TSTP Solution File: LCL161-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:03:43 EDT 2022
% Result : Unsatisfiable 1.75s 1.94s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 2 RR)
% Number of literals : 17 ( 16 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
implies(truth,x) != x,
file('LCL161-1.p',unknown),
[] ).
cnf(5,axiom,
xor(A,falsehood) = A,
file('LCL161-1.p',unknown),
[] ).
cnf(7,axiom,
xor(A,A) = falsehood,
file('LCL161-1.p',unknown),
[] ).
cnf(10,axiom,
and_star(A,truth) = A,
file('LCL161-1.p',unknown),
[] ).
cnf(15,axiom,
xor(A,xor(truth,B)) = xor(xor(A,truth),B),
file('LCL161-1.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('LCL161-1.p',unknown),
[] ).
cnf(22,axiom,
and_star(A,B) = and_star(B,A),
file('LCL161-1.p',unknown),
[] ).
cnf(23,axiom,
implies(A,B) = xor(truth,and_star(A,xor(truth,B))),
file('LCL161-1.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(27,plain,
xor(falsehood,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,5])]),
[iquote('para_into,19.1.1,5.1.1,flip.1')] ).
cnf(34,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(40,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]),27])]),
[iquote('para_into,16.1.1.1,7.1.1,demod,27,flip.1')] ).
cnf(84,plain,
xor(truth,A) = implies(A,falsehood),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,5]),10]),
[iquote('para_into,24.1.1.2.2,5.1.1,demod,10')] ).
cnf(86,plain,
implies(implies(A,falsehood),falsehood) = implies(truth,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,34]),84,84]),
[iquote('para_into,24.1.1.2,34.1.1,demod,84,84')] ).
cnf(126,plain,
implies(truth,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),84,84,86]),
[iquote('back_demod,40,demod,84,84,86')] ).
cnf(128,plain,
$false,
inference(binary,[status(thm)],[126,1]),
[iquote('binary,126.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Jul 27 09:30:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.75/1.93 ----- Otter 3.3f, August 2004 -----
% 1.75/1.93 The process was started by sandbox2 on n019.cluster.edu,
% 1.75/1.93 Wed Jul 27 09:30:37 2022
% 1.75/1.93 The command was "./otter". The process ID is 4207.
% 1.75/1.93
% 1.75/1.93 set(prolog_style_variables).
% 1.75/1.93 set(auto).
% 1.75/1.93 dependent: set(auto1).
% 1.75/1.93 dependent: set(process_input).
% 1.75/1.93 dependent: clear(print_kept).
% 1.75/1.93 dependent: clear(print_new_demod).
% 1.75/1.93 dependent: clear(print_back_demod).
% 1.75/1.93 dependent: clear(print_back_sub).
% 1.75/1.93 dependent: set(control_memory).
% 1.75/1.93 dependent: assign(max_mem, 12000).
% 1.75/1.93 dependent: assign(pick_given_ratio, 4).
% 1.75/1.93 dependent: assign(stats_level, 1).
% 1.75/1.93 dependent: assign(max_seconds, 10800).
% 1.75/1.93 clear(print_given).
% 1.75/1.93
% 1.75/1.93 list(usable).
% 1.75/1.93 0 [] A=A.
% 1.75/1.93 0 [] not(X)=xor(X,truth).
% 1.75/1.93 0 [] xor(X,falsehood)=X.
% 1.75/1.93 0 [] xor(X,X)=falsehood.
% 1.75/1.93 0 [] and_star(X,truth)=X.
% 1.75/1.93 0 [] and_star(X,falsehood)=falsehood.
% 1.75/1.93 0 [] and_star(xor(truth,X),X)=falsehood.
% 1.75/1.93 0 [] xor(X,xor(truth,Y))=xor(xor(X,truth),Y).
% 1.75/1.93 0 [] and_star(xor(and_star(xor(truth,X),Y),truth),Y)=and_star(xor(and_star(xor(truth,Y),X),truth),X).
% 1.75/1.93 0 [] xor(X,Y)=xor(Y,X).
% 1.75/1.93 0 [] and_star(and_star(X,Y),Z)=and_star(X,and_star(Y,Z)).
% 1.75/1.93 0 [] and_star(X,Y)=and_star(Y,X).
% 1.75/1.93 0 [] not(truth)=falsehood.
% 1.75/1.93 0 [] implies(X,Y)=xor(truth,and_star(X,xor(truth,Y))).
% 1.75/1.93 0 [] implies(truth,x)!=x.
% 1.75/1.93 end_of_list.
% 1.75/1.93
% 1.75/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.93
% 1.75/1.93 All clauses are units, and equality is present; the
% 1.75/1.93 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.93
% 1.75/1.93 dependent: set(knuth_bendix).
% 1.75/1.93 dependent: set(anl_eq).
% 1.75/1.93 dependent: set(para_from).
% 1.75/1.93 dependent: set(para_into).
% 1.75/1.93 dependent: clear(para_from_right).
% 1.75/1.93 dependent: clear(para_into_right).
% 1.75/1.93 dependent: set(para_from_vars).
% 1.75/1.93 dependent: set(eq_units_both_ways).
