%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET617+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 1.74s 1.91s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 12 unt; 0 nHn; 3 RR)
% Number of literals : 14 ( 13 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(11,axiom,
( symmetric_difference(dollar_c1,empty_set) != dollar_c1
| symmetric_difference(empty_set,dollar_c1) != dollar_c1 ),
file('SET617+3.p',unknown),
[] ).
cnf(14,axiom,
A = A,
file('SET617+3.p',unknown),
[] ).
cnf(15,axiom,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
file('SET617+3.p',unknown),
[] ).
cnf(16,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(19,axiom,
union(A,empty_set) = A,
file('SET617+3.p',unknown),
[] ).
cnf(21,axiom,
difference(A,empty_set) = A,
file('SET617+3.p',unknown),
[] ).
cnf(23,axiom,
difference(empty_set,A) = empty_set,
file('SET617+3.p',unknown),
[] ).
cnf(24,axiom,
union(A,B) = union(B,A),
file('SET617+3.p',unknown),
[] ).
cnf(35,plain,
union(empty_set,A) = symmetric_difference(empty_set,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,23]),21]),
[iquote('para_into,16.1.1.1,22.1.1,demod,21')] ).
cnf(37,plain,
symmetric_difference(A,empty_set) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,21]),23,19])]),
[iquote('para_into,16.1.1.1,20.1.1,demod,23,19,flip.1')] ).
cnf(42,plain,
symmetric_difference(empty_set,dollar_c1) != dollar_c1,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),37]),14]),
[iquote('back_demod,11,demod,37,unit_del,14')] ).
cnf(52,plain,
symmetric_difference(empty_set,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,19]),35])]),
[iquote('para_into,24.1.1,18.1.1,demod,35,flip.1')] ).
cnf(54,plain,
$false,
inference(binary,[status(thm)],[52,42]),
[iquote('binary,52.1,42.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET617+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:44:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.70/1.91 ----- Otter 3.3f, August 2004 -----
% 1.70/1.91 The process was started by sandbox on n028.cluster.edu,
% 1.70/1.91 Wed Jul 27 10:44:49 2022
% 1.70/1.91 The command was "./otter". The process ID is 29866.
% 1.70/1.91
% 1.70/1.91 set(prolog_style_variables).
% 1.70/1.91 set(auto).
% 1.70/1.91 dependent: set(auto1).
% 1.70/1.91 dependent: set(process_input).
% 1.70/1.91 dependent: clear(print_kept).
% 1.70/1.91 dependent: clear(print_new_demod).
% 1.70/1.91 dependent: clear(print_back_demod).
% 1.70/1.91 dependent: clear(print_back_sub).
% 1.70/1.91 dependent: set(control_memory).
% 1.70/1.91 dependent: assign(max_mem, 12000).
% 1.70/1.91 dependent: assign(pick_given_ratio, 4).
% 1.70/1.91 dependent: assign(stats_level, 1).
% 1.70/1.91 dependent: assign(max_seconds, 10800).
% 1.70/1.91 clear(print_given).
% 1.70/1.91
% 1.70/1.91 formula_list(usable).
% 1.70/1.91 all A (A=A).
% 1.70/1.91 all B C (symmetric_difference(B,C)=union(difference(B,C),difference(C,B))).
% 1.70/1.91 all B (union(B,empty_set)=B).
% 1.70/1.91 all B (difference(B,empty_set)=B).
% 1.70/1.91 all B (difference(empty_set,B)=empty_set).
% 1.70/1.91 all B (-member(B,empty_set)).
% 1.70/1.91 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.70/1.91 all B C (union(B,C)=union(C,B)).
% 1.70/1.91 all B C (symmetric_difference(B,C)=symmetric_difference(C,B)).
% 1.70/1.91 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.70/1.91 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.70/1.91 all B subset(B,B).
% 1.70/1.91 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.70/1.91 -(all B (symmetric_difference(B,empty_set)=B&symmetric_difference(empty_set,B)=B)).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 -------> usable clausifies to:
% 1.70/1.91
% 1.70/1.91 list(usable).
