%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 1.96s 2.14s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 9 equ; 3 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
difference(dollar_c3,symmetric_difference(dollar_c2,dollar_c1)) != union(difference(dollar_c3,union(dollar_c2,dollar_c1)),intersection(intersection(dollar_c3,dollar_c2),dollar_c1)),
file('SET622+3.p',unknown),
[] ).
cnf(19,plain,
union(difference(dollar_c3,union(dollar_c2,dollar_c1)),intersection(intersection(dollar_c3,dollar_c2),dollar_c1)) != difference(dollar_c3,symmetric_difference(dollar_c2,dollar_c1)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18])]),
[iquote('copy,18,flip.1')] ).
cnf(24,axiom,
A = A,
file('SET622+3.p',unknown),
[] ).
cnf(26,axiom,
intersection(intersection(A,B),C) = intersection(A,intersection(B,C)),
file('SET622+3.p',unknown),
[] ).
cnf(27,axiom,
difference(A,difference(B,C)) = union(difference(A,B),intersection(A,C)),
file('SET622+3.p',unknown),
[] ).
cnf(29,plain,
union(difference(A,B),intersection(A,C)) = difference(A,difference(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])]),
[iquote('copy,27,flip.1')] ).
cnf(30,axiom,
symmetric_difference(A,B) = difference(union(A,B),intersection(A,B)),
file('SET622+3.p',unknown),
[] ).
cnf(32,plain,
difference(union(A,B),intersection(A,B)) = symmetric_difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[30])]),
[iquote('copy,30,flip.1')] ).
cnf(42,plain,
difference(dollar_c3,symmetric_difference(dollar_c2,dollar_c1)) != difference(dollar_c3,symmetric_difference(dollar_c2,dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),26,29,32]),
[iquote('back_demod,19,demod,26,29,32')] ).
cnf(43,plain,
$false,
inference(binary,[status(thm)],[42,24]),
[iquote('binary,42.1,24.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 10:39:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.14 ----- Otter 3.3f, August 2004 -----
% 1.96/2.14 The process was started by sandbox2 on n025.cluster.edu,
% 1.96/2.14 Wed Jul 27 10:39:30 2022
% 1.96/2.14 The command was "./otter". The process ID is 26984.
% 1.96/2.14
% 1.96/2.14 set(prolog_style_variables).
% 1.96/2.14 set(auto).
% 1.96/2.14 dependent: set(auto1).
% 1.96/2.14 dependent: set(process_input).
% 1.96/2.14 dependent: clear(print_kept).
% 1.96/2.14 dependent: clear(print_new_demod).
% 1.96/2.14 dependent: clear(print_back_demod).
% 1.96/2.14 dependent: clear(print_back_sub).
% 1.96/2.14 dependent: set(control_memory).
% 1.96/2.14 dependent: assign(max_mem, 12000).
% 1.96/2.14 dependent: assign(pick_given_ratio, 4).
% 1.96/2.14 dependent: assign(stats_level, 1).
% 1.96/2.14 dependent: assign(max_seconds, 10800).
% 1.96/2.14 clear(print_given).
% 1.96/2.14
% 1.96/2.14 formula_list(usable).
% 1.96/2.14 all A (A=A).
% 1.96/2.14 all B C D (intersection(intersection(B,C),D)=intersection(B,intersection(C,D))).
% 1.96/2.14 all B C D (difference(B,difference(C,D))=union(difference(B,C),intersection(B,D))).
% 1.96/2.14 all B C (symmetric_difference(B,C)=difference(union(B,C),intersection(B,C))).
% 1.96/2.14 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.96/2.14 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.96/2.14 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.96/2.14 all B C (symmetric_difference(B,C)=union(difference(B,C),difference(C,B))).
% 1.96/2.14 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.96/2.14 all B C (union(B,C)=union(C,B)).
% 1.96/2.14 all B C (intersection(B,C)=intersection(C,B)).
% 1.96/2.14 all B C (symmetric_difference(B,C)=symmetric_difference(C,B)).
% 1.96/2.14 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.96/2.14 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.96/2.14 all B subset(B,B).
% 1.96/2.14 -(all B C D (difference(B,symmetric_difference(C,D))=union(difference(B,union(C,D)),intersection(intersection(B,C),D)))).
% 1.96/2.14 end_of_list.
% 1.96/2.14
% 1.96/2.14 -------> usable clausifies to:
% 1.96/2.14
% 1.96/2.14 list(usable).
% 1.96/2.14 0 [] A=A.
% 1.96/2.14 0 [] intersection(intersection(B,C),D)=intersection(B,intersection(C,D)).
