%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:25:41 EDT 2022
% Result : Unsatisfiable 1.95s 2.16s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of clauses : 33 ( 31 unt; 0 nHn; 25 RR)
% Number of literals : 35 ( 8 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 13 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ d(A)
| d(s(A)) ),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(2,axiom,
~ d(f(s(s(one)),s(s(one)))),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(4,axiom,
f(A,one) = s(one),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(5,axiom,
f(one,s(A)) = s(s(f(one,A))),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(7,plain,
s(s(f(one,A))) = f(one,s(A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(9,axiom,
f(s(A),s(B)) = f(A,f(s(A),B)),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(10,axiom,
d(one),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(11,plain,
s(one) = f(A,one),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(12,plain,
~ d(f(s(one),f(s(one),f(s(s(one)),one)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),9,9]),
[iquote('back_demod,2,demod,9,9')] ).
cnf(13,plain,
d(s(one)),
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(14,plain,
d(s(s(one))),
inference(hyper,[status(thm)],[13,1]),
[iquote('hyper,13,1')] ).
cnf(15,plain,
d(s(s(s(one)))),
inference(hyper,[status(thm)],[14,1]),
[iquote('hyper,14,1')] ).
cnf(16,plain,
d(s(s(s(s(one))))),
inference(hyper,[status(thm)],[15,1]),
[iquote('hyper,15,1')] ).
cnf(21,plain,
d(s(s(s(s(s(one)))))),
inference(hyper,[status(thm)],[16,1]),
[iquote('hyper,16,1')] ).
cnf(24,plain,
s(s(s(one))) = f(one,s(one)),
inference(para_into,[status(thm),theory(equality)],[7,4]),
[iquote('para_into,6.1.1.1.1,4.1.1')] ).
cnf(25,plain,
d(f(one,s(s(one)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),24,7]),
[iquote('back_demod,21,demod,24,7')] ).
cnf(28,plain,
( ~ d(s(f(one,A)))
| d(f(one,s(A))) ),
inference(para_from,[status(thm),theory(equality)],[7,1]),
[iquote('para_from,6.1.1,1.2.1')] ).
cnf(30,plain,
d(s(f(one,s(s(one))))),
inference(hyper,[status(thm)],[25,1]),
[iquote('hyper,25,1')] ).
cnf(36,plain,
f(s(A),f(B,one)) = f(A,f(s(A),one)),
inference(para_into,[status(thm),theory(equality)],[9,11]),
[iquote('para_into,8.1.1.2,11.1.1')] ).
cnf(38,plain,
f(s(A),f(one,s(B))) = f(A,f(A,f(s(A),f(one,B)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,7]),9]),
[iquote('para_into,8.1.1.2,6.1.1,demod,9')] ).
cnf(41,plain,
~ d(f(s(one),f(one,f(s(one),one)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),36]),
[iquote('back_demod,12,demod,36')] ).
cnf(44,plain,
d(f(one,f(one,s(one)))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[30,1]),7,24]),
[iquote('hyper,30,1,demod,7,24')] ).
cnf(48,plain,
d(s(f(one,f(one,s(one))))),
inference(hyper,[status(thm)],[44,1]),
[iquote('hyper,44,1')] ).
cnf(50,plain,
d(f(one,s(f(one,s(one))))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[48,1]),7]),
[iquote('hyper,48,1,demod,7')] ).
cnf(53,plain,
d(s(f(one,s(f(one,s(one)))))),
inference(hyper,[status(thm)],[50,1]),
[iquote('hyper,50,1')] ).
cnf(55,plain,
d(f(one,f(one,s(s(one))))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[53,28]),7]),
[iquote('hyper,53,28,demod,7')] ).
cnf(63,plain,
d(s(f(one,f(one,s(s(one)))))),
inference(hyper,[status(thm)],[55,1]),
[iquote('hyper,55,1')] ).
cnf(65,plain,
d(f(one,s(f(one,s(s(one)))))),
inference(hyper,[status(thm)],[63,28]),
[iquote('hyper,63,28')] ).
cnf(79,plain,
d(s(f(one,s(f(one,s(s(one))))))),
inference(hyper,[status(thm)],[65,1]),
[iquote('hyper,65,1')] ).
cnf(84,plain,
~ d(f(one,f(one,f(one,f(s(one),one))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[41,4]),38,36]),
[iquote('para_into,41.1.1.2.2,4.1.1,demod,38,36')] ).
cnf(95,plain,
d(f(one,f(one,f(one,s(one))))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[79,28]),7,24]),
[iquote('hyper,79,28,demod,7,24')] ).
cnf(98,plain,
d(f(one,f(one,f(one,f(A,one))))),
inference(para_into,[status(thm),theory(equality)],[95,11]),
[iquote('para_into,95.1.1.2.2.2,11.1.1')] ).
cnf(99,plain,
$false,
inference(binary,[status(thm)],[98,84]),
[iquote('binary,98.1,84.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n011.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 10:20:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.95/2.16 ----- Otter 3.3f, August 2004 -----
% 1.95/2.16 The process was started by sandbox2 on n011.cluster.edu,
% 1.95/2.16 Wed Jul 27 10:20:26 2022
% 1.95/2.16 The command was "./otter". The process ID is 9107.
% 1.95/2.16
% 1.95/2.16 set(prolog_style_variables).
% 1.95/2.16 set(auto).
% 1.95/2.16 dependent: set(auto1).
% 1.95/2.16 dependent: set(process_input).
% 1.95/2.16 dependent: clear(print_kept).
% 1.95/2.16 dependent: clear(print_new_demod).
% 1.95/2.16 dependent: clear(print_back_demod).
% 1.95/2.16 dependent: clear(print_back_sub).
