TSTP Solution File: SEU128+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU128+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 13:14:50 EDT 2022
% Result : Theorem 2.78s 3.00s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 10 unt; 1 nHn; 12 RR)
% Number of literals : 21 ( 2 equ; 7 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU128+1.p',unknown),
[] ).
cnf(3,axiom,
( subset(A,B)
| ~ in(dollar_f1(A,B),B) ),
file('SEU128+1.p',unknown),
[] ).
cnf(6,axiom,
( A != set_intersection2(B,C)
| in(D,A)
| ~ in(D,B)
| ~ in(D,C) ),
file('SEU128+1.p',unknown),
[] ).
cnf(9,axiom,
~ subset(dollar_c5,set_intersection2(dollar_c4,dollar_c3)),
file('SEU128+1.p',unknown),
[] ).
cnf(21,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SEU128+1.p',unknown),
[] ).
cnf(22,axiom,
( subset(A,B)
| in(dollar_f1(A,B),A) ),
file('SEU128+1.p',unknown),
[] ).
cnf(30,axiom,
subset(dollar_c5,dollar_c4),
file('SEU128+1.p',unknown),
[] ).
cnf(31,axiom,
subset(dollar_c5,dollar_c3),
file('SEU128+1.p',unknown),
[] ).
cnf(88,plain,
in(dollar_f1(dollar_c5,set_intersection2(dollar_c4,dollar_c3)),dollar_c5),
inference(hyper,[status(thm)],[22,9]),
[iquote('hyper,22,9')] ).
cnf(751,plain,
in(dollar_f1(dollar_c5,set_intersection2(dollar_c4,dollar_c3)),dollar_c3),
inference(hyper,[status(thm)],[88,2,31]),
[iquote('hyper,88,2,31')] ).
cnf(752,plain,
in(dollar_f1(dollar_c5,set_intersection2(dollar_c4,dollar_c3)),dollar_c4),
inference(hyper,[status(thm)],[88,2,30]),
[iquote('hyper,88,2,30')] ).
cnf(1230,plain,
in(dollar_f1(dollar_c5,set_intersection2(dollar_c4,dollar_c3)),set_intersection2(dollar_c4,dollar_c3)),
inference(hyper,[status(thm)],[752,6,21,751]),
[iquote('hyper,752,6,21,751')] ).
cnf(3751,plain,
subset(dollar_c5,set_intersection2(dollar_c4,dollar_c3)),
inference(hyper,[status(thm)],[1230,3]),
[iquote('hyper,1230,3')] ).
cnf(3752,plain,
$false,
inference(binary,[status(thm)],[3751,9]),
[iquote('binary,3751.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU128+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 07:53:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.98 ----- Otter 3.3f, August 2004 -----
% 1.73/1.98 The process was started by sandbox2 on n024.cluster.edu,
% 1.73/1.98 Wed Jul 27 07:53:55 2022
% 1.73/1.98 The command was "./otter". The process ID is 18790.
% 1.73/1.98
% 1.73/1.98 set(prolog_style_variables).
% 1.73/1.98 set(auto).
% 1.73/1.98 dependent: set(auto1).
% 1.73/1.98 dependent: set(process_input).
% 1.73/1.98 dependent: clear(print_kept).
% 1.73/1.98 dependent: clear(print_new_demod).
% 1.73/1.98 dependent: clear(print_back_demod).
% 1.73/1.98 dependent: clear(print_back_sub).
% 1.73/1.98 dependent: set(control_memory).
% 1.73/1.98 dependent: assign(max_mem, 12000).
% 1.73/1.98 dependent: assign(pick_given_ratio, 4).
% 1.73/1.98 dependent: assign(stats_level, 1).
% 1.73/1.98 dependent: assign(max_seconds, 10800).
% 1.73/1.98 clear(print_given).
% 1.73/1.98
% 1.73/1.98 formula_list(usable).
% 1.73/1.98 all A (A=A).
% 1.73/1.98 all A B (in(A,B)-> -in(B,A)).
% 1.73/1.98 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.73/1.98 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.73/1.98 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.73/1.98 $T.
% 1.73/1.98 $T.
% 1.73/1.98 empty(empty_set).
% 1.73/1.98 all A B (set_intersection2(A,A)=A).
% 1.73/1.98 exists A empty(A).
