TSTP Solution File: LCL672+1.001 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL672+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:05:03 EDT 2022
% Result : Theorem 32.47s 32.64s
% Output : Refutation 32.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of clauses : 18 ( 13 unt; 3 nHn; 17 RR)
% Number of literals : 47 ( 0 equ; 26 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r1(A,B)
| ~ r1(B,C)
| r1(A,C) ),
file('LCL672+1.001.p',unknown),
[] ).
cnf(4,axiom,
( ~ r1(dollar_c6,A)
| p2(A)
| ~ r1(dollar_c6,B)
| ~ r1(B,C)
| ~ r1(C,D)
| r1(D,dollar_f2(B,C,D))
| ~ r1(C,E)
| p1(E)
| ~ r1(dollar_c6,F)
| p1(F) ),
file('LCL672+1.001.p',unknown),
[] ).
cnf(5,axiom,
( ~ r1(dollar_c6,A)
| p2(A)
| ~ r1(dollar_c6,B)
| ~ r1(B,C)
| ~ r1(C,D)
| ~ p1(dollar_f2(B,C,D))
| ~ r1(C,E)
| p1(E)
| ~ r1(dollar_c6,F)
| p1(F) ),
file('LCL672+1.001.p',unknown),
[] ).
cnf(11,axiom,
~ p2(dollar_c1),
file('LCL672+1.001.p',unknown),
[] ).
cnf(12,axiom,
( ~ r1(dollar_c2,A)
| p1(A) ),
file('LCL672+1.001.p',unknown),
[] ).
cnf(13,axiom,
~ p1(dollar_c3),
file('LCL672+1.001.p',unknown),
[] ).
cnf(14,axiom,
~ p1(dollar_c5),
file('LCL672+1.001.p',unknown),
[] ).
cnf(57,plain,
( ~ r1(dollar_c6,A)
| p2(A)
| ~ r1(dollar_c6,B)
| ~ r1(B,C)
| ~ r1(C,D)
| ~ p1(dollar_f2(B,C,D))
| ~ r1(C,E)
| p1(E)
| ~ r1(dollar_c6,E) ),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.8.10')] ).
cnf(510,axiom,
r1(A,A),
file('LCL672+1.001.p',unknown),
[] ).
cnf(511,axiom,
r1(dollar_c6,dollar_c1),
file('LCL672+1.001.p',unknown),
[] ).
cnf(512,axiom,
r1(dollar_c6,dollar_c4),
file('LCL672+1.001.p',unknown),
[] ).
cnf(513,axiom,
r1(dollar_c4,dollar_c2),
file('LCL672+1.001.p',unknown),
[] ).
cnf(514,axiom,
r1(dollar_c4,dollar_c3),
file('LCL672+1.001.p',unknown),
[] ).
cnf(515,axiom,
r1(dollar_c6,dollar_c5),
file('LCL672+1.001.p',unknown),
[] ).
cnf(814,plain,
r1(dollar_c6,dollar_c3),
inference(hyper,[status(thm)],[514,1,512]),
[iquote('hyper,514,1,512')] ).
cnf(1055,plain,
r1(dollar_c2,dollar_f2(dollar_c4,dollar_c4,dollar_c2)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[515,4,511,512,510,513,514]),11,13,14]),
[iquote('hyper,515,4,511,512,510,513,514,unit_del,11,13,14')] ).
cnf(9222,plain,
p1(dollar_f2(dollar_c4,dollar_c4,dollar_c2)),
inference(hyper,[status(thm)],[1055,12]),
[iquote('hyper,1055,12')] ).
cnf(9269,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[9222,57,511,512,510,513,514,814]),11,13]),
[iquote('hyper,9222,57,511,512,510,513,514,814,unit_del,11,13')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL672+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n024.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 09:33:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.37/2.57 ----- Otter 3.3f, August 2004 -----
% 2.37/2.57 The process was started by sandbox on n024.cluster.edu,
% 2.37/2.57 Wed Jul 27 09:33:55 2022
% 2.37/2.57 The command was "./otter". The process ID is 27973.
