TSTP Solution File: LCL155-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.66s 1.86s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 6 RR)
% Number of literals : 35 ( 34 equ; 3 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 : 44 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
xor(x,x) != falsehood,
file('LCL155-1.p',unknown),
[] ).
cnf(4,axiom,
implies(truth,A) = A,
file('LCL155-1.p',unknown),
[] ).
cnf(5,axiom,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
file('LCL155-1.p',unknown),
[] ).
cnf(7,axiom,
implies(implies(A,B),B) = implies(implies(B,A),A),
file('LCL155-1.p',unknown),
[] ).
cnf(8,axiom,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
file('LCL155-1.p',unknown),
[] ).
cnf(10,axiom,
or(A,B) = implies(not(A),B),
file('LCL155-1.p',unknown),
[] ).
cnf(13,axiom,
or(A,B) = or(B,A),
file('LCL155-1.p',unknown),
[] ).
cnf(14,axiom,
and(A,B) = not(or(not(A),not(B))),
file('LCL155-1.p',unknown),
[] ).
cnf(15,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(20,axiom,
xor(A,B) = or(and(A,not(B)),and(not(A),B)),
file('LCL155-1.p',unknown),
[] ).
cnf(26,axiom,
not(truth) = falsehood,
file('LCL155-1.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(31,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(35,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(41,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(42,plain,
implies(not(A),B) = or(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[41])]),
[iquote('copy,41,flip.1')] ).
cnf(57,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(82,plain,
implies(implies(not(A),falsehood),A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,26]),4]),
[iquote('para_into,8.1.1.1.2,25.1.1,demod,4')] ).
cnf(118,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(para_into,[status(thm),theory(equality)],[82,26]),
[iquote('para_into,82.1.1.1.1,25.1.1')] ).
cnf(120,plain,
implies(or(falsehood,A),A) = truth,
inference(para_into,[status(thm),theory(equality)],[82,42]),
[iquote('para_into,82.1.1.1,42.1.1')] ).
cnf(138,plain,
implies(implies(implies(falsehood,falsehood),A),implies(A,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[118,5]),57]),
[iquote('para_from,118.1.1,5.1.1.2.2,demod,57')] ).
cnf(146,plain,
implies(implies(not(falsehood),A),A) = truth,
inference(para_into,[status(thm),theory(equality)],[120,10]),
[iquote('para_into,120.1.1.1,10.1.1')] ).
cnf(193,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)],[146,7]),4])]),
[iquote('para_from,146.1.1,7.1.1.1,demod,4,flip.1')] ).
cnf(206,plain,
implies(A,A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,4]),4]),
[iquote('para_into,31.1.1.2.1,3.1.1,demod,4')] ).
cnf(214,plain,
implies(A,truth) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[138]),206,4,206]),
[iquote('back_demod,138,demod,206,4,206')] ).
cnf(220,plain,
implies(A,implies(B,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[35]),214,4]),
[iquote('back_demod,35,demod,214,4')] ).
cnf(225,plain,
implies(not(falsehood),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[193]),220,4]),
[iquote('back_demod,193,demod,220,4')] ).
cnf(233,plain,
or(not(A),A) = truth,
inference(para_into,[status(thm),theory(equality)],[206,42]),
[iquote('para_into,205.1.1,42.1.1')] ).
cnf(235,plain,
or(A,not(A)) = truth,
inference(para_into,[status(thm),theory(equality)],[206,27]),
[iquote('para_into,205.1.1,27.1.1')] ).
cnf(267,plain,
or(A,falsehood) = A,
inference(para_into,[status(thm),theory(equality)],[225,42]),
[iquote('para_into,225.1.1,42.1.1')] ).
cnf(288,plain,
or(and(x,not(x)),and(not(x),x)) != falsehood,
inference(para_from,[status(thm),theory(equality)],[20,1]),
[iquote('para_from,20.1.1,1.1.1')] ).
cnf(292,plain,
and(not(A),A) = falsehood,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[233,15]),26])]),
[iquote('para_from,233.1.1,15.1.1.1,demod,26,flip.1')] ).
cnf(295,plain,
and(x,not(x)) != falsehood,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[288]),292,267]),
[iquote('back_demod,288,demod,292,267')] ).
cnf(298,plain,
and(A,not(A)) = falsehood,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[235,15]),26])]),
[iquote('para_from,235.1.1,15.1.1.1,demod,26,flip.1')] ).
cnf(300,plain,
$false,
inference(binary,[status(thm)],[298,295]),
[iquote('binary,298.1,295.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n018.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 09:26:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.66/1.86 ----- Otter 3.3f, August 2004 -----
% 1.66/1.86 The process was started by sandbox2 on n018.cluster.edu,
% 1.66/1.86 Wed Jul 27 09:26:31 2022
% 1.66/1.86 The command was "./otter". The process ID is 31267.