% 1.95/2.16 dependent: set(control_memory).
% 1.95/2.16 dependent: assign(max_mem, 12000).
% 1.95/2.16 dependent: assign(pick_given_ratio, 4).
% 1.95/2.16 dependent: assign(stats_level, 1).
% 1.95/2.16 dependent: assign(max_seconds, 10800).
% 1.95/2.16 clear(print_given).
% 1.95/2.16
% 1.95/2.16 list(usable).
% 1.95/2.16 0 [] A=A.
% 1.95/2.16 0 [] f(N,one)=s(one).
% 1.95/2.16 0 [] f(one,s(X))=s(s(f(one,X))).
% 1.95/2.16 0 [] f(s(N),s(X))=f(N,f(s(N),X)).
% 1.95/2.16 0 [] d(one).
% 1.95/2.16 0 [] -d(X)|d(s(X)).
% 1.95/2.16 0 [] -d(f(s(s(one)),s(s(one)))).
% 1.95/2.16 end_of_list.
% 1.95/2.16
% 1.95/2.16 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.95/2.16
% 1.95/2.16 This is a Horn set with equality. The strategy will be
% 1.95/2.16 Knuth-Bendix and hyper_res, with positive clauses in
% 1.95/2.16 sos and nonpositive clauses in usable.
% 1.95/2.16
% 1.95/2.16 dependent: set(knuth_bendix).
% 1.95/2.16 dependent: set(anl_eq).
% 1.95/2.16 dependent: set(para_from).
% 1.95/2.16 dependent: set(para_into).
% 1.95/2.16 dependent: clear(para_from_right).
% 1.95/2.16 dependent: clear(para_into_right).
% 1.95/2.16 dependent: set(para_from_vars).
% 1.95/2.16 dependent: set(eq_units_both_ways).
% 1.95/2.16 dependent: set(dynamic_demod_all).
% 1.95/2.16 dependent: set(dynamic_demod).
% 1.95/2.16 dependent: set(order_eq).
% 1.95/2.16 dependent: set(back_demod).
% 1.95/2.16 dependent: set(lrpo).
% 1.95/2.16 dependent: set(hyper_res).
% 1.95/2.16 dependent: clear(order_hyper).
% 1.95/2.16
% 1.95/2.16 ------------> process usable:
% 1.95/2.16 ** KEPT (pick-wt=5): 1 [] -d(A)|d(s(A)).
% 1.95/2.16 ** KEPT (pick-wt=8): 2 [] -d(f(s(s(one)),s(s(one)))).
% 1.95/2.16
% 1.95/2.16 ------------> process sos:
% 1.95/2.16 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.95/2.16 ** KEPT (pick-wt=6): 4 [] f(A,one)=s(one).
% 1.95/2.16 ** KEPT (pick-wt=10): 6 [copy,5,flip.1] s(s(f(one,A)))=f(one,s(A)).
% 1.95/2.16 ---> New Demodulator: 7 [new_demod,6] s(s(f(one,A)))=f(one,s(A)).
% 1.95/2.16 ** KEPT (pick-wt=12): 8 [] f(s(A),s(B))=f(A,f(s(A),B)).
% 1.95/2.16 ---> New Demodulator: 9 [new_demod,8] f(s(A),s(B))=f(A,f(s(A),B)).
% 1.95/2.16 ** KEPT (pick-wt=2): 10 [] d(one).
% 1.95/2.16 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.95/2.16 ** KEPT (pick-wt=6): 11 [copy,4,flip.1] s(one)=f(A,one).
% 1.95/2.16 >>>> Starting back demodulation with 7.
% 1.95/2.16 >>>> Starting back demodulation with 9.
% 1.95/2.16 >> back demodulating 2 with 9.
% 1.95/2.16 Following clause subsumed by 4 during input processing: 0 [copy,11,flip.1] f(A,one)=s(one).
% 1.95/2.16
% 1.95/2.16 ======= end of input processing =======
% 1.95/2.16
% 1.95/2.16 =========== start of search ===========
% 1.95/2.16
% 1.95/2.16 -------- PROOF --------
% 1.95/2.16
% 1.95/2.16 ----> UNIT CONFLICT at 0.00 sec ----> 99 [binary,98.1,84.1] $F.
% 1.95/2.16
% 1.95/2.16 Length of proof is 26. Level of proof is 17.
% 1.95/2.16
% 1.95/2.16 ---------------- PROOF ----------------
% 1.95/2.16 % SZS status Unsatisfiable
% 1.95/2.16 % SZS output start Refutation
% See solution above
% 1.95/2.16 ------------ end of proof -------------
% 1.95/2.16
% 1.95/2.16
% 1.95/2.16 Search stopped by max_proofs option.
% 1.95/2.16
% 1.95/2.16
% 1.95/2.16 Search stopped by max_proofs option.
% 1.95/2.16
% 1.95/2.16 ============ end of search ============
% 1.95/2.16
% 1.95/2.16 -------------- statistics -------------
% 1.95/2.16 clauses given 45
% 1.95/2.16 clauses generated 161
% 1.95/2.16 clauses kept 87
% 1.95/2.16 clauses forward subsumed 118
% 1.95/2.16 clauses back subsumed 3
% 1.95/2.16 Kbytes malloced 1953
% 1.95/2.16
% 1.95/2.16 ----------- times (seconds) -----------
% 1.95/2.16 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.16 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.95/2.16
% 1.95/2.16 That finishes the proof of the theorem.
% 1.95/2.16
% 1.95/2.16 Process 9107 finished Wed Jul 27 10:20:27 2022
% 1.95/2.16 Otter interrupted
% 1.95/2.16 PROOF FOUND
%------------------------------------------------------------------------------