TSTP Solution File: SET909+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:14:30 EDT 2022
% Result : Theorem 1.75s 1.98s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 5 RR)
% Number of literals : 14 ( 7 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SET909+1.p',unknown),
[] ).
cnf(5,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != C ),
file('SET909+1.p',unknown),
[] ).
cnf(9,axiom,
( A != set_union2(B,C)
| in(D,A)
| ~ in(D,B) ),
file('SET909+1.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('SET909+1.p',unknown),
[] ).
cnf(29,axiom,
set_union2(A,A) = A,
file('SET909+1.p',unknown),
[] ).
cnf(31,axiom,
set_union2(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = empty_set,
file('SET909+1.p',unknown),
[] ).
cnf(38,plain,
in(A,unordered_pair(B,A)),
inference(hyper,[status(thm)],[21,5,21]),
[iquote('hyper,21,5,21')] ).
cnf(66,plain,
in(A,set_union2(unordered_pair(B,A),C)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[38,9,29]),29]),
[iquote('hyper,38,9,28,demod,29')] ).
cnf(914,plain,
$false,
inference(hyper,[status(thm)],[66,2,31]),
[iquote('hyper,66,2,31')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.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 10:46:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.70/1.90 ----- Otter 3.3f, August 2004 -----
% 1.70/1.90 The process was started by sandbox2 on n008.cluster.edu,
% 1.70/1.90 Wed Jul 27 10:46:38 2022
% 1.70/1.90 The command was "./otter". The process ID is 29971.
% 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 (A=A).
% 1.70/1.90 all A B (in(A,B)-> -in(B,A)).
% 1.70/1.90 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.70/1.90 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.70/1.90 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.70/1.90 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.70/1.90 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.70/1.90 empty(empty_set).
% 1.70/1.90 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.70/1.90 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.70/1.90 all A B (set_union2(A,A)=A).
% 1.70/1.90 exists A empty(A).
% 1.70/1.90 exists A (-empty(A)).
% 1.70/1.90 -(all A B C (set_union2(unordered_pair(A,B),C)!=empty_set)).
% 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 [] A=A.
% 1.70/1.90 0 [] -in(A,B)| -in(B,A).
% 1.70/1.90 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.90 0 [] set_union2(A,B)=set_union2(B,A).
% 1.70/1.90 0 [] A!=empty_set| -in(B,A).
% 1.70/1.90 0 [] A=empty_set|in($f1(A),A).
% 1.70/1.90 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.70/1.90 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.70/1.90 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.70/1.90 0 [] C=unordered_pair(A,B)|in($f2(A,B,C),C)|$f2(A,B,C)=A|$f2(A,B,C)=B.
% 1.70/1.90 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=A.
% 1.70/1.90 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=B.
% 1.70/1.90 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.70/1.90 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.70/1.90 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.70/1.90 0 [] C=set_union2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A)|in($f3(A,B,C),B).
% 1.70/1.90 0 [] C=set_union2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A).
% 1.70/1.90 0 [] C=set_union2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),B).
% 1.70/1.90 0 [] empty(empty_set).
% 1.70/1.90 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.70/1.90 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.70/1.90 0 [] set_union2(A,A)=A.
% 1.70/1.90 0 [] empty($c1).
% 1.70/1.90 0 [] -empty($c2).
% 1.70/1.90 0 [] set_union2(unordered_pair($c5,$c4),$c3)=empty_set.
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.70/1.90
% 1.70/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.90 deletion, with positive clauses in sos and nonpositive
% 1.70/1.90 clauses in usable.
% 1.70/1.90
% 1.70/1.90 dependent: set(knuth_bendix).
% 1.70/1.90 dependent: set(anl_eq).
% 1.70/1.90 dependent: set(para_from).
% 1.70/1.90 dependent: set(para_into).
% 1.70/1.90 dependent: clear(para_from_right).
% 1.70/1.90 dependent: clear(para_into_right).
% 1.70/1.90 dependent: set(para_from_vars).
% 1.70/1.90 dependent: set(eq_units_both_ways).
% 1.70/1.90 dependent: set(dynamic_demod_all).
% 1.70/1.90 dependent: set(dynamic_demod).
% 1.70/1.90 dependent: set(order_eq).
% 1.70/1.90 dependent: set(back_demod).
% 1.70/1.90 dependent: set(lrpo).
% 1.70/1.90 dependent: set(hyper_res).
% 1.70/1.90 dependent: set(unit_deletion).
% 1.70/1.90 dependent: set(factor).
