses kept 54
% 1.68/1.88 clauses forward subsumed 47
% 1.68/1.88 clauses back subsumed 7
% 1.68/1.88 Kbytes malloced 976
% 1.68/1.88
% 1.68/1.88 ----------- times (seconds) -----------
% 1.68/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.88
% 1.68/1.88 That finishes the proof of the theorem.
% 1.68/1.88
% 1.68/1.88 Process 21739 finished Wed Jul 27 08:00:07 2022
% 1.68/1.88 Otter interrupted
% 1.68/1.88 PROOF FOUND
%------------------------------------------------------------------------------