TSTP Solution File: SYN356+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN356+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:24:21 EDT 2022
% Result : Theorem 1.57s 2.15s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 11 RR)
% Number of literals : 15 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 6 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big_r(A,B)
| big_r(B,A) ),
file('SYN356+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ big_r(A,B)
| big_q(A,B) ),
file('SYN356+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ big_q(A,B)
| big_q(A,A) ),
file('SYN356+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ big_q(a,a)
| ~ big_q(b,b) ),
file('SYN356+1.p',unknown),
[] ).
cnf(5,axiom,
big_r(a,b),
file('SYN356+1.p',unknown),
[] ).
cnf(6,plain,
big_q(a,b),
inference(hyper,[status(thm)],[5,2]),
[iquote('hyper,5,2')] ).
cnf(7,plain,
big_r(b,a),
inference(hyper,[status(thm)],[5,1]),
[iquote('hyper,5,1')] ).
cnf(8,plain,
big_q(a,a),
inference(hyper,[status(thm)],[6,3]),
[iquote('hyper,6,3')] ).
cnf(9,plain,
big_q(b,a),
inference(hyper,[status(thm)],[7,2]),
[iquote('hyper,7,2')] ).
cnf(10,plain,
big_q(b,b),
inference(hyper,[status(thm)],[9,3]),
[iquote('hyper,9,3')] ).
cnf(11,plain,
$false,
inference(hyper,[status(thm)],[10,4,8]),
[iquote('hyper,10,4,8')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN356+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.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 11:32:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.57/2.15 ----- Otter 3.3f, August 2004 -----
% 1.57/2.15 The process was started by sandbox2 on n026.cluster.edu,
% 1.57/2.15 Wed Jul 27 11:32:39 2022
% 1.57/2.15 The command was "./otter". The process ID is 17658.
% 1.57/2.15
% 1.57/2.15 set(prolog_style_variables).
% 1.57/2.15 set(auto).
% 1.57/2.15 dependent: set(auto1).
% 1.57/2.15 dependent: set(process_input).
% 1.57/2.15 dependent: clear(print_kept).
% 1.57/2.15 dependent: clear(print_new_demod).
% 1.57/2.15 dependent: clear(print_back_demod).
% 1.57/2.15 dependent: clear(print_back_sub).
% 1.57/2.15 dependent: set(control_memory).
% 1.57/2.15 dependent: assign(max_mem, 12000).
% 1.57/2.15 dependent: assign(pick_given_ratio, 4).
% 1.57/2.15 dependent: assign(stats_level, 1).
% 1.57/2.15 dependent: assign(max_seconds, 10800).
% 1.57/2.15 clear(print_given).
% 1.57/2.15
% 1.57/2.15 formula_list(usable).
% 1.57/2.15 -(big_r(a,b)& (all X Y (big_r(X,Y)->big_r(Y,X)&big_q(X,Y)))& (all U V (big_q(U,V)->big_q(U,U)))->big_q(a,a)&big_q(b,b)).
% 1.57/2.15 end_of_list.
% 1.57/2.15
% 1.57/2.15 -------> usable clausifies to:
% 1.57/2.15
% 1.57/2.15 list(usable).
% 1.57/2.15 0 [] big_r(a,b).
% 1.57/2.15 0 [] -big_r(X,Y)|big_r(Y,X).
% 1.57/2.15 0 [] -big_r(X,Y)|big_q(X,Y).
% 1.57/2.15 0 [] -big_q(U,V)|big_q(U,U).
% 1.57/2.15 0 [] -big_q(a,a)| -big_q(b,b).
% 1.57/2.15 end_of_list.
% 1.57/2.15
% 1.57/2.15 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=2.
% 1.57/2.15
% 1.57/2.15 This is a Horn set without equality. The strategy will
% 1.57/2.15 be hyperresolution, with satellites in sos and nuclei
% 1.57/2.15 in usable.
% 1.57/2.15
% 1.57/2.15 dependent: set(hyper_res).
% 1.57/2.15 dependent: clear(order_hyper).
% 1.57/2.15
% 1.57/2.15 ------------> process usable:
% 1.57/2.15 ** KEPT (pick-wt=6): 1 [] -big_r(A,B)|big_r(B,A).
% 1.57/2.15 ** KEPT (pick-wt=6): 2 [] -big_r(A,B)|big_q(A,B).
% 1.57/2.15 ** KEPT (pick-wt=6): 3 [] -big_q(A,B)|big_q(A,A).
% 1.57/2.15 ** KEPT (pick-wt=6): 4 [] -big_q(a,a)| -big_q(b,b).
% 1.57/2.15
% 1.57/2.15 ------------> process sos:
% 1.57/2.15 ** KEPT (pick-wt=3): 5 [] big_r(a,b).
% 1.57/2.15
% 1.57/2.15 ======= end of input processing =======
% 1.57/2.15
% 1.57/2.15 =========== start of search ===========
% 1.57/2.15
% 1.57/2.15 -------- PROOF --------
% 1.57/2.15
% 1.57/2.15 -----> EMPTY CLAUSE at 0.00 sec ----> 11 [hyper,10,4,8] $F.
% 1.57/2.15
% 1.57/2.15 Length of proof is 5. Level of proof is 3.
% 1.57/2.15
% 1.57/2.15 ---------------- PROOF ----------------
% 1.57/2.15 % SZS status Theorem
% 1.57/2.15 % SZS output start Refutation
% See solution above
% 1.57/2.15 ------------ end of proof -------------
% 1.57/2.15
% 1.57/2.15
% 1.57/2.15 Search stopped by max_proofs option.
% 1.57/2.15
% 1.57/2.15
% 1.57/2.15 Search stopped by max_proofs option.
% 1.57/2.15
% 1.57/2.15 ============ end of search ============
% 1.57/2.15
% 1.57/2.15 -------------- statistics -------------
% 1.57/2.15 clauses given 6
% 1.57/2.15 clauses generated 8
% 1.57/2.15 clauses kept 10
% 1.57/2.15 clauses forward subsumed 2
% 1.57/2.15 clauses back subsumed 0
% 1.57/2.15 Kbytes malloced 976
% 1.57/2.15
% 1.57/2.15 ----------- times (seconds) -----------
% 1.57/2.15 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/2.15 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/2.15 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.57/2.15
% 1.57/2.15 That finishes the proof of the theorem.
% 1.57/2.15
% 1.57/2.15 Process 17658 finished Wed Jul 27 11:32:41 2022
% 1.57/2.15 Otter interrupted
% 1.57/2.15 PROOF FOUND
%------------------------------------------------------------------------------