TSTP Solution File: LCL156-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 13:03:42 EDT 2022
% Result : Unsatisfiable 1.69s 1.90s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 5 RR)
% Number of literals : 41 ( 40 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
and_star(x,truth) != x,
file('LCL156-1.p',unknown),
[] ).
cnf(4,axiom,
implies(truth,A) = A,
file('LCL156-1.p',unknown),
[] ).
cnf(5,axiom,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
file('LCL156-1.p',unknown),
[] ).
cnf(7,axiom,
implies(implies(A,B),B) = implies(implies(B,A),A),
file('LCL156-1.p',unknown),
[] ).
cnf(8,axiom,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
file('LCL156-1.p',unknown),
[] ).
cnf(10,axiom,
or(A,B) = implies(not(A),B),
file('LCL156-1.p',unknown),
[] ).
cnf(13,axiom,
or(A,B) = or(B,A),
file('LCL156-1.p',unknown),
[] ).
cnf(14,axiom,
and(A,B) = not(or(not(A),not(B))),
file('LCL156-1.p',unknown),
[] ).
cnf(16,plain,
not(or(not(A),not(B))) = and(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(22,axiom,
and_star(A,B) = not(or(not(A),not(B))),
file('LCL156-1.p',unknown),
[] ).
cnf(24,plain,
and_star(A,B) = and(A,B),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22]),16]),
[iquote('copy,22,demod,16')] ).
cnf(25,axiom,
not(truth) = falsehood,
file('LCL156-1.p',unknown),
[] ).
cnf(27,plain,
implies(not(A),B) = or(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(29,plain,
and(x,truth) != x,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),24]),
[iquote('back_demod,1,demod,24')] ).
cnf(32,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(36,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(48,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(57,plain,
or(A,B) = implies(not(B),A),
inference(para_into,[status(thm),theory(equality)],[10,13]),
[iquote('para_into,10.1.1,13.1.1')] ).
cnf(58,plain,
implies(not(A),B) = or(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[57])]),
[iquote('copy,57,flip.1')] ).
cnf(59,plain,
or(truth,A) = implies(falsehood,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,25])]),
[iquote('para_into,27.1.1.1,25.1.1,flip.1')] ).
cnf(69,plain,
or(A,truth) = implies(falsehood,A),
inference(para_into,[status(thm),theory(equality)],[59,13]),
[iquote('para_into,59.1.1,13.1.1')] ).
cnf(71,plain,
implies(not(A),truth) = implies(falsehood,A),
inference(para_into,[status(thm),theory(equality)],[69,10]),
[iquote('para_into,69.1.1,10.1.1')] ).
cnf(75,plain,
implies(implies(not(A),falsehood),A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,25]),4]),
[iquote('para_into,8.1.1.1.2,25.1.1,demod,4')] ).
cnf(120,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(para_into,[status(thm),theory(equality)],[75,25]),
[iquote('para_into,75.1.1.1.1,25.1.1')] ).
cnf(122,plain,
implies(or(falsehood,A),A) = truth,
inference(para_into,[status(thm),theory(equality)],[75,58]),
[iquote('para_into,75.1.1.1,58.1.1')] ).
cnf(155,plain,
implies(implies(implies(falsehood,falsehood),A),implies(A,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[120,5]),48]),
[iquote('para_from,120.1.1,5.1.1.2.2,demod,48')] ).
cnf(163,plain,
implies(implies(not(falsehood),A),A) = truth,
inference(para_into,[status(thm),theory(equality)],[122,10]),
[iquote('para_into,122.1.1.1,10.1.1')] ).
cnf(195,plain,
implies(implies(A,implies(not(falsehood),A)),implies(not(falsehood),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[163,7]),4])]),
[iquote('para_from,163.1.1,7.1.1.1,demod,4,flip.1')] ).
cnf(203,plain,
not(or(not(A),falsehood)) = and(A,truth),
inference(para_into,[status(thm),theory(equality)],[16,25]),
[iquote('para_into,15.1.1.1.2,25.1.1')] ).
