TSTP Solution File: LCL115-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL115-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:03:36 EDT 2022
% Result : Unsatisfiable 2.00s 2.18s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 5 RR)
% Number of literals : 30 ( 29 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
implies(not(implies(a,b)),not(b)) != truth,
file('LCL115-2.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('LCL115-2.p',unknown),
[] ).
cnf(4,axiom,
implies(truth,A) = A,
file('LCL115-2.p',unknown),
[] ).
cnf(5,axiom,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
file('LCL115-2.p',unknown),
[] ).
cnf(7,axiom,
implies(implies(A,B),B) = implies(implies(B,A),A),
file('LCL115-2.p',unknown),
[] ).
cnf(8,axiom,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
file('LCL115-2.p',unknown),
[] ).
cnf(10,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(para_into,[status(thm),theory(equality)],[7,7]),
[iquote('para_into,7.1.1.1,7.1.1')] ).
cnf(12,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,4])]),
[iquote('para_into,7.1.1.1,3.1.1,flip.1')] ).
cnf(22,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(para_into,[status(thm),theory(equality)],[8,4]),
[iquote('para_into,8.1.1.2,3.1.1')] ).
cnf(24,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)],[8,7]),4])]),
[iquote('para_from,8.1.1,7.1.1.1,demod,4,flip.1')] ).
cnf(28,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)],[5,8]),4]),
[iquote('para_into,5.1.1.1,8.1.1,demod,4')] ).
cnf(34,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,4]),4]),
[iquote('para_into,5.1.1.1,3.1.1,demod,4')] ).
cnf(44,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(para_into,[status(thm),theory(equality)],[5,4]),
[iquote('para_into,5.1.1.2.1,3.1.1')] ).
cnf(83,plain,
implies(A,A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,4]),4]),
[iquote('para_into,34.1.1.2.1,3.1.1,demod,4')] ).
cnf(87,plain,
implies(A,truth) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,12]),83]),
[iquote('para_into,34.1.1.2,12.1.1,demod,83')] ).
cnf(91,plain,
implies(A,implies(B,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),87,4]),
[iquote('back_demod,44,demod,87,4')] ).
cnf(92,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[10]),91,4]),
[iquote('back_demod,10,demod,91,4')] ).
cnf(120,plain,
implies(implies(A,B),implies(A,implies(C,B))) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[91,5]),4]),
[iquote('para_from,90.1.1,5.1.1.2.1,demod,4')] ).
cnf(130,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)],[92,22]),4])]),
[iquote('para_into,92.1.1.1,22.1.1,demod,4,flip.1')] ).
cnf(174,plain,
implies(A,implies(B,implies(C,A))) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[120,91]),4]),
[iquote('para_into,120.1.1.1,90.1.1,demod,4')] ).
cnf(206,plain,
implies(not(A),implies(A,B)) = truth,
inference(para_into,[status(thm),theory(equality)],[174,24]),
[iquote('para_into,174.1.1.2,24.1.1')] ).
cnf(231,plain,
implies(not(truth),A) = truth,
inference(para_into,[status(thm),theory(equality)],[206,4]),
[iquote('para_into,206.1.1.2,3.1.1')] ).
cnf(237,plain,
not(not(truth)) = truth,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[130]),231])]),
[iquote('back_demod,130,demod,231,flip.1')] ).
cnf(269,plain,
implies(not(not(A)),A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,22]),237,4,4]),
[iquote('para_into,28.1.1.1,22.1.1,demod,237,4,4')] ).
cnf(301,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)],[269,24]),269,87,83])]),
[iquote('para_from,268.1.1,24.1.1.2,demod,269,87,83,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)],[269,7]),4,301,4])]),
[iquote('para_from,268.1.1,7.1.1.1,demod,4,301,4,flip.1')] ).
cnf(319,plain,
implies(implies(not(A),B),implies(not(B),A)) = truth,
inference(para_from,[status(thm),theory(equality)],[311,8]),
[iquote('para_from,310.1.1,8.1.1.1.2')] ).
cnf(328,plain,
implies(not(A),B) = implies(not(B),A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[311,24]),311,319,4]),
[iquote('para_from,310.1.1,24.1.1.2.2,demod,311,319,4')] ).
cnf(631,plain,
truth != truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[328,1]),311,91]),
[iquote('para_from,328.1.1,1.1.1,demod,311,91')] ).
cnf(632,plain,
$false,
inference(binary,[status(thm)],[631,2]),
[iquote('binary,631.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL115-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 09:22:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.00/2.18 ----- Otter 3.3f, August 2004 -----
% 2.00/2.18 The process was started by sandbox on n020.cluster.edu,
% 2.00/2.18 Wed Jul 27 09:22:08 2022
% 2.00/2.18 The command was "./otter". The process ID is 11337.
