TSTP Solution File: LCL654+1.001 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL654+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:04:54 EDT 2022
% Result : Theorem 1.94s 2.11s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 22 ( 12 unt; 6 nHn; 21 RR)
% Number of literals : 54 ( 0 equ; 27 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ r1(dollar_c4,A)
| ~ r1(A,B)
| ~ r1(B,C)
| r1(C,dollar_f2(A,B,C))
| ~ r1(B,D)
| p1(D) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(4,axiom,
( ~ r1(dollar_c4,A)
| ~ r1(A,B)
| ~ r1(B,C)
| ~ p1(dollar_f2(A,B,C))
| ~ r1(B,D)
| p1(D) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(5,axiom,
( ~ r1(dollar_c4,A)
| ~ r1(A,B)
| r1(B,dollar_f3(A,B))
| ~ r1(A,C)
| r1(C,dollar_f4(A,C)) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(6,axiom,
( ~ r1(dollar_c4,A)
| ~ r1(A,B)
| r1(B,dollar_f3(A,B))
| ~ r1(A,C)
| ~ p1(dollar_f4(A,C)) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(7,axiom,
( ~ r1(dollar_c4,A)
| ~ r1(A,B)
| ~ r1(dollar_f3(A,B),C)
| p1(C)
| ~ r1(A,D)
| r1(D,dollar_f4(A,D)) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(8,axiom,
( ~ r1(dollar_c4,A)
| ~ r1(A,B)
| ~ r1(dollar_f3(A,B),C)
| p1(C)
| ~ r1(A,D)
| ~ p1(dollar_f4(A,D)) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(10,axiom,
~ p1(dollar_c1),
file('LCL654+1.001.p',unknown),
[] ).
cnf(11,axiom,
( ~ r1(dollar_c3,A)
| p1(A) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(54,axiom,
r1(A,A),
file('LCL654+1.001.p',unknown),
[] ).
cnf(55,axiom,
r1(dollar_c4,dollar_c3),
file('LCL654+1.001.p',unknown),
[] ).
cnf(56,axiom,
r1(dollar_c3,dollar_c2),
file('LCL654+1.001.p',unknown),
[] ).
cnf(57,axiom,
r1(dollar_c2,dollar_c1),
file('LCL654+1.001.p',unknown),
[] ).
cnf(85,plain,
( r1(dollar_c2,dollar_f3(dollar_c3,dollar_c2))
| r1(dollar_c3,dollar_f4(dollar_c3,dollar_c3)) ),
inference(hyper,[status(thm)],[56,5,55,54]),
[iquote('hyper,56,5,55,54')] ).
cnf(452,plain,
( r1(dollar_c2,dollar_f3(dollar_c3,dollar_c2))
| p1(dollar_f4(dollar_c3,dollar_c3)) ),
inference(hyper,[status(thm)],[85,11]),
[iquote('hyper,85,11')] ).
cnf(476,plain,
r1(dollar_c2,dollar_f3(dollar_c3,dollar_c2)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[452,6,55,56,54])]),
[iquote('hyper,452,6,55,56,54,factor_simp')] ).
cnf(479,plain,
r1(dollar_f3(dollar_c3,dollar_c2),dollar_f2(dollar_c3,dollar_c2,dollar_f3(dollar_c3,dollar_c2))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[476,3,55,56,57]),10]),
[iquote('hyper,476,3,55,56,57,unit_del,10')] ).
cnf(509,plain,
( p1(dollar_f2(dollar_c3,dollar_c2,dollar_f3(dollar_c3,dollar_c2)))
| r1(dollar_c3,dollar_f4(dollar_c3,dollar_c3)) ),
inference(hyper,[status(thm)],[479,7,55,56,54]),
[iquote('hyper,479,7,55,56,54')] ).
cnf(1212,plain,
r1(dollar_c3,dollar_f4(dollar_c3,dollar_c3)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[509,4,55,56,476,57]),10]),
[iquote('hyper,509,4,55,56,476,57,unit_del,10')] ).
cnf(1219,plain,
p1(dollar_f4(dollar_c3,dollar_c3)),
inference(hyper,[status(thm)],[1212,11]),
[iquote('hyper,1212,11')] ).
cnf(1249,plain,
p1(dollar_f2(dollar_c3,dollar_c2,dollar_f3(dollar_c3,dollar_c2))),
inference(hyper,[status(thm)],[1219,8,55,56,479,54]),
[iquote('hyper,1219,8,55,56,479,54')] ).
cnf(1312,plain,
p1(dollar_c1),
inference(hyper,[status(thm)],[1249,4,55,56,476,57]),
[iquote('hyper,1249,4,55,56,476,57')] ).
cnf(1313,plain,
$false,
inference(binary,[status(thm)],[1312,10]),
[iquote('binary,1312.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL654+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:21:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.94/2.11 ----- Otter 3.3f, August 2004 -----
% 1.94/2.11 The process was started by sandbox2 on n019.cluster.edu,
% 1.94/2.11 Wed Jul 27 09:21:07 2022
% 1.94/2.11 The command was "./otter". The process ID is 31106.
% 1.94/2.11
% 1.94/2.11 set(prolog_style_variables).
% 1.94/2.11 set(auto).
% 1.94/2.11 dependent: set(auto1).
% 1.94/2.11 dependent: set(process_input).
% 1.94/2.11 dependent: clear(print_kept).
% 1.94/2.11 dependent: clear(print_new_demod).
% 1.94/2.11 dependent: clear(print_back_demod).
% 1.94/2.11 dependent: clear(print_back_sub).
% 1.94/2.11 dependent: set(control_memory).
% 1.94/2.11 dependent: assign(max_mem, 12000).
% 1.94/2.11 dependent: assign(pick_given_ratio, 4).
% 1.94/2.11 dependent: assign(stats_level, 1).
% 1.94/2.11 dependent: assign(max_seconds, 10800).
% 1.94/2.11 clear(print_given).
% 1.94/2.11
% 1.94/2.11 formula_list(usable).
% 1.94/2.11 all X r1(X,X).
% 1.94/2.11 -(-(exists X (-(-(all Y (-r1(X,Y)| -(-(all X (-r1(Y,X)| -(all Y (-r1(X,Y)| -p1(Y)))))&p1(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)| -(-(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)| -(all X (-r1(Y,X)))))| (all Y (-r1(X,Y)| (all X (-r1(Y,X)| (all Y (-r1(X,Y)|p1(Y)))))| -(all X (-r1(Y,X)|p1(X))))))))).
% 1.94/2.11 end_of_list.
% 1.94/2.11
% 1.94/2.11 -------> usable clausifies to:
% 1.94/2.11