cnf(230,plain,
implies(A,A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,4]),4]),
[iquote('para_into,32.1.1.2.1,3.1.1,demod,4')] ).
cnf(238,plain,
implies(A,truth) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[155]),230,4,230]),
[iquote('back_demod,155,demod,230,4,230')] ).
cnf(244,plain,
implies(falsehood,A) = truth,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[71]),238])]),
[iquote('back_demod,71,demod,238,flip.1')] ).
cnf(246,plain,
implies(A,implies(B,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[36]),238,4]),
[iquote('back_demod,36,demod,238,4')] ).
cnf(251,plain,
implies(not(falsehood),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[195]),246,4]),
[iquote('back_demod,195,demod,246,4')] ).
cnf(266,plain,
implies(implies(A,falsehood),falsehood) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[244,7]),4])]),
[iquote('para_from,243.1.1,7.1.1.1,demod,4,flip.1')] ).
cnf(273,plain,
or(A,falsehood) = A,
inference(para_into,[status(thm),theory(equality)],[251,58]),
[iquote('para_into,251.1.1,58.1.1')] ).
cnf(276,plain,
not(not(A)) = and(A,truth),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[203]),273]),
[iquote('back_demod,203,demod,273')] ).
cnf(292,plain,
implies(not(A),falsehood) = A,
inference(para_into,[status(thm),theory(equality)],[273,10]),
[iquote('para_into,272.1.1,10.1.1')] ).
cnf(355,plain,
not(A) = implies(A,falsehood),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[292,7]),244,4])]),
[iquote('para_from,292.1.1,7.1.1.1,demod,244,4,flip.1')] ).
cnf(407,plain,
and(A,truth) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[276]),355,355,266])]),
[iquote('back_demod,276,demod,355,355,266,flip.1')] ).
cnf(409,plain,
$false,
inference(binary,[status(thm)],[407,29]),
[iquote('binary,407.1,29.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL156-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.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 09:12:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.89 ----- Otter 3.3f, August 2004 -----
% 1.69/1.89 The process was started by sandbox2 on n010.cluster.edu,
% 1.69/1.89 Wed Jul 27 09:12:10 2022
% 1.69/1.89 The command was "./otter". The process ID is 23680.
% 1.69/1.89
% 1.69/1.89 set(prolog_style_variables).
% 1.69/1.89 set(auto).
% 1.69/1.89 dependent: set(auto1).
% 1.69/1.89 dependent: set(process_input).
% 1.69/1.89 dependent: clear(print_kept).
% 1.69/1.89 dependent: clear(print_new_demod).
% 1.69/1.89 dependent: clear(print_back_demod).
% 1.69/1.89 dependent: clear(print_back_sub).
% 1.69/1.89 dependent: set(control_memory).
% 1.69/1.89 dependent: assign(max_mem, 12000).
% 1.69/1.89 dependent: assign(pick_given_ratio, 4).
% 1.69/1.89 dependent: assign(stats_level, 1).
% 1.69/1.89 dependent: assign(max_seconds, 10800).
% 1.69/1.89 clear(print_given).
% 1.69/1.89
% 1.69/1.89 list(usable).
% 1.69/1.89 0 [] A=A.
% 1.69/1.89 0 [] implies(truth,X)=X.
% 1.69/1.89 0 [] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))=truth.
% 1.69/1.89 0 [] implies(implies(X,Y),Y)=implies(implies(Y,X),X).
% 1.69/1.89 0 [] implies(implies(not(X),not(Y)),implies(Y,X))=truth.
% 1.69/1.89 0 [] or(X,Y)=implies(not(X),Y).
% 1.69/1.89 0 [] or(or(X,Y),Z)=or(X,or(Y,Z)).
% 1.69/1.89 0 [] or(X,Y)=or(Y,X).