% 2.37/2.57
% 2.37/2.57 set(prolog_style_variables).
% 2.37/2.57 set(auto).
% 2.37/2.57 dependent: set(auto1).
% 2.37/2.57 dependent: set(process_input).
% 2.37/2.57 dependent: clear(print_kept).
% 2.37/2.57 dependent: clear(print_new_demod).
% 2.37/2.57 dependent: clear(print_back_demod).
% 2.37/2.57 dependent: clear(print_back_sub).
% 2.37/2.57 dependent: set(control_memory).
% 2.37/2.57 dependent: assign(max_mem, 12000).
% 2.37/2.57 dependent: assign(pick_given_ratio, 4).
% 2.37/2.57 dependent: assign(stats_level, 1).
% 2.37/2.57 dependent: assign(max_seconds, 10800).
% 2.37/2.57 clear(print_given).
% 2.37/2.57
% 2.37/2.57 formula_list(usable).
% 2.37/2.57 all X r1(X,X).
% 2.37/2.57 all X Y Z (r1(X,Y)&r1(Y,Z)->r1(X,Z)).
% 2.37/2.57 -(-(exists X (-(-(all Y (-r1(X,Y)|p2(Y)))& -(all Y (-r1(X,Y)| -(-(all X (-r1(Y,X)| -(all Y (-r1(X,Y)| -p1(Y)))))&p1(Y))))& -(all Y (-r1(X,Y)|p1(Y)))| -(all Y (-r1(X,Y)|p2(Y)))& -(all Y (-r1(X,Y)| (all X (-r1(Y,X)| -(-(all Y (-r1(X,Y)| -(all X (-r1(Y,X)|p1(X)))))& -(all Y (-r1(X,Y)|p1(Y))))))))& -(all Y (-r1(X,Y)|p1(Y)))| -(all Y (-r1(X,Y)|p2(Y)))& -(all Y (-r1(X,Y)| -(-(all X (-r1(Y,X)| -(all Y (-r1(X,Y)| -(all X (-r1(Y,X)|p1(X)))))))& -(all X (-r1(Y,X)| -(all Y (-r1(X,Y)|p1(Y))))))))& -(all Y (-r1(X,Y)|p1(Y)))| -(all Y (-r1(X,Y)|p2(Y)))& -(all Y (-r1(X,Y)| -(all X (-r1(Y,X)))))& -(all Y (-r1(X,Y)|p1(Y)))| (all Y (-r1(X,Y)|p2(Y)))| (all Y (-r1(X,Y)| (all X (-r1(Y,X)| -(all Y (-r1(X,Y)|p1(Y)))))| (all X (-r1(Y,X)|p1(X)))))| (all Y (-r1(X,Y)|p1(Y))))))).
% 2.37/2.57 end_of_list.
% 2.37/2.57
% 2.37/2.57 -------> usable clausifies to:
% 2.37/2.57
% 2.37/2.57 list(usable).
% 2.37/2.57 0 [] r1(X,X).
% 2.37/2.57 0 [] -r1(X,Y)| -r1(Y,Z)|r1(X,Z).
% 2.37/2.57 0 [] -r1($c6,Y)|p2(Y)| -r1($c6,X4)| -r1(X4,X)|r1(X,$f1(X4,X))| -p1(X4)| -r1($c6,X5)|p1(X5).
% 2.37/2.57 0 [] -r1($c6,Y)|p2(Y)| -r1($c6,X4)| -r1(X4,X)|p1($f1(X4,X))| -p1(X4)| -r1($c6,X5)|p1(X5).
% 2.37/2.57 0 [] -r1($c6,X6)|p2(X6)| -r1($c6,X7)| -r1(X7,X8)| -r1(X8,X1)|r1(X1,$f2(X7,X8,X1))| -r1(X8,X2)|p1(X2)| -r1($c6,X9)|p1(X9).
% 2.37/2.57 0 [] -r1($c6,X6)|p2(X6)| -r1($c6,X7)| -r1(X7,X8)| -r1(X8,X1)| -p1($f2(X7,X8,X1))| -r1(X8,X2)|p1(X2)| -r1($c6,X9)|p1(X9).
