TSTP Solution File: SET914+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:14:31 EDT 2022
% Result : Theorem 1.91s 2.10s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 19 ( 8 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SET914+1.p',unknown),
[] ).
cnf(4,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SET914+1.p',unknown),
[] ).
cnf(10,axiom,
( A != set_intersection2(B,C)
| in(D,A)
| ~ in(D,B)
| ~ in(D,C) ),
file('SET914+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
file('SET914+1.p',unknown),
[] ).
cnf(23,axiom,
A = A,
file('SET914+1.p',unknown),
[] ).
cnf(32,axiom,
set_intersection2(A,A) = A,
file('SET914+1.p',unknown),
[] ).
cnf(34,axiom,
disjoint(unordered_pair(dollar_c5,dollar_c4),dollar_c3),
file('SET914+1.p',unknown),
[] ).
cnf(35,axiom,
in(dollar_c5,dollar_c3),
file('SET914+1.p',unknown),
[] ).
cnf(42,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[23,4,23]),
[iquote('hyper,23,4,23')] ).
cnf(120,plain,
set_intersection2(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = empty_set,
inference(hyper,[status(thm)],[34,12]),
[iquote('hyper,34,12')] ).
cnf(175,plain,
in(dollar_c5,set_intersection2(unordered_pair(dollar_c5,A),dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[42,10,32,35]),32]),
[iquote('hyper,42,10,31,35,demod,32')] ).
cnf(1586,plain,
$false,
inference(hyper,[status(thm)],[175,2,120]),
[iquote('hyper,175,2,120')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n022.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 10:44:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.94 ----- Otter 3.3f, August 2004 -----
% 1.74/1.94 The process was started by sandbox2 on n022.cluster.edu,
% 1.74/1.94 Wed Jul 27 10:44:05 2022
% 1.74/1.94 The command was "./otter". The process ID is 1941.
% 1.74/1.94
% 1.74/1.94 set(prolog_style_variables).
% 1.74/1.94 set(auto).
% 1.74/1.94 dependent: set(auto1).
% 1.74/1.94 dependent: set(process_input).
% 1.74/1.94 dependent: clear(print_kept).
% 1.74/1.94 dependent: clear(print_new_demod).
% 1.74/1.94 dependent: clear(print_back_demod).
% 1.74/1.94 dependent: clear(print_back_sub).
% 1.74/1.94 dependent: set(control_memory).
% 1.74/1.94 dependent: assign(max_mem, 12000).
% 1.74/1.94 dependent: assign(pick_given_ratio, 4).
% 1.74/1.94 dependent: assign(stats_level, 1).
% 1.74/1.94 dependent: assign(max_seconds, 10800).
% 1.74/1.94 clear(print_given).
% 1.74/1.94
% 1.74/1.94 formula_list(usable).
% 1.74/1.94 all A (A=A).
% 1.74/1.94 all A B (in(A,B)-> -in(B,A)).
% 1.74/1.94 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.74/1.94 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.74/1.94 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.74/1.94 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.74/1.94 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.74/1.94 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.74/1.94 empty(empty_set).
% 1.74/1.94 all A B (set_intersection2(A,A)=A).
% 1.74/1.94 exists A empty(A).
% 1.74/1.94 exists A (-empty(A)).
% 1.74/1.94 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.74/1.94 -(all A B C (-(disjoint(unordered_pair(A,B),C)&in(A,C)))).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 -------> usable clausifies to:
% 1.74/1.94
% 1.74/1.94 list(usable).
% 1.74/1.94 0 [] A=A.
% 1.74/1.94 0 [] -in(A,B)| -in(B,A).
% 1.74/1.94 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.74/1.94 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.74/1.94 0 [] A!=empty_set| -in(B,A).
% 1.74/1.94 0 [] A=empty_set|in($f1(A),A).
% 1.74/1.94 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.74/1.94 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.74/1.94 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.74/1.94 0 [] C=unordered_pair(A,B)|in($f2(A,B,C),C)|$f2(A,B,C)=A|$f2(A,B,C)=B.
% 1.74/1.94 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=A.
% 1.74/1.94 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=B.
% 1.74/1.94 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.74/1.94 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.74/1.94 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.74/1.94 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A).
% 1.74/1.94 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),B).
% 1.74/1.94 0 [] C=set_intersection2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A)| -in($f3(A,B,C),B).
% 1.74/1.94 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.74/1.94 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.74/1.94 0 [] empty(empty_set).
% 1.74/1.94 0 [] set_intersection2(A,A)=A.
% 1.74/1.94 0 [] empty($c1).
% 1.74/1.94 0 [] -empty($c2).
% 1.74/1.94 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.74/1.94 0 [] disjoint(unordered_pair($c5,$c4),$c3).
