TSTP Solution File: SET621+3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:13:53 EDT 2022
% Result : Theorem 1.71s 1.92s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 5 RR)
% Number of literals : 13 ( 12 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
difference(symmetric_difference(dollar_c3,dollar_c2),dollar_c1) != union(difference(dollar_c3,union(dollar_c2,dollar_c1)),difference(dollar_c2,union(dollar_c3,dollar_c1))),
file('SET621+3.p',unknown),
[] ).
cnf(16,plain,
union(difference(dollar_c3,union(dollar_c2,dollar_c1)),difference(dollar_c2,union(dollar_c3,dollar_c1))) != difference(symmetric_difference(dollar_c3,dollar_c2),dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(20,axiom,
A = A,
file('SET621+3.p',unknown),
[] ).
cnf(21,axiom,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
file('SET621+3.p',unknown),
[] ).
cnf(23,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(24,axiom,
difference(difference(A,B),C) = difference(A,union(B,C)),
file('SET621+3.p',unknown),
[] ).
cnf(25,axiom,
difference(union(A,B),C) = union(difference(A,C),difference(B,C)),
file('SET621+3.p',unknown),
[] ).
cnf(26,plain,
union(difference(A,B),difference(C,B)) = difference(union(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.1')] ).
cnf(33,plain,
difference(A,union(B,C)) = difference(difference(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24])]),
[iquote('copy,24,flip.1')] ).
cnf(130,plain,
union(difference(dollar_c3,union(dollar_c2,dollar_c1)),difference(difference(dollar_c2,dollar_c3),dollar_c1)) != difference(symmetric_difference(dollar_c3,dollar_c2),dollar_c1),
inference(para_from,[status(thm),theory(equality)],[33,16]),
[iquote('para_from,33.1.1,16.1.1.2')] ).
cnf(140,plain,
union(difference(A,union(B,C)),difference(D,C)) = difference(union(difference(A,B),D),C),
inference(para_into,[status(thm),theory(equality)],[26,24]),
[iquote('para_into,26.1.1.1,24.1.1')] ).
cnf(151,plain,
difference(symmetric_difference(dollar_c3,dollar_c2),dollar_c1) != difference(symmetric_difference(dollar_c3,dollar_c2),dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[130]),140,23]),
[iquote('back_demod,130,demod,140,23')] ).
cnf(152,plain,
$false,
inference(binary,[status(thm)],[151,20]),
[iquote('binary,151.1,20.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:24:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.92 ----- Otter 3.3f, August 2004 -----
% 1.71/1.92 The process was started by sandbox2 on n009.cluster.edu,
% 1.71/1.92 Wed Jul 27 10:24:51 2022
% 1.71/1.92 The command was "./otter". The process ID is 10951.
% 1.71/1.92
% 1.71/1.92 set(prolog_style_variables).
% 1.71/1.92 set(auto).
% 1.71/1.92 dependent: set(auto1).
% 1.71/1.92 dependent: set(process_input).
% 1.71/1.92 dependent: clear(print_kept).
% 1.71/1.92 dependent: clear(print_new_demod).
% 1.71/1.92 dependent: clear(print_back_demod).
% 1.71/1.92 dependent: clear(print_back_sub).
% 1.71/1.92 dependent: set(control_memory).
% 1.71/1.92 dependent: assign(max_mem, 12000).
% 1.71/1.92 dependent: assign(pick_given_ratio, 4).
% 1.71/1.92 dependent: assign(stats_level, 1).
% 1.71/1.92 dependent: assign(max_seconds, 10800).
% 1.71/1.92 clear(print_given).
% 1.71/1.92
% 1.71/1.92 formula_list(usable).
% 1.71/1.92 all A (A=A).
% 1.71/1.92 all B C (symmetric_difference(B,C)=union(difference(B,C),difference(C,B))).
% 1.71/1.92 all B C D (difference(difference(B,C),D)=difference(B,union(C,D))).
% 1.71/1.92 all B C D (difference(union(B,C),D)=union(difference(B,D),difference(C,D))).
% 1.71/1.92 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.71/1.92 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.71/1.92 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.71/1.92 all B C (union(B,C)=union(C,B)).
% 1.71/1.92 all B C (symmetric_difference(B,C)=symmetric_difference(C,B)).