% 1.75/1.93 dependent: set(dynamic_demod_all).
% 1.75/1.93 dependent: set(dynamic_demod).
% 1.75/1.93 dependent: set(order_eq).
% 1.75/1.93 dependent: set(back_demod).
% 1.75/1.93 dependent: set(lrpo).
% 1.75/1.93
% 1.75/1.93 ------------> process usable:
% 1.75/1.93 ** KEPT (pick-wt=5): 1 [] implies(truth,x)!=x.
% 1.75/1.93
% 1.75/1.93 ------------> process sos:
% 1.75/1.93 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.93 ** KEPT (pick-wt=6): 3 [] not(A)=xor(A,truth).
% 1.75/1.93 ---> New Demodulator: 4 [new_demod,3] not(A)=xor(A,truth).
% 1.75/1.93 ** KEPT (pick-wt=5): 5 [] xor(A,falsehood)=A.
% 1.75/1.93 ---> New Demodulator: 6 [new_demod,5] xor(A,falsehood)=A.
% 1.75/1.93 ** KEPT (pick-wt=5): 7 [] xor(A,A)=falsehood.
% 1.75/1.93 ---> New Demodulator: 8 [new_demod,7] xor(A,A)=falsehood.
% 1.75/1.93 ** KEPT (pick-wt=5): 9 [] and_star(A,truth)=A.
% 1.75/1.93 ---> New Demodulator: 10 [new_demod,9] and_star(A,truth)=A.
% 1.75/1.93 ** KEPT (pick-wt=5): 11 [] and_star(A,falsehood)=falsehood.
% 1.75/1.93 ---> New Demodulator: 12 [new_demod,11] and_star(A,falsehood)=falsehood.
% 1.75/1.93 ** KEPT (pick-wt=7): 13 [] and_star(xor(truth,A),A)=falsehood.
% 1.75/1.93 ---> New Demodulator: 14 [new_demod,13] and_star(xor(truth,A),A)=falsehood.
% 1.75/1.93 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.75/1.93 ---> New Demodulator: 17 [new_demod,16] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.75/1.93 ** 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).
% 1.75/1.93 ** KEPT (pick-wt=7): 19 [] xor(A,B)=xor(B,A).
% 1.75/1.93 ** KEPT (pick-wt=11): 20 [] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.75/1.93 ---> New Demodulator: 21 [new_demod,20] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.75/1.93 ** KEPT (pick-wt=7): 22 [] and_star(A,B)=and_star(B,A).
% 1.75/1.93 Following clause subsumed by 2 during input processing: 0 [demod,4,8] falsehood=falsehood.
% 1.75/1.93 ** KEPT (pick-wt=11): 24 [copy,23,flip.1] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.75/1.93 ---> New Demodulator: 25 [new_demod,24] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.75/1.93 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.75/1.93 >>>> Starting back demodulation with 4.
% 1.75/1.93 >>>> Starting back demodulation with 6.
% 1.75/1.93 >>>> Starting back demodulation with 8.
% 1.75/1.93 >>>> Starting back demodulation with 10.
% 1.75/1.93 >>>> Starting back demodulation with 12.
% 1.75/1.93 >>>> Starting back demodulation with 14.
% 1.75/1.93 >>>> Starting back demodulation with 17.
% 1.75/1.93 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).
% 1.75/1.93 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] xor(A,B)=xor(B,A).
% 1.75/1.94 >>>> Starting back demodulation with 21.
% 1.75/1.94 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] and_star(A,B)=and_star(B,A).
% 1.75/1.94 >>>> Starting back demodulation with 25.
% 1.75/1.94
% 1.75/1.94 ======= end of input processing =======
% 1.75/1.94
% 1.75/1.94 =========== start of search ===========
% 1.75/1.94
% 1.75/1.94 -------- PROOF --------
% 1.75/1.94
% 1.75/1.94 ----> UNIT CONFLICT at 0.00 sec ----> 128 [binary,126.1,1.1] $F.
% 1.75/1.94
% 1.75/1.94 Length of proof is 8. Level of proof is 4.
% 1.75/1.94
% 1.75/1.94 ---------------- PROOF ----------------
% 1.75/1.94 % SZS status Unsatisfiable
% 1.75/1.94 % SZS output start Refutation
% See solution above
% 1.75/1.94 ------------ end of proof -------------
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94 ============ end of search ============
% 1.75/1.94
% 1.75/1.94 -------------- statistics -------------
% 1.75/1.94 clauses given 21
% 1.75/1.94 clauses generated 188
% 1.75/1.94 clauses kept 72
% 1.75/1.94 clauses forward subsumed 165
% 1.75/1.94 clauses back subsumed 0
% 1.75/1.94 Kbytes malloced 1953
% 1.75/1.94
% 1.75/1.94 ----------- times (seconds) -----------
% 1.75/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.94
% 1.75/1.94 That finishes the proof of the theorem.
% 1.75/1.94
% 1.75/1.94 Process 4207 finished Wed Jul 27 09:30:38 2022
% 1.75/1.94 Otter interrupted
% 1.75/1.94 PROOF FOUND
%------------------------------------------------------------------------------