% 1.74/1.94 0 [] in($c5,$c3).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.74/1.94
% 1.74/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.94 deletion, with positive clauses in sos and nonpositive
% 1.74/1.94 clauses in usable.
% 1.74/1.94
% 1.74/1.94 dependent: set(knuth_bendix).
% 1.74/1.94 dependent: set(anl_eq).
% 1.74/1.94 dependent: set(para_from).
% 1.74/1.94 dependent: set(para_into).
% 1.74/1.94 dependent: clear(para_from_right).
% 1.74/1.94 dependent: clear(para_into_right).
% 1.74/1.94 dependent: set(para_from_vars).
% 1.74/1.94 dependent: set(eq_units_both_ways).
% 1.74/1.94 dependent: set(dynamic_demod_all).
% 1.74/1.94 dependent: set(dynamic_demod).
% 1.74/1.94 dependent: set(order_eq).
% 1.74/1.94 dependent: set(back_demod).
% 1.74/1.94 dependent: set(lrpo).
% 1.74/1.94 dependent: set(hyper_res).
% 1.74/1.94 dependent: set(unit_deletion).
% 1.74/1.94 dependent: set(factor).
% 1.74/1.94
% 1.74/1.94 ------------> process usable:
% 1.74/1.94 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.74/1.94 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.74/1.94 ** KEPT (pick-wt=14): 3 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.74/1.94 ** KEPT (pick-wt=11): 4 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.74/1.94 ** KEPT (pick-wt=11): 5 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.74/1.94 ** KEPT (pick-wt=17): 6 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=B.
% 1.74/1.94 ** KEPT (pick-wt=17): 7 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=C.
% 1.74/1.94 ** KEPT (pick-wt=11): 8 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.74/1.94 ** KEPT (pick-wt=11): 9 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.74/1.94 ** KEPT (pick-wt=14): 10 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.74/1.94 ** KEPT (pick-wt=23): 11 [] A=set_intersection2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B)| -in($f3(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=8): 12 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=8): 13 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.91/2.10 ** KEPT (pick-wt=2): 14 [] -empty($c2).
% 1.91/2.10 ** KEPT (pick-wt=6): 15 [] -disjoint(A,B)|disjoint(B,A).
% 1.91/2.10
% 1.91/2.10 ------------> process sos:
% 1.91/2.10 ** KEPT (pick-wt=3): 23 [] A=A.
% 1.91/2.10 ** KEPT (pick-wt=7): 24 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.10 ** KEPT (pick-wt=7): 25 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.91/2.10 ** KEPT (pick-wt=7): 26 [] A=empty_set|in($f1(A),A).
% 1.91/2.10 ** KEPT (pick-wt=23): 27 [] A=unordered_pair(B,C)|in($f2(B,C,A),A)|$f2(B,C,A)=B|$f2(B,C,A)=C.
% 1.91/2.10 ** KEPT (pick-wt=17): 28 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B).
% 1.91/2.10 ** KEPT (pick-wt=17): 29 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),C).
% 1.91/2.10 ** KEPT (pick-wt=2): 30 [] empty(empty_set).
% 1.91/2.10 ** KEPT (pick-wt=5): 31 [] set_intersection2(A,A)=A.
% 1.91/2.10 ---> New Demodulator: 32 [new_demod,31] set_intersection2(A,A)=A.
% 1.91/2.10 ** KEPT (pick-wt=2): 33 [] empty($c1).
% 1.91/2.10 ** KEPT (pick-wt=5): 34 [] disjoint(unordered_pair($c5,$c4),$c3).
% 1.91/2.10 ** KEPT (pick-wt=3): 35 [] in($c5,$c3).
% 1.91/2.10 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 1.91/2.10 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.10 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.91/2.10 >>>> Starting back demodulation with 32.
% 1.91/2.10 >> back demodulating 22 with 32.
% 1.91/2.10 >> back demodulating 21 with 32.
% 1.91/2.10 >> back demodulating 18 with 32.
% 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 -----> EMPTY CLAUSE at 0.16 sec ----> 1586 [hyper,175,2,120] $F.
% 1.91/2.10
% 1.91/2.10 Length of proof is 3. Level of proof is 2.
% 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 34
% 1.91/2.10 clauses generated 2586
% 1.91/2.10 clauses kept 1580
% 1.91/2.10 clauses forward subsumed 1031
% 1.91/2.10 clauses back subsumed 2
% 1.91/2.10 Kbytes malloced 3906
% 1.91/2.10
% 1.91/2.10 ----------- times (seconds) -----------
% 1.91/2.10 user CPU time 0.16 (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 1941 finished Wed Jul 27 10:44:07 2022
% 1.91/2.10 Otter interrupted
% 1.91/2.10 PROOF FOUND
%------------------------------------------------------------------------------