TSTP Solution File: SEU263+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:15:23 EDT 2022
% Result : Theorem 1.75s 1.95s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 12 unt; 0 nHn; 20 RR)
% Number of literals : 30 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element(A,powerset(cartesian_product2(B,C)))
| relation(A) ),
file('SEU263+1.p',unknown),
[] ).
cnf(3,axiom,
( relation_of2(A,B,C)
| ~ subset(A,cartesian_product2(B,C)) ),
file('SEU263+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ relation_of2_as_subset(A,B,C)
| element(A,powerset(cartesian_product2(B,C))) ),
file('SEU263+1.p',unknown),
[] ).
cnf(6,axiom,
( relation_of2_as_subset(A,B,C)
| ~ relation_of2(A,B,C) ),
file('SEU263+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset(A,B)
| ~ subset(C,D)
| subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('SEU263+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ relation_of2_as_subset(A,B,C)
| subset(relation_dom(A),B) ),
file('SEU263+1.p',unknown),
[] ).
cnf(10,axiom,
~ relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
file('SEU263+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SEU263+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ relation(A)
| subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('SEU263+1.p',unknown),
[] ).
cnf(19,axiom,
relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c4),
file('SEU263+1.p',unknown),
[] ).
cnf(20,axiom,
subset(relation_rng(dollar_c1),dollar_c3),
file('SEU263+1.p',unknown),
[] ).
cnf(28,plain,
subset(relation_dom(dollar_c1),dollar_c2),
inference(hyper,[status(thm)],[19,8]),
[iquote('hyper,19,8')] ).
cnf(30,plain,
element(dollar_c1,powerset(cartesian_product2(dollar_c2,dollar_c4))),
inference(hyper,[status(thm)],[19,4]),
[iquote('hyper,19,4')] ).
cnf(52,plain,
subset(cartesian_product2(relation_dom(dollar_c1),relation_rng(dollar_c1)),cartesian_product2(dollar_c2,dollar_c3)),
inference(hyper,[status(thm)],[28,7,20]),
[iquote('hyper,28,7,20')] ).
cnf(101,plain,
relation(dollar_c1),
inference(hyper,[status(thm)],[30,1]),
[iquote('hyper,30,1')] ).
cnf(102,plain,
subset(dollar_c1,cartesian_product2(relation_dom(dollar_c1),relation_rng(dollar_c1))),
inference(hyper,[status(thm)],[101,12]),
[iquote('hyper,101,12')] ).
cnf(3622,plain,
subset(dollar_c1,cartesian_product2(dollar_c2,dollar_c3)),
inference(hyper,[status(thm)],[52,11,102]),
[iquote('hyper,52,11,102')] ).
cnf(3864,plain,
relation_of2(dollar_c1,dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[3622,3]),
[iquote('hyper,3622,3')] ).
cnf(3865,plain,
relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[3864,6]),
[iquote('hyper,3864,6')] ).
cnf(3866,plain,
$false,
inference(binary,[status(thm)],[3865,10]),
[iquote('binary,3865.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:52:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.70/1.90 ----- Otter 3.3f, August 2004 -----
% 1.70/1.90 The process was started by sandbox2 on n024.cluster.edu,
% 1.70/1.90 Wed Jul 27 07:52:25 2022
% 1.70/1.90 The command was "./otter". The process ID is 15093.
% 1.70/1.90
% 1.70/1.90 set(prolog_style_variables).
% 1.70/1.90 set(auto).
% 1.70/1.90 dependent: set(auto1).
% 1.70/1.90 dependent: set(process_input).
% 1.70/1.90 dependent: clear(print_kept).
% 1.70/1.90 dependent: clear(print_new_demod).
% 1.70/1.90 dependent: clear(print_back_demod).
% 1.70/1.90 dependent: clear(print_back_sub).
% 1.70/1.90 dependent: set(control_memory).
% 1.70/1.90 dependent: assign(max_mem, 12000).
% 1.70/1.90 dependent: assign(pick_given_ratio, 4).
% 1.70/1.90 dependent: assign(stats_level, 1).
% 1.70/1.90 dependent: assign(max_seconds, 10800).
% 1.70/1.90 clear(print_given).
% 1.70/1.90
% 1.70/1.90 formula_list(usable).
% 1.70/1.90 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 1.70/1.90 all A B C (relation_of2(C,A,B)<->subset(C,cartesian_product2(A,B))).
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 $T.
% 1.70/1.90 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 1.70/1.90 all A B exists C relation_of2(C,A,B).
% 1.70/1.90 all A exists B element(B,A).
% 1.70/1.90 all A B exists C relation_of2_as_subset(C,A,B).
% 1.70/1.90 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 1.70/1.90 all A B subset(A,A).
% 1.70/1.90 all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.70/1.90 all A B C (relation_of2_as_subset(C,A,B)->subset(relation_dom(C),A)&subset(relation_rng(C),B)).
% 1.70/1.90 -(all A B C D (relation_of2_as_subset(D,C,A)-> (subset(relation_rng(D),B)->relation_of2_as_subset(D,C,B)))).
% 1.70/1.90 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.70/1.90 all A (relation(A)->subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))).
% 1.70/1.90 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 -------> usable clausifies to:
% 1.70/1.90
% 1.70/1.90 list(usable).
% 1.70/1.90 0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 1.70/1.90 0 [] -relation_of2(C,A,B)|subset(C,cartesian_product2(A,B)).