% 1.96/2.14 0 [] difference(B,difference(C,D))=union(difference(B,C),intersection(B,D)).
% 1.96/2.14 0 [] symmetric_difference(B,C)=difference(union(B,C),intersection(B,C)).
% 1.96/2.14 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.96/2.14 0 [] member(D,union(B,C))| -member(D,B).
% 1.96/2.14 0 [] member(D,union(B,C))| -member(D,C).
% 1.96/2.14 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.96/2.14 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.96/2.14 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.96/2.14 0 [] -member(D,difference(B,C))|member(D,B).
% 1.96/2.14 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.96/2.14 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.96/2.14 0 [] symmetric_difference(B,C)=union(difference(B,C),difference(C,B)).
% 1.96/2.14 0 [] B!=C|subset(B,C).
% 1.96/2.14 0 [] B!=C|subset(C,B).
% 1.96/2.14 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.96/2.14 0 [] union(B,C)=union(C,B).
% 1.96/2.14 0 [] intersection(B,C)=intersection(C,B).
% 1.96/2.14 0 [] symmetric_difference(B,C)=symmetric_difference(C,B).
% 1.96/2.14 0 [] B!=C| -member(D,B)|member(D,C).
% 1.96/2.14 0 [] B!=C|member(D,B)| -member(D,C).
% 1.96/2.14 0 [] B=C|member($f1(B,C),B)|member($f1(B,C),C).
% 1.96/2.14 0 [] B=C| -member($f1(B,C),B)| -member($f1(B,C),C).
% 1.96/2.14 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.96/2.14 0 [] subset(B,C)|member($f2(B,C),B).
% 1.96/2.14 0 [] subset(B,C)| -member($f2(B,C),C).
% 1.96/2.14 0 [] subset(B,B).
% 1.96/2.14 0 [] difference($c3,symmetric_difference($c2,$c1))!=union(difference($c3,union($c2,$c1)),intersection(intersection($c3,$c2),$c1)).
% 1.96/2.14 end_of_list.
% 1.96/2.14
% 1.96/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.96/2.14
% 1.96/2.14 This ia a non-Horn set with equality. The strategy will be
% 1.96/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.96/2.14 deletion, with positive clauses in sos and nonpositive
% 1.96/2.14 clauses in usable.
% 1.96/2.14
% 1.96/2.14 dependent: set(knuth_bendix).
% 1.96/2.14 dependent: set(anl_eq).
% 1.96/2.14 dependent: set(para_from).
% 1.96/2.14 dependent: set(para_into).
% 1.96/2.14 dependent: clear(para_from_right).
% 1.96/2.14 dependent: clear(para_into_right).
% 1.96/2.14 dependent: set(para_from_vars).
% 1.96/2.14 dependent: set(eq_units_both_ways).
% 1.96/2.14 dependent: set(dynamic_demod_all).
% 1.96/2.14 dependent: set(dynamic_demod).
% 1.96/2.14 dependent: set(order_eq).
% 1.96/2.14 dependent: set(back_demod).
% 1.96/2.14 dependent: set(lrpo).
% 1.96/2.14 dependent: set(hyper_res).
% 1.96/2.14 dependent: set(unit_deletion).
% 1.96/2.14 dependent: set(factor).
% 1.96/2.14
% 1.96/2.14 ------------> process usable:
% 1.96/2.14 ** KEPT (pick-wt=11): 1 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.96/2.14 ** KEPT (pick-wt=8): 2 [] member(A,union(B,C))| -member(A,B).
% 1.96/2.14 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,C
% 1.96/2.14 -------- PROOF --------
% 1.96/2.14 ).
% 1.96/2.14 ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,B).
% 1.96/2.14 ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,C).
% 1.96/2.14 ** KEPT (pick-wt=11): 6 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.96/2.14 ** KEPT (pick-wt=8): 7 [] -member(A,difference(B,C))|member(A,B).
% 1.96/2.14 ** KEPT (pick-wt=8): 8 [] -member(A,difference(B,C))| -member(A,C).
% 1.96/2.14 ** KEPT (pick-wt=11): 9 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.96/2.14 ** KEPT (pick-wt=6): 10 [] A!=B|subset(A,B).
% 1.96/2.14 ** KEPT (pick-wt=6): 11 [] A!=B|subset(B,A).
% 1.96/2.14 ** KEPT (pick-wt=9): 12 [] A=B| -subset(A,B)| -subset(B,A).
% 1.96/2.14 ** KEPT (pick-wt=9): 13 [] A!=B| -member(C,A)|member(C,B).
