%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:05:47 EDT 2022
% Result : Unsatisfiable 1.71s 1.91s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 19 RR)
% Number of literals : 31 ( 30 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
f(f(n3,n2),u) != f(f(u,u),u),
file('LDA001-1.p',unknown),
[] ).
cnf(2,plain,
f(f(u,u),u) != f(f(n3,n2),u),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('LDA001-1.p',unknown),
[] ).
cnf(4,axiom,
f(A,f(B,C)) = f(f(A,B),f(A,C)),
file('LDA001-1.p',unknown),
[] ).
cnf(5,plain,
f(f(A,B),f(A,C)) = f(A,f(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(7,axiom,
n2 = f(n1,n1),
file('LDA001-1.p',unknown),
[] ).
cnf(9,plain,
f(n1,n1) = n2,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,axiom,
n3 = f(n2,n1),
file('LDA001-1.p',unknown),
[] ).
cnf(12,plain,
f(n2,n1) = n3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,axiom,
u = f(n2,n2),
file('LDA001-1.p',unknown),
[] ).
cnf(15,plain,
f(n2,n2) = u,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(16,plain,
f(u,f(n2,A)) = f(n2,f(n2,A)),
inference(para_into,[status(thm),theory(equality)],[5,15]),
[iquote('para_into,5.1.1.1,14.1.1')] ).
cnf(18,plain,
f(n3,f(n2,A)) = f(n2,f(n1,A)),
inference(para_into,[status(thm),theory(equality)],[5,12]),
[iquote('para_into,5.1.1.1,11.1.1')] ).
cnf(21,plain,
f(n2,f(n1,A)) = f(n1,f(n1,A)),
inference(para_into,[status(thm),theory(equality)],[5,9]),
[iquote('para_into,5.1.1.1,8.1.1')] ).
cnf(25,plain,
f(f(n2,A),u) = f(n2,f(A,n2)),
inference(para_into,[status(thm),theory(equality)],[5,15]),
[iquote('para_into,5.1.1.2,14.1.1')] ).
cnf(26,plain,
f(f(n2,A),n3) = f(n2,f(A,n1)),
inference(para_into,[status(thm),theory(equality)],[5,12]),
[iquote('para_into,5.1.1.2,11.1.1')] ).
cnf(28,plain,
f(f(n1,A),n2) = f(n1,f(A,n1)),
inference(para_into,[status(thm),theory(equality)],[5,9]),
[iquote('para_into,5.1.1.2,8.1.1')] ).
cnf(33,plain,
f(n3,f(n2,A)) = f(n1,f(n1,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),21]),
[iquote('back_demod,18,demod,21')] ).
cnf(35,plain,
f(u,u) = f(n2,u),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,15]),15]),
[iquote('para_into,16.1.1.2,14.1.1,demod,15')] ).
cnf(38,plain,
f(f(n3,n2),u) != f(n2,f(u,n2)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),35,25])]),
[iquote('back_demod,2,demod,35,25,flip.1')] ).
cnf(52,plain,
f(n1,n2) = u,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,9]),15,9])]),
[iquote('para_into,20.1.1.2,8.1.1,demod,15,9,flip.1')] ).
cnf(59,plain,
f(n2,u) = f(n1,u),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[52,21]),52]),
[iquote('para_from,51.1.1,20.1.1.2,demod,52')] ).
cnf(62,plain,
f(f(n1,A),u) = f(n1,f(A,n2)),
inference(para_from,[status(thm),theory(equality)],[52,5]),
[iquote('para_from,51.1.1,5.1.1.2')] ).
cnf(128,plain,
f(n2,f(u,n2)) = f(n1,f(u,n2)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,59]),62])]),
[iquote('para_into,24.1.1.1,59.1.1,demod,62,flip.1')] ).
cnf(131,plain,
f(f(n3,n2),u) != f(n1,f(u,n2)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[38]),128]),
[iquote('back_demod,38,demod,128')] ).
cnf(146,plain,
f(n3,n3) = u,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,12]),9,15]),
[iquote('para_into,26.1.1.1,11.1.1,demod,9,15')] ).
cnf(151,plain,
f(f(n3,A),u) = f(n3,f(A,n3)),
inference(para_from,[status(thm),theory(equality)],[146,5]),
[iquote('para_from,146.1.1,5.1.1.2')] ).
cnf(158,plain,
f(n1,f(u,n2)) != f(n1,f(n1,n3)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[131]),151,33])]),
[iquote('back_demod,131,demod,151,33,flip.1')] ).
cnf(166,plain,
f(u,n2) = f(n1,n3),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,52]),12]),
[iquote('para_into,28.1.1.1,51.1.1,demod,12')] ).
cnf(167,plain,
f(n1,f(n1,n3)) != f(n1,f(n1,n3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[158]),166]),
[iquote('back_demod,158,demod,166')] ).
cnf(168,plain,
$false,
inference(binary,[status(thm)],[167,3]),
[iquote('binary,167.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.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 02:00:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.71/1.91 ----- Otter 3.3f, August 2004 -----
% 1.71/1.91 The process was started by sandbox on n021.cluster.edu,
% 1.71/1.91 Wed Jul 27 02:00:38 2022
% 1.71/1.91 The command was "./otter". The process ID is 20712.