% 1.70/1.90 0 [] relation_of2(C,A,B)| -subset(C,cartesian_product2(A,B)).
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] $T.
% 1.70/1.90 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 1.70/1.90 0 [] relation_of2($f1(A,B),A,B).
% 1.70/1.90 0 [] element($f2(A),A).
% 1.70/1.90 0 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.70/1.90 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 1.70/1.90 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 1.70/1.90 0 [] subset(A,A).
% 1.70/1.90 0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.90 0 [] -relation_of2_as_subset(C,A,B)|subset(relation_dom(C),A).
% 1.70/1.90 0 [] -relation_of2_as_subset(C,A,B)|subset(relation_rng(C),B).
% 1.70/1.90 0 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.70/1.90 0 [] subset(relation_rng($c1),$c3).
% 1.70/1.90 0 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.70/1.90 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.70/1.90 0 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 1.70/1.90 0 [] -element(A,powerset(B))|subset(A,B).
% 1.70/1.90 0 [] element(A,powerset(B))| -subset(A,B).
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.70/1.90
% 1.70/1.90 This is a Horn set without equality. The strategy will
% 1.70/1.90 be hyperresolution, with satellites in sos and nuclei
% 1.70/1.90 in usable.
% 1.70/1.90
% 1.70/1.90 dependent: set(hyper_res).
% 1.70/1.90 dependent: clear(order_hyper).
% 1.70/1.90
% 1.70/1.90 ------------> process usable:
% 1.70/1.90 ** KEPT (pick-wt=8): 1 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 1.70/1.90 ** KEPT (pick-wt=9): 2 [] -relation_of2(A,B,C)|subset(A,cartesian_product2(B,C)).
% 1.70/1.90 ** KEPT (pick-wt=9): 3 [] relation_of2(A,B,C)| -subset(A,cartesian_product2(B,C)).
% 1.70/1.90 ** KEPT (pick-wt=10): 4 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 1.70/1.90 ** KEPT (pick-wt=8): 5 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 1.70/1.90 ** KEPT (pick-wt=8): 6 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 1.70/1.90 ** KEPT (pick-wt=13): 7 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.90 ** KEPT (pick-wt=8): 8 [] -relation_of2_as_subset(A,B,C)|subset(relation_dom(A),B).
% 1.70/1.90 ** KEPT (pick-wt=8): 9 [] -relation_of2_as_subset(A,B,C)|subset(relation_rng(A),C).
% 1.70/1.90 ** KEPT (pick-wt=4): 10 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.70/1.90 ** KEPT (pick-wt=9): 11 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.70/1.90 ** KEPT (pick-wt=9): 12 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 1.70/1.90 ** KEPT (pick-wt=7): 13 [] -element(A,powerset(B))|subset(A,B).
% 1.75/1.95 ** KEPT (pick-wt=7): 14 [] element(A,powerset(B))| -subset(A,B).
% 1.75/1.95
% 1.75/1.95 ------------> process sos:
% 1.75/1.95 ** KEPT (pick-wt=6): 15 [] relation_of2($f1(A,B),A,B).
% 1.75/1.95 ** KEPT (pick-wt=4): 16 [] element($f2(A),A).
% 1.75/1.95 ** KEPT (pick-wt=6): 17 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.75/1.95 ** KEPT (pick-wt=3): 18 [] subset(A,A).
% 1.75/1.95 ** KEPT (pick-wt=4): 19 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.75/1.95 ** KEPT (pick-wt=4): 20 [] subset(relation_rng($c1),$c3).
% 1.75/1.95
% 1.75/1.95 ======= end of input processing =======
% 1.75/1.95
% 1.75/1.95 =========== start of search ===========
% 1.75/1.95
% 1.75/1.95 -------- PROOF --------
% 1.75/1.95
% 1.75/1.95 ----> UNIT CONFLICT at 0.05 sec ----> 3866 [binary,3865.1,10.1] $F.
% 1.75/1.95
% 1.75/1.95 Length of proof is 8. Level of proof is 6.
% 1.75/1.95
% 1.75/1.95 ---------------- PROOF ----------------
% 1.75/1.95 % SZS status Theorem
% 1.75/1.95 % SZS output start Refutation
% See solution above
% 1.75/1.95 ------------ end of proof -------------
% 1.75/1.95
% 1.75/1.95
% 1.75/1.95 Search stopped by max_proofs option.
% 1.75/1.95
% 1.75/1.95
% 1.75/1.95 Search stopped by max_proofs option.
% 1.75/1.95
% 1.75/1.95 ============ end of search ============
% 1.75/1.95
% 1.75/1.95 -------------- statistics -------------
% 1.75/1.95 clauses given 98
% 1.75/1.95 clauses generated 4093
% 1.75/1.95 clauses kept 3865
% 1.75/1.95 clauses forward subsumed 248
% 1.75/1.95 clauses back subsumed 0
% 1.75/1.95 Kbytes malloced 3906
% 1.75/1.95
% 1.75/1.95 ----------- times (seconds) -----------
% 1.75/1.95 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.75/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.95 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.95
% 1.75/1.95 That finishes the proof of the theorem.
% 1.75/1.95
% 1.75/1.95 Process 15093 finished Wed Jul 27 07:52:26 2022
% 1.75/1.95 Otter interrupted
% 1.75/1.95 PROOF FOUND
%------------------------------------------------------------------------------