% 1.71/1.92 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.71/1.92 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.71/1.92 all B subset(B,B).
% 1.71/1.92 -(all B C D (difference(symmetric_difference(B,C),D)=union(difference(B,union(C,D)),difference(C,union(B,D))))).
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 -------> usable clausifies to:
% 1.71/1.92
% 1.71/1.92 list(usable).
% 1.71/1.92 0 [] A=A.
% 1.71/1.92 0 [] symmetric_difference(B,C)=union(difference(B,C),difference(C,B)).
% 1.71/1.92 0 [] difference(difference(B,C),D)=difference(B,union(C,D)).
% 1.71/1.92 0 [] difference(union(B,C),D)=union(difference(B,D),difference(C,D)).
% 1.71/1.92 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.71/1.92 0 [] member(D,union(B,C))| -member(D,B).
% 1.71/1.92 0 [] member(D,union(B,C))| -member(D,C).
% 1.71/1.92 0 [] -member(D,difference(B,C))|member(D,B).
% 1.71/1.92 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.71/1.92 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.71/1.92 0 [] B!=C|subset(B,C).
% 1.71/1.92 0 [] B!=C|subset(C,B).
% 1.71/1.92 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.71/1.92 0 [] union(B,C)=union(C,B).
% 1.71/1.92 0 [] symmetric_difference(B,C)=symmetric_difference(C,B).
% 1.71/1.92 0 [] B!=C| -member(D,B)|member(D,C).
% 1.71/1.92 0 [] B!=C|member(D,B)| -member(D,C).
% 1.71/1.92 0 [] B=C|member($f1(B,C),B)|member($f1(B,C),C).
% 1.71/1.92 0 [] B=C| -member($f1(B,C),B)| -member($f1(B,C),C).
% 1.71/1.92 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.71/1.92 0 [] subset(B,C)|member($f2(B,C),B).
% 1.71/1.92 0 [] subset(B,C)| -member($f2(B,C),C).
% 1.71/1.92 0 [] subset(B,B).
% 1.71/1.92 0 [] difference(symmetric_difference($c3,$c2),$c1)!=union(difference($c3,union($c2,$c1)),difference($c2,union($c3,$c1))).
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.71/1.92
% 1.71/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.92 deletion, with positive clauses in sos and nonpositive
% 1.71/1.92 clauses in usable.
% 1.71/1.92
% 1.71/1.92 dependent: set(knuth_bendix).
% 1.71/1.92 dependent: set(anl_eq).
% 1.71/1.92 dependent: set(para_from).
% 1.71/1.92 dependent: set(para_into).
% 1.71/1.92 dependent: clear(para_from_right).
% 1.71/1.92 dependent: clear(para_into_right).
% 1.71/1.92 dependent: set(para_from_vars).
% 1.71/1.92 dependent: set(eq_units_both_ways).
% 1.71/1.92 dependent: set(dynamic_demod_all).
% 1.71/1.92 dependent: set(dynamic_demod).
% 1.71/1.92 dependent: set(order_eq).
% 1.71/1.92 dependent: set(back_demod).
% 1.71/1.92 dependent: set(lrpo).
% 1.71/1.92 dependent: set(hyper_res).
% 1.71/1.92 dependent: set(unit_deletion).
% 1.71/1.92 dependent: set(factor).
% 1.71/1.92
% 1.71/1.92 ------------> process usable:
% 1.71/1.92 ** KEPT (pick-wt=11): 1 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.71/1.92 ** KEPT (pick-wt=8): 2 [] member(A,union(B,C))| -member(A,B).
% 1.71/1.92 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,C).
% 1.71/1.92 ** KEPT (pick-wt=8): 4 [] -member(A,difference(B,C))|member(A,B).
% 1.71/1.92 ** KEPT (pick-wt=8): 5 [] -member(A,difference(B,C))| -member(A,C).
% 1.71/1.92 ** KEPT (pick-wt=11): 6 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.71/1.92 ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.71/1.92 ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.71/1.92 ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.71/1.92 ** KEPT (pick-wt=9): 10 [] A!=B| -member(C,A)|member(C,B).
% 1.71/1.92 ** KEPT (pick-wt=9): 11 [] A!=B|member(C,A)| -member(C,B).
