TSTP Solution File: NUM020-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:07:27 EDT 2022
% Result : Unsatisfiable 1.91s 2.10s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 6 unt; 0 nHn; 4 RR)
% Number of literals : 11 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ e_qualish(A,B)
| e_qualish(successor(A),successor(B)) ),
file('NUM020-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ e_qualish(A,B)
| ~ e_qualish(B,C)
| e_qualish(A,C) ),
file('NUM020-1.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(add(a,successor(n0)),successor(a)),
file('NUM020-1.p',unknown),
[] ).
cnf(7,axiom,
e_qualish(add(A,n0),A),
file('NUM020-1.p',unknown),
[] ).
cnf(8,axiom,
e_qualish(add(A,successor(B)),successor(add(A,B))),
file('NUM020-1.p',unknown),
[] ).
cnf(15,plain,
e_qualish(successor(add(A,n0)),successor(A)),
inference(hyper,[status(thm)],[7,2]),
[iquote('hyper,7,2')] ).
cnf(73,plain,
e_qualish(add(A,successor(n0)),successor(A)),
inference(hyper,[status(thm)],[15,4,8]),
[iquote('hyper,15,4,8')] ).
cnf(74,plain,
$false,
inference(binary,[status(thm)],[73,5]),
[iquote('binary,73.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n023.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 10:19:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.91/2.10 ----- Otter 3.3f, August 2004 -----
% 1.91/2.10 The process was started by sandbox on n023.cluster.edu,
% 1.91/2.10 Wed Jul 27 10:19:18 2022
% 1.91/2.10 The command was "./otter". The process ID is 2813.
% 1.91/2.10
% 1.91/2.10 set(prolog_style_variables).
% 1.91/2.10 set(auto).
% 1.91/2.10 dependent: set(auto1).
% 1.91/2.10 dependent: set(process_input).
% 1.91/2.10 dependent: clear(print_kept).
% 1.91/2.10 dependent: clear(print_new_demod).
% 1.91/2.10 dependent: clear(print_back_demod).
% 1.91/2.10 dependent: clear(print_back_sub).
% 1.91/2.10 dependent: set(control_memory).
% 1.91/2.10 dependent: assign(max_mem, 12000).
% 1.91/2.10 dependent: assign(pick_given_ratio, 4).
% 1.91/2.10 dependent: assign(stats_level, 1).
% 1.91/2.10 dependent: assign(max_seconds, 10800).
% 1.91/2.10 clear(print_given).
% 1.91/2.10
% 1.91/2.10 list(usable).
% 1.91/2.10 0 [] e_qualish(add(A,n0),A).
% 1.91/2.10 0 [] e_qualish(add(A,successor(B)),successor(add(A,B))).
% 1.91/2.10 0 [] e_qualish(multiply(A,n0),n0).
% 1.91/2.10 0 [] e_qualish(multiply(A,successor(B)),add(multiply(A,B),A)).
% 1.91/2.10 0 [] -e_qualish(successor(A),successor(B))|e_qualish(A,B).
% 1.91/2.10 0 [] -e_qualish(A,B)|e_qualish(successor(A),successor(B)).
% 1.91/2.10 0 [] e_qualish(X,X).
% 1.91/2.10 0 [] -e_qualish(X,Y)|e_qualish(Y,X).
% 1.91/2.10 0 [] -e_qualish(X,Y)| -e_qualish(Y,Z)|e_qualish(X,Z).
% 1.91/2.10 0 [] e_qualish(n1,successor(n0)).
% 1.91/2.10 0 [] -e_qualish(add(a,successor(n0)),successor(a)).
% 1.91/2.10 0 [] -e_qualish(successor(A),n0).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.91/2.10
% 1.91/2.10 This is a Horn set without equality. The strategy will
% 1.91/2.10 be hyperresolution, with satellites in sos and nuclei
% 1.91/2.10 in usable.
% 1.91/2.10
% 1.91/2.10 dependent: set(hyper_res).
% 1.91/2.10 dependent: clear(order_hyper).
% 1.91/2.10
% 1.91/2.10 ------------> process usable:
% 1.91/2.10 ** KEPT (pick-wt=8): 1 [] -e_qualish(successor(A),successor(B))|e_qualish(A,B).
% 1.91/2.10 ** KEPT (pick-wt=8): 2 [] -e_qualish(A,B)|e_qualish(successor(A),successor(B)).
% 1.91/2.10 ** KEPT (pick-wt=6): 3 [] -e_qualish(A,B)|e_qualish(B,A).
% 1.91/2.10 ** KEPT (pick-wt=9): 4 [] -e_qualish(A,B)| -e_qualish(B,C)|e_qualish(A,C).
% 1.91/2.10 ** KEPT (pick-wt=7): 5 [] -e_qualish(add(a,successor(n0)),successor(a)).
% 1.91/2.10 ** KEPT (pick-wt=4): 6 [] -e_qualish(successor(A),n0).
% 1.91/2.10
% 1.91/2.10 ------------> process sos:
% 1.91/2.10 ** KEPT (pick-wt=5): 7 [] e_qualish(add(A,n0),A).
% 1.91/2.10 ** KEPT (pick-wt=9): 8 [] e_qualish(add(A,successor(B)),successor(add(A,B))).
% 1.91/2.10 ** KEPT (pick-wt=5): 9 [] e_qualish(multiply(A,n0),n0).
% 1.91/2.10 ** KEPT (pick-wt=10): 10 [] e_qualish(multiply(A,successor(B)),add(multiply(A,B),A)).
% 1.91/2.10 ** KEPT (pick-wt=3): 11 [] e_qualish(A,A).
% 1.91/2.10 ** KEPT (pick-wt=4): 12 [] e_qualish(n1,successor(n0)).
% 1.91/2.10
% 1.91/2.10 ======= end of input processing =======
% 1.91/2.10
% 1.91/2.10 =========== start of search ===========
% 1.91/2.10
% 1.91/2.10 -------- PROOF --------
% 1.91/2.10
% 1.91/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 74 [binary,73.1,5.1] $F.
% 1.91/2.10
% 1.91/2.10 Length of proof is 2. Level of proof is 2.
% 1.91/2.10
% 1.91/2.10 ---------------- PROOF ----------------
% 1.91/2.10 % SZS status Unsatisfiable
% 1.91/2.10 % SZS output start Refutation
% See solution above
% 1.91/2.10 ------------ end of proof -------------
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10 ============ end of search ============
% 1.91/2.10
% 1.91/2.10 -------------- statistics -------------
% 1.91/2.10 clauses given 17
% 1.91/2.10 clauses generated 139
% 1.91/2.10 clauses kept 73
% 1.91/2.10 clauses forward subsumed 78
% 1.91/2.10 clauses back subsumed 0
% 1.91/2.10 Kbytes malloced 976
% 1.91/2.10
% 1.91/2.10 ----------- times (seconds) -----------
% 1.91/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.10
% 1.91/2.10 That finishes the proof of the theorem.
% 1.91/2.10
% 1.91/2.10 Process 2813 finished Wed Jul 27 10:19:20 2022
% 1.91/2.10 Otter interrupted
% 1.91/2.10 PROOF FOUND
%------------------------------------------------------------------------------