%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : REL014+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:11:49 EDT 2022
% Result : Theorem 2.00s 2.19s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 12 unt; 0 nHn; 4 RR)
% Number of literals : 16 ( 15 equ; 5 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( composition(dollar_c1,one) != dollar_c1
| composition(one,dollar_c1) != dollar_c1 ),
file('REL014+1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('REL014+1.p',unknown),
[] ).
cnf(13,axiom,
composition(A,composition(B,C)) = composition(composition(A,B),C),
file('REL014+1.p',unknown),
[] ).
cnf(14,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(17,axiom,
composition(A,one) = A,
file('REL014+1.p',unknown),
[] ).
cnf(22,axiom,
converse(converse(A)) = A,
file('REL014+1.p',unknown),
[] ).
cnf(25,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)),
file('REL014+1.p',unknown),
[] ).
cnf(37,plain,
( dollar_c1 != dollar_c1
| composition(one,dollar_c1) != dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),17]),
[iquote('back_demod,1,demod,17')] ).
cnf(83,plain,
composition(A,composition(one,B)) = composition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,17])]),
[iquote('para_into,14.1.1.1,16.1.1,flip.1')] ).
cnf(166,plain,
composition(converse(one),converse(A)) = converse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,17])]),
[iquote('para_into,25.1.1.1,16.1.1,flip.1')] ).
cnf(173,plain,
composition(converse(one),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[166,22]),22]),
[iquote('para_into,166.1.1.2,21.1.1,demod,22')] ).
cnf(175,plain,
composition(one,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[173,83]),173])]),
[iquote('para_into,172.1.1,83.1.1,demod,173,flip.1')] ).
cnf(178,plain,
dollar_c1 != dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),175]),
[iquote('back_demod,37,demod,175')] ).
cnf(179,plain,
$false,
inference(binary,[status(thm)],[178,2]),
[iquote('binary,178.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL014+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n006.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 10:05:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.00/2.18 ----- Otter 3.3f, August 2004 -----
% 2.00/2.18 The process was started by sandbox on n006.cluster.edu,
% 2.00/2.18 Wed Jul 27 10:05:17 2022
% 2.00/2.18 The command was "./otter". The process ID is 30859.
% 2.00/2.18
% 2.00/2.18 set(prolog_style_variables).
% 2.00/2.18 set(auto).
% 2.00/2.18 dependent: set(auto1).
% 2.00/2.18 dependent: set(process_input).
% 2.00/2.18 dependent: clear(print_kept).
% 2.00/2.18 dependent: clear(print_new_demod).
% 2.00/2.18 dependent: clear(print_back_demod).
% 2.00/2.18 dependent: clear(print_back_sub).
% 2.00/2.18 dependent: set(control_memory).
% 2.00/2.18 dependent: assign(max_mem, 12000).
% 2.00/2.18 dependent: assign(pick_given_ratio, 4).
% 2.00/2.18 dependent: assign(stats_level, 1).
% 2.00/2.18 dependent: assign(max_seconds, 10800).
% 2.00/2.18 clear(print_given).
% 2.00/2.18
% 2.00/2.18 formula_list(usable).
% 2.00/2.18 all A (A=A).
% 2.00/2.18 all X0 X1 (join(X0,X1)=join(X1,X0)).
% 2.00/2.18 all X0 X1 X2 (join(X0,join(X1,X2))=join(join(X0,X1),X2)).
% 2.00/2.18 all X0 X1 (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))).
% 2.00/2.18 all X0 X1 (meet(X0,X1)=complement(join(complement(X0),complement(X1)))).
% 2.00/2.18 all X0 X1 X2 (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2)).
% 2.00/2.18 all X0 (composition(X0,one)=X0).
% 2.00/2.18 all X0 X1 X2 (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2))).
% 2.00/2.18 all X0 (converse(converse(X0))=X0).
% 2.00/2.18 all X0 X1 (converse(join(X0,X1))=join(converse(X0),converse(X1))).
% 2.00/2.18 all X0 X1 (converse(composition(X0,X1))=composition(converse(X1),converse(X0))).
% 2.00/2.18 all X0 X1 (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1)).
% 2.00/2.18 all X0 (top=join(X0,complement(X0))).
% 2.00/2.18 all X0 (zero=meet(X0,complement(X0))).
