TSTP Solution File: SET983+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:14:38 EDT 2022
% Result : Theorem 1.66s 1.89s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 6 RR)
% Number of literals : 12 ( 4 equ; 4 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; 5 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A != set_intersection2(B,C)
| in(D,A)
| ~ in(D,B)
| ~ in(D,C) ),
file('SET983+1.p',unknown),
[] ).
cnf(7,axiom,
~ in(dollar_c7,cartesian_product2(set_intersection2(dollar_c6,dollar_c4),set_intersection2(dollar_c5,dollar_c3))),
file('SET983+1.p',unknown),
[] ).
cnf(19,axiom,
set_intersection2(A,A) = A,
file('SET983+1.p',unknown),
[] ).
cnf(21,axiom,
cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('SET983+1.p',unknown),
[] ).
cnf(23,plain,
set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D)) = cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(24,axiom,
in(dollar_c7,cartesian_product2(dollar_c6,dollar_c5)),
file('SET983+1.p',unknown),
[] ).
cnf(25,axiom,
in(dollar_c7,cartesian_product2(dollar_c4,dollar_c3)),
file('SET983+1.p',unknown),
[] ).
cnf(52,plain,
in(dollar_c7,cartesian_product2(set_intersection2(dollar_c6,dollar_c4),set_intersection2(dollar_c5,dollar_c3))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,4,19,24]),23,23,19]),
[iquote('hyper,25,4,18,24,demod,23,23,19')] ).
cnf(53,plain,
$false,
inference(binary,[status(thm)],[52,7]),
[iquote('binary,52.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 10:49:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.88 ----- Otter 3.3f, August 2004 -----
% 1.66/1.88 The process was started by sandbox2 on n028.cluster.edu,
% 1.66/1.88 Wed Jul 27 10:49:49 2022
% 1.66/1.88 The command was "./otter". The process ID is 7294.
% 1.66/1.88
% 1.66/1.88 set(prolog_style_variables).
% 1.66/1.88 set(auto).
% 1.66/1.88 dependent: set(auto1).
% 1.66/1.88 dependent: set(process_input).
% 1.66/1.88 dependent: clear(print_kept).
% 1.66/1.88 dependent: clear(print_new_demod).
% 1.66/1.88 dependent: clear(print_back_demod).
% 1.66/1.88 dependent: clear(print_back_sub).
% 1.66/1.88 dependent: set(control_memory).
% 1.66/1.88 dependent: assign(max_mem, 12000).
% 1.66/1.88 dependent: assign(pick_given_ratio, 4).
% 1.66/1.88 dependent: assign(stats_level, 1).
% 1.66/1.88 dependent: assign(max_seconds, 10800).
% 1.66/1.88 clear(print_given).
% 1.66/1.88
% 1.66/1.88 formula_list(usable).
% 1.66/1.88 all A (A=A).
% 1.66/1.88 all A B (in(A,B)-> -in(B,A)).
% 1.66/1.88 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.66/1.88 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.66/1.88 all A B (set_intersection2(A,A)=A).
% 1.66/1.88 exists A empty(A).
% 1.66/1.88 exists A (-empty(A)).
% 1.66/1.88 all A B C D (cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.66/1.88 -(all A B C D E (in(A,cartesian_product2(B,C))&in(A,cartesian_product2(D,E))->in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))))).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 -------> usable clausifies to:
% 1.66/1.88
% 1.66/1.88 list(usable).
% 1.66/1.88 0 [] A=A.
% 1.66/1.88 0 [] -in(A,B)| -in(B,A).
% 1.66/1.88 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.66/1.88 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.66/1.88 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.66/1.88 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.66/1.88 0 [] C=set_intersection2(A,B)|in($f1(A,B,C),C)|in($f1(A,B,C),A).
% 1.66/1.88 0 [] C=set_intersection2(A,B)|in($f1(A,B,C),C)|in($f1(A,B,C),B).
% 1.66/1.88 0 [] C=set_intersection2(A,B)| -in($f1(A,B,C),C)| -in($f1(A,B,C),A)| -in($f1(A,B,C),B).
% 1.66/1.88 0 [] set_intersection2(A,A)=A.
% 1.66/1.88 0 [] empty($c1).
% 1.66/1.88 0 [] -empty($c2).
% 1.66/1.88 0 [] cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.66/1.88 0 [] in($c7,cartesian_product2($c6,$c5)).
% 1.66/1.88 0 [] in($c7,cartesian_product2($c4,$c3)).
% 1.66/1.88 0 [] -in($c7,cartesian_product2(set_intersection2($c6,$c4),set_intersection2($c5,$c3))).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.66/1.88
% 1.66/1.88 This ia a non-Horn set with equality. The strategy will be
% 1.66/1.88 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.66/1.88 deletion, with positive clauses in sos and nonpositive
% 1.66/1.88 clauses in usable.
