TSTP Solution File: REL049+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:11:59 EDT 2022
% Result : Theorem 1.66s 1.87s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 5 RR)
% Number of literals : 8 ( 7 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
join(join(dollar_c3,dollar_c1),dollar_c2) != dollar_c2,
file('REL049+1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('REL049+1.p',unknown),
[] ).
cnf(4,axiom,
join(A,join(B,C)) = join(join(A,B),C),
file('REL049+1.p',unknown),
[] ).
cnf(6,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(36,axiom,
join(dollar_c3,dollar_c2) = dollar_c2,
file('REL049+1.p',unknown),
[] ).
cnf(38,axiom,
join(dollar_c1,dollar_c2) = dollar_c2,
file('REL049+1.p',unknown),
[] ).
cnf(39,plain,
dollar_c2 != dollar_c2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6,38,36]),
[iquote('back_demod,1,demod,6,38,36')] ).
cnf(40,plain,
$false,
inference(binary,[status(thm)],[39,2]),
[iquote('binary,39.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n003.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 10:06:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.66/1.87 ----- Otter 3.3f, August 2004 -----
% 1.66/1.87 The process was started by sandbox on n003.cluster.edu,
% 1.66/1.87 Wed Jul 27 10:06:41 2022
% 1.66/1.87 The command was "./otter". The process ID is 8023.
% 1.66/1.87
% 1.66/1.87 set(prolog_style_variables).
% 1.66/1.87 set(auto).
% 1.66/1.87 dependent: set(auto1).
% 1.66/1.87 dependent: set(process_input).
% 1.66/1.87 dependent: clear(print_kept).
% 1.66/1.87 dependent: clear(print_new_demod).
% 1.66/1.87 dependent: clear(print_back_demod).
% 1.66/1.87 dependent: clear(print_back_sub).
% 1.66/1.87 dependent: set(control_memory).
% 1.66/1.87 dependent: assign(max_mem, 12000).
% 1.66/1.87 dependent: assign(pick_given_ratio, 4).
% 1.66/1.87 dependent: assign(stats_level, 1).
% 1.66/1.87 dependent: assign(max_seconds, 10800).
% 1.66/1.87 clear(print_given).
% 1.66/1.87
% 1.66/1.87 formula_list(usable).
% 1.66/1.87 all A (A=A).
% 1.66/1.87 all X0 X1 (join(X0,X1)=join(X1,X0)).
% 1.66/1.87 all X0 X1 X2 (join(X0,join(X1,X2))=join(join(X0,X1),X2)).
% 1.66/1.87 all X0 X1 (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))).
% 1.66/1.87 all X0 X1 (meet(X0,X1)=complement(join(complement(X0),complement(X1)))).
% 1.66/1.87 all X0 X1 X2 (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2)).
% 1.66/1.87 all X0 (composition(X0,one)=X0).
% 1.66/1.87 all X0 X1 X2 (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2))).
% 1.66/1.87 all X0 (converse(converse(X0))=X0).
% 1.66/1.87 all X0 X1 (converse(join(X0,X1))=join(converse(X0),converse(X1))).
% 1.66/1.87 all X0 X1 (converse(composition(X0,X1))=composition(converse(X1),converse(X0))).
% 1.66/1.87 all X0 X1 (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1)).
% 1.66/1.87 all X0 (top=join(X0,complement(X0))).
% 1.66/1.87 all X0 (zero=meet(X0,complement(X0))).
% 1.66/1.87 -(all X0 X1 X2 (join(X0,X1)=X1&join(X2,X1)=X1->join(join(X0,X2),X1)=X1)).
% 1.66/1.87 end_of_list.
% 1.66/1.87
% 1.66/1.87 -------> usable clausifies to:
% 1.66/1.87
% 1.66/1.87 list(usable).
% 1.66/1.87 0 [] A=A.
% 1.66/1.87 0 [] join(X0,X1)=join(X1,X0).
% 1.66/1.87 0 [] join(X0,join(X1,X2))=join(join(X0,X1),X2).
% 1.66/1.87 0 [] X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))).
% 1.66/1.87 0 [] meet(X0,X1)=complement(join(complement(X0),complement(X1))).
% 1.66/1.87 0 [] composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2).
% 1.66/1.87 0 [] composition(X0,one)=X0.
% 1.66/1.87 0 [] composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)).
% 1.66/1.87 0 [] converse(converse(X0))=X0.
% 1.66/1.87 0 [] converse(join(X0,X1))=join(converse(X0),converse(X1)).
% 1.66/1.87 0 [] converse(composition(X0,X1))=composition(converse(X1),converse(X0)).
% 1.66/1.87 0 [] join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1).
% 1.66/1.87 0 [] top=join(X0,complement(X0)).
% 1.66/1.87 0 [] zero=meet(X0,complement(X0)).
% 1.66/1.87 0 [] join($c3,$c2)=$c2.
% 1.66/1.87 0 [] join($c1,$c2)=$c2.
% 1.66/1.87 0 [] join(join($c3,$c1),$c2)!=$c2.
% 1.66/1.87 end_of_list.
% 1.66/1.87
% 1.66/1.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.87
% 1.66/1.87 All clauses are units, and equality is present; the
% 1.66/1.87 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.87
% 1.66/1.87 dependent: set(knuth_bendix).
% 1.66/1.87 dependent: set(anl_eq).
% 1.66/1.87 dependent: set(para_from).
% 1.66/1.87 dependent: set(para_into).
% 1.66/1.87 dependent: clear(para_from_right).
% 1.66/1.87 dependent: clear(para_into_right).
