TSTP Solution File: SEU126+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 1.77s 1.95s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 7 unt; 3 nHn; 8 RR)
% Number of literals : 26 ( 9 equ; 7 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
( A = set_union2(B,C)
| ~ in(dollar_f1(B,C,A),A)
| ~ in(dollar_f1(B,C,A),B) ),
file('SEU126+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU126+1.p',unknown),
[] ).
cnf(15,axiom,
set_union2(dollar_c4,dollar_c3) != dollar_c3,
file('SEU126+1.p',unknown),
[] ).
cnf(22,plain,
( set_union2(A,B) = A
| ~ in(dollar_f1(A,B,A),A) ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[8])]),
[iquote('factor,8.2.3,flip.1')] ).
cnf(25,axiom,
A = A,
file('SEU126+1.p',unknown),
[] ).
cnf(26,axiom,
set_union2(A,B) = set_union2(B,A),
file('SEU126+1.p',unknown),
[] ).
cnf(27,axiom,
( A = set_union2(B,C)
| in(dollar_f1(B,C,A),A)
| in(dollar_f1(B,C,A),B)
| in(dollar_f1(B,C,A),C) ),
file('SEU126+1.p',unknown),
[] ).
cnf(34,axiom,
subset(dollar_c4,dollar_c3),
file('SEU126+1.p',unknown),
[] ).
cnf(77,plain,
set_union2(dollar_c3,dollar_c4) != dollar_c3,
inference(para_from,[status(thm),theory(equality)],[26,15]),
[iquote('para_from,26.1.1,15.1.1')] ).
cnf(120,plain,
( A = set_union2(B,dollar_c4)
| in(dollar_f1(B,dollar_c4,A),A)
| in(dollar_f1(B,dollar_c4,A),B)
| in(dollar_f1(B,dollar_c4,A),dollar_c3) ),
inference(hyper,[status(thm)],[27,10,34]),
[iquote('hyper,27,10,34')] ).
cnf(153,plain,
( set_union2(A,dollar_c4) = A
| in(dollar_f1(A,dollar_c4,A),A)
| in(dollar_f1(A,dollar_c4,A),dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[120])]),
[iquote('factor,120.2.3,flip.1')] ).
cnf(179,plain,
in(dollar_f1(dollar_c3,dollar_c4,dollar_c3),dollar_c3),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[153]),77]),
[iquote('factor,153.2.3,unit_del,77')] ).
cnf(355,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[77,22]),25,179]),
[iquote('para_into,77.1.1,22.1.1,unit_del,25,179')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.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 07:52:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.73/1.93 ----- Otter 3.3f, August 2004 -----
% 1.73/1.93 The process was started by sandbox on n003.cluster.edu,
% 1.73/1.93 Wed Jul 27 07:52:11 2022
% 1.73/1.93 The command was "./otter". The process ID is 30188.
% 1.73/1.93
% 1.73/1.93 set(prolog_style_variables).
% 1.73/1.93 set(auto).
% 1.73/1.93 dependent: set(auto1).
% 1.73/1.93 dependent: set(process_input).
% 1.73/1.93 dependent: clear(print_kept).
% 1.73/1.93 dependent: clear(print_new_demod).
% 1.73/1.93 dependent: clear(print_back_demod).
% 1.73/1.93 dependent: clear(print_back_sub).
% 1.73/1.93 dependent: set(control_memory).
% 1.73/1.93 dependent: assign(max_mem, 12000).
% 1.73/1.93 dependent: assign(pick_given_ratio, 4).
% 1.73/1.93 dependent: assign(stats_level, 1).
% 1.73/1.93 dependent: assign(max_seconds, 10800).
% 1.73/1.93 clear(print_given).
% 1.73/1.93
% 1.73/1.93 formula_list(usable).
% 1.73/1.93 all A (A=A).
% 1.73/1.93 all A B (in(A,B)-> -in(B,A)).
% 1.73/1.93 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.73/1.93 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.73/1.93 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.73/1.93 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.73/1.93 $T.
% 1.73/1.93 $T.
% 1.73/1.93 empty(empty_set).
% 1.73/1.93 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.73/1.93 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.73/1.93 all A B (set_union2(A,A)=A).
% 1.73/1.93 exists A empty(A).
% 1.73/1.93 exists A (-empty(A)).
% 1.73/1.93 all A B subset(A,A).
% 1.73/1.93 -(all A B (subset(A,B)->set_union2(A,B)=B)).