% 1.70/1.91 0 [] A=A.
% 1.70/1.91 0 [] symmetric_difference(B,C)=union(difference(B,C),difference(C,B)).
% 1.70/1.91 0 [] union(B,empty_set)=B.
% 1.70/1.91 0 [] difference(B,empty_set)=B.
% 1.70/1.91 0 [] difference(empty_set,B)=empty_set.
% 1.70/1.91 0 [] -member(B,empty_set).
% 1.70/1.91 0 [] B!=C|subset(B,C).
% 1.70/1.91 0 [] B!=C|subset(C,B).
% 1.70/1.91 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.70/1.91 0 [] union(B,C)=union(C,B).
% 1.70/1.91 0 [] symmetric_difference(B,C)=symmetric_difference(C,B).
% 1.70/1.91 0 [] B!=C| -member(D,B)|member(D,C).
% 1.70/1.91 0 [] B!=C|member(D,B)| -member(D,C).
% 1.70/1.91 0 [] B=C|member($f1(B,C),B)|member($f1(B,C),C).
% 1.70/1.91 0 [] B=C| -member($f1(B,C),B)| -member($f1(B,C),C).
% 1.70/1.91 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.70/1.91 0 [] subset(B,C)|member($f2(B,C),B).
% 1.70/1.91 0 [] subset(B,C)| -member($f2(B,C),C).
% 1.70/1.91 0 [] subset(B,B).
% 1.70/1.91 0 [] -empty(B)| -member(C,B).
% 1.70/1.91 0 [] empty(B)|member($f3(B),B).
% 1.70/1.91 0 [] symmetric_difference($c1,empty_set)!=$c1|symmetric_difference(empty_set,$c1)!=$c1.
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.70/1.91
% 1.70/1.91 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.91 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.91 deletion, with positive clauses in sos and nonpositive
% 1.70/1.91 clauses in usable.
% 1.70/1.91
% 1.70/1.91 dependent: set(knuth_bendix).
% 1.70/1.91 dependent: set(anl_eq).
% 1.70/1.91 dependent: set(para_from).
% 1.70/1.91 dependent: set(para_into).
% 1.70/1.91 dependent: clear(para_from_right).
% 1.70/1.91 dependent: clear(para_into_right).
% 1.70/1.91 dependent: set(para_from_vars).
% 1.70/1.91 dependent: set(eq_units_both_ways).
% 1.70/1.91 dependent: set(dynamic_demod_all).
% 1.70/1.91 dependent: set(dynamic_demod).
% 1.70/1.91 dependent: set(order_eq).
% 1.70/1.91 dependent: set(back_demod).
% 1.70/1.91 dependent: set(lrpo).
% 1.70/1.91 dependent: set(hyper_res).
% 1.70/1.91 dependent: set(unit_deletion).
% 1.70/1.91 dependent: set(factor).
% 1.70/1.91
% 1.70/1.91 ------------> process usable:
% 1.70/1.91 ** KEPT (pick-wt=3): 1 [] -member(A,empty_set).
% 1.70/1.91 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.70/1.91 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.70/1.91 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.70/1.91 ** KEPT (pick-wt=9): 5 [] A!=B| -member(C,A)|member(C,B).
% 1.70/1.91 ** KEPT (pick-wt=9): 6 [] A!=B|member(C,A)| -member(C,B).
% 1.70/1.91 ** KEPT (pick-wt=13): 7 [] A=B| -member($f1(A,B),A)| -member($f1(A,B),B).
% 1.70/1.91 ** KEPT (pick-wt=9): 8 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.70/1.91 ** KEPT (pick-wt=8): 9 [] subset(A,B)| -member($f2(A,B),B).
% 1.70/1.91 ** KEPT (pick-wt=5): 10 [] -empty(A)| -member(B,A).
% 1.70/1.91 ** KEPT (pick-wt=10): 11 [] symmetric_difference($c1,empty_set)!=$c1|symmetric_difference(empty_set,$c1)!=$c1.
