TSTP Solution File: LCL164-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:03:44 EDT 2022
% Result : Unsatisfiable 1.69s 1.91s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 6 RR)
% Number of literals : 42 ( 41 equ; 5 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; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file('LCL164-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('LCL164-1.p',unknown),
[] ).
cnf(4,axiom,
not(A) = xor(A,truth),
file('LCL164-1.p',unknown),
[] ).
cnf(6,axiom,
xor(A,falsehood) = A,
file('LCL164-1.p',unknown),
[] ).
cnf(7,axiom,
xor(A,A) = falsehood,
file('LCL164-1.p',unknown),
[] ).
cnf(10,axiom,
and_star(A,truth) = A,
file('LCL164-1.p',unknown),
[] ).
cnf(13,axiom,
and_star(xor(truth,A),A) = falsehood,
file('LCL164-1.p',unknown),
[] ).
cnf(15,axiom,
xor(A,xor(truth,B)) = xor(xor(A,truth),B),
file('LCL164-1.p',unknown),
[] ).
cnf(16,plain,
xor(xor(A,truth),B) = xor(A,xor(truth,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(19,axiom,
xor(A,B) = xor(B,A),
file('LCL164-1.p',unknown),
[] ).
cnf(20,axiom,
and_star(and_star(A,B),C) = and_star(A,and_star(B,C)),
file('LCL164-1.p',unknown),
[] ).
cnf(22,axiom,
and_star(A,B) = and_star(B,A),
file('LCL164-1.p',unknown),
[] ).
cnf(23,axiom,
implies(A,B) = xor(truth,and_star(A,xor(truth,B))),
file('LCL164-1.p',unknown),
[] ).
cnf(24,plain,
xor(truth,and_star(A,xor(truth,B))) = implies(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
[iquote('copy,23,flip.1')] ).
cnf(26,plain,
implies(implies(xor(x,truth),xor(y,truth)),implies(y,x)) != truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),4,4]),
[iquote('back_demod,1,demod,4,4')] ).
cnf(28,plain,
xor(falsehood,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,6])]),
[iquote('para_into,19.1.1,5.1.1,flip.1')] ).
cnf(31,plain,
and_star(A,xor(truth,A)) = falsehood,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,13])]),
[iquote('para_into,22.1.1,13.1.1,flip.1')] ).
cnf(35,plain,
and_star(truth,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,10])]),
[iquote('para_into,22.1.1,9.1.1,flip.1')] ).
cnf(41,plain,
xor(truth,xor(truth,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,7]),28])]),
[iquote('para_into,16.1.1.1,7.1.1,demod,28,flip.1')] ).
cnf(60,plain,
xor(truth,xor(A,truth)) = A,
inference(para_into,[status(thm),theory(equality)],[41,19]),
[iquote('para_into,41.1.1.2,19.1.1')] ).
cnf(77,plain,
xor(truth,and_star(A,B)) = implies(A,xor(B,truth)),
inference(para_into,[status(thm),theory(equality)],[24,60]),
[iquote('para_into,24.1.1.2.2,60.1.1')] ).
cnf(79,plain,
xor(truth,and_star(A,B)) = implies(A,xor(truth,B)),
inference(para_into,[status(thm),theory(equality)],[24,41]),
[iquote('para_into,24.1.1.2.2,41.1.1')] ).
cnf(80,plain,
implies(A,xor(truth,implies(B,C))) = implies(A,and_star(B,xor(truth,C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,24]),79]),
[iquote('para_into,24.1.1.2.2,24.1.1,demod,79')] ).
cnf(85,plain,
xor(truth,A) = implies(A,falsehood),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,6]),10]),
[iquote('para_into,24.1.1.2.2,5.1.1,demod,10')] ).
cnf(87,plain,
implies(implies(A,falsehood),falsehood) = implies(truth,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,35]),85,85]),
[iquote('para_into,24.1.1.2,35.1.1,demod,85,85')] ).
cnf(91,plain,
implies(A,A) = truth,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,31]),6])]),
[iquote('para_into,24.1.1.2,31.1.1,demod,6,flip.1')] ).