% 1.66/1.86
% 1.66/1.86 set(prolog_style_variables).
% 1.66/1.86 set(auto).
% 1.66/1.86 dependent: set(auto1).
% 1.66/1.86 dependent: set(process_input).
% 1.66/1.86 dependent: clear(print_kept).
% 1.66/1.86 dependent: clear(print_new_demod).
% 1.66/1.86 dependent: clear(print_back_demod).
% 1.66/1.86 dependent: clear(print_back_sub).
% 1.66/1.86 dependent: set(control_memory).
% 1.66/1.86 dependent: assign(max_mem, 12000).
% 1.66/1.86 dependent: assign(pick_given_ratio, 4).
% 1.66/1.86 dependent: assign(stats_level, 1).
% 1.66/1.86 dependent: assign(max_seconds, 10800).
% 1.66/1.86 clear(print_given).
% 1.66/1.86
% 1.66/1.86 list(usable).
% 1.66/1.86 0 [] A=A.
% 1.66/1.86 0 [] implies(truth,X)=X.
% 1.66/1.86 0 [] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))=truth.
% 1.66/1.86 0 [] implies(implies(X,Y),Y)=implies(implies(Y,X),X).
% 1.66/1.86 0 [] implies(implies(not(X),not(Y)),implies(Y,X))=truth.
% 1.66/1.86 0 [] or(X,Y)=implies(not(X),Y).
% 1.66/1.86 0 [] or(or(X,Y),Z)=or(X,or(Y,Z)).
% 1.66/1.86 0 [] or(X,Y)=or(Y,X).
% 1.66/1.86 0 [] and(X,Y)=not(or(not(X),not(Y))).
% 1.66/1.86 0 [] and(and(X,Y),Z)=and(X,and(Y,Z)).
% 1.66/1.86 0 [] and(X,Y)=and(Y,X).
% 1.66/1.86 0 [] xor(X,Y)=or(and(X,not(Y)),and(not(X),Y)).
% 1.66/1.86 0 [] xor(X,Y)=xor(Y,X).
% 1.66/1.86 0 [] and_star(X,Y)=not(or(not(X),not(Y))).
% 1.66/1.86 0 [] and_star(and_star(X,Y),Z)=and_star(X,and_star(Y,Z)).
% 1.66/1.86 0 [] and_star(X,Y)=and_star(Y,X).
% 1.66/1.86 0 [] not(truth)=falsehood.
% 1.66/1.86 0 [] xor(x,x)!=falsehood.
% 1.66/1.86 end_of_list.
% 1.66/1.86
% 1.66/1.86 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.86
% 1.66/1.86 All clauses are units, and equality is present; the
% 1.66/1.86 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.86
% 1.66/1.86 dependent: set(knuth_bendix).
% 1.66/1.86 dependent: set(anl_eq).
% 1.66/1.86 dependent: set(para_from).
% 1.66/1.86 dependent: set(para_into).
% 1.66/1.86 dependent: clear(para_from_right).
% 1.66/1.86 dependent: clear(para_into_right).
% 1.66/1.86 dependent: set(para_from_vars).
% 1.66/1.86 dependent: set(eq_units_both_ways).
% 1.66/1.86 dependent: set(dynamic_demod_all).
% 1.66/1.86 dependent: set(dynamic_demod).
% 1.66/1.86 dependent: set(order_eq).
% 1.66/1.86 dependent: set(back_demod).
% 1.66/1.86 dependent: set(lrpo).
% 1.66/1.86
% 1.66/1.86 ------------> process usable:
% 1.66/1.86 ** KEPT (pick-wt=5): 1 [] xor(x,x)!=falsehood.
% 1.66/1.86
% 1.66/1.86 ------------> process sos:
% 1.66/1.86 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.66/1.86 ** KEPT (pick-wt=5): 3 [] implies(truth,A)=A.
% 1.66/1.86 ---> New Demodulator: 4 [new_demod,3] implies(truth,A)=A.
% 1.66/1.86 ** KEPT (pick-wt=13): 5 [] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.66/1.86 ---> New Demodulator: 6 [new_demod,5] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.66/1.86 ** KEPT (pick-wt=11): 7 [] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.66/1.86 ** KEPT (pick-wt=11): 8 [] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.66/1.86 ---> New Demodulator: 9 [new_demod,8] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.66/1.86 ** KEPT (pick-wt=8): 10 [] or(A,B)=implies(not(A),B).
% 1.66/1.86 ** KEPT (pick-wt=11): 11 [] or(or(A,B),C)=or(A,or(B,C)).
% 1.66/1.86 ---> New Demodulator: 12 [new_demod,11] or(or(A,B),C)=or(A,or(B,C)).
