TSTP Solution File: LCL139-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL139-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 13:03:40 EDT 2022
% Result : Unsatisfiable 1.64s 1.88s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 5 RR)
% Number of literals : 32 ( 31 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 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 : 45 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
implies(x,not(truth)) != not(x),
file('LCL139-1.p',unknown),
[] ).
cnf(2,plain,
not(x) != implies(x,not(truth)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
implies(truth,A) = A,
file('LCL139-1.p',unknown),
[] ).
cnf(6,axiom,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
file('LCL139-1.p',unknown),
[] ).
cnf(8,axiom,
implies(implies(A,B),B) = implies(implies(B,A),A),
file('LCL139-1.p',unknown),
[] ).
cnf(9,axiom,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
file('LCL139-1.p',unknown),
[] ).
cnf(11,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1,8.1.1')] ).
cnf(13,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,5])]),
[iquote('para_into,8.1.1.1,4.1.1,flip.1')] ).
cnf(23,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(para_into,[status(thm),theory(equality)],[9,5]),
[iquote('para_into,9.1.1.2,4.1.1')] ).
cnf(25,plain,
implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,8]),5])]),
[iquote('para_from,9.1.1,8.1.1.1,demod,5,flip.1')] ).
cnf(29,plain,
implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,9]),5]),
[iquote('para_into,6.1.1.1,9.1.1,demod,5')] ).
cnf(35,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,5]),5]),
[iquote('para_into,6.1.1.1,4.1.1,demod,5')] ).
cnf(45,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(para_into,[status(thm),theory(equality)],[6,5]),
[iquote('para_into,6.1.1.2.1,4.1.1')] ).
cnf(75,plain,
implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[23,8]),5])]),
[iquote('para_from,23.1.1,8.1.1.1,demod,5,flip.1')] ).
cnf(84,plain,
implies(A,A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,5]),5]),
[iquote('para_into,35.1.1.2.1,4.1.1,demod,5')] ).
cnf(88,plain,
implies(A,truth) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,13]),84]),
[iquote('para_into,35.1.1.2,13.1.1,demod,84')] ).
cnf(92,plain,
implies(A,implies(B,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[45]),88,5]),
[iquote('back_demod,45,demod,88,5')] ).
cnf(93,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),92,5]),
[iquote('back_demod,11,demod,92,5')] ).
cnf(121,plain,
implies(implies(A,B),implies(A,implies(C,B))) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[92,6]),5]),
[iquote('para_from,91.1.1,6.1.1.2.1,demod,5')] ).
cnf(131,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[93,23]),5])]),
[iquote('para_into,93.1.1.1,23.1.1,demod,5,flip.1')] ).
cnf(175,plain,
implies(A,implies(B,implies(C,A))) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[121,92]),5]),
[iquote('para_into,121.1.1.1,91.1.1,demod,5')] ).
cnf(207,plain,
implies(not(A),implies(A,B)) = truth,
inference(para_into,[status(thm),theory(equality)],[175,25]),
[iquote('para_into,175.1.1.2,25.1.1')] ).
cnf(232,plain,
implies(not(truth),A) = truth,
inference(para_into,[status(thm),theory(equality)],[207,5]),
[iquote('para_into,207.1.1.2,4.1.1')] ).
cnf(238,plain,
not(not(truth)) = truth,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[131]),232])]),
[iquote('back_demod,131,demod,232,flip.1')] ).
cnf(270,plain,
implies(not(not(A)),A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,23]),238,5,5]),
[iquote('para_into,29.1.1.1,23.1.1,demod,238,5,5')] ).
cnf(302,plain,
implies(A,not(not(A))) = truth,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[270,25]),270,88,84])]),
[iquote('para_from,269.1.1,25.1.1.2,demod,270,88,84,flip.1')] ).
cnf(311,plain,
not(not(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[270,8]),5,302,5])]),
[iquote('para_from,269.1.1,8.1.1.1,demod,5,302,5,flip.1')] ).
cnf(322,plain,
implies(A,implies(not(A),B)) = truth,
inference(para_from,[status(thm),theory(equality)],[311,207]),
[iquote('para_from,311.1.1,207.1.1.1')] ).
cnf(334,plain,
implies(not(A),not(truth)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[75]),322,5]),
[iquote('back_demod,75,demod,322,5')] ).
cnf(337,plain,
implies(A,not(truth)) = not(A),
inference(para_into,[status(thm),theory(equality)],[334,311]),
[iquote('para_into,334.1.1.1,311.1.1')] ).
cnf(338,plain,
not(A) = implies(A,not(truth)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[337])]),
[iquote('copy,337,flip.1')] ).
cnf(339,plain,
$false,
inference(binary,[status(thm)],[338,2]),
[iquote('binary,338.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL139-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 08:53:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.64/1.88 ----- Otter 3.3f, August 2004 -----
% 1.64/1.88 The process was started by sandbox2 on n017.cluster.edu,
% 1.64/1.88 Wed Jul 27 08:53:48 2022
% 1.64/1.88 The command was "./otter". The process ID is 1835.
% 1.64/1.88
% 1.64/1.88 set(prolog_style_variables).
% 1.64/1.88 set(auto).