% 1.96/2.14 ** KEPT (pick-wt=9): 14 [] A!=B|member(C,A)| -member(C,B).
% 1.96/2.14 ** KEPT (pick-wt=13): 15 [] A=B| -member($f1(A,B),A)| -member($f1(A,B),B).
% 1.96/2.14 ** KEPT (pick-wt=9): 16 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.96/2.14 ** KEPT (pick-wt=8): 17 [] subset(A,B)| -member($f2(A,B),B).
% 1.96/2.14 ** KEPT (pick-wt=17): 19 [copy,18,flip.1] union(difference($c3,union($c2,$c1)),intersection(intersection($c3,$c2),$c1))!=difference($c3,symmetric_difference($c2,$c1)).
% 1.96/2.14
% 1.96/2.14 ------------> process sos:
% 1.96/2.14 ** KEPT (pick-wt=3): 24 [] A=A.
% 1.96/2.14 ** KEPT (pick-wt=11): 25 [] intersection(intersection(A,B),C)=intersection(A,intersection(B,C)).
% 1.96/2.14 ---> New Demodulator: 26 [new_demod,25] intersection(intersection(A,B),C)=intersection(A,intersection(B,C)).
% 1.96/2.14 ** KEPT (pick-wt=13): 28 [copy,27,flip.1] union(difference(A,B),intersection(A,C))=difference(A,difference(B,C)).
% 1.96/2.14 ---> New Demodulator: 29 [new_demod,28] union(difference(A,B),intersection(A,C))=difference(A,difference(B,C)).
% 1.96/2.14 ** KEPT (pick-wt=11): 31 [copy,30,flip.1] difference(union(A,B),intersection(A,B))=symmetric_difference(A,B).
% 1.96/2.14 ---> New Demodulator: 32 [new_demod,31] difference(union(A,B),intersection(A,B))=symmetric_difference(A,B).
% 1.96/2.14 ** KEPT (pick-wt=11): 34 [copy,33,flip.1] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.96/2.14 ---> New Demodulator: 35 [new_demod,34] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.96/2.14 ** KEPT (pick-wt=7): 36 [] union(A,B)=union(B,A).
% 1.96/2.14 ** KEPT (pick-wt=7): 37 [] intersection(A,B)=intersection(B,A).
% 1.96/2.14 ** KEPT (pick-wt=7): 38 [] symmetric_difference(A,B)=symmetric_difference(B,A).
% 1.96/2.14 ** KEPT (pick-wt=13): 39 [] A=B|member($f1(A,B),A)|member($f1(A,B),B).
% 1.96/2.14 ** KEPT (pick-wt=8): 40 [] subset(A,B)|member($f2(A,B),A).
% 1.96/2.14 ** KEPT (pick-wt=3): 41 [] subset(A,A).
% 1.96/2.14 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] A=A.
% 1.96/2.14 24 back subsumes 23.
% 1.96/2.14 24 back subsumes 22.
% 1.96/2.14 >>>> Starting back demodulation with 26.
% 1.96/2.14 >> back demodulating 19 with 26.
% 1.96/2.14
% 1.96/2.14 ----> UNIT CONFLICT at 0.00 sec ----> 43 [binary,42.1,24.1] $F.
% 1.96/2.14
% 1.96/2.14 Length of proof is 4. Level of proof is 2.
% 1.96/2.14
% 1.96/2.14 ---------------- PROOF ----------------
% 1.96/2.14 % SZS status Theorem
% 1.96/2.14 % SZS output start Refutation
% See solution above
% 1.96/2.14 ------------ end of proof -------------
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14 Search stopped by max_proofs option.
% 1.96/2.14
% 1.96/2.14
% 1.96/2.14 Search stopped by max_proofs option.
% 1.96/2.14
% 1.96/2.14 ============ end of search ============
% 1.96/2.14
% 1.96/2.14 -------------- statistics -------------
% 1.96/2.14 clauses given 0
% 1.96/2.14 clauses generated 4
% 1.96/2.14 clauses kept 34
% 1.96/2.14 clauses forward subsumed 1
% 1.96/2.14 clauses back subsumed 2
% 1.96/2.14 Kbytes malloced 976
% 1.96/2.14
% 1.96/2.14 ----------- times (seconds) -----------
% 1.96/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.14
% 1.96/2.14 That finishes the proof of the theorem.
% 1.96/2.14
% 1.96/2.14 Process 26984 finished Wed Jul 27 10:39:32 2022
% 1.96/2.14 Otter interrupted
% 1.96/2.14 PROOF FOUND
%------------------------------------------------------------------------------