% 1.66/1.86 ** KEPT (pick-wt=7): 13 [] or(A,B)=or(B,A).
% 1.66/1.86 ** KEPT (pick-wt=10): 15 [copy,14,flip.1] not(or(not(A),not(B)))=and(A,B).
% 1.66/1.86 ---> New Demodulator: 16 [new_demod,15] not(or(not(A),not(B)))=and(A,B).
% 1.66/1.86 ** KEPT (pick-wt=11): 17 [] and(and(A,B),C)=and(A,and(B,C)).
% 1.66/1.86 ---> New Demodulator: 18 [new_demod,17] and(and(A,B),C)=and(A,and(B,C)).
% 1.66/1.86 ** KEPT (pick-wt=7): 19 [] and(A,B)=and(B,A).
% 1.66/1.86 ** KEPT (pick-wt=13): 20 [] xor(A,B)=or(and(A,not(B)),and(not(A),B)).
% 1.66/1.86 ** KEPT (pick-wt=7): 21 [] xor(A,B)=xor(B,A).
% 1.66/1.86 ** KEPT (pick-wt=7): 23 [copy,22,demod,16] and_star(A,B)=and(A,B).
% 1.66/1.86 ---> New Demodulator: 24 [new_demod,23] and_star(A,B)=and(A,B).
% 1.66/1.86 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)).
% 1.66/1.86 Following clause subsumed by 19 during input processing: 0 [demod,24,24] and(A,B)=and(B,A).
% 1.66/1.86 ** KEPT (pick-wt=4): 25 [] not(truth)=falsehood.
% 1.66/1.86 ---> New Demodulator: 26 [new_demod,25] not(truth)=falsehood.
% 1.66/1.86 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.66/1.86 >>>> Starting back demodulation with 4.
% 1.66/1.86 >>>> Starting back demodulation with 6.
% 1.66/1.86 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.66/1.86 >>>> Starting back demodulation with 9.
% 1.66/1.86 ** KEPT (pick-wt=8): 27 [copy,10,flip.1] implies(not(A),B)=or(A,B).
% 1.66/1.86 >>>> Starting back demodulation with 12.
% 1.66/1.86 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] or(A,B)=or(B,A).
% 1.66/1.86 >>>> Starting back demodulation with 16.
% 1.66/1.86 >>>> Starting back demodulation with 18.
% 1.66/1.86 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] and(A,B)=and(B,A).
% 1.66/1.86 ** KEPT (pick-wt=13): 28 [copy,20,flip.1] or(and(A,not(B)),and(not(A),B))=xor(A,B).
% 1.66/1.86 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] xor(A,B)=xor(B,A).
% 1.66/1.86 >>>> Starting back demodulation with 24.
% 1.66/1.86 >>>> Starting back demodulation with 26.
% 1.66/1.86 Following clause subsumed by 10 during input processing: 0 [copy,27,flip.1] or(A,B)=implies(not(A),B).
% 1.66/1.86 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)).
% 1.66/1.86
% 1.66/1.86 ======= end of input processing =======
% 1.66/1.86
% 1.66/1.86 =========== start of search ===========
% 1.66/1.86
% 1.66/1.86 -------- PROOF --------
% 1.66/1.86
% 1.66/1.86 ----> UNIT CONFLICT at 0.01 sec ----> 300 [binary,298.1,295.1] $F.
% 1.66/1.86
% 1.66/1.86 Length of proof is 24. Level of proof is 8.
% 1.66/1.86
% 1.66/1.86 ---------------- PROOF ----------------
% 1.66/1.86 % SZS status Unsatisfiable
% 1.66/1.86 % SZS output start Refutation
% See solution above
% 1.66/1.86 ------------ end of proof -------------
% 1.66/1.86
% 1.66/1.86
% 1.66/1.86 Search stopped by max_proofs option.
% 1.66/1.86
% 1.66/1.86
% 1.66/1.86 Search stopped by max_proofs option.
% 1.66/1.86
% 1.66/1.86 ============ end of search ============
% 1.66/1.86
% 1.66/1.86 -------------- statistics -------------
% 1.66/1.86 clauses given 40
% 1.66/1.86 clauses generated 410
% 1.66/1.86 clauses kept 164
% 1.66/1.86 clauses forward subsumed 358
% 1.66/1.86 clauses back subsumed 0
% 1.66/1.86 Kbytes malloced 1953
% 1.66/1.86
% 1.66/1.86 ----------- times (seconds) -----------
% 1.66/1.86 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.66/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.86 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.86
% 1.66/1.86 That finishes the proof of the theorem.
% 1.66/1.86
% 1.66/1.86 Process 31267 finished Wed Jul 27 09:26:33 2022
% 1.66/1.86 Otter interrupted
% 1.66/1.86 PROOF FOUND
%------------------------------------------------------------------------------