cnf(94,plain,
implies(and_star(implies(A,falsehood),B),falsehood) = implies(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,22]),85,85]),
[iquote('para_into,24.1.1.2,22.1.1,demod,85,85')] ).
cnf(96,plain,
implies(and_star(A,and_star(B,implies(C,falsehood))),falsehood) = implies(and_star(A,B),C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,20]),85,85]),
[iquote('para_into,24.1.1.2,20.1.1,demod,85,85')] ).
cnf(102,plain,
implies(A,xor(B,truth)) = implies(and_star(A,B),falsehood),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[77])]),85]),
[iquote('copy,77,flip.1,demod,85')] ).
cnf(115,plain,
implies(A,implies(implies(B,C),falsehood)) = implies(A,and_star(B,implies(C,falsehood))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),85,85]),
[iquote('back_demod,80,demod,85,85')] ).
cnf(118,plain,
implies(and_star(A,B),falsehood) = implies(A,implies(B,falsehood)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),85,85]),
[iquote('back_demod,78,demod,85,85')] ).
cnf(128,plain,
implies(truth,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),85,85,87]),
[iquote('back_demod,41,demod,85,85,87')] ).
cnf(138,plain,
implies(A,xor(B,truth)) = implies(A,implies(B,falsehood)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[102])]),118])]),
[iquote('copy,102,flip.1,demod,118,flip.1')] ).
cnf(142,plain,
implies(and_star(A,B),C) = implies(A,implies(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),118,118,87,128])]),
[iquote('back_demod,96,demod,118,118,87,128,flip.1')] ).
cnf(143,plain,
implies(implies(A,falsehood),implies(B,falsehood)) = implies(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[94]),142]),
[iquote('back_demod,94,demod,142')] ).
cnf(146,plain,
implies(implies(xor(x,truth),implies(y,falsehood)),implies(y,x)) != truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),138]),
[iquote('back_demod,26,demod,138')] ).
cnf(147,plain,
implies(A,B) = implies(implies(B,falsehood),implies(A,falsehood)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[143])]),
[iquote('copy,143,flip.1')] ).
cnf(155,plain,
xor(A,truth) = implies(A,falsehood),
inference(para_into,[status(thm),theory(equality)],[85,19]),
[iquote('para_into,84.1.1,19.1.1')] ).
cnf(162,plain,
implies(implies(implies(x,falsehood),implies(y,falsehood)),implies(y,x)) != truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[146]),155]),
[iquote('back_demod,146,demod,155')] ).
cnf(224,plain,
implies(implies(A,B),falsehood) = and_star(A,implies(B,falsehood)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[115,128]),128]),
[iquote('para_into,115.1.1,127.1.1,demod,128')] ).
cnf(400,plain,
truth != truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[162,147]),224,91,10,224,91,10,91]),
[iquote('para_into,162.1.1.1,147.1.1,demod,224,91,10,224,91,10,91')] ).
cnf(401,plain,
$false,
inference(binary,[status(thm)],[400,2]),
[iquote('binary,400.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 09:32:21 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.69/1.88 ----- Otter 3.3f, August 2004 -----
% 1.69/1.88 The process was started by sandbox2 on n027.cluster.edu,
% 1.69/1.88 Wed Jul 27 09:32:22 2022
% 1.69/1.88 The command was "./otter". The process ID is 15727.
% 1.69/1.88
% 1.69/1.88 set(prolog_style_variables).
% 1.69/1.88 set(auto).
% 1.69/1.88 dependent: set(auto1).
% 1.69/1.88 dependent: set(process_input).
% 1.69/1.88 dependent: clear(print_kept).
% 1.69/1.88 dependent: clear(print_new_demod).
% 1.69/1.88 dependent: clear(print_back_demod).
% 1.69/1.88 dependent: clear(print_back_sub).
% 1.69/1.88 dependent: set(control_memory).
% 1.69/1.88 dependent: assign(max_mem, 12000).
% 1.69/1.88 dependent: assign(pick_given_ratio, 4).
