TSTP Solution File: SEU159+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU159+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 13:14:58 EDT 2022
% Result : Theorem 74.14s 74.37s
% Output : Refutation 74.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 14 unt; 5 nHn; 20 RR)
% Number of literals : 43 ( 14 equ; 18 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 : 26 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU159+3.p',unknown),
[] ).
cnf(3,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU159+3.p',unknown),
[] ).
cnf(4,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != C ),
file('SEU159+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU159+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SEU159+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ subset(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| ~ in(dollar_c5,dollar_c3)
| ~ in(dollar_c4,dollar_c3) ),
file('SEU159+3.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('SEU159+3.p',unknown),
[] ).
cnf(14,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SEU159+3.p',unknown),
[] ).
cnf(16,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SEU159+3.p',unknown),
[] ).
cnf(19,axiom,
( subset(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| in(dollar_c5,dollar_c3) ),
file('SEU159+3.p',unknown),
[] ).
cnf(20,axiom,
( subset(unordered_pair(dollar_c5,dollar_c4),dollar_c3)
| in(dollar_c4,dollar_c3) ),
file('SEU159+3.p',unknown),
[] ).
cnf(22,plain,
in(A,unordered_pair(B,A)),
inference(hyper,[status(thm)],[13,4,13]),
[iquote('hyper,13,4,13')] ).
cnf(23,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[13,3,13]),
[iquote('hyper,13,3,13')] ).
cnf(46,plain,
( ~ subset(unordered_pair(dollar_c4,dollar_c5),dollar_c3)
| ~ in(dollar_c5,dollar_c3)
| ~ in(dollar_c4,dollar_c3) ),
inference(para_from,[status(thm),theory(equality)],[14,10]),
[iquote('para_from,14.1.1,10.1.1')] ).
cnf(54,plain,
in(dollar_c5,dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,7,23])]),
[iquote('hyper,19,7,23,factor_simp')] ).
cnf(66,plain,
in(dollar_c4,dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[20,7,22])]),
[iquote('hyper,20,7,22,factor_simp')] ).
cnf(163,plain,
in(dollar_f2(unordered_pair(dollar_c5,dollar_c4),dollar_c3),unordered_pair(dollar_c5,dollar_c4)),
inference(hyper,[status(thm)],[66,10,16,54]),
[iquote('hyper,66,10,16,54')] ).
cnf(360,plain,
( dollar_f2(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = dollar_c4
| dollar_f2(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = dollar_c5 ),
inference(hyper,[status(thm)],[163,2,14]),
[iquote('hyper,163,2,14')] ).
cnf(1130,plain,
~ subset(unordered_pair(dollar_c5,dollar_c4),dollar_c3),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[46,14]),54,66]),
[iquote('para_into,46.1.1,14.1.1,unit_del,54,66')] ).
cnf(1236,plain,
~ subset(unordered_pair(dollar_c4,dollar_c5),dollar_c3),
inference(para_into,[status(thm),theory(equality)],[1130,14]),
[iquote('para_into,1130.1.1,14.1.1')] ).
cnf(2683,plain,
dollar_f2(unordered_pair(dollar_c5,dollar_c4),dollar_c3) = dollar_c5,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[360,8]),1130,66]),
[iquote('para_from,360.1.1,8.2.1,unit_del,1130,66')] ).
cnf(2687,plain,
dollar_c5 = dollar_c4,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[360,8]),2683]),1130,54]),
[iquote('para_from,360.2.1,8.2.1,demod,2683,unit_del,1130,54')] ).
cnf(2691,plain,
dollar_f2(unordered_pair(dollar_c4,dollar_c4),dollar_c3) = dollar_c4,
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[360]),2687,2687,2687])]),
[iquote('back_demod,360,demod,2687,2687,2687,factor_simp')] ).
cnf(2702,plain,
~ subset(unordered_pair(dollar_c4,dollar_c4),dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1236]),2687]),
[iquote('back_demod,1236,demod,2687')] ).
cnf(2706,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2691,8]),2702,66]),
[iquote('para_from,2691.1.1,8.2.1,unit_del,2702,66')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU159+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n010.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 07:26:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.11/2.29 ----- Otter 3.3f, August 2004 -----
% 2.11/2.29 The process was started by sandbox2 on n010.cluster.edu,
% 2.11/2.29 Wed Jul 27 07:26:25 2022
% 2.11/2.29 The command was "./otter". The process ID is 23785.
% 2.11/2.29
% 2.11/2.29 set(prolog_style_variables).