% 1.73/1.93 all A (set_union2(A,empty_set)=A).
% 1.73/1.93 all A (empty(A)->A=empty_set).
% 1.73/1.93 all A B (-(in(A,B)&empty(B))).
% 1.73/1.93 all A B (-(empty(A)&A!=B&empty(B))).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 -------> usable clausifies to:
% 1.73/1.93
% 1.73/1.93 list(usable).
% 1.73/1.93 0 [] A=A.
% 1.73/1.93 0 [] -in(A,B)| -in(B,A).
% 1.73/1.93 0 [] set_union2(A,B)=set_union2(B,A).
% 1.73/1.93 0 [] A!=B|subset(A,B).
% 1.73/1.93 0 [] A!=B|subset(B,A).
% 1.73/1.93 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.73/1.93 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.73/1.93 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.73/1.93 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.73/1.93 0 [] C=set_union2(A,B)|in($f1(A,B,C),C)|in($f1(A,B,C),A)|in($f1(A,B,C),B).
% 1.73/1.93 0 [] C=set_union2(A,B)| -in($f1(A,B,C),C)| -in($f1(A,B,C),A).
% 1.73/1.93 0 [] C=set_union2(A,B)| -in($f1(A,B,C),C)| -in($f1(A,B,C),B).
% 1.73/1.93 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.73/1.93 0 [] subset(A,B)|in($f2(A,B),A).
% 1.73/1.93 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.73/1.93 0 [] $T.
% 1.73/1.93 0 [] $T.
% 1.73/1.93 0 [] empty(empty_set).
% 1.73/1.93 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.73/1.93 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.73/1.93 0 [] set_union2(A,A)=A.
% 1.73/1.93 0 [] empty($c1).
% 1.73/1.93 0 [] -empty($c2).
% 1.73/1.93 0 [] subset(A,A).
% 1.73/1.93 0 [] subset($c4,$c3).
% 1.73/1.93 0 [] set_union2($c4,$c3)!=$c3.
% 1.73/1.93 0 [] set_union2(A,empty_set)=A.
% 1.73/1.93 0 [] -empty(A)|A=empty_set.
% 1.73/1.93 0 [] -in(A,B)| -empty(B).
% 1.73/1.93 0 [] -empty(A)|A=B| -empty(B).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.73/1.93
% 1.73/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.73/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.93 deletion, with positive clauses in sos and nonpositive
% 1.73/1.93 clauses in usable.
% 1.73/1.93
% 1.73/1.93 dependent: set(knuth_bendix).
% 1.73/1.93 dependent: set(anl_eq).
% 1.73/1.93 dependent: set(para_from).
% 1.73/1.93 dependent: set(para_into).
% 1.73/1.93 dependent: clear(para_from_right).
% 1.73/1.93 dependent: clear(para_into_right).
% 1.73/1.93 dependent: set(para_from_vars).
% 1.73/1.93 dependent: set(eq_units_both_ways).
% 1.73/1.93 dependent: set(dynamic_demod_all).
% 1.73/1.93 dependent: set(dynamic_demod).
% 1.73/1.93 dependent: set(order_eq).
% 1.73/1.93 dependent: set(back_demod).
% 1.73/1.93 dependent: set(lrpo).
% 1.73/1.93 dependent: set(hyper_res).
% 1.73/1.93 dependent: set(unit_deletion).
% 1.73/1.93 dependent: set(factor).
% 1.73/1.93
% 1.73/1.93 ------------> process usable:
% 1.73/1.93 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.73/1.93 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.73/1.93 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.73/1.93 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.73/1.93 ** KEPT (pick-wt=14): 5 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.73/1.93 ** KEPT (pick-wt=11): 6 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.73/1.93 ** KEPT (pick-wt=11): 7 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.73/1.93 ** KEPT (pick-wt=17): 8 [] A=set_union2(B,C)| -in($f1(B,C,A),A)| -in($f1(B,C,A),B).
% 1.73/1.93 ** KEPT (pick-wt=17): 9 [] A=set_union2(B,C)| -in($f1(B,C,A),A)| -in($f1(B,C,A),C).
% 1.73/1.93 ** KEPT (pick-wt=9): 10 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.73/1.93 ** KEPT (pick-wt=8): 11 [] subset(A,B)| -in($f2(A,B),B).
% 1.73/1.93 ** KEPT (pick-wt=6): 12 [] empty(A)| -empty(set_union2(A,B)).