% 1.73/1.98 exists A (-empty(A)).
% 1.73/1.98 all A B subset(A,A).
% 1.73/1.98 -(all A B C (subset(A,B)&subset(A,C)->subset(A,set_intersection2(B,C)))).
% 1.73/1.98 all A (set_intersection2(A,empty_set)=empty_set).
% 1.73/1.98 all A (empty(A)->A=empty_set).
% 1.73/1.98 all A B (-(in(A,B)&empty(B))).
% 1.73/1.98 all A B (-(empty(A)&A!=B&empty(B))).
% 1.73/1.98 end_of_list.
% 1.73/1.98
% 1.73/1.98 -------> usable clausifies to:
% 1.73/1.98
% 1.73/1.98 list(usable).
% 1.73/1.98 0 [] A=A.
% 1.73/1.98 0 [] -in(A,B)| -in(B,A).
% 1.73/1.98 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.73/1.98 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.73/1.98 0 [] subset(A,B)|in($f1(A,B),A).
% 1.73/1.98 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.73/1.98 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.73/1.98 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.73/1.98 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.73/1.98 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A).
% 1.73/1.98 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),B).
% 1.73/1.98 0 [] C=set_intersection2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A)| -in($f2(A,B,C),B).
% 1.73/1.98 0 [] $T.
% 1.73/1.98 0 [] $T.
% 1.73/1.98 0 [] empty(empty_set).
% 1.73/1.98 0 [] set_intersection2(A,A)=A.
% 1.73/1.98 0 [] empty($c1).
% 1.73/1.98 0 [] -empty($c2).
% 1.73/1.98 0 [] subset(A,A).
% 1.73/1.98 0 [] subset($c5,$c4).
% 1.73/1.98 0 [] subset($c5,$c3).
% 1.73/1.98 0 [] -subset($c5,set_intersection2($c4,$c3)).
% 1.73/1.98 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.73/1.98 0 [] -empty(A)|A=empty_set.
% 1.73/1.98 0 [] -in(A,B)| -empty(B).
% 1.73/1.98 0 [] -empty(A)|A=B| -empty(B).
% 1.73/1.98 end_of_list.
% 1.73/1.98
% 1.73/1.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.73/1.98
% 1.73/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.73/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.98 deletion, with positive clauses in sos and nonpositive
% 1.73/1.98 clauses in usable.
% 1.73/1.98
% 1.73/1.98 dependent: set(knuth_bendix).
% 1.73/1.98 dependent: set(anl_eq).
% 1.73/1.98 dependent: set(para_from).
% 1.73/1.98 dependent: set(para_into).
% 1.73/1.98 dependent: clear(para_from_right).
% 1.73/1.98 dependent: clear(para_into_right).
% 1.73/1.98 dependent: set(para_from_vars).
% 1.73/1.98 dependent: set(eq_units_both_ways).
% 1.73/1.98 dependent: set(dynamic_demod_all).
% 1.73/1.98 dependent: set(dynamic_demod).
% 1.73/1.98 dependent: set(order_eq).
% 1.73/1.98 dependent: set(back_demod).
% 1.73/1.98 dependent: set(lrpo).
% 1.73/1.98 dependent: set(hyper_res).
% 1.73/1.98 dependent: set(unit_deletion).
% 1.73/1.98 dependent: set(factor).
% 1.73/1.98
% 1.73/1.98 ------------> process usable:
% 1.73/1.98 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.73/1.98 ** KEPT (pick-wt=9): 2 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.73/1.98 ** KEPT (pick-wt=8): 3 [] subset(A,B)| -in($f1(A,B),B).
% 1.73/1.98 ** KEPT (pick-wt=11): 4 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.73/1.98 ** KEPT (pick-wt=11): 5 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.73/1.98 ** KEPT (pick-wt=14): 6 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.73/1.98 ** KEPT (pick-wt=23): 7 [] A=set_intersection2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B)| -in($f2(B,C,A),C).
% 1.73/1.98 ** KEPT (pick-wt=2): 8 [] -empty($c2).
% 1.73/1.98 ** KEPT (pick-wt=5): 9 [] -subset($c5,set_intersection2($c4,$c3)).
% 1.73/1.98 ** KEPT (pick-wt=5): 10 [] -empty(A)|A=empty_set.