% 2.11/2.29 set(auto).
% 2.11/2.29 dependent: set(auto1).
% 2.11/2.29 dependent: set(process_input).
% 2.11/2.29 dependent: clear(print_kept).
% 2.11/2.29 dependent: clear(print_new_demod).
% 2.11/2.29 dependent: clear(print_back_demod).
% 2.11/2.29 dependent: clear(print_back_sub).
% 2.11/2.29 dependent: set(control_memory).
% 2.11/2.29 dependent: assign(max_mem, 12000).
% 2.11/2.29 dependent: assign(pick_given_ratio, 4).
% 2.11/2.29 dependent: assign(stats_level, 1).
% 2.11/2.29 dependent: assign(max_seconds, 10800).
% 2.11/2.29 clear(print_given).
% 2.11/2.29
% 2.11/2.29 formula_list(usable).
% 2.11/2.29 all A (A=A).
% 2.11/2.29 all A B (in(A,B)-> -in(B,A)).
% 2.11/2.29 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.11/2.29 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 2.11/2.29 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.11/2.29 exists A empty(A).
% 2.11/2.29 exists A (-empty(A)).
% 2.11/2.29 all A B subset(A,A).
% 2.11/2.29 -(all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C))).
% 2.11/2.29 end_of_list.
% 2.11/2.29
% 2.11/2.29 -------> usable clausifies to:
% 2.11/2.29
% 2.11/2.29 list(usable).
% 2.11/2.29 0 [] A=A.
% 2.11/2.29 0 [] -in(A,B)| -in(B,A).
% 2.11/2.29 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.11/2.29 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 2.11/2.29 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 2.11/2.29 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 2.11/2.29 0 [] C=unordered_pair(A,B)|in($f1(A,B,C),C)|$f1(A,B,C)=A|$f1(A,B,C)=B.
% 2.11/2.29 0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=A.
% 2.11/2.29 0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=B.
% 2.11/2.29 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.11/2.29 0 [] subset(A,B)|in($f2(A,B),A).
% 2.11/2.29 0 [] subset(A,B)| -in($f2(A,B),B).
% 2.11/2.29 0 [] empty($c1).
% 2.11/2.29 0 [] -empty($c2).
% 2.11/2.29 0 [] subset(A,A).
% 2.11/2.29 0 [] subset(unordered_pair($c5,$c4),$c3)|in($c5,$c3).
% 2.11/2.29 0 [] subset(unordered_pair($c5,$c4),$c3)|in($c4,$c3).
% 2.11/2.29 0 [] -subset(unordered_pair($c5,$c4),$c3)| -in($c5,$c3)| -in($c4,$c3).
% 2.11/2.29 end_of_list.
% 2.11/2.29
% 2.11/2.29 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.11/2.29
% 2.11/2.29 This ia a non-Horn set with equality. The strategy will be
% 2.11/2.29 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.11/2.29 deletion, with positive clauses in sos and nonpositive
% 2.11/2.29 clauses in usable.
% 2.11/2.29
% 2.11/2.29 dependent: set(knuth_bendix).
% 2.11/2.29 dependent: set(anl_eq).
% 2.11/2.29 dependent: set(para_from).
% 2.11/2.29 dependent: set(para_into).
% 2.11/2.29 dependent: clear(para_from_right).
% 2.11/2.29 dependent: clear(para_into_right).
% 2.11/2.29 dependent: set(para_from_vars).
% 2.11/2.29 dependent: set(eq_units_both_ways).
% 2.11/2.29 dependent: set(dynamic_demod_all).
% 2.11/2.29 dependent: set(dynamic_demod).
% 2.11/2.29 dependent: set(order_eq).
% 2.11/2.29 dependent: set(back_demod).
% 2.11/2.29 dependent: set(lrpo).
% 2.11/2.29 dependent: set(hyper_res).
% 2.11/2.29 dependent: set(unit_deletion).
% 2.11/2.29 dependent: set(factor).
% 2.11/2.29
% 2.11/2.29 ------------> process usable:
% 2.11/2.29 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.11/2.29 ** KEPT (pick-wt=14): 2 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 2.11/2.29 ** KEPT (pick-wt=11): 3 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 2.11/2.29 ** KEPT (pick-wt=11): 4 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 2.11/2.29 ** KEPT (pick-wt=17): 5 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=B.
% 2.11/2.29 ** KEPT (pick-wt=17): 6 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=C.
% 2.11/2.29 ** KEPT (pick-wt=9): 7 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.11/2.29 ** KEPT (pick-wt=8): 8 [] subset(A,B)| -in($f2(A,B),B).
% 2.11/2.29 ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 2.11/2.29 ** KEPT (pick-wt=11): 10 [] -subset(unordered_pair($c5,$c4),$c3)| -in($c5,$c3)| -in($c4,$c3).
% 2.11/2.29
% 2.11/2.29 ------------> process sos:
% 2.11/2.29 ** KEPT (pick-wt=3): 13 [] A=A.
% 2.11/2.29 ** KEPT (pick-wt=7): 14 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.11/2.29 ** KEPT (pick-wt=23): 15 [] A=unordered_pair(B,C)|in($f1(B,C,A),A)|$f1(B,C,A)=B|$f1(B,C,A)=C.
% 2.11/2.29 ** KEPT (pick-wt=8): 16 [] subset(A,B)|in($f2(A,B),A).
% 2.11/2.29 ** KEPT (pick-wt=2): 17 [] empty($c1).
% 2.11/2.29 ** KEPT (pick-wt=3): 18 [] subset(A,A).
% 2.11/2.29 ** KEPT (pick-wt=8): 19 [] subset(unordered_pair($c5,$c4),$c3)|in($c5,$c3).
% 2.11/2.29 ** KEPT (pick-wt=8): 20 [] subset(unordered_pair($c5,$c4),$c3)|in($c4,$c3).
% 2.11/2.29 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 2.11/2.29 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.11/2.29
% 2.11/2.29 ======= end of input processing =======
% 2.11/2.29
% 2.11/2.29 =========== start of search ===========
% 2.11/2.29
% 2.11/2.29
% 2.11/2.29 Resetting weight limit to 15.
% 74.14/74.37
% 74.14/74.37
% 74.14/74.37 Resetting weight limit to 15.
% 74.14/74.37
% 74.14/74.37 sos_size=2119
% 74.14/74.37
% 74.14/74.37
% 74.14/74.37 Resetting weight limit to 14.
% 74.14/74.37
% 74.14/74.37
% 74.14/74.37 Resetting weight limit to 14.
% 74.14/74.37
% 74.14/74.37 sos_size=2149
% 74.14/74.37
% 74.14/74.37
% 74.14/74.37 Resetting weight limit to 13.
% 74.14/74.37
% 74.14/74.37
% 74.14/74.37 Resetting weight limit to 13.
% 74.14/74.37
% 74.14/74.37 sos_size=2248
% 74.14/74.37
% 74.14/74.37 -- HEY sandbox2, WE HAVE A PROOF!! --
% 74.14/74.37
% 74.14/74.37 -----> EMPTY CLAUSE at 72.45 sec ----> 2706 [para_from,2691.1.1,8.2.1,unit_del,2702,66] $F.
% 74.14/74.37
% 74.14/74.37 Length of proof is 13. Level of proof is 7.
% 74.14/74.37
% 74.14/74.37 ---------------- PROOF ----------------
% 74.14/74.37 % SZS status Theorem
% 74.14/74.37 % SZS output start Refutation
% See solution above
% 74.14/74.37 ------------ end of proof -------------
% 74.14/74.37
% 74.14/74.37
% 74.14/74.37 Search stopped by max_proofs option.
% 74.14/74.37
% 74.14/74.37
% 74.14/74.37 Search stopped by max_proofs option.
% 74.14/74.37
% 74.14/74.37 ============ end of search ============
% 74.14/74.37
% 74.14/74.37 -------------- statistics -------------
% 74.14/74.37 clauses given 520
% 74.14/74.37 clauses generated 755145
% 74.14/74.37 clauses kept 2659
% 74.14/74.37 clauses forward subsumed 16087
% 74.14/74.37 clauses back subsumed 52
% 74.14/74.37 Kbytes malloced 5859
% 74.14/74.37
% 74.14/74.37 ----------- times (seconds) -----------
% 74.14/74.37 user CPU time 72.45 (0 hr, 1 min, 12 sec)
% 74.14/74.37 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 74.14/74.37 wall-clock time 73 (0 hr, 1 min, 13 sec)
% 74.14/74.37
% 74.14/74.37 That finishes the proof of the theorem.
% 74.14/74.37
% 74.14/74.37 Process 23785 finished Wed Jul 27 07:27:38 2022
% 74.14/74.37 Otter interrupted
% 74.14/74.37 PROOF FOUND
%------------------------------------------------------------------------------