% 2.00/2.18 -(all X0 (composition(X0,one)=X0&composition(one,X0)=X0)).
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 -------> usable clausifies to:
% 2.00/2.18
% 2.00/2.18 list(usable).
% 2.00/2.18 0 [] A=A.
% 2.00/2.18 0 [] join(X0,X1)=join(X1,X0).
% 2.00/2.18 0 [] join(X0,join(X1,X2))=join(join(X0,X1),X2).
% 2.00/2.18 0 [] X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))).
% 2.00/2.18 0 [] meet(X0,X1)=complement(join(complement(X0),complement(X1))).
% 2.00/2.18 0 [] composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2).
% 2.00/2.18 0 [] composition(X0,one)=X0.
% 2.00/2.18 0 [] composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)).
% 2.00/2.18 0 [] converse(converse(X0))=X0.
% 2.00/2.18 0 [] converse(join(X0,X1))=join(converse(X0),converse(X1)).
% 2.00/2.18 0 [] converse(composition(X0,X1))=composition(converse(X1),converse(X0)).
% 2.00/2.18 0 [] join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1).
% 2.00/2.18 0 [] top=join(X0,complement(X0)).
% 2.00/2.18 0 [] zero=meet(X0,complement(X0)).
% 2.00/2.18 0 [] composition($c1,one)!=$c1|composition(one,$c1)!=$c1.
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 2.00/2.18
% 2.00/2.18 This is a Horn set with equality. The strategy will be
% 2.00/2.18 Knuth-Bendix and hyper_res, with positive clauses in
% 2.00/2.18 sos and nonpositive clauses in usable.
% 2.00/2.18
% 2.00/2.18 dependent: set(knuth_bendix).
% 2.00/2.18 dependent: set(anl_eq).
% 2.00/2.18 dependent: set(para_from).
% 2.00/2.18 dependent: set(para_into).
% 2.00/2.18 dependent: clear(para_from_right).
% 2.00/2.18 dependent: clear(para_into_right).
% 2.00/2.18 dependent: set(para_from_vars).
% 2.00/2.18 dependent: set(eq_units_both_ways).
% 2.00/2.18 dependent: set(dynamic_demod_all).
% 2.00/2.18 dependent: set(dynamic_demod).
% 2.00/2.18 dependent: set(order_eq).
% 2.00/2.18 dependent: set(back_demod).
% 2.00/2.18 dependent: set(lrpo).
% 2.00/2.18 dependent: set(hyper_res).
% 2.00/2.18 dependent: clear(order_hyper).
% 2.00/2.18
% 2.00/2.18 ------------> process usable:
% 2.00/2.18 ** KEPT (pick-wt=10): 1 [] composition($c1,one)!=$c1|composition(one,$c1)!=$c1.
% 2.00/2.18
% 2.00/2.18 ------------> process sos:
% 2.00/2.18 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.00/2.18 ** KEPT (pick-wt=7): 3 [] join(A,B)=join(B,A).
% 2.00/2.18 ** KEPT (pick-wt=11): 5 [copy,4,flip.1] join(join(A,B),C)=join(A,join(B,C)).
% 2.00/2.18 ---> New Demodulator: 6 [new_demod,5] join(join(A,B),C)=join(A,join(B,C)).
% 2.00/2.18 ** KEPT (pick-wt=14): 8 [copy,7,flip.1] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 2.00/2.18 ---> New Demodulator: 9 [new_demod,8] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 2.00/2.18 ** KEPT (pick-wt=10): 11 [copy,10,flip.1] complement(join(complement(A),complement(B)))=meet(A,B).
% 2.00/2.18 ---> New Demodulator: 12 [new_demod,11] complement(join(complement(A),complement(B)))=meet(A,B).
% 2.00/2.18 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 2.00/2.19 ---> New Demodulator: 15 [new_demod,14] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 2.00/2.19 ** KEPT (pick-wt=5): 16 [] composition(A,one)=A.
% 2.00/2.19 ---> New Demodulator: 17 [new_demod,16] composition(A,one)=A.
% 2.00/2.19 ** KEPT (pick-wt=13): 19 [copy,18,flip.1] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 2.00/2.19 ---> New Demodulator: 20 [new_demod,19] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 2.00/2.19 ** KEPT (pick-wt=5): 21 [] converse(converse(A))=A.