% 2.37/2.57 0 [] -r1($c6,X10)|p2(X10)| -r1($c6,X11)| -r1(X11,X12)|r1(X12,$f3(X11,X12))| -r1(X11,X13)|r1(X13,$f4(X11,X13))| -r1($c6,X14)|p1(X14).
% 2.37/2.57 0 [] -r1($c6,X10)|p2(X10)| -r1($c6,X11)| -r1(X11,X12)|r1(X12,$f3(X11,X12))| -r1(X11,X13)| -p1($f4(X11,X13))| -r1($c6,X14)|p1(X14).
% 2.37/2.57 0 [] -r1($c6,X10)|p2(X10)| -r1($c6,X11)| -r1(X11,X12)| -r1($f3(X11,X12),X3)|p1(X3)| -r1(X11,X13)|r1(X13,$f4(X11,X13))| -r1($c6,X14)|p1(X14).
% 2.37/2.57 0 [] -r1($c6,X10)|p2(X10)| -r1($c6,X11)| -r1(X11,X12)| -r1($f3(X11,X12),X3)|p1(X3)| -r1(X11,X13)| -p1($f4(X11,X13))| -r1($c6,X14)|p1(X14).
% 2.37/2.57 0 [] -r1($c6,X15)|p2(X15)| -r1($c6,X16)|r1(X16,$f5(X16))| -r1($c6,X17)|p1(X17).
% 2.37/2.57 0 [] r1($c6,$c1).
% 2.37/2.57 0 [] -p2($c1).
% 2.37/2.57 0 [] r1($c6,$c4).
% 2.37/2.57 0 [] r1($c4,$c2).
% 2.37/2.57 0 [] -r1($c2,X18)|p1(X18).
% 2.37/2.57 0 [] r1($c4,$c3).
% 2.37/2.57 0 [] -p1($c3).
% 2.37/2.57 0 [] r1($c6,$c5).
% 2.37/2.57 0 [] -p1($c5).
% 2.37/2.57 end_of_list.
% 2.37/2.57
% 2.37/2.57 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=10.
% 2.37/2.57
% 2.37/2.57 This is a non-Horn set without equality. The strategy will
% 2.37/2.57 be ordered hyper_res, unit deletion, and factoring, with
% 2.37/2.57 satellites in sos and with nuclei in usable.
% 2.37/2.57
% 2.37/2.57 dependent: set(hyper_res).
% 2.37/2.57 dependent: set(factor).
% 2.37/2.57 dependent: set(unit_deletion).
% 2.37/2.57
% 2.37/2.57 ------------> process usable:
% 2.37/2.57 ** KEPT (pick-wt=9): 1 [] -r1(A,B)| -r1(B,C)|r1(A,C).
% 2.37/2.57 ** KEPT (pick-wt=23): 2 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)|r1(C,$f1(B,C))| -p1(B)| -r1($c6,D)|p1(D).
% 2.37/2.57 ** KEPT (pick-wt=22): 3 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)|p1($f1(B,C))| -p1(B)| -r1($c6,D)|p1(D).
% 2.37/2.57 ** KEPT (pick-wt=30): 4 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)| -r1(C,D)|r1(D,$f2(B,C,D))| -r1(C,E)|p1(E)| -r1($c6,F)|p1(F).
% 2.37/2.57 ** KEPT (pick-wt=29): 5 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)| -r1(C,D)| -p1($f2(B,C,D))| -r1(C,E)|p1(E)| -r1($c6,F)|p1(F).
% 2.37/2.57 ** KEPT (pick-wt=29): 6 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)|r1(C,$f3(B,C))| -r1(B,D)|r1(D,$f4(B,D))| -r1($c6,E)|p1(E).
% 2.37/2.57 ** KEPT (pick-wt=28): 7 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)|r1(C,$f3(B,C))| -r1(B,D)| -p1($f4(B,D))| -r1($c6,E)|p1(E).
% 2.37/2.57 ** KEPT (pick-wt=31): 8 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)| -r1($f3(B,C),D)|p1(D)| -r1(B,E)|r1(E,$f4(B,E))| -r1($c6,F)|p1(F).