% 1.73/1.98 ** KEPT (pick-wt=5): 11 [] -in(A,B)| -empty(B).
% 1.73/1.98 ** KEPT (pick-wt=7): 12 [] -empty(A)|A=B| -empty(B).
% 1.73/1.98
% 1.73/1.98 ------------> process sos:
% 1.73/1.98 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.73/1.98 ** KEPT (pick-wt=7): 21 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.73/1.98 ** KEPT (pick-wt=8): 22 [] subset(A,B)|in($f1(A,B),A).
% 1.73/1.98 ** KEPT (pick-wt=17): 23 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B).
% 1.73/1.98 ** KEPT (pick-wt=17): 24 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),C).
% 2.78/3.00 ** KEPT (pick-wt=2): 25 [] empty(empty_set).
% 2.78/3.00 ** KEPT (pick-wt=5): 26 [] set_intersection2(A,A)=A.
% 2.78/3.00 ---> New Demodulator: 27 [new_demod,26] set_intersection2(A,A)=A.
% 2.78/3.00 ** KEPT (pick-wt=2): 28 [] empty($c1).
% 2.78/3.00 ** KEPT (pick-wt=3): 29 [] subset(A,A).
% 2.78/3.00 ** KEPT (pick-wt=3): 30 [] subset($c5,$c4).
% 2.78/3.00 ** KEPT (pick-wt=3): 31 [] subset($c5,$c3).
% 2.78/3.00 ** KEPT (pick-wt=5): 32 [] set_intersection2(A,empty_set)=empty_set.
% 2.78/3.00 ---> New Demodulator: 33 [new_demod,32] set_intersection2(A,empty_set)=empty_set.
% 2.78/3.00 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 2.78/3.00 20 back subsumes 18.
% 2.78/3.00 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.78/3.00 >>>> Starting back demodulation with 27.
% 2.78/3.00 >> back demodulating 19 with 27.
% 2.78/3.00 >> back demodulating 17 with 27.
% 2.78/3.00 >> back demodulating 14 with 27.
% 2.78/3.00 >>>> Starting back demodulation with 33.
% 2.78/3.00
% 2.78/3.00 ======= end of input processing =======
% 2.78/3.00
% 2.78/3.00 =========== start of search ===========
% 2.78/3.00
% 2.78/3.00
% 2.78/3.00 Resetting weight limit to 11.
% 2.78/3.00
% 2.78/3.00
% 2.78/3.00 Resetting weight limit to 11.
% 2.78/3.00
% 2.78/3.00 sos_size=3382
% 2.78/3.00
% 2.78/3.00 -------- PROOF --------
% 2.78/3.00
% 2.78/3.00 ----> UNIT CONFLICT at 1.01 sec ----> 3752 [binary,3751.1,9.1] $F.
% 2.78/3.00
% 2.78/3.00 Length of proof is 5. Level of proof is 4.
% 2.78/3.00
% 2.78/3.00 ---------------- PROOF ----------------
% 2.78/3.00 % SZS status Theorem
% 2.78/3.00 % SZS output start Refutation
% See solution above
% 2.78/3.00 ------------ end of proof -------------
% 2.78/3.00
% 2.78/3.00
% 2.78/3.00 Search stopped by max_proofs option.
% 2.78/3.00
% 2.78/3.00
% 2.78/3.00 Search stopped by max_proofs option.
% 2.78/3.00
% 2.78/3.00 ============ end of search ============
% 2.78/3.00
% 2.78/3.00 -------------- statistics -------------
% 2.78/3.00 clauses given 130
% 2.78/3.00 clauses generated 16198
% 2.78/3.00 clauses kept 3746
% 2.78/3.00 clauses forward subsumed 8678
% 2.78/3.00 clauses back subsumed 212
% 2.78/3.00 Kbytes malloced 4882
% 2.78/3.00
% 2.78/3.00 ----------- times (seconds) -----------
% 2.78/3.00 user CPU time 1.01 (0 hr, 0 min, 1 sec)
% 2.78/3.00 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.78/3.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.78/3.00
% 2.78/3.00 That finishes the proof of the theorem.
% 2.78/3.00
% 2.78/3.00 Process 18790 finished Wed Jul 27 07:53:57 2022
% 2.78/3.00 Otter interrupted
% 2.78/3.00 PROOF FOUND
%------------------------------------------------------------------------------