% 1.66/1.87 dependent: set(para_from_vars).
% 1.66/1.87 dependent: set(eq_units_both_ways).
% 1.66/1.87 dependent: set(dynamic_demod_all).
% 1.66/1.87 dependent: set(dynamic_demod).
% 1.66/1.87 dependent: set(order_eq).
% 1.66/1.87 dependent: set(back_demod).
% 1.66/1.87 dependent: set(lrpo).
% 1.66/1.87
% 1.66/1.87 ------------> process usable:
% 1.66/1.87 ** KEPT (pick-wt=7): 1 [] join(join($c3,$c1),$c2)!=$c2.
% 1.66/1.87
% 1.66/1.87 ------------> process sos:
% 1.66/1.87 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.66/1.87 ** KEPT (pick-wt=7): 3 [] join(A,B)=join(B,A).
% 1.66/1.87 ** KEPT (pick-wt=11): 5 [copy,4,flip.1] join(join(A,B),C)=join(A,join(B,C)).
% 1.66/1.87 ---> New Demodulator: 6 [new_demod,5] join(join(A,B),C)=join(A,join(B,C)).
% 1.66/1.87 ** KEPT (pick-wt=14): 8 [copy,7,flip.1] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.66/1.87 ---> New Demodulator: 9 [new_demod,8] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.66/1.87 ** KEPT (pick-wt=10): 11 [copy,10,flip.1] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.66/1.87 ---> New Demodulator: 12 [new_demod,11] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.66/1.87 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 1.66/1.87 ---> New Demodulator: 15 [new_demod,14] composition(composition(A,B),
% 1.66/1.87 -------- PROOF --------
% 1.66/1.87 C)=composition(A,composition(B,C)).
% 1.66/1.87 ** KEPT (pick-wt=5): 16 [] composition(A,one)=A.
% 1.66/1.87 ---> New Demodulator: 17 [new_demod,16] composition(A,one)=A.
% 1.66/1.87 ** KEPT (pick-wt=13): 19 [copy,18,flip.1] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.66/1.87 ---> New Demodulator: 20 [new_demod,19] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.66/1.87 ** KEPT (pick-wt=5): 21 [] converse(converse(A))=A.
% 1.66/1.87 ---> New Demodulator: 22 [new_demod,21] converse(converse(A))=A.
% 1.66/1.87 ** KEPT (pick-wt=10): 23 [] converse(join(A,B))=join(converse(A),converse(B)).
% 1.66/1.87 ---> New Demodulator: 24 [new_demod,23] converse(join(A,B))=join(converse(A),converse(B)).
% 1.66/1.87 ** KEPT (pick-wt=10): 25 [] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.66/1.87 ---> New Demodulator: 26 [new_demod,25] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.66/1.87 ** KEPT (pick-wt=13): 27 [] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.66/1.87 ---> New Demodulator: 28 [new_demod,27] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.66/1.87 ** KEPT (pick-wt=6): 30 [copy,29,flip.1] join(A,complement(A))=top.
% 1.66/1.87 ---> New Demodulator: 31 [new_demod,30] join(A,complement(A))=top.
% 1.66/1.87 ** KEPT (pick-wt=6): 33 [copy,32,flip.1] meet(A,complement(A))=zero.
% 1.66/1.87 ---> New Demodulator: 34 [new_demod,33] meet(A,complement(A))=zero.
% 1.66/1.87 ** KEPT (pick-wt=5): 35 [] join($c3,$c2)=$c2.
% 1.66/1.87 ---> New Demodulator: 36 [new_demod,35] join($c3,$c2)=$c2.
% 1.66/1.87 ** KEPT (pick-wt=5): 37 [] join($c1,$c2)=$c2.
% 1.66/1.87 ---> New Demodulator: 38 [new_demod,37] join($c1,$c2)=$c2.
% 1.66/1.87 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.66/1.87 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] join(A,B)=join(B,A).
% 1.66/1.87 >>>> Starting back demodulation with 6.
% 1.66/1.87 >> back demodulating 1 with 6.
% 1.66/1.87
% 1.66/1.87 ----> UNIT CONFLICT at 0.00 sec ----> 40 [binary,39.1,2.1] $F.
% 1.66/1.87
% 1.66/1.87 Length of proof is 2. Level of proof is 2.
% 1.66/1.87
% 1.66/1.87 ---------------- PROOF ----------------
% 1.66/1.87 % SZS status Theorem
% 1.66/1.87 % SZS output start Refutation
% See solution above
% 1.66/1.87 ------------ end of proof -------------
% 1.66/1.87
% 1.66/1.87
% 1.66/1.87 Search stopped by max_proofs option.
% 1.66/1.87
% 1.66/1.87
% 1.66/1.87 Search stopped by max_proofs option.
% 1.66/1.87
% 1.66/1.87 ============ end of search ============
% 1.66/1.87
% 1.66/1.87 -------------- statistics -------------
% 1.66/1.87 clauses given 0
% 1.66/1.87 clauses generated 0
% 1.66/1.87 clauses kept 18
% 1.66/1.87 clauses forward subsumed 2
% 1.66/1.87 clauses back subsumed 0
% 1.66/1.87 Kbytes malloced 976
% 1.66/1.87
% 1.66/1.87 ----------- times (seconds) -----------
% 1.66/1.87 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.87 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.87
% 1.66/1.87 That finishes the proof of the theorem.
% 1.66/1.87
% 1.66/1.87 Process 8023 finished Wed Jul 27 10:06:43 2022
% 1.66/1.87 Otter interrupted
% 1.66/1.87 PROOF FOUND
%------------------------------------------------------------------------------