% 1.73/1.93 ** KEPT (pick-wt=6): 13 [] empty(A)| -empty(set_union2(B,A)).
% 1.73/1.93 ** KEPT (pick-wt=2): 14 [] -empty($c2).
% 1.73/1.93 ** KEPT (pick-wt=5): 15 [] set_union2($c4,$c3)!=$c3.
% 1.73/1.93 ** KEPT (pick-wt=5): 16 [] -empty(A)|A=empty_set.
% 1.73/1.93 ** KEPT (pick-wt=5): 17 [] -in(A,B)| -empty(B).
% 1.77/1.95 ** KEPT (pick-wt=7): 18 [] -empty(A)|A=B| -empty(B).
% 1.77/1.95
% 1.77/1.95 ------------> process sos:
% 1.77/1.95 ** KEPT (pick-wt=3): 25 [] A=A.
% 1.77/1.95 ** KEPT (pick-wt=7): 26 [] set_union2(A,B)=set_union2(B,A).
% 1.77/1.95 ** KEPT (pick-wt=23): 27 [] A=set_union2(B,C)|in($f1(B,C,A),A)|in($f1(B,C,A),B)|in($f1(B,C,A),C).
% 1.77/1.95 ** KEPT (pick-wt=8): 28 [] subset(A,B)|in($f2(A,B),A).
% 1.77/1.95 ** KEPT (pick-wt=2): 29 [] empty(empty_set).
% 1.77/1.95 ** KEPT (pick-wt=5): 30 [] set_union2(A,A)=A.
% 1.77/1.95 ---> New Demodulator: 31 [new_demod,30] set_union2(A,A)=A.
% 1.77/1.95 ** KEPT (pick-wt=2): 32 [] empty($c1).
% 1.77/1.95 ** KEPT (pick-wt=3): 33 [] subset(A,A).
% 1.77/1.95 ** KEPT (pick-wt=3): 34 [] subset($c4,$c3).
% 1.77/1.95 ** KEPT (pick-wt=5): 35 [] set_union2(A,empty_set)=A.
% 1.77/1.95 ---> New Demodulator: 36 [new_demod,35] set_union2(A,empty_set)=A.
% 1.77/1.95 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] A=A.
% 1.77/1.95 25 back subsumes 24.
% 1.77/1.95 25 back subsumes 20.
% 1.77/1.95 Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.77/1.95 >>>> Starting back demodulation with 31.
% 1.77/1.95 >> back demodulating 21 with 31.
% 1.77/1.95 >>>> Starting back demodulation with 36.
% 1.77/1.95
% 1.77/1.95 ======= end of input processing =======
% 1.77/1.95
% 1.77/1.95 =========== start of search ===========
% 1.77/1.95
% 1.77/1.95 -------- PROOF --------
% 1.77/1.95
% 1.77/1.95 -----> EMPTY CLAUSE at 0.02 sec ----> 355 [para_into,77.1.1,22.1.1,unit_del,25,179] $F.
% 1.77/1.95
% 1.77/1.95 Length of proof is 5. Level of proof is 3.
% 1.77/1.95
% 1.77/1.95 ---------------- PROOF ----------------
% 1.77/1.95 % SZS status Theorem
% 1.77/1.95 % SZS output start Refutation
% See solution above
% 1.77/1.95 ------------ end of proof -------------
% 1.77/1.95
% 1.77/1.95
% 1.77/1.95 Search stopped by max_proofs option.
% 1.77/1.95
% 1.77/1.95
% 1.77/1.95 Search stopped by max_proofs option.
% 1.77/1.95
% 1.77/1.95 ============ end of search ============
% 1.77/1.95
% 1.77/1.95 -------------- statistics -------------
% 1.77/1.95 clauses given 13
% 1.77/1.95 clauses generated 692
% 1.77/1.95 clauses kept 349
% 1.77/1.95 clauses forward subsumed 377
% 1.77/1.95 clauses back subsumed 6
% 1.77/1.95 Kbytes malloced 1953
% 1.77/1.95
% 1.77/1.95 ----------- times (seconds) -----------
% 1.77/1.95 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.77/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.77/1.95
% 1.77/1.95 That finishes the proof of the theorem.
% 1.77/1.95
% 1.77/1.95 Process 30188 finished Wed Jul 27 07:52:13 2022
% 1.77/1.95 Otter interrupted
% 1.77/1.95 PROOF FOUND
%------------------------------------------------------------------------------