% 2.00/2.19 ---> New Demodulator: 22 [new_demod,21] converse(converse(A))=A.
% 2.00/2.19 ** KEPT (pick-wt=10): 23 [] converse(join(A,B))=join(converse(A),converse(B)).
% 2.00/2.19 ---> New Demodulator: 24 [new_demod,23] converse(join(A,B))=join(converse(A),converse(B)).
% 2.00/2.19 ** KEPT (pick-wt=10): 25 [] converse(composition(A,B))=composition(converse(B),converse(A)).
% 2.00/2.19 ---> New Demodulator: 26 [new_demod,25] converse(composition(A,B))=composition(converse(B),converse(A)).
% 2.00/2.19 ** KEPT (pick-wt=13): 27 [] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 2.00/2.19 ---> New Demodulator: 28 [new_demod,27] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 2.00/2.19 ** KEPT (pick-wt=6): 30 [copy,29,flip.1] join(A,complement(A))=top.
% 2.00/2.19 ---> New Demodulator: 31 [new_demod,30] join(A,complement(A))=top.
% 2.00/2.19 ** KEPT (pick-wt=6): 33 [copy,32,flip.1] meet(A,complement(A))=zero.
% 2.00/2.19 ---> New Demodulator: 34 [new_demod,33] meet(A,complement(A))=zero.
% 2.00/2.19 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.00/2.19 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] join(A,B)=join(B,A).
% 2.00/2.19 >>>> Starting back demodulation with 6.
% 2.00/2.19 >>>> Starting back demodulation with 9.
% 2.00/2.19 >>>> Starting back demodulation with 12.
% 2.00/2.19 >> back demodulating 8 with 12.
% 2.00/2.19 >>>> Starting back demodulation with 15.
% 2.00/2.19 >>>> Starting back demodulation with 17.
% 2.00/2.19 >> back demodulating 1 with 17.
% 2.00/2.19 >>>> Starting back demodulation with 20.
% 2.00/2.19 >>>> Starting back demodulation with 22.
% 2.00/2.19 >>>> Starting back demodulation with 24.
% 2.00/2.19 >>>> Starting back demodulation with 26.
% 2.00/2.19 >>>> Starting back demodulation with 28.
% 2.00/2.19 >>>> Starting back demodulation with 31.
% 2.00/2.19 >>>> Starting back demodulation with 34.
% 2.00/2.19 >>>> Starting back demodulation with 36.
% 2.00/2.19
% 2.00/2.19 ======= end of input processing =======
% 2.00/2.19
% 2.00/2.19 =========== start of search ===========
% 2.00/2.19
% 2.00/2.19 -------- PROOF --------
% 2.00/2.19
% 2.00/2.19 ----> UNIT CONFLICT at 0.01 sec ----> 179 [binary,178.1,2.1] $F.
% 2.00/2.19
% 2.00/2.19 Length of proof is 7. Level of proof is 4.
% 2.00/2.19
% 2.00/2.19 ---------------- PROOF ----------------
% 2.00/2.19 % SZS status Theorem
% 2.00/2.19 % SZS output start Refutation
% See solution above
% 2.00/2.19 ------------ end of proof -------------
% 2.00/2.19
% 2.00/2.19
% 2.00/2.19 Search stopped by max_proofs option.
% 2.00/2.19
% 2.00/2.19
% 2.00/2.19 Search stopped by max_proofs option.
% 2.00/2.19
% 2.00/2.19 ============ end of search ============
% 2.00/2.19
% 2.00/2.19 -------------- statistics -------------
% 2.00/2.19 clauses given 33
% 2.00/2.19 clauses generated 211
% 2.00/2.19 clauses kept 91
% 2.00/2.19 clauses forward subsumed 158
% 2.00/2.19 clauses back subsumed 0
% 2.00/2.19 Kbytes malloced 1953
% 2.00/2.19
% 2.00/2.19 ----------- times (seconds) -----------
% 2.00/2.19 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.00/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.19 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.00/2.19
% 2.00/2.19 That finishes the proof of the theorem.
% 2.00/2.19
% 2.00/2.19 Process 30859 finished Wed Jul 27 10:05:18 2022
% 2.00/2.19 Otter interrupted
% 2.00/2.19 PROOF FOUND
%------------------------------------------------------------------------------