% 1.64/1.88 dependent: set(auto1).
% 1.64/1.88 dependent: set(process_input).
% 1.64/1.88 dependent: clear(print_kept).
% 1.64/1.88 dependent: clear(print_new_demod).
% 1.64/1.88 dependent: clear(print_back_demod).
% 1.64/1.88 dependent: clear(print_back_sub).
% 1.64/1.88 dependent: set(control_memory).
% 1.64/1.88 dependent: assign(max_mem, 12000).
% 1.64/1.88 dependent: assign(pick_given_ratio, 4).
% 1.64/1.88 dependent: assign(stats_level, 1).
% 1.64/1.88 dependent: assign(max_seconds, 10800).
% 1.64/1.88 clear(print_given).
% 1.64/1.88
% 1.64/1.88 list(usable).
% 1.64/1.88 0 [] A=A.
% 1.64/1.88 0 [] implies(truth,X)=X.
% 1.64/1.88 0 [] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))=truth.
% 1.64/1.88 0 [] implies(implies(X,Y),Y)=implies(implies(Y,X),X).
% 1.64/1.88 0 [] implies(implies(not(X),not(Y)),implies(Y,X))=truth.
% 1.64/1.88 0 [] implies(x,not(truth))!=not(x).
% 1.64/1.88 end_of_list.
% 1.64/1.88
% 1.64/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.64/1.88
% 1.64/1.88 All clauses are units, and equality is present; the
% 1.64/1.88 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.64/1.88
% 1.64/1.88 dependent: set(knuth_bendix).
% 1.64/1.88 dependent: set(anl_eq).
% 1.64/1.88 dependent: set(para_from).
% 1.64/1.88 dependent: set(para_into).
% 1.64/1.88 dependent: clear(para_from_right).
% 1.64/1.88 dependent: clear(para_into_right).
% 1.64/1.88 dependent: set(para_from_vars).
% 1.64/1.88 dependent: set(eq_units_both_ways).
% 1.64/1.88 dependent: set(dynamic_demod_all).
% 1.64/1.88 dependent: set(dynamic_demod).
% 1.64/1.88 dependent: set(order_eq).
% 1.64/1.88 dependent: set(back_demod).
% 1.64/1.88 dependent: set(lrpo).
% 1.64/1.88
% 1.64/1.88 ------------> process usable:
% 1.64/1.88 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] not(x)!=implies(x,not(truth)).
% 1.64/1.88
% 1.64/1.88 ------------> process sos:
% 1.64/1.88 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.64/1.88 ** KEPT (pick-wt=5): 4 [] implies(truth,A)=A.
% 1.64/1.88 ---> New Demodulator: 5 [new_demod,4] implies(truth,A)=A.
% 1.64/1.88 ** KEPT (pick-wt=13): 6 [] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.64/1.88 ---> New Demodulator: 7 [new_demod,6] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.64/1.88 ** KEPT (pick-wt=11): 8 [] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.64/1.88 ** KEPT (pick-wt=11): 9 [] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.64/1.88 ---> New Demodulator: 10 [new_demod,9] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.64/1.88 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.64/1.88 >>>> Starting back demodulation with 5.
% 1.64/1.88 >>>> Starting back demodulation with 7.
% 1.64/1.88 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.64/1.88 >>>> Starting back demodulation with 10.
% 1.64/1.88
% 1.64/1.88 ======= end of input processing =======
% 1.64/1.88
% 1.64/1.88 =========== start of search ===========
% 1.64/1.88
% 1.64/1.88 -------- PROOF --------
% 1.64/1.88
% 1.64/1.88 ----> UNIT CONFLICT at 0.01 sec ----> 339 [binary,338.1,2.1] $F.
% 1.64/1.88
% 1.64/1.88 Length of proof is 26. Level of proof is 16.
% 1.64/1.88
% 1.64/1.88 ---------------- PROOF ----------------
% 1.64/1.88 % SZS status Unsatisfiable
% 1.64/1.88 % SZS output start Refutation
% See solution above
% 1.64/1.88 ------------ end of proof -------------
% 1.64/1.88
% 1.64/1.88
% 1.64/1.88 Search stopped by max_proofs option.
% 1.64/1.88
% 1.64/1.88
% 1.64/1.88 Search stopped by max_proofs option.
% 1.64/1.88
% 1.64/1.88 ============ end of search ============
% 1.64/1.88
% 1.64/1.88 -------------- statistics -------------
% 1.64/1.88 clauses given 25
% 1.64/1.88 clauses generated 589
% 1.64/1.88 clauses kept 173
% 1.64/1.88 clauses forward subsumed 495
% 1.64/1.88 clauses back subsumed 0
% 1.64/1.88 Kbytes malloced 1953
% 1.64/1.88
% 1.64/1.88 ----------- times (seconds) -----------
% 1.64/1.88 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.64/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.64/1.88
% 1.64/1.88 That finishes the proof of the theorem.
% 1.64/1.88
% 1.64/1.88 Process 1835 finished Wed Jul 27 08:53:49 2022
% 1.64/1.88 Otter interrupted
% 1.64/1.88 PROOF FOUND
%------------------------------------------------------------------------------