TSTP Solution File: LCL109-5 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL109-5 : 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 13:03:34 EDT 2022
% Result : Unsatisfiable 1.65s 1.84s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 8 RR)
% Number of literals : 26 ( 13 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ordered(A,B)
| implies(A,B) = truth ),
file('LCL109-5.p',unknown),
[] ).
cnf(2,axiom,
( implies(A,B) != truth
| ordered(A,B) ),
file('LCL109-5.p',unknown),
[] ).
cnf(3,axiom,
( ~ ordered(A,B)
| ordered(implies(A,C),implies(B,C)) ),
file('LCL109-5.p',unknown),
[] ).
cnf(5,axiom,
( ~ ordered(A,implies(B,C))
| ordered(B,implies(A,C)) ),
file('LCL109-5.p',unknown),
[] ).
cnf(6,axiom,
big_V(implies(x,y),implies(y,x)) != truth,
file('LCL109-5.p',unknown),
[] ).
cnf(9,axiom,
implies(truth,A) = A,
file('LCL109-5.p',unknown),
[] ).
cnf(12,axiom,
implies(implies(A,B),B) = implies(implies(B,A),A),
file('LCL109-5.p',unknown),
[] ).
cnf(15,axiom,
big_V(A,B) = implies(implies(A,B),B),
file('LCL109-5.p',unknown),
[] ).
cnf(17,plain,
implies(implies(A,B),B) = big_V(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(29,plain,
big_V(A,B) = big_V(B,A),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),17,17]),
[iquote('copy,12,flip.1,demod,17,17')] ).
cnf(32,plain,
ordered(truth,truth),
inference(hyper,[status(thm)],[9,2]),
[iquote('hyper,8,2')] ).
cnf(33,plain,
( truth = A
| ~ ordered(truth,A) ),
inference(para_into,[status(thm),theory(equality)],[9,1]),
[iquote('para_into,8.1.1,1.2.1')] ).
cnf(41,plain,
ordered(A,A),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[32,3]),9,9]),
[iquote('hyper,32,3,demod,9,9')] ).
cnf(42,plain,
ordered(A,big_V(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[41,5]),17]),
[iquote('hyper,41,5,demod,17')] ).
cnf(77,plain,
big_V(truth,A) = truth,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[33,42])]),
[iquote('hyper,33,42,flip.1')] ).
cnf(130,plain,
big_V(A,truth) = truth,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,77])]),
[iquote('para_into,29.1.1,77.1.1,flip.1')] ).
cnf(135,plain,
big_V(implies(y,x),implies(x,y)) != truth,
inference(para_from,[status(thm),theory(equality)],[29,6]),
[iquote('para_from,29.1.1,6.1.1')] ).
cnf(137,plain,
ordered(A,truth),
inference(para_from,[status(thm),theory(equality)],[130,42]),
[iquote('para_from,130.1.1,42.1.2')] ).
cnf(139,plain,
ordered(implies(A,B),B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[137,3]),9]),
[iquote('hyper,137,3,demod,9')] ).
cnf(180,plain,
big_V(A,B) = truth,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[139,1]),17]),
[iquote('hyper,139,1,demod,17')] ).
cnf(182,plain,
$false,
inference(binary,[status(thm)],[180,135]),
[iquote('binary,180.1,135.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 09:13:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.65/1.84 ----- Otter 3.3f, August 2004 -----
% 1.65/1.84 The process was started by sandbox on n018.cluster.edu,
% 1.65/1.84 Wed Jul 27 09:13:31 2022
% 1.65/1.84 The command was "./otter". The process ID is 22109.
% 1.65/1.84
% 1.65/1.84 set(prolog_style_variables).
% 1.65/1.84 set(auto).
% 1.65/1.84 dependent: set(auto1).
% 1.65/1.84 dependent: set(process_input).
% 1.65/1.84 dependent: clear(print_kept).
% 1.65/1.84 dependent: clear(print_new_demod).
% 1.65/1.84 dependent: clear(print_back_demod).
% 1.65/1.84 dependent: clear(print_back_sub).
% 1.65/1.84 dependent: set(control_memory).
% 1.65/1.84 dependent: assign(max_mem, 12000).
% 1.65/1.84 dependent: assign(pick_given_ratio, 4).
% 1.65/1.84 dependent: assign(stats_level, 1).
% 1.65/1.84 dependent: assign(max_seconds, 10800).
% 1.65/1.84 clear(print_given).
% 1.65/1.84
% 1.65/1.84 list(usable).
% 1.65/1.84 0 [] A=A.
% 1.65/1.84 0 [] implies(truth,X)=X.
% 1.65/1.84 0 [] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))=truth.
