TSTP Solution File: SEU264+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 1.91s 2.10s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 10 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ relation_of2_as_subset(A,B,C)
| subset(relation_rng(A),C) ),
file('SEU264+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ relation_of2_as_subset(A,B,C)
| ~ subset(relation_rng(A),D)
| relation_of2_as_subset(A,B,D) ),
file('SEU264+1.p',unknown),
[] ).
cnf(8,axiom,
~ relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
file('SEU264+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SEU264+1.p',unknown),
[] ).
cnf(16,axiom,
relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c4),
file('SEU264+1.p',unknown),
[] ).
cnf(17,axiom,
subset(dollar_c4,dollar_c3),
file('SEU264+1.p',unknown),
[] ).
cnf(24,plain,
subset(relation_rng(dollar_c1),dollar_c4),
inference(hyper,[status(thm)],[16,6]),
[iquote('hyper,16,6')] ).
cnf(35,plain,
subset(relation_rng(dollar_c1),dollar_c3),
inference(hyper,[status(thm)],[24,9,17]),
[iquote('hyper,24,9,17')] ).
cnf(42,plain,
relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[35,7,16]),
[iquote('hyper,35,7,16')] ).
cnf(43,plain,
$false,
inference(binary,[status(thm)],[42,8]),
[iquote('binary,42.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 07:58:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.10 ----- Otter 3.3f, August 2004 -----
% 1.91/2.10 The process was started by sandbox on n015.cluster.edu,
% 1.91/2.10 Wed Jul 27 07:58:11 2022
% 1.91/2.10 The command was "./otter". The process ID is 5049.
% 1.91/2.10
% 1.91/2.10 set(prolog_style_variables).
% 1.91/2.10 set(auto).
% 1.91/2.10 dependent: set(auto1).
% 1.91/2.10 dependent: set(process_input).
% 1.91/2.10 dependent: clear(print_kept).
% 1.91/2.10 dependent: clear(print_new_demod).
% 1.91/2.10 dependent: clear(print_back_demod).
% 1.91/2.10 dependent: clear(print_back_sub).
% 1.91/2.10 dependent: set(control_memory).
% 1.91/2.10 dependent: assign(max_mem, 12000).
% 1.91/2.10 dependent: assign(pick_given_ratio, 4).
% 1.91/2.10 dependent: assign(stats_level, 1).
% 1.91/2.10 dependent: assign(max_seconds, 10800).
% 1.91/2.10 clear(print_given).
% 1.91/2.10
% 1.91/2.10 formula_list(usable).
% 1.91/2.10 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 $T.
% 1.91/2.10 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 1.91/2.10 all A B exists C relation_of2(C,A,B).
% 1.91/2.10 all A exists B element(B,A).
% 1.91/2.10 all A B exists C relation_of2_as_subset(C,A,B).
% 1.91/2.10 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 1.91/2.10 all A B subset(A,A).
% 1.91/2.10 all A B C (relation_of2_as_subset(C,A,B)->subset(relation_dom(C),A)&subset(relation_rng(C),B)).
% 1.91/2.10 all A B C D (relation_of2_as_subset(D,C,A)-> (subset(relation_rng(D),B)->relation_of2_as_subset(D,C,B))).
% 1.91/2.10 -(all A B C D (relation_of2_as_subset(D,C,A)-> (subset(A,B)->relation_of2_as_subset(D,C,B)))).
% 1.91/2.10 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.91/2.10 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 -------> usable clausifies to:
% 1.91/2.10
% 1.91/2.10 list(usable).
% 1.91/2.10 0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] $T.
% 1.91/2.10 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 1.91/2.10 0 [] relation_of2($f1(A,B),A,B).
% 1.91/2.10 0 [] element($f2(A),A).
% 1.91/2.10 0 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.91/2.10 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 1.91/2.10 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 1.91/2.10 0 [] subset(A,A).
% 1.91/2.10 0 [] -relation_of2_as_subset(C,A,B)|subset(relation_dom(C),A).
% 1.91/2.10 0 [] -relation_of2_as_subset(C,A,B)|subset(relation_rng(C),B).