% 1.66/1.88
% 1.66/1.88 dependent: set(knuth_bendix).
% 1.66/1.88 dependent: set(anl_eq).
% 1.66/1.88 dependent: set(para_from).
% 1.66/1.88 dependent: set(para_into).
% 1.66/1.88 dependent: clear(para_from_right).
% 1.66/1.88 dependent: clear(para_into_right).
% 1.66/1.88 dependent: set(para_from_vars).
% 1.66/1.88 dependent: set(eq_units_both_ways).
% 1.66/1.88 dependent: set(dynamic_demod_all).
% 1.66/1.88 dependent: set(dynamic_demod).
% 1.66/1.88 dependent: set(order_eq).
% 1.66/1.88 dependent: set(back_demod).
% 1.66/1.88 dependent: set(lrpo).
% 1.66/1.88 dependent: set(hyper_res).
% 1.66/1.88 dependent: set(unit_deletion).
% 1.66/1.88 dependent: set(factor).
% 1.66/1.88
% 1.66/1.88 ------------> process usable:
% 1.66/1.88 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.66/1.88 ** KEPT (pick-wt=11): 2 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.66/1.88 ** KEPT (pick-wt=11): 3 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.66/1.88 ** KEPT (pick-wt=14): 4 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.66/1.88 ** KEPT (pick-wt=23): 5 [] A=set_intersection2(B,C)| -in($f1(B,C,A),A)| -in($f1(B,C,A),B)| -in($f1(B,C,A),C).
% 1.66/1.88 ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.66/1.88 ** KEPT (pick-wt=9): 7 [] -in($c7,cartesian_product2(set_intersection2($c6,$c4),set_intersection2($c5,$c3))).
% 1.66/1.88
% 1.66/1.88 ------------> process sos:
% 1.66/1.88 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.66/1.88 ** KEPT (pick-wt=7): 15 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.66/1.88 ** KEPT (pick-wt=17): 16 [] A=set_intersection2(B,C)|in($f1(B,C,A),A)|in($f1(B,C,A),B).
% 1.66/1.88 ** KEPT (pick-wt=17): 17 [] A=set_intersection2(B,C)|in($f1(B,C,A),A)|in($f1(B,C,A),C).
% 1.66/1.88 ** KEPT (pick-wt=5): 18 [] set_intersection2(A,A)=A.
% 1.66/1.88 ---> New Demodulator: 19 [new_demod,18] set_intersection2(A,A)=A.
% 1.66/1.88 ** KEPT (pick-wt=2): 20 [] empty($c1).
% 1.66/1.88 ** KEPT (pick-wt=15): 22 [copy,21,flip.1] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 1.66/1.89 ---> New Demodulator: 23 [new_demod,22] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 1.66/1.89 ** KEPT (pick-wt=5): 24 [] in($c7,cartesian_product2($c6,$c5)).
% 1.66/1.89 ** KEPT (pick-wt=5): 25 [] in($c7,cartesian_product2($c4,$c3)).
% 1.66/1.89 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.66/1.89 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.66/1.89 >>>> Starting back demodulation with 19.
% 1.66/1.89 >> back demodulating 13 with 19.
% 1.66/1.89 >> back demodulating 12 with 19.
% 1.66/1.89 >> back demodulating 9 with 19.
% 1.66/1.89 >>>> Starting back demodulation with 23.
% 1.66/1.89
% 1.66/1.89 ======= end of input processing =======
% 1.66/1.89
% 1.66/1.89 =========== start of search ===========
% 1.66/1.89
% 1.66/1.89 -------- PROOF --------
% 1.66/1.89
% 1.66/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 53 [binary,52.1,7.1] $F.
% 1.66/1.89
% 1.66/1.89 Length of proof is 2. Level of proof is 2.
% 1.66/1.89
% 1.66/1.89 ---------------- PROOF ----------------
% 1.66/1.89 % SZS status Theorem
% 1.66/1.89 % SZS output start Refutation
% See solution above
% 1.66/1.89 ------------ end of proof -------------
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89 ============ end of search ============
% 1.66/1.89
% 1.66/1.89 -------------- statistics -------------
% 1.66/1.89 clauses given 5
% 1.66/1.89 clauses generated 63
% 1.66/1.89 clauses kept 49
% 1.66/1.89 clauses forward subsumed 35
% 1.66/1.89 clauses back subsumed 0
% 1.66/1.89 Kbytes malloced 976
% 1.66/1.89
% 1.66/1.89 ----------- times (seconds) -----------
% 1.66/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.89
% 1.66/1.89 That finishes the proof of the theorem.
% 1.66/1.89
% 1.66/1.89 Process 7294 finished Wed Jul 27 10:49:50 2022
% 1.66/1.89 Otter interrupted
% 1.66/1.89 PROOF FOUND
%------------------------------------------------------------------------------