TSTP Solution File: SYN986+1.002 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN986+1.002 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:25:37 EDT 2022
% Result : Theorem 1.88s 2.08s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 10 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 10 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r(A,B,C)
| ~ r(C,B,D)
| r(A,succ(B),D) ),
file('SYN986+1.002.p',unknown),
[] ).
cnf(2,axiom,
( ~ r(zero,zero,A)
| ~ r(zero,A,B)
| ~ r(zero,B,C) ),
file('SYN986+1.002.p',unknown),
[] ).
cnf(3,axiom,
r(A,zero,succ(A)),
file('SYN986+1.002.p',unknown),
[] ).
cnf(4,plain,
r(A,succ(zero),succ(succ(A))),
inference(hyper,[status(thm)],[3,1,3]),
[iquote('hyper,3,1,3')] ).
cnf(5,plain,
r(A,succ(succ(zero)),succ(succ(succ(succ(A))))),
inference(hyper,[status(thm)],[4,1,4]),
[iquote('hyper,4,1,4')] ).
cnf(6,plain,
$false,
inference(hyper,[status(thm)],[5,2,3,4]),
[iquote('hyper,5,2,3,4')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN986+1.002 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:21:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.88/2.08 ----- Otter 3.3f, August 2004 -----
% 1.88/2.08 The process was started by sandbox on n006.cluster.edu,
% 1.88/2.08 Wed Jul 27 11:21:32 2022
% 1.88/2.08 The command was "./otter". The process ID is 28813.
% 1.88/2.08
% 1.88/2.08 set(prolog_style_variables).
% 1.88/2.08 set(auto).
% 1.88/2.08 dependent: set(auto1).
% 1.88/2.08 dependent: set(process_input).
% 1.88/2.08 dependent: clear(print_kept).
% 1.88/2.08 dependent: clear(print_new_demod).
% 1.88/2.08 dependent: clear(print_back_demod).
% 1.88/2.08 dependent: clear(print_back_sub).
% 1.88/2.08 dependent: set(control_memory).
% 1.88/2.08 dependent: assign(max_mem, 12000).
% 1.88/2.08 dependent: assign(pick_given_ratio, 4).
% 1.88/2.08 dependent: assign(stats_level, 1).
% 1.88/2.08 dependent: assign(max_seconds, 10800).
% 1.88/2.08 clear(print_given).
% 1.88/2.08
% 1.88/2.08 formula_list(usable).
% 1.88/2.08 all Y r(Y,zero,succ(Y)).
% 1.88/2.08 all Y X Z Z1 (r(Y,X,Z)-> (r(Z,X,Z1)->r(Y,succ(X),Z1))).
% 1.88/2.08 -(exists Z2 Z1 Z0 (r(zero,zero,Z2)&r(zero,Z2,Z1)&r(zero,Z1,Z0))).
% 1.88/2.08 end_of_list.
% 1.88/2.08
% 1.88/2.08 -------> usable clausifies to:
% 1.88/2.08
% 1.88/2.08 list(usable).
% 1.88/2.08 0 [] r(Y,zero,succ(Y)).
% 1.88/2.08 0 [] -r(Y,X,Z)| -r(Z,X,Z1)|r(Y,succ(X),Z1).
% 1.88/2.08 0 [] -r(zero,zero,Z2)| -r(zero,Z2,Z1)| -r(zero,Z1,Z0).
% 1.88/2.08 end_of_list.
% 1.88/2.08
% 1.88/2.08 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.88/2.08
% 1.88/2.08 This is a Horn set without equality. The strategy will
% 1.88/2.08 be hyperresolution, with satellites in sos and nuclei
% 1.88/2.08 in usable.
% 1.88/2.08
% 1.88/2.08 dependent: set(hyper_res).
% 1.88/2.08 dependent: clear(order_hyper).
% 1.88/2.08
% 1.88/2.08 ------------> process usable:
% 1.88/2.08 ** KEPT (pick-wt=13): 1 [] -r(A,B,C)| -r(C,B,D)|r(A,succ(B),D).
% 1.88/2.08 ** KEPT (pick-wt=12): 2 [] -r(zero,zero,A)| -r(zero,A,B)| -r(zero,B,C).
% 1.88/2.08
% 1.88/2.08 ------------> process sos:
% 1.88/2.08 ** KEPT (pick-wt=5): 3 [] r(A,zero,succ(A)).
% 1.88/2.08
% 1.88/2.08 ======= end of input processing =======
% 1.88/2.08
% 1.88/2.08 =========== start of search ===========
% 1.88/2.08
% 1.88/2.08 -------- PROOF --------
% 1.88/2.08
% 1.88/2.08 -----> EMPTY CLAUSE at 0.00 sec ----> 6 [hyper,5,2,3,4] $F.
% 1.88/2.08
% 1.88/2.08 Length of proof is 2. Level of proof is 2.
% 1.88/2.08
% 1.88/2.08 ---------------- PROOF ----------------
% 1.88/2.08 % SZS status Theorem
% 1.88/2.08 % SZS output start Refutation
% See solution above
% 1.88/2.08 ------------ end of proof -------------
% 1.88/2.08
% 1.88/2.08
% 1.88/2.08 Search stopped by max_proofs option.
% 1.88/2.08
% 1.88/2.08
% 1.88/2.08 Search stopped by max_proofs option.
% 1.88/2.08
% 1.88/2.08 ============ end of search ============
% 1.88/2.08
% 1.88/2.08 -------------- statistics -------------
% 1.88/2.08 clauses given 3
% 1.88/2.08 clauses generated 5
% 1.88/2.08 clauses kept 5
% 1.88/2.08 clauses forward subsumed 2
% 1.88/2.08 clauses back subsumed 0
% 1.88/2.08 Kbytes malloced 976
% 1.88/2.08
% 1.88/2.08 ----------- times (seconds) -----------
% 1.88/2.08 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.08 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.88/2.08
% 1.88/2.08 That finishes the proof of the theorem.
% 1.88/2.08
% 1.88/2.08 Process 28813 finished Wed Jul 27 11:21:33 2022
% 1.88/2.08 Otter interrupted
% 1.88/2.08 PROOF FOUND
%------------------------------------------------------------------------------