% 1.91/2.10 0 [] -relation_of2_as_subset(D,C,A)| -subset(relation_rng(D),B)|relation_of2_as_subset(D,C,B).
% 1.91/2.10 0 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.91/2.10 0 [] subset($c4,$c3).
% 1.91/2.10 0 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.91/2.10 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.91/2.10 0 [] -element(A,powerset(B))|subset(A,B).
% 1.91/2.10 0 [] element(A,powerset(B))| -subset(A,B).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.91/2.10
% 1.91/2.10 This is a Horn set without equality. The strategy will
% 1.91/2.10 be hyperresolution, with satellites in sos and nuclei
% 1.91/2.10 in usable.
% 1.91/2.10
% 1.91/2.10 dependent: set(hyper_res).
% 1.91/2.10 dependent: clear(order_hyper).
% 1.91/2.10
% 1.91/2.10 ------------> process usable:
% 1.91/2.10 ** KEPT (pick-wt=8): 1 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 1.91/2.10 ** KEPT (pick-wt=10): 2 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 1.91/2.10 ** KEPT (pick-wt=8): 3 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 1.91/2.10 ** KEPT (pick-wt=8): 4 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 1.91/2.10 ** KEPT (pick-wt=8): 5 [] -relation_of2_as_subset(A,B,C)|subset(relation_dom(A),B).
% 1.91/2.10 ** KEPT (pick-wt=8): 6 [] -relation_of2_as_subset(A,B,C)|subset(relation_rng(A),C).
% 1.91/2.10 ** KEPT (pick-wt=12): 7 [] -relation_of2_as_subset(A,B,C)| -subset(relation_rng(A),D)|relation_of2_as_subset(A,B,D).
% 1.91/2.10 ** KEPT (pick-wt=4): 8 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.91/2.10 ** KEPT (pick-wt=9): 9 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.91/2.10 ** KEPT (pick-wt=7): 10 [] -element(A,powerset(B))|subset(A,B).
% 1.91/2.10 ** KEPT (pick-wt=7): 11 [] element(A,powerset(B))| -subset(A,B).
% 1.91/2.10
% 1.91/2.10 ------------> process sos:
% 1.91/2.10 ** KEPT (pick-wt=6): 12 [] relation_of2($f1(A,B),A,B).
% 1.91/2.10 ** KEPT (pick-wt=4): 13 [] element($f2(A),A).
% 1.91/2.10 ** KEPT (pick-wt=6): 14 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.91/2.10 ** KEPT (pick-wt=3): 15 [] subset(A,A).
% 1.91/2.10 ** KEPT (pick-wt=4): 16 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.91/2.10 ** KEPT (pick-wt=3): 17 [] subset($c4,$c3).
% 1.91/2.10
% 1.91/2.10 ======= end of input processing =======
% 1.91/2.10
% 1.91/2.10 =========== start of search ===========
% 1.91/2.10
% 1.91/2.10 -------- PROOF --------
% 1.91/2.10
% 1.91/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 43 [binary,42.1,8.1] $F.
% 1.91/2.10
% 1.91/2.10 Length of proof is 3. Level of proof is 3.
% 1.91/2.10
% 1.91/2.10 ---------------- PROOF ----------------
% 1.91/2.10 % SZS status Theorem
% 1.91/2.10 % SZS output start Refutation
% See solution above
% 1.91/2.10 ------------ end of proof -------------
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10 ============ end of search ============
% 1.91/2.10
% 1.91/2.10 -------------- statistics -------------
% 1.91/2.10 clauses given 14
% 1.91/2.10 clauses generated 40
% 1.91/2.10 clauses kept 42
% 1.91/2.10 clauses forward subsumed 15
% 1.91/2.10 clauses back subsumed 0
% 1.91/2.10 Kbytes malloced 976
% 1.91/2.10
% 1.91/2.10 ----------- times (seconds) -----------
% 1.91/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.10
% 1.91/2.10 That finishes the proof of the theorem.
% 1.91/2.10
% 1.91/2.10 Process 5049 finished Wed Jul 27 07:58:13 2022
% 1.91/2.10 Otter interrupted
% 1.91/2.10 PROOF FOUND
%------------------------------------------------------------------------------