% 1.69/1.88 dependent: assign(stats_level, 1).
% 1.69/1.88 dependent: assign(max_seconds, 10800).
% 1.69/1.88 clear(print_given).
% 1.69/1.88
% 1.69/1.88 list(usable).
% 1.69/1.88 0 [] A=A.
% 1.69/1.88 0 [] not(X)=xor(X,truth).
% 1.69/1.88 0 [] xor(X,falsehood)=X.
% 1.69/1.88 0 [] xor(X,X)=falsehood.
% 1.69/1.88 0 [] and_star(X,truth)=X.
% 1.69/1.88 0 [] and_star(X,falsehood)=falsehood.
% 1.69/1.88 0 [] and_star(xor(truth,X),X)=falsehood.
% 1.69/1.88 0 [] xor(X,xor(truth,Y))=xor(xor(X,truth),Y).
% 1.69/1.88 0 [] and_star(xor(and_star(xor(truth,X),Y),truth),Y)=and_star(xor(and_star(xor(truth,Y),X),truth),X).
% 1.69/1.88 0 [] xor(X,Y)=xor(Y,X).
% 1.69/1.88 0 [] and_star(and_star(X,Y),Z)=and_star(X,and_star(Y,Z)).
% 1.69/1.88 0 [] and_star(X,Y)=and_star(Y,X).
% 1.69/1.88 0 [] not(truth)=falsehood.
% 1.69/1.88 0 [] implies(X,Y)=xor(truth,and_star(X,xor(truth,Y))).
% 1.69/1.88 0 [] implies(implies(not(x),not(y)),implies(y,x))!=truth.
% 1.69/1.88 end_of_list.
% 1.69/1.88
% 1.69/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.69/1.88
% 1.69/1.88 All clauses are units, and equality is present; the
% 1.69/1.88 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.69/1.88
% 1.69/1.88 dependent: set(knuth_bendix).
% 1.69/1.88 dependent: set(anl_eq).
% 1.69/1.88 dependent: set(para_from).
% 1.69/1.88 dependent: set(para_into).
% 1.69/1.88 dependent: clear(para_from_right).
% 1.69/1.88 dependent: clear(para_into_right).
% 1.69/1.88 dependent: set(para_from_vars).
% 1.69/1.88 dependent: set(eq_units_both_ways).
% 1.69/1.88 dependent: set(dynamic_demod_all).
% 1.69/1.88 dependent: set(dynamic_demod).
% 1.69/1.88 dependent: set(order_eq).
% 1.69/1.88 dependent: set(back_demod).
% 1.69/1.88 dependent: set(lrpo).
% 1.69/1.88
% 1.69/1.88 ------------> process usable:
% 1.69/1.88 ** KEPT (pick-wt=11): 1 [] implies(implies(not(x),not(y)),implies(y,x))!=truth.
% 1.69/1.88
% 1.69/1.88 ------------> process sos:
% 1.69/1.88 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.88 ** KEPT (pick-wt=6): 3 [] not(A)=xor(A,truth).
% 1.69/1.88 ---> New Demodulator: 4 [new_demod,3] not(A)=xor(A,truth).
% 1.69/1.88 ** KEPT (pick-wt=5): 5 [] xor(A,falsehood)=A.
% 1.69/1.88 ---> New Demodulator: 6 [new_demod,5] xor(A,falsehood)=A.
% 1.69/1.88 ** KEPT (pick-wt=5): 7 [] xor(A,A)=falsehood.
% 1.69/1.88 ---> New Demodulator: 8 [new_demod,7] xor(A,A)=falsehood.
% 1.69/1.88 ** KEPT (pick-wt=5): 9 [] and_star(A,truth)=A.
% 1.69/1.88 ---> New Demodulator: 10 [new_demod,9] and_star(A,truth)=A.
% 1.69/1.88 ** KEPT (pick-wt=5): 11 [] and_star(A,falsehood)=falsehood.
% 1.69/1.88 ---> New Demodulator: 12 [new_demod,11] and_star(A,falsehood)=falsehood.