% 1.69/1.89 0 [] and(X,Y)=not(or(not(X),not(Y))).
% 1.69/1.89 0 [] and(and(X,Y),Z)=and(X,and(Y,Z)).
% 1.69/1.89 0 [] and(X,Y)=and(Y,X).
% 1.69/1.89 0 [] xor(X,Y)=or(and(X,not(Y)),and(not(X),Y)).
% 1.69/1.89 0 [] xor(X,Y)=xor(Y,X).
% 1.69/1.89 0 [] and_star(X,Y)=not(or(not(X),not(Y))).
% 1.69/1.89 0 [] and_star(and_star(X,Y),Z)=and_star(X,and_star(Y,Z)).
% 1.69/1.89 0 [] and_star(X,Y)=and_star(Y,X).
% 1.69/1.89 0 [] not(truth)=falsehood.
% 1.69/1.89 0 [] and_star(x,truth)!=x.
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.69/1.89
% 1.69/1.89 All clauses are units, and equality is present; the
% 1.69/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.69/1.89
% 1.69/1.89 dependent: set(knuth_bendix).
% 1.69/1.89 dependent: set(anl_eq).
% 1.69/1.89 dependent: set(para_from).
% 1.69/1.89 dependent: set(para_into).
% 1.69/1.89 dependent: clear(para_from_right).
% 1.69/1.89 dependent: clear(para_into_right).
% 1.69/1.89 dependent: set(para_from_vars).
% 1.69/1.89 dependent: set(eq_units_both_ways).
% 1.69/1.89 dependent: set(dynamic_demod_all).
% 1.69/1.89 dependent: set(dynamic_demod).
% 1.69/1.89 dependent: set(order_eq).
% 1.69/1.89 dependent: set(back_demod).
% 1.69/1.89 dependent: set(lrpo).
% 1.69/1.89
% 1.69/1.89 ------------> process usable:
% 1.69/1.89 ** KEPT (pick-wt=5): 1 [] and_star(x,truth)!=x.
% 1.69/1.89
% 1.69/1.89 ------------> process sos:
% 1.69/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.89 ** KEPT (pick-wt=5): 3 [] implies(truth,A)=A.
% 1.69/1.89 ---> New Demodulator: 4 [new_demod,3] implies(truth,A)=A.
% 1.69/1.89 ** KEPT (pick-wt=13): 5 [] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.69/1.89 ---> New Demodulator: 6 [new_demod,5] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.69/1.89 ** KEPT (pick-wt=11): 7 [] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.69/1.89 ** KEPT (pick-wt=11): 8 [] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.69/1.89 ---> New Demodulator: 9 [new_demod,8] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.69/1.89 ** KEPT (pick-wt=8): 10 [] or(A,B)=implies(not(A),B).
% 1.69/1.89 ** KEPT (pick-wt=11): 11 [] or(or(A,B),C)=or(A,or(B,C)).
% 1.69/1.89 ---> New Demodulator: 12 [new_demod,11] or(or(A,B),C)=or(A,or(B,C)).
% 1.69/1.89 ** KEPT (pick-wt=7): 13 [] or(A,B)=or(B,A).
% 1.69/1.89 ** KEPT (pick-wt=10): 15 [copy,14,flip.1] not(or(not(A),not(B)))=and(A,B).
% 1.69/1.89 ---> New Demodulator: 16 [new_demod,15] not(or(not(A),not(B)))=and(A,B).
% 1.69/1.89 ** KEPT (pick-wt=11): 17 [] and(and(A,B),C)=and(A,and(B,C)).
% 1.69/1.89 ---> New Demodulator: 18 [new_demod,17] and(and(A,B),C)=and(A,and(B,C)).
% 1.69/1.89 ** KEPT (pick-wt=7): 19 [] and(A,B)=and(B,A).
% 1.69/1.89 ** KEPT (pick-wt=13): 20 [] xor(A,B)=or(and(A,not(B)),and(not(A),B)).