% 1.65/1.84 0 [] implies(implies(X,Y),Y)=implies(implies(Y,X),X).
% 1.65/1.84 0 [] implies(implies(not(X),not(Y)),implies(Y,X))=truth.
% 1.65/1.84 0 [] big_V(X,Y)=implies(implies(X,Y),Y).
% 1.65/1.84 0 [] big_hat(X,Y)=not(big_V(not(X),not(Y))).
% 1.65/1.84 0 [] -ordered(X,Y)|implies(X,Y)=truth.
% 1.65/1.84 0 [] implies(X,Y)!=truth|ordered(X,Y).
% 1.65/1.84 0 [] -ordered(X,Y)|ordered(implies(X,Z),implies(Y,Z)).
% 1.65/1.84 0 [] -ordered(X,Y)|ordered(implies(Z,X),implies(Z,Y)).
% 1.65/1.84 0 [] -ordered(X,implies(Y,Z))|ordered(Y,implies(X,Z)).
% 1.65/1.84 0 [] -ordered(Y,implies(X,Z))|ordered(X,implies(Y,Z)).
% 1.65/1.84 0 [] not(big_V(X,Y))=big_hat(not(X),not(Y)).
% 1.65/1.84 0 [] not(big_hat(X,Y))=big_V(not(X),not(Y)).
% 1.65/1.84 0 [] implies(big_V(X,Y),Z)=big_hat(implies(X,Z),implies(Y,Z)).
% 1.65/1.84 0 [] implies(X,big_hat(Y,Z))=big_hat(implies(X,Y),implies(X,Z)).
% 1.65/1.84 0 [] big_V(implies(x,y),implies(y,x))!=truth.
% 1.65/1.84 end_of_list.
% 1.65/1.84
% 1.65/1.84 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.65/1.84
% 1.65/1.84 This is a Horn set with equality. The strategy will be
% 1.65/1.84 Knuth-Bendix and hyper_res, with positive clauses in
% 1.65/1.84 sos and nonpositive clauses in usable.
% 1.65/1.84
% 1.65/1.84 dependent: set(knuth_bendix).
% 1.65/1.84 dependent: set(anl_eq).
% 1.65/1.84 dependent: set(para_from).
% 1.65/1.84 dependent: set(para_into).
% 1.65/1.84 dependent: clear(para_from_right).
% 1.65/1.84 dependent: clear(para_into_right).
% 1.65/1.84 dependent: set(para_from_vars).
% 1.65/1.84 dependent: set(eq_units_both_ways).
% 1.65/1.84 dependent: set(dynamic_demod_all).
% 1.65/1.84 dependent: set(dynamic_demod).
% 1.65/1.84 dependent: set(order_eq).
% 1.65/1.84 dependent: set(back_demod).
% 1.65/1.84 dependent: set(lrpo).
% 1.65/1.84 dependent: set(hyper_res).
% 1.65/1.84 dependent: clear(order_hyper).
% 1.65/1.84
% 1.65/1.84 ------------> process usable:
% 1.65/1.84 ** KEPT (pick-wt=8): 1 [] -ordered(A,B)|implies(A,B)=truth.
% 1.65/1.84 ** KEPT (pick-wt=8): 2 [] implies(A,B)!=truth|ordered(A,B).
% 1.65/1.84 ** KEPT (pick-wt=10): 3 [] -ordered(A,B)|ordered(implies(A,C),implies(B,C)).
% 1.65/1.84 ** KEPT (pick-wt=10): 4 [] -ordered(A,B)|ordered(implies(C,A),implies(C,B)).
% 1.65/1.84 ** KEPT (pick-wt=10): 5 [] -ordered(A,implies(B,C))|ordered(B,implies(A,C)).
% 1.65/1.84 Following clause subsumed by 5 during input processing: 0 [] -ordered(A,implies(B,C))|ordered(B,implies(A,C)).
% 1.65/1.84 ** KEPT (pick-wt=9): 6 [] big_V(implies(x,y),implies(y,x))!=truth.
% 1.65/1.84
% 1.65/1.84 ------------> process sos:
% 1.65/1.84 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.65/1.84 ** KEPT (pick-wt=5): 8 [] implies(truth,A)=A.
% 1.65/1.84 ---> New Demodulator: 9 [new_demod,8] implies(truth,A)=A.
% 1.65/1.84 ** KEPT (pick-wt=13): 10 [] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.65/1.84 ---> New Demodulator: 11 [new_demod,10] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.65/1.84 ** KEPT (pick-wt=11): 12 [] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.65/1.84 ** KEPT (pick-wt=11): 13 [] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.65/1.84 ---> New Demodulator: 14 [new_demod,13] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.65/1.84 ** KEPT (pick-wt=9): 16 [copy,15,flip.1] implies(implies(A,B),B)=big_V(A,B).