% 2.37/2.57 ** KEPT (pick-wt=30): 9 [] -r1($c6,A)|p2(A)| -r1($c6,B)| -r1(B,C)| -r1($f3(B,C),D)|p1(D)| -r1(B,E)| -p1($f4(B,E))| -r1($c6,F)|p1(F).
% 32.47/32.64 ** KEPT (pick-wt=17): 10 [] -r1($c6,A)|p2(A)| -r1($c6,B)|r1(B,$f5(B))| -r1($c6,C)|p1(C).
% 32.47/32.64 ** KEPT (pick-wt=2): 11 [] -p2($c1).
% 32.47/32.64 ** KEPT (pick-wt=5): 12 [] -r1($c2,A)|p1(A).
% 32.47/32.64 ** KEPT (pick-wt=2): 13 [] -p1($c3).
% 32.47/32.64 ** KEPT (pick-wt=2): 14 [] -p1($c5).
% 32.47/32.64
% 32.47/32.64 ------------> process sos:
% 32.47/32.64 ** KEPT (pick-wt=3): 510 [] r1(A,A).
% 32.47/32.64 ** KEPT (pick-wt=3): 511 [] r1($c6,$c1).
% 32.47/32.64 ** KEPT (pick-wt=3): 512 [] r1($c6,$c4).
% 32.47/32.64 ** KEPT (pick-wt=3): 513 [] r1($c4,$c2).
% 32.47/32.64 ** KEPT (pick-wt=3): 514 [] r1($c4,$c3).
% 32.47/32.64 ** KEPT (pick-wt=3): 515 [] r1($c6,$c5).
% 32.47/32.64
% 32.47/32.64 ======= end of input processing =======
% 32.47/32.64
% 32.47/32.64 =========== start of search ===========
% 32.47/32.64
% 32.47/32.64
% 32.47/32.64 Resetting weight limit to 6.
% 32.47/32.64
% 32.47/32.64
% 32.47/32.64 Resetting weight limit to 6.
% 32.47/32.64
% 32.47/32.64 sos_size=396
% 32.47/32.64
% 32.47/32.64 -- HEY sandbox, WE HAVE A PROOF!! --
% 32.47/32.64
% 32.47/32.64 -----> EMPTY CLAUSE at 30.62 sec ----> 9269 [hyper,9222,57,511,512,510,513,514,814,unit_del,11,13] $F.
% 32.47/32.64
% 32.47/32.64 Length of proof is 4. Level of proof is 2.
% 32.47/32.64
% 32.47/32.64 ---------------- PROOF ----------------
% 32.47/32.64 % SZS status Theorem
% 32.47/32.64 % SZS output start Refutation
% See solution above
% 32.47/32.64 ------------ end of proof -------------
% 32.47/32.64
% 32.47/32.64
% 32.47/32.64 Search stopped by max_proofs option.
% 32.47/32.64
% 32.47/32.64
% 32.47/32.64 Search stopped by max_proofs option.
% 32.47/32.64
% 32.47/32.64 ============ end of search ============
% 32.47/32.64
% 32.47/32.64 -------------- statistics -------------
% 32.47/32.64 clauses given 45
% 32.47/32.64 clauses generated 506986
% 32.47/32.64 clauses kept 9268
% 32.47/32.64 clauses forward subsumed 160588
% 32.47/32.64 clauses back subsumed 8286
% 32.47/32.64 Kbytes malloced 4882
% 32.47/32.64
% 32.47/32.64 ----------- times (seconds) -----------
% 32.47/32.64 user CPU time 30.62 (0 hr, 0 min, 30 sec)
% 32.47/32.64 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 32.47/32.64 wall-clock time 32 (0 hr, 0 min, 32 sec)
% 32.47/32.64
% 32.47/32.64 That finishes the proof of the theorem.
% 32.47/32.64
% 32.47/32.64 Process 27973 finished Wed Jul 27 09:34:27 2022
% 32.47/32.64 Otter interrupted
% 32.47/32.64 PROOF FOUND
%------------------------------------------------------------------------------