TSTP Solution File: SET599+3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:13:47 EDT 2022
% Result : Theorem 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 2 RR)
% Number of literals : 6 ( 2 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
~ subset(difference(dollar_c2,dollar_c1),symmetric_difference(dollar_c2,dollar_c1)),
file('SET599+3.p',unknown),
[] ).
cnf(12,axiom,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
file('SET599+3.p',unknown),
[] ).
cnf(13,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(15,axiom,
subset(A,union(A,B)),
file('SET599+3.p',unknown),
[] ).
cnf(29,plain,
subset(difference(A,B),symmetric_difference(A,B)),
inference(para_from,[status(thm),theory(equality)],[13,15]),
[iquote('para_from,13.1.1,15.1.2')] ).
cnf(30,plain,
$false,
inference(binary,[status(thm)],[29,9]),
[iquote('binary,29.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 10:44:50 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox2 on n012.cluster.edu,
% 1.68/1.89 Wed Jul 27 10:44:50 2022
% 1.68/1.89 The command was "./otter". The process ID is 29169.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 formula_list(usable).
% 1.68/1.89 all A (A=A).
% 1.68/1.89 all B C (symmetric_difference(B,C)=union(difference(B,C),difference(C,B))).
% 1.68/1.89 all B C subset(B,union(B,C)).
% 1.68/1.89 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.68/1.89 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.68/1.89 all B C (union(B,C)=union(C,B)).
% 1.68/1.89 all B C (symmetric_difference(B,C)=symmetric_difference(C,B)).
% 1.68/1.89 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.68/1.89 all B subset(B,B).
% 1.68/1.89 -(all B C subset(difference(B,C),symmetric_difference(B,C))).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 -------> usable clausifies to:
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] symmetric_difference(B,C)=union(difference(B,C),difference(C,B)).
% 1.68/1.89 0 [] subset(B,union(B,C)).
% 1.68/1.89 0 [] -member(D,difference(B,C))|member(D,B).
% 1.68/1.89 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.68/1.89 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.68/1.89 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.68/1.89 0 [] subset(B,C)|member($f1(B,C),B).
% 1.68/1.89 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.68/1.89 0 [] union(B,C)=union(C,B).
% 1.68/1.89 0 [] symmetric_difference(B,C)=symmetric_difference(C,B).
% 1.68/1.89 0 [] B!=C| -member(D,B)|member(D,C).
% 1.68/1.89 0 [] B!=C|member(D,B)| -member(D,C).
% 1.68/1.89 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.68/1.89 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.68/1.89 0 [] subset(B,B).
% 1.68/1.89 0 [] -subset(difference($c2,$c1),symmetric_difference($c2,$c1)).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.89
% 1.68/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.89 deletion, with positive clauses in sos and nonpositive
% 1.68/1.89 clauses in usable.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89 dependent: set(hyper_res).
% 1.68/1.89 dependent: set(unit_deletion).
% 1.68/1.89 dependent: set(factor).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=8): 1 [] -member(A,difference(B,C))|member(A,B).
% 1.68/1.89 ** KEPT (pick-wt=8): 2 [] -member(A,difference(B,C))| -member(A,C).
% 1.68/1.89 ** KEPT (pick-wt=11): 3 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.68/1.89 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.68/1.89 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f1(A,B),B).
% 1.68/1.89 ** KEPT (pick-wt=9): 6 [] A!=B| -member(C,A)|member(C,B).
% 1.68/1.89 ** KEPT (pick-wt=9): 7 [] A!=B|member(C,A)| -member(C,B).
% 1.68/1.89 ** KEPT (pick-wt=13): 8 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.68/1.89 ** KEPT (pick-wt=7): 9 [] -subset(difference($c2,$c1),symmetric_difference($c2,$c1)).
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=11): 13 [copy,12,flip.1] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.68/1.89 ---> New Demodulator: 14 [new_demod,13] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.68/1.89 ** KEPT (pick-wt=5): 15 [] subset(A,union(A,B)).
% 1.68/1.89 ** KEPT (pick-wt=8): 16 [] subset(A,B)|member($f1(A,B),A).
% 1.68/1.89 ** KEPT (pick-wt=7): 17 [] union(A,B)=union(B,A).
% 1.68/1.89 ** KEPT (pick-wt=7): 18 [] symmetric_difference(A,B)=symmetric_difference(B,A).
% 1.68/1.89 ** KEPT (pick-wt=13): 19 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.68/1.89 ** KEPT (pick-wt=3): 20 [] subset(A,A).
% 1.68/1.89 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.68/1.89 11 back subsumes 10.
% 1.68/1.89 >>>> Starting back demodulation with 14.
% 1.68/1.89 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] union(A,B)=union(B,A).
% 1.68/1.89 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] symmetric_difference(A,B)=symmetric_difference(B,A).
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 30 [binary,29.1,9.1] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 2. Level of proof is 2.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Theorem
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 6
% 1.68/1.89 clauses generated 23
% 1.68/1.89 clauses kept 27
% 1.68/1.89 clauses forward subsumed 16
% 1.68/1.89 clauses back subsumed 1
% 1.68/1.89 Kbytes malloced 976
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 29169 finished Wed Jul 27 10:44:52 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------