% 1.71/1.91
% 1.71/1.91 set(prolog_style_variables).
% 1.71/1.91 set(auto).
% 1.71/1.91 dependent: set(auto1).
% 1.71/1.91 dependent: set(process_input).
% 1.71/1.91 dependent: clear(print_kept).
% 1.71/1.91 dependent: clear(print_new_demod).
% 1.71/1.91 dependent: clear(print_back_demod).
% 1.71/1.91 dependent: clear(print_back_sub).
% 1.71/1.91 dependent: set(control_memory).
% 1.71/1.91 dependent: assign(max_mem, 12000).
% 1.71/1.91 dependent: assign(pick_given_ratio, 4).
% 1.71/1.91 dependent: assign(stats_level, 1).
% 1.71/1.91 dependent: assign(max_seconds, 10800).
% 1.71/1.91 clear(print_given).
% 1.71/1.91
% 1.71/1.91 list(usable).
% 1.71/1.91 0 [] A=A.
% 1.71/1.91 0 [] f(X,f(Y,Z))=f(f(X,Y),f(X,Z)).
% 1.71/1.91 0 [] n2=f(n1,n1).
% 1.71/1.91 0 [] n3=f(n2,n1).
% 1.71/1.91 0 [] u=f(n2,n2).
% 1.71/1.91 0 [] f(f(n3,n2),u)!=f(f(u,u),u).
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.91
% 1.71/1.91 All clauses are units, and equality is present; the
% 1.71/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.91
% 1.71/1.91 dependent: set(knuth_bendix).
% 1.71/1.91 dependent: set(anl_eq).
% 1.71/1.91 dependent: set(para_from).
% 1.71/1.91 dependent: set(para_into).
% 1.71/1.91 dependent: clear(para_from_right).
% 1.71/1.91 dependent: clear(para_into_right).
% 1.71/1.91 dependent: set(para_from_vars).
% 1.71/1.91 dependent: set(eq_units_both_ways).
% 1.71/1.91 dependent: set(dynamic_demod_all).
% 1.71/1.91 dependent: set(dynamic_demod).
% 1.71/1.91 dependent: set(order_eq).
% 1.71/1.91 dependent: set(back_demod).
% 1.71/1.91 dependent: set(lrpo).
% 1.71/1.91
% 1.71/1.91 ------------> process usable:
% 1.71/1.91 ** KEPT (pick-wt=11): 2 [copy,1,flip.1] f(f(u,u),u)!=f(f(n3,n2),u).
% 1.71/1.91
% 1.71/1.91 ------------> process sos:
% 1.71/1.91 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.71/1.91 ** KEPT (pick-wt=13): 5 [copy,4,flip.1] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.71/1.91 ---> New Demodulator: 6 [new_demod,5] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.71/1.91 ** KEPT (pick-wt=5): 8 [copy,7,flip.1] f(n1,n1)=n2.
% 1.71/1.91 ---> New Demodulator: 9 [new_demod,8] f(n1,n1)=n2.
% 1.71/1.91 ** KEPT (pick-wt=5): 11 [copy,10,flip.1] f(n2,n1)=n3.
% 1.71/1.91 ---> New Demodulator: 12 [new_demod,11] f(n2,n1)=n3.
% 1.71/1.91 ** KEPT (pick-wt=5): 14 [copy,13,flip.1] f(n2,n2)=u.
% 1.71/1.91 ---> New Demodulator: 15 [new_demod,14] f(n2,n2)=u.
% 1.71/1.91 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.71/1.91 >>>> Starting back demodulation with 6.
% 1.71/1.91 >>>> Starting back demodulation with 9.
% 1.71/1.91 >>>> Starting back demodulation with 12.
% 1.71/1.91 >>>> Starting back demodulation with 15.
% 1.71/1.91
% 1.71/1.91 ======= end of input processing =======
% 1.71/1.91
% 1.71/1.91 =========== start of search ===========
% 1.71/1.91
% 1.71/1.91 -------- PROOF --------
% 1.71/1.91
% 1.71/1.91 ----> UNIT CONFLICT at 0.01 sec ----> 168 [binary,167.1,3.1] $F.
% 1.71/1.91
% 1.71/1.91 Length of proof is 24. Level of proof is 8.
% 1.71/1.91
% 1.71/1.91 ---------------- PROOF ----------------
% 1.71/1.91 % SZS status Unsatisfiable
% 1.71/1.91 % SZS output start Refutation
% See solution above
% 1.71/1.91 ------------ end of proof -------------
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91 ============ end of search ============
% 1.71/1.91
% 1.71/1.91 -------------- statistics -------------
% 1.71/1.91 clauses given 18
% 1.71/1.91 clauses generated 125
% 1.71/1.91 clauses kept 86
% 1.71/1.91 clauses forward subsumed 63
% 1.71/1.91 clauses back subsumed 0
% 1.71/1.91 Kbytes malloced 976
% 1.71/1.91
% 1.71/1.91 ----------- times (seconds) -----------
% 1.71/1.91 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.71/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.91
% 1.71/1.91 That finishes the proof of the theorem.
% 1.71/1.91
% 1.71/1.91 Process 20712 finished Wed Jul 27 02:00:39 2022
% 1.71/1.91 Otter interrupted
% 1.71/1.91 PROOF FOUND
%------------------------------------------------------------------------------