% 1.69/1.89 ** KEPT (pick-wt=7): 21 [] xor(A,B)=xor(B,A).
% 1.69/1.89 ** KEPT (pick-wt=7): 23 [copy,22,demod,16] and_star(A,B)=and(A,B).
% 1.69/1.89 ---> New Demodulator: 24 [new_demod,23] and_star(A,B)=and(A,B).
% 1.69/1.89 Following clause subsumed by 2 during input processing: 0 [demod,24,24,18,24,24] and(A,and(B,C))=and(A,and(B,C)).
% 1.69/1.89 Following clause subsumed by 19 during input processing: 0 [demod,24,24] and(A,B)=and(B,A).
% 1.69/1.89 ** KEPT (pick-wt=4): 25 [] not(truth)=falsehood.
% 1.69/1.89 ---> New Demodulator: 26 [new_demod,25] not(truth)=falsehood.
% 1.69/1.89 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.89 >>>> Starting back demodulation with 4.
% 1.69/1.89 >>>> Starting back demodulation with 6.
% 1.69/1.89 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.69/1.89 >>>> Starting back demodulation with 9.
% 1.69/1.89 ** KEPT (pick-wt=8): 27 [copy,10,flip.1] implies(not(A),B)=or(A,B).
% 1.69/1.90 >>>> Starting back demodulation with 12.
% 1.69/1.90 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] or(A,B)=or(B,A).
% 1.69/1.90 >>>> Starting back demodulation with 16.
% 1.69/1.90 >>>> Starting back demodulation with 18.
% 1.69/1.90 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] and(A,B)=and(B,A).
% 1.69/1.90 ** KEPT (pick-wt=13): 28 [copy,20,flip.1] or(and(A,not(B)),and(not(A),B))=xor(A,B).
% 1.69/1.90 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] xor(A,B)=xor(B,A).
% 1.69/1.90 >>>> Starting back demodulation with 24.
% 1.69/1.90 >> back demodulating 1 with 24.
% 1.69/1.90 >>>> Starting back demodulation with 26.
% 1.69/1.90 Following clause subsumed by 10 during input processing: 0 [copy,27,flip.1] or(A,B)=implies(not(A),B).
% 1.69/1.90 Following clause subsumed by 20 during input processing: 0 [copy,28,flip.1] xor(A,B)=or(and(A,not(B)),and(not(A),B)).
% 1.69/1.90
% 1.69/1.90 ======= end of input processing =======
% 1.69/1.90
% 1.69/1.90 =========== start of search ===========
% 1.69/1.90
% 1.69/1.90 -------- PROOF --------
% 1.69/1.90
% 1.69/1.90 ----> UNIT CONFLICT at 0.01 sec ----> 409 [binary,407.1,29.1] $F.
% 1.69/1.90
% 1.69/1.90 Length of proof is 30. Level of proof is 10.
% 1.69/1.90
% 1.69/1.90 ---------------- PROOF ----------------
% 1.69/1.90 % SZS status Unsatisfiable
% 1.69/1.90 % SZS output start Refutation
% See solution above
% 1.69/1.90 ------------ end of proof -------------
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90 ============ end of search ============
% 1.69/1.90
% 1.69/1.90 -------------- statistics -------------
% 1.69/1.90 clauses given 44
% 1.69/1.90 clauses generated 450
% 1.69/1.90 clauses kept 229
% 1.69/1.90 clauses forward subsumed 403
% 1.69/1.90 clauses back subsumed 0
% 1.69/1.90 Kbytes malloced 2929
% 1.69/1.90
% 1.69/1.90 ----------- times (seconds) -----------
% 1.69/1.90 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.90
% 1.69/1.90 That finishes the proof of the theorem.
% 1.69/1.90
% 1.69/1.90 Process 23680 finished Wed Jul 27 09:12:11 2022
% 1.69/1.90 Otter interrupted
% 1.69/1.90 PROOF FOUND
%------------------------------------------------------------------------------