% 1.71/1.92 ** KEPT (pick-wt=13): 12 [] A=B| -member($f1(A,B),A)| -member($f1(A,B),B).
% 1.71/1.92 ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.71/1.92 ** KEPT (pick-wt=8): 14 [] subset(A,B)| -member($f2(A,B),B).
% 1.71/1.92 ** KEPT (pick-wt=17): 16 [copy,15,flip.1] union(difference($c3,union($c2,$c1)),difference($c2,union($c3,$c1)))!=difference(symmetric_difference($c3,$c2),$c1).
% 1.71/1.92
% 1.71/1.92 ------------> process sos:
% 1.71/1.92 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.71/1.92 ** KEPT (pick-wt=11): 22 [copy,21,flip.1] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.71/1.92 ---> New Demodulator: 23 [new_demod,22] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.71/1.92 ** KEPT (pick-wt=11): 24 [] difference(difference(A,B),C)=difference(A,union(B,C)).
% 1.71/1.92 ** KEPT (pick-wt=13): 26 [copy,25,flip.1] union(difference(A,B),difference(C,B))=difference(union(A,C),B).
% 1.71/1.92 ---> New Demodulator: 27 [new_demod,26] union(difference(A,B),difference(C,B))=difference(union(A,C),B).
% 1.71/1.92 ** KEPT (pick-wt=7): 28 [] union(A,B)=union(B,A).
% 1.71/1.92 ** KEPT (pick-wt=7): 29 [] symmetric_difference(A,B)=symmetric_difference(B,A).
% 1.71/1.92 ** KEPT (pick-wt=13): 30 [] A=B|member($f1(A,B),A)|member($f1(A,B),B).
% 1.71/1.92 ** KEPT (pick-wt=8): 31 [] subset(A,B)|member($f2(A,B),A).
% 1.71/1.92 ** KEPT (pick-wt=3): 32 [] subset(A,A).
% 1.71/1.92 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 1.71/1.92 20 back subsumes 19.
% 1.71/1.92 20 back subsumes 18.
% 1.71/1.92 >>>> Starting back demodulation with 23.
% 1.71/1.92 ** KEPT (pick-wt=11): 33 [copy,24,flip.1] difference(A,union(B,C))=difference(difference(A,B),C).
% 1.71/1.92 >>>> Starting back demodulation with 27.
% 1.71/1.92 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] union(A,B)=union(B,A).
% 1.71/1.92 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] symmetric_difference(A,B)=symmetric_difference(B,A).
% 1.71/1.92 Following clause subsumed by 24 during input processing: 0 [copy,33,flip.1] difference(difference(A,B),C)=difference(A,union(B,C)).
% 1.71/1.92
% 1.71/1.92 ======= end of input processing =======
% 1.71/1.92
% 1.71/1.92 =========== start of search ===========
% 1.71/1.92
% 1.71/1.92 -------- PROOF --------
% 1.71/1.92
% 1.71/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 152 [binary,151.1,20.1] $F.
% 1.71/1.92
% 1.71/1.92 Length of proof is 7. Level of proof is 3.
% 1.71/1.92
% 1.71/1.92 ---------------- PROOF ----------------
% 1.71/1.92 % SZS status Theorem
% 1.71/1.92 % SZS output start Refutation
% See solution above
% 1.71/1.92 ------------ end of proof -------------
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92 ============ end of search ============
% 1.71/1.92
% 1.71/1.92 -------------- statistics -------------
% 1.71/1.92 clauses given 16
% 1.71/1.92 clauses generated 236
% 1.71/1.92 clauses kept 138
% 1.71/1.92 clauses forward subsumed 135
% 1.71/1.92 clauses back subsumed 2
% 1.71/1.92 Kbytes malloced 1953
% 1.71/1.92
% 1.71/1.92 ----------- times (seconds) -----------
% 1.71/1.92 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.92
% 1.71/1.92 That finishes the proof of the theorem.
% 1.71/1.92
% 1.71/1.92 Process 10951 finished Wed Jul 27 10:24:52 2022
% 1.71/1.92 Otter interrupted
% 1.71/1.92 PROOF FOUND
%------------------------------------------------------------------------------