% 1.70/1.90
% 1.70/1.90 ------------> process usable:
% 1.70/1.90 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.70/1.90 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.70/1.90 ** KEPT (pick-wt=14): 3 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.70/1.90 ** KEPT (pick-wt=11): 4 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.70/1.90 ** KEPT (pick-wt=11): 5 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.70/1.90 ** KEPT (pick-wt=17): 6 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=B.
% 1.70/1.90 ** KEPT (pick-wt=17): 7 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=C.
% 1.70/1.90 ** KEPT (pick-wt=14): 8 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.70/1.90 ** KEPT (pick-wt=11): 9 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.70/1.90 ** KEPT (pick-wt=11): 10 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.70/1.90 ** KEPT (pick-wt=17): 11 [] A=set_union2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B).
% 1.70/1.90 ** KEPT (pick-wt=17): 12 [] A=set_union2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),C).
% 1.70/1.90 ** KEPT (pick-wt=6): 13 [] empty(A)| -empty(set_union2(A,B)).
% 1.70/1.90 ** KEPT (pick-wt=6): 14 [] empty(A)| -empty(set_union2(B,A)).
% 1.75/1.98 ** KEPT (pick-wt=2): 15 [] -empty($c2).
% 1.75/1.98
% 1.75/1.98 ------------> process sos:
% 1.75/1.98 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.75/1.98 ** KEPT (pick-wt=7): 22 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.75/1.98 ** KEPT (pick-wt=7): 23 [] set_union2(A,B)=set_union2(B,A).
% 1.75/1.98 ** KEPT (pick-wt=7): 24 [] A=empty_set|in($f1(A),A).
% 1.75/1.98 ** KEPT (pick-wt=23): 25 [] A=unordered_pair(B,C)|in($f2(B,C,A),A)|$f2(B,C,A)=B|$f2(B,C,A)=C.
% 1.75/1.98 ** KEPT (pick-wt=23): 26 [] A=set_union2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B)|in($f3(B,C,A),C).
% 1.75/1.98 ** KEPT (pick-wt=2): 27 [] empty(empty_set).
% 1.75/1.98 ** KEPT (pick-wt=5): 28 [] set_union2(A,A)=A.
% 1.75/1.98 ---> New Demodulator: 29 [new_demod,28] set_union2(A,A)=A.
% 1.75/1.98 ** KEPT (pick-wt=2): 30 [] empty($c1).
% 1.75/1.98 ** KEPT (pick-wt=7): 31 [] set_union2(unordered_pair($c5,$c4),$c3)=empty_set.
% 1.75/1.98 ---> New Demodulator: 32 [new_demod,31] set_union2(unordered_pair($c5,$c4),$c3)=empty_set.
% 1.75/1.98 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 1.75/1.98 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.75/1.98 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.75/1.98 >>>> Starting back demodulation with 29.
% 1.75/1.98 >> back demodulating 18 with 29.
% 1.75/1.98 >>>> Starting back demodulation with 32.
% 1.75/1.98
% 1.75/1.98 ======= end of input processing =======
% 1.75/1.98
% 1.75/1.98 =========== start of search ===========
% 1.75/1.98
% 1.75/1.98 -------- PROOF --------
% 1.75/1.98
% 1.75/1.98 -----> EMPTY CLAUSE at 0.08 sec ----> 914 [hyper,66,2,31] $F.
% 1.75/1.98
% 1.75/1.98 Length of proof is 2. Level of proof is 2.
% 1.75/1.98
% 1.75/1.98 ---------------- PROOF ----------------
% 1.75/1.98 % SZS status Theorem
% 1.75/1.98 % SZS output start Refutation
% See solution above
% 1.75/1.98 ------------ end of proof -------------
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Search stopped by max_proofs option.
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Search stopped by max_proofs option.
% 1.75/1.98
% 1.75/1.98 ============ end of search ============
% 1.75/1.98
% 1.75/1.98 -------------- statistics -------------
% 1.75/1.98 clauses given 20
% 1.75/1.98 clauses generated 1518
% 1.75/1.98 clauses kept 909
% 1.75/1.98 clauses forward subsumed 629
% 1.75/1.98 clauses back subsumed 1
% 1.75/1.98 Kbytes malloced 2929
% 1.75/1.98
% 1.75/1.98 ----------- times (seconds) -----------
% 1.75/1.98 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.75/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.98
% 1.75/1.98 That finishes the proof of the theorem.
% 1.75/1.98
% 1.75/1.98 Process 29971 finished Wed Jul 27 10:46:40 2022
% 1.75/1.98 Otter interrupted
% 1.75/1.98 PROOF FOUND
%------------------------------------------------------------------------------