% 1.70/1.91
% 1.70/1.91 ------------> process sos:
% 1.70/1.91 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.70/1.91 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.70/1.91 ---> New Demodulator: 17 [new_demod,16] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 1.70/1.91 ** KEPT (pick-wt=5): 18 [] union(A,empty_set)=A.
% 1.70/1.91 ---> New Demodulator: 19 [new_demod,18] union(A,empty_set)=A.
% 1.70/1.91 ** KEPT (pick-wt=5): 20 [] difference(A,empty_set)=A.
% 1.70/1.91 ---> New Demodulator: 21 [new_demod,20] difference(A,empty_set)=A.
% 1.70/1.91 ** KEPT (pick-wt=5): 22 [] difference(empty_set,A)=empty_set.
% 1.70/1.91 ---> New Demodulator: 23 [new_demod,22] difference(empty_set,A)=empty_set.
% 1.70/1.91 ** KEPT (pick-wt=7): 24 [] union(A,B)=union(B,A).
% 1.70/1.91 ** KEPT (pick-wt=7): 25 [] symmetric_difference(A,B)=symmetric_difference(B,A).
% 1.70/1.91 ** KEPT (pick-wt=13): 26 [] A=B|member($f1(A,B),A)|member($f1(A,B),B).
% 1.70/1.91 ** KEPT (pick-wt=8): 27 [] subset(A,B)|member($f2(A,B),A).
% 1.70/1.91 ** KEPT (pick-wt=3): 28 [] subset(A,A).
% 1.70/1.91 ** KEPT (pick-wt=6): 29 [] empty(A)|member($f3(A),A).
% 1.70/1.91 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.70/1.91 14 back subsumes 13.
% 1.70/1.91 14 back subsumes 12.
% 1.70/1.91 >>>> Starting back demodulation with 17.
% 1.70/1.91 >>>> Starting back demodulation with 19.
% 1.70/1.91 >>>> Starting back demodulation with 21.
% 1.70/1.91 >>>> Starting back demodulation with 23.
% 1.70/1.91 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] union(A,B)=union(B,A).
% 1.70/1.91 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] symmetric_difference(A,B)=symmetric_difference(B,A).
% 1.74/1.91
% 1.74/1.91 ======= end of input processing =======
% 1.74/1.91
% 1.74/1.91 =========== start of search ===========
% 1.74/1.91
% 1.74/1.91 -------- PROOF --------
% 1.74/1.91
% 1.74/1.91 ----> UNIT CONFLICT at 0.00 sec ----> 54 [binary,52.1,42.1] $F.
% 1.74/1.91
% 1.74/1.91 Length of proof is 5. Level of proof is 3.
% 1.74/1.91
% 1.74/1.91 ---------------- PROOF ----------------
% 1.74/1.91 % SZS status Theorem
% 1.74/1.91 % SZS output start Refutation
% See solution above
% 1.74/1.91 ------------ end of proof -------------
% 1.74/1.91
% 1.74/1.91
% 1.74/1.91 Search stopped by max_proofs option.
% 1.74/1.91
% 1.74/1.91
% 1.74/1.91 Search stopped by max_proofs option.
% 1.74/1.91
% 1.74/1.91 ============ end of search ============
% 1.74/1.91
% 1.74/1.91 -------------- statistics -------------
% 1.74/1.91 clauses given 10
% 1.74/1.91 clauses generated 83
% 1.74/1.91 clauses kept 45
% 1.74/1.91 clauses forward subsumed 64
% 1.74/1.91 clauses back subsumed 2
% 1.74/1.91 Kbytes malloced 976
% 1.74/1.91
% 1.74/1.91 ----------- times (seconds) -----------
% 1.74/1.91 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.91
% 1.74/1.91 That finishes the proof of the theorem.
% 1.74/1.91
% 1.74/1.91 Process 29866 finished Wed Jul 27 10:44:50 2022
% 1.74/1.91 Otter interrupted
% 1.74/1.91 PROOF FOUND
%------------------------------------------------------------------------------