TSTP Solution File: LCL686+1.001 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 13:05:10 EDT 2022
% Result : Theorem 1.98s 2.16s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 5 unt; 2 nHn; 10 RR)
% Number of literals : 23 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ r1(dollar_c3,A)
| ~ r1(A,B)
| ~ p2(B)
| p1(B) ),
file('LCL686+1.001.p',unknown),
[] ).
cnf(4,axiom,
( ~ r1(dollar_c3,A)
| ~ r1(A,B)
| p2(B)
| ~ p1(B) ),
file('LCL686+1.001.p',unknown),
[] ).
cnf(7,axiom,
( ~ r1(dollar_c3,A)
| r1(A,dollar_f3(A)) ),
file('LCL686+1.001.p',unknown),
[] ).
cnf(8,axiom,
( ~ r1(dollar_c3,A)
| p1(dollar_f3(A))
| p2(dollar_f3(A)) ),
file('LCL686+1.001.p',unknown),
[] ).
cnf(9,axiom,
( ~ r1(dollar_c3,A)
| ~ p2(dollar_f3(A))
| ~ p1(dollar_f3(A)) ),
file('LCL686+1.001.p',unknown),
[] ).
cnf(12,axiom,
r1(A,A),
file('LCL686+1.001.p',unknown),
[] ).
cnf(18,plain,
( p1(dollar_f3(dollar_c3))
| p2(dollar_f3(dollar_c3)) ),
inference(hyper,[status(thm)],[12,8]),
[iquote('hyper,12,8')] ).
cnf(19,plain,
r1(dollar_c3,dollar_f3(dollar_c3)),
inference(hyper,[status(thm)],[12,7]),
[iquote('hyper,12,7')] ).
cnf(38,plain,
p1(dollar_f3(dollar_c3)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[18,3,19,12])]),
[iquote('hyper,18,3,19,12,factor_simp')] ).
cnf(39,plain,
p2(dollar_f3(dollar_c3)),
inference(hyper,[status(thm)],[38,4,19,12]),
[iquote('hyper,38,4,19,12')] ).
cnf(40,plain,
$false,
inference(hyper,[status(thm)],[39,9,12,38]),
[iquote('hyper,39,9,12,38')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 09:29:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.98/2.16 ----- Otter 3.3f, August 2004 -----
% 1.98/2.16 The process was started by sandbox2 on n011.cluster.edu,
% 1.98/2.16 Wed Jul 27 09:29:10 2022
% 1.98/2.16 The command was "./otter". The process ID is 18840.
% 1.98/2.16
% 1.98/2.16 set(prolog_style_variables).
% 1.98/2.16 set(auto).
% 1.98/2.16 dependent: set(auto1).
% 1.98/2.16 dependent: set(process_input).
% 1.98/2.16 dependent: clear(print_kept).
% 1.98/2.16 dependent: clear(print_new_demod).
% 1.98/2.16 dependent: clear(print_back_demod).
% 1.98/2.16 dependent: clear(print_back_sub).
% 1.98/2.16 dependent: set(control_memory).
% 1.98/2.16 dependent: assign(max_mem, 12000).
% 1.98/2.16 dependent: assign(pick_given_ratio, 4).
% 1.98/2.16 dependent: assign(stats_level, 1).
% 1.98/2.16 dependent: assign(max_seconds, 10800).
% 1.98/2.16 clear(print_given).
% 1.98/2.16
% 1.98/2.16 formula_list(usable).
% 1.98/2.16 all X r1(X,X).
% 1.98/2.16 all X Y Z (r1(X,Y)&r1(Y,Z)->r1(X,Z)).
% 1.98/2.16 -(-(exists X (-((all Y (-r1(X,Y)| -p3(Y)| (all X (-r1(Y,X)| -p1(X)))))| (all Y (-r1(X,Y)| -(all X (-r1(Y,X)| -((all Y (-r1(X,Y)))| -(all Y (-r1(X,Y)| -(p2(Y)& -p1(Y)| -p2(Y)&p1(Y))))| (all Y (-r1(X,Y)|p3(Y)))| (all Y (-r1(X,Y)| -p1(Y)& -p2(Y)|p2(Y)&p1(Y)))))))))))).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 -------> usable clausifies to:
% 1.98/2.16
% 1.98/2.16 list(usable).
% 1.98/2.16 0 [] r1(X,X).
% 1.98/2.16 0 [] -r1(X,Y)| -r1(Y,Z)|r1(X,Z).
% 1.98/2.16 0 [] r1($c4,$c2).
% 1.98/2.16 0 [] p3($c2).
% 1.98/2.16 0 [] r1($c2,$c1).
% 1.98/2.16 0 [] p1($c1).
% 1.98/2.16 0 [] r1($c4,$c3).
% 1.98/2.16 0 [] -r1($c3,X)|r1(X,$f1(X)).