% 1.69/1.88 ** KEPT (pick-wt=7): 13 [] and_star(xor(truth,A),A)=falsehood.
% 1.69/1.88 ---> New Demodulator: 14 [new_demod,13] and_star(xor(truth,A),A)=falsehood.
% 1.69/1.88 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.69/1.88 ---> New Demodulator: 17 [new_demod,16] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.69/1.88 ** KEPT (pick-wt=19): 18 [] and_star(xor(and_star(xor(truth,A),B),truth),B)=and_star(xor(and_star(xor(truth,B),A),truth),A).
% 1.69/1.88 ** KEPT (pick-wt=7): 19 [] xor(A,B)=xor(B,A).
% 1.69/1.88 ** KEPT (pick-wt=11): 20 [] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.69/1.88 ---> New Demodulator: 21 [new_demod,20] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.69/1.88 ** KEPT (pick-wt=7): 22 [] and_star(A,B)=and_star(B,A).
% 1.69/1.88 Following clause subsumed by 2 during input processing: 0 [demod,4,8] falsehood=falsehood.
% 1.69/1.88 ** KEPT (pick-wt=11): 24 [copy,23,flip.1] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.69/1.88 ---> New Demodulator: 25 [new_demod,24] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.69/1.88 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.88 >>>> Starting back demodulation with 4.
% 1.69/1.88 >> back demodulating 1 with 4.
% 1.69/1.88 >>>> Starting back demodulation with 6.
% 1.69/1.88 >>>> Starting back demodulation with 8.
% 1.69/1.88 >>>> Starting back demodulation with 10.
% 1.69/1.88 >>>> Starting back demodulation with 12.
% 1.69/1.88 >>>> Starting back demodulation with 14.
% 1.69/1.88 >>>> Starting back demodulation with 17.
% 1.69/1.88 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] and_star(xor(and_star(xor(truth,A),B),truth),B)=and_star(xor(and_star(xor(truth,B),A),truth),A).
% 1.69/1.91 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] xor(A,B)=xor(B,A).
% 1.69/1.91 >>>> Starting back demodulation with 21.
% 1.69/1.91 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] and_star(A,B)=and_star(B,A).
% 1.69/1.91 >>>> Starting back demodulation with 25.
% 1.69/1.91
% 1.69/1.91 ======= end of input processing =======
% 1.69/1.91
% 1.69/1.91 =========== start of search ===========
% 1.69/1.91
% 1.69/1.91 -------- PROOF --------
% 1.69/1.91
% 1.69/1.91 ----> UNIT CONFLICT at 0.02 sec ----> 401 [binary,400.1,2.1] $F.
% 1.69/1.91
% 1.69/1.91 Length of proof is 29. Level of proof is 9.
% 1.69/1.91
% 1.69/1.91 ---------------- PROOF ----------------
% 1.69/1.91 % SZS status Unsatisfiable
% 1.69/1.91 % SZS output start Refutation
% See solution above
% 1.69/1.91 ------------ end of proof -------------
% 1.69/1.91
% 1.69/1.91
% 1.69/1.91 Search stopped by max_proofs option.
% 1.69/1.91
% 1.69/1.91
% 1.69/1.91 Search stopped by max_proofs option.
% 1.69/1.91
% 1.69/1.91 ============ end of search ============
% 1.69/1.91
% 1.69/1.91 -------------- statistics -------------
% 1.69/1.91 clauses given 61
% 1.69/1.91 clauses generated 1403
% 1.69/1.91 clauses kept 244
% 1.69/1.91 clauses forward subsumed 1319
% 1.69/1.91 clauses back subsumed 1
% 1.69/1.91 Kbytes malloced 2929
% 1.69/1.91
% 1.69/1.91 ----------- times (seconds) -----------
% 1.69/1.91 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.69/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.91
% 1.69/1.91 That finishes the proof of the theorem.
% 1.69/1.91
% 1.69/1.91 Process 15727 finished Wed Jul 27 09:32:23 2022
% 1.69/1.91 Otter interrupted
% 1.69/1.91 PROOF FOUND
%------------------------------------------------------------------------------