% 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 list(usable).
% 2.00/2.18 0 [] A=A.
% 2.00/2.18 0 [] implies(truth,X)=X.
% 2.00/2.18 0 [] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))=truth.
% 2.00/2.18 0 [] implies(implies(X,Y),Y)=implies(implies(Y,X),X).
% 2.00/2.18 0 [] implies(implies(not(X),not(Y)),implies(Y,X))=truth.
% 2.00/2.18 0 [] implies(not(implies(a,b)),not(b))!=truth.
% 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=1.
% 2.00/2.18
% 2.00/2.18 All clauses are units, and equality is present; the
% 2.00/2.18 strategy will be Knuth-Bendix with positive clauses in sos.
% 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
% 2.00/2.18 ------------> process usable:
% 2.00/2.18 ** KEPT (pick-wt=9): 1 [] implies(not(implies(a,b)),not(b))!=truth.
% 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=5): 3 [] implies(truth,A)=A.
% 2.00/2.18 ---> New Demodulator: 4 [new_demod,3] implies(truth,A)=A.
% 2.00/2.18 ** KEPT (pick-wt=13): 5 [] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 2.00/2.18 ---> New Demodulator: 6 [new_demod,5] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 2.00/2.18 ** KEPT (pick-wt=11): 7 [] implies(implies(A,B),B)=implies(implies(B,A),A).
% 2.00/2.18 ** KEPT (pick-wt=11): 8 [] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 2.00/2.18 ---> New Demodulator: 9 [new_demod,8] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 2.00/2.18 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.00/2.18 >>>> Starting back demodulation with 4.
% 2.00/2.18 >>>> Starting back demodulation with 6.
% 2.00/2.18 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] implies(implies(A,B),B)=implies(implies(B,A),A).
% 2.00/2.18 >>>> Starting back demodulation with 9.
% 2.00/2.18
% 2.00/2.18 ======= end of input processing =======
% 2.00/2.18
% 2.00/2.18 =========== start of search ===========
% 2.00/2.18
% 2.00/2.18 -------- PROOF --------
% 2.00/2.18
% 2.00/2.18 ----> UNIT CONFLICT at 0.02 sec ----> 632 [binary,631.1,2.1] $F.
% 2.00/2.18
% 2.00/2.18 Length of proof is 23. Level of proof is 15.
% 2.00/2.18
% 2.00/2.18 ---------------- PROOF ----------------
% 2.00/2.18 % SZS status Unsatisfiable
% 2.00/2.18 % SZS output start Refutation
% See solution above
% 2.00/2.18 ------------ end of proof -------------
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Search stopped by max_proofs option.
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Search stopped by max_proofs option.
% 2.00/2.18
% 2.00/2.18 ============ end of search ============
% 2.00/2.18
% 2.00/2.18 -------------- statistics -------------
% 2.00/2.18 clauses given 34
% 2.00/2.18 clauses generated 1155
% 2.00/2.18 clauses kept 325
% 2.00/2.18 clauses forward subsumed 923
% 2.00/2.18 clauses back subsumed 0
% 2.00/2.18 Kbytes malloced 2929
% 2.00/2.18
% 2.00/2.18 ----------- times (seconds) -----------
% 2.00/2.18 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 2.00/2.18 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.18
% 2.00/2.18 That finishes the proof of the theorem.
% 2.00/2.18
% 2.00/2.18 Process 11337 finished Wed Jul 27 09:22:10 2022
% 2.00/2.18 Otter interrupted
% 2.00/2.18 PROOF FOUND
%------------------------------------------------------------------------------