% 1.98/2.16 0 [] -r1($c3,X)| -r1(X,Y)| -p2(Y)|p1(Y).
% 1.98/2.16 0 [] -r1($c3,X)| -r1(X,Y)|p2(Y)| -p1(Y).
% 1.98/2.16 0 [] -r1($c3,X)|r1(X,$f2(X)).
% 1.98/2.16 0 [] -r1($c3,X)| -p3($f2(X)).
% 1.98/2.16 0 [] -r1($c3,X)|r1(X,$f3(X)).
% 1.98/2.16 0 [] -r1($c3,X)|p1($f3(X))|p2($f3(X)).
% 1.98/2.16 0 [] -r1($c3,X)| -p2($f3(X))| -p1($f3(X)).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.98/2.16
% 1.98/2.16 This is a non-Horn set without equality. The strategy will
% 1.98/2.16 be ordered hyper_res, unit deletion, and factoring, with
% 1.98/2.16 satellites in sos and with nuclei in usable.
% 1.98/2.16
% 1.98/2.16 dependent: set(hyper_res).
% 1.98/2.16 dependent: set(factor).
% 1.98/2.16 dependent: set(unit_deletion).
% 1.98/2.16
% 1.98/2.16 ------------> process usable:
% 1.98/2.16 ** KEPT (pick-wt=9): 1 [] -r1(A,B)| -r1(B,C)|r1(A,C).
% 1.98/2.16 ** KEPT (pick-wt=7): 2 [] -r1($c3,A)|r1(A,$f1(A)).
% 1.98/2.16 ** KEPT (pick-wt=10): 3 [] -r1($c3,A)| -r1(A,B)| -p2(B)|p1(B).
% 1.98/2.16 ** KEPT (pick-wt=10): 4 [] -r1($c3,A)| -r1(A,B)|p2(B)| -p1(B).
% 1.98/2.16 ** KEPT (pick-wt=7): 5 [] -r1($c3,A)|r1(A,$f2(A)).
% 1.98/2.16 ** KEPT (pick-wt=6): 6 [] -r1($c3,A)| -p3($f2(A)).
% 1.98/2.16 ** KEPT (pick-wt=7): 7 [] -r1($c3,A)|r1(A,$f3(A)).
% 1.98/2.16 ** KEPT (pick-wt=9): 8 [] -r1($c3,A)|p1($f3(A))|p2($f3(A)).
% 1.98/2.16 ** KEPT (pick-wt=9): 9 [] -r1($c3,A)| -p2($f3(A))| -p1($f3(A)).
% 1.98/2.16
% 1.98/2.16 ------------> process sos:
% 1.98/2.16 ** KEPT (pick-wt=3): 12 [] r1(A,A).
% 1.98/2.16 ** KEPT (pick-wt=3): 13 [] r1($c4,$c2).
% 1.98/2.16 ** KEPT (pick-wt=2): 14 [] p3($c2).
% 1.98/2.16 ** KEPT (pick-wt=3): 15 [] r1($c2,$c1).
% 1.98/2.16 ** KEPT (pick-wt=2): 16 [] p1($c1).
% 1.98/2.16 ** KEPT (pick-wt=3): 17 [] r1($c4,$c3).
% 1.98/2.16
% 1.98/2.16 ======= end of input processing =======
% 1.98/2.16
% 1.98/2.16 =========== start of search ===========
% 1.98/2.16
% 1.98/2.16 -------- PROOF --------
% 1.98/2.16
% 1.98/2.16 -----> EMPTY CLAUSE at 0.00 sec ----> 40 [hyper,39,9,12,38] $F.
% 1.98/2.16
% 1.98/2.16 Length of proof is 4. Level of proof is 3.
% 1.98/2.16
% 1.98/2.16 ---------------- PROOF ----------------
% 1.98/2.16 % SZS status Theorem
% 1.98/2.16 % SZS output start Refutation
% See solution above
% 1.98/2.16 ------------ end of proof -------------
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16 ============ end of search ============
% 1.98/2.16
% 1.98/2.16 -------------- statistics -------------
% 1.98/2.16 clauses given 13
% 1.98/2.16 clauses generated 44
% 1.98/2.16 clauses kept 39
% 1.98/2.16 clauses forward subsumed 18
% 1.98/2.16 clauses back subsumed 1
% 1.98/2.16 Kbytes malloced 976
% 1.98/2.16
% 1.98/2.16 ----------- times (seconds) -----------
% 1.98/2.16 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.16
% 1.98/2.16 That finishes the proof of the theorem.
% 1.98/2.16
% 1.98/2.16 Process 18840 finished Wed Jul 27 09:29:12 2022
% 1.98/2.16 Otter interrupted
% 1.98/2.16 PROOF FOUND
%------------------------------------------------------------------------------