% 1.65/1.84 ---> New Demodulator: 17 [new_demod,16] implies(implies(A,B),B)=big_V(A,B).
% 1.65/1.84 ** KEPT (pick-wt=10): 19 [copy,18,flip.1] not(big_V(not(A),not(B)))=big_hat(A,B).
% 1.65/1.84 ---> New Demodulator: 20 [new_demod,19] not(big_V(not(A),not(B)))=big_hat(A,B).
% 1.65/1.84 ** KEPT (pick-wt=10): 21 [] not(big_V(A,B))=big_hat(not(A),not(B)).
% 1.65/1.84 ---> New Demodulator: 22 [new_demod,21] not(big_V(A,B))=big_hat(not(A),not(B)).
% 1.65/1.84 ** KEPT (pick-wt=10): 23 [] not(big_hat(A,B))=big_V(not(A),not(B)).
% 1.65/1.84 ---> New Demodulator: 24 [new_demod,23] not(big_hat(A,B))=big_V(not(A),not(B)).
% 1.65/1.84 ** KEPT (pick-wt=13): 25 [] implies(big_V(A,B),C)=big_hat(implies(A,C),implies(B,C)).
% 1.65/1.84 ---> New Demodulator: 26 [new_demod,25] implies(big_V(A,B),C)=big_hat(implies(A,C),implies(B,C)).
% 1.65/1.84 ** KEPT (pick-wt=13): 27 [] implies(A,big_hat(B,C))=big_hat(implies(A,B),implies(A,C)).
% 1.65/1.84 ---> New Demodulator: 28 [new_demod,27] implies(A,big_hat(B,C))=big_hat(implies(A,B),implies(A,C)).
% 1.65/1.84 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.65/1.84 >>>> Starting back demodulation with 9.
% 1.65/1.84 >>>> Starting back demodulation with 11.
% 1.65/1.84 ** KEPT (pick-wt=7): 29 [copy,12,flip.1,demod,17,17] big_V(A,B)=big_V(B,A).
% 1.65/1.84 >>>> Starting back demodulation with 14.
% 1.65/1.84 >>>> Starting back demodulation with 17.
% 1.65/1.84 >> back demodulating 12 with 17.
% 1.65/1.84 >>>> Starting back demodulation with 20.
% 1.65/1.84 >>>> Starting back demodulation with 22.
% 1.65/1.84 >> back demodulating 19 with 22.
% 1.65/1.84 >>>> Starting back demodulation with 24.
% 1.65/1.84 >>>> Starting back demodulation with 26.
% 1.65/1.84 >>>> Starting back demodulation with 28.
% 1.65/1.84 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] big_V(A,B)=big_V(B,A).
% 1.65/1.84 >>>> Starting back demodulation with 31.
% 1.65/1.84
% 1.65/1.84 ======= end of input processing =======
% 1.65/1.84
% 1.65/1.84 =========== start of search ===========
% 1.65/1.84
% 1.65/1.84 -------- PROOF --------
% 1.65/1.84
% 1.65/1.84 ----> UNIT CONFLICT at 0.01 sec ----> 182 [binary,180.1,135.1] $F.
% 1.65/1.84
% 1.65/1.84 Length of proof is 12. Level of proof is 8.
% 1.65/1.84
% 1.65/1.84 ---------------- PROOF ----------------
% 1.65/1.84 % SZS status Unsatisfiable
% 1.65/1.84 % SZS output start Refutation
% See solution above
% 1.65/1.84 ------------ end of proof -------------
% 1.65/1.84
% 1.65/1.84
% 1.65/1.84 Search stopped by max_proofs option.
% 1.65/1.84
% 1.65/1.84
% 1.65/1.84 Search stopped by max_proofs option.
% 1.65/1.84
% 1.65/1.84 ============ end of search ============
% 1.65/1.84
% 1.65/1.84 -------------- statistics -------------
% 1.65/1.84 clauses given 18
% 1.65/1.84 clauses generated 210
% 1.65/1.84 clauses kept 140
% 1.65/1.84 clauses forward subsumed 110
% 1.65/1.84 clauses back subsumed 16
% 1.65/1.84 Kbytes malloced 1953
% 1.65/1.84
% 1.65/1.84 ----------- times (seconds) -----------
% 1.65/1.84 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.84 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.84 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.84
% 1.65/1.84 That finishes the proof of the theorem.
% 1.65/1.84
% 1.65/1.84 Process 22109 finished Wed Jul 27 09:13:33 2022
% 1.65/1.84 Otter interrupted
% 1.65/1.84 PROOF FOUND
%------------------------------------------------------------------------------