TSTP Solution File: SET616+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:13:52 EDT 2022
% Result : Theorem 2.90s 3.13s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 7 unt; 6 nHn; 13 RR)
% Number of literals : 38 ( 7 equ; 15 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; 0-2 aty)
% Number of variables : 19 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(dollar_f1(A,B),A)
| ~ member(dollar_f1(A,B),B)
| A = B ),
file('SET616+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(A,difference(B,C))
| ~ member(A,C) ),
file('SET616+3.p',unknown),
[] ).
cnf(4,axiom,
( member(A,difference(B,C))
| ~ member(A,B)
| member(A,C) ),
file('SET616+3.p',unknown),
[] ).
cnf(7,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET616+3.p',unknown),
[] ).
cnf(13,axiom,
dollar_c2 != dollar_c1,
file('SET616+3.p',unknown),
[] ).
cnf(18,axiom,
( member(dollar_f1(A,B),A)
| member(dollar_f1(A,B),B)
| A = B ),
file('SET616+3.p',unknown),
[] ).
cnf(21,axiom,
subset(A,A),
file('SET616+3.p',unknown),
[] ).
cnf(22,axiom,
difference(dollar_c2,dollar_c1) = difference(dollar_c1,dollar_c2),
file('SET616+3.p',unknown),
[] ).
cnf(32,plain,
( member(A,difference(dollar_c1,dollar_c2))
| ~ member(A,dollar_c2)
| member(A,dollar_c1) ),
inference(para_from,[status(thm),theory(equality)],[22,4]),
[iquote('para_from,22.1.1,4.1.2')] ).
cnf(33,plain,
( ~ member(A,difference(dollar_c1,dollar_c2))
| ~ member(A,dollar_c1) ),
inference(para_from,[status(thm),theory(equality)],[22,3]),
[iquote('para_from,22.1.1,3.1.2')] ).
cnf(43,plain,
( ~ member(A,difference(dollar_c1,B))
| ~ member(A,dollar_c1)
| ~ subset(dollar_c2,B)
| ~ subset(B,dollar_c2) ),
inference(para_into,[status(thm),theory(equality)],[33,7]),
[iquote('para_into,33.1.2.2,7.1.1')] ).
cnf(121,plain,
( member(dollar_f1(A,dollar_c2),difference(dollar_c1,dollar_c2))
| member(dollar_f1(A,dollar_c2),dollar_c1)
| member(dollar_f1(A,dollar_c2),A)
| A = dollar_c2 ),
inference(hyper,[status(thm)],[32,18]),
[iquote('hyper,32,18')] ).
cnf(124,plain,
( member(dollar_f1(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c2))
| member(dollar_f1(dollar_c1,dollar_c2),dollar_c1) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[121]),13]),
[iquote('factor,121.2.3,unit_del,13')] ).
cnf(674,plain,
member(dollar_f1(dollar_c1,dollar_c2),dollar_c1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[124,3,18]),13])]),
[iquote('hyper,124,3,18,unit_del,13,factor_simp')] ).
cnf(689,plain,
( member(dollar_f1(dollar_c1,dollar_c2),difference(dollar_c1,A))
| member(dollar_f1(dollar_c1,dollar_c2),A) ),
inference(hyper,[status(thm)],[674,4]),
[iquote('hyper,674,4')] ).
cnf(2931,plain,
member(dollar_f1(dollar_c1,dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[689,43,674,21,21]),
[iquote('hyper,689,43,674,21,21')] ).
cnf(2980,plain,
dollar_c2 = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2931,1,674])]),
[iquote('hyper,2931,1,674,flip.1')] ).
cnf(2982,plain,
$false,
inference(binary,[status(thm)],[2980,13]),
[iquote('binary,2980.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 10:59:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.90 ----- Otter 3.3f, August 2004 -----
% 1.70/1.90 The process was started by sandbox on n028.cluster.edu,
% 1.70/1.90 Wed Jul 27 10:59:19 2022
% 1.70/1.90 The command was "./otter". The process ID is 19897.
% 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 B C ((all D (member(D,B)<->member(D,C)))->B=C).
% 1.70/1.90 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.70/1.90 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.70/1.90 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.70/1.90 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.70/1.90 all B subset(B,B).
% 1.70/1.90 -(all B C (difference(B,C)=difference(C,B)->B=C)).
% 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 [] member($f1(B,C),B)|member($f1(B,C),C)|B=C.
% 1.70/1.90 0 [] -member($f1(B,C),B)| -member($f1(B,C),C)|B=C.
% 1.70/1.90 0 [] -member(D,difference(B,C))|member(D,B).
% 1.70/1.90 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.70/1.90 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.70/1.90 0 [] B!=C|subset(B,C).
% 1.70/1.90 0 [] B!=C|subset(C,B).
% 1.70/1.90 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.70/1.90 0 [] B!=C| -member(D,B)|member(D,C).
% 1.70/1.90 0 [] B!=C|member(D,B)| -member(D,C).
% 1.70/1.90 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.70/1.90 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.70/1.90 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.70/1.90 0 [] subset(B,C)|member($f3(B,C),B).
% 1.70/1.90 0 [] subset(B,C)| -member($f3(B,C),C).
% 1.70/1.90 0 [] subset(B,B).
% 1.70/1.90 0 [] difference($c2,$c1)=difference($c1,$c2).
% 1.70/1.90 0 [] $c2!=$c1.
% 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=3.
% 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=13): 1 [] -member($f1(A,B),A)| -member($f1(A,B),B)|A=B.
% 1.70/1.90 ** KEPT (pick-wt=8): 2 [] -member(A,difference(B,C))|member(A,B).
% 1.70/1.90 ** KEPT (pick-wt=8): 3 [] -member(A,difference(B,C))| -member(A,C).
% 1.70/1.90 ** KEPT (pick-wt=11): 4 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.70/1.90 ** KEPT (pick-wt=6): 5 [] A!=B|subset(A,B).
% 1.70/1.90 ** KEPT (pick-wt=6): 6 [] A!=B|subset(B,A).
% 1.70/1.90 ** KEPT (pick-wt=9): 7 [] A=B| -subset(A,B)| -subset(B,A).
% 1.70/1.90 ** KEPT (pick-wt=9): 8 [] A!=B| -member(C,A)|member(C,B).
% 1.70/1.90 ** KEPT (pick-wt=9): 9 [] A!=B|member(C,A)| -member(C,B).
% 1.70/1.90 ** KEPT (pick-wt=13): 10 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.70/1.90 ** KEPT (pick-wt=9): 11 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.70/1.90 ** KEPT (pick-wt=8): 12 [] subset(A,B)| -member($f3(A,B),B).
% 1.70/1.90 ** KEPT (pick-wt=3): 13 [] $c2!=$c1.
% 1.70/1.90
% 1.70/1.90 ------------> process sos:
% 1.70/1.90 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.70/1.90 ** KEPT (pick-wt=13): 18 [] member($f1(A,B),A)|member($f1(A,B),B)|A=B.
% 1.70/1.90 ** KEPT (pick-wt=13): 19 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.70/1.90 ** KEPT (pick-wt=8): 20 [] subset(A,B)|member($f3(A,B),A).
% 1.70/1.90 ** KEPT (pick-wt=3): 21 [] subset(A,A).
% 1.70/1.90 ** KEPT (pick-wt=7): 22 [] difference($c2,$c1)=difference($c1,$c2).
% 1.70/1.90 ---> New Demodulator: 23 [new_demod,22] difference($c2,$c1)=difference($c1,$c2).
% 1.70/1.90 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.70/1.90 17 back subsumes 16.
% 1.70/1.90 17 back subsumes 15.
% 1.70/1.90 17 back subsumes 14.
% 1.70/1.90 >>>> Starting back demodulation with 23.
% 1.70/1.90
% 1.70/1.90 ======= end of input processing =======
% 1.70/1.90
% 1.70/1.90 =========== start of search ===========
% 2.90/3.13
% 2.90/3.13
% 2.90/3.13 Resetting weight limit to 15.
% 2.90/3.13
% 2.90/3.13
% 2.90/3.13 Resetting weight limit to 15.
% 2.90/3.13
% 2.90/3.13 sos_size=2396
% 2.90/3.13
% 2.90/3.13 -------- PROOF --------
% 2.90/3.13
% 2.90/3.13 ----> UNIT CONFLICT at 1.23 sec ----> 2982 [binary,2980.1,13.1] $F.
% 2.90/3.13
% 2.90/3.13 Length of proof is 9. Level of proof is 7.
% 2.90/3.13
% 2.90/3.13 ---------------- PROOF ----------------
% 2.90/3.13 % SZS status Theorem
% 2.90/3.13 % SZS output start Refutation
% See solution above
% 2.90/3.13 ------------ end of proof -------------
% 2.90/3.13
% 2.90/3.13
% 2.90/3.13 Search stopped by max_proofs option.
% 2.90/3.13
% 2.90/3.13
% 2.90/3.13 Search stopped by max_proofs option.
% 2.90/3.13
% 2.90/3.13 ============ end of search ============
% 2.90/3.13
% 2.90/3.13 -------------- statistics -------------
% 2.90/3.13 clauses given 104
% 2.90/3.13 clauses generated 13287
% 2.90/3.13 clauses kept 2978
% 2.90/3.13 clauses forward subsumed 5795
% 2.90/3.13 clauses back subsumed 381
% 2.90/3.13 Kbytes malloced 4882
% 2.90/3.13
% 2.90/3.13 ----------- times (seconds) -----------
% 2.90/3.13 user CPU time 1.23 (0 hr, 0 min, 1 sec)
% 2.90/3.13 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.90/3.13 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.90/3.13
% 2.90/3.13 That finishes the proof of the theorem.
% 2.90/3.13
% 2.90/3.13 Process 19897 finished Wed Jul 27 10:59:21 2022
% 2.90/3.13 Otter interrupted
% 2.90/3.13 PROOF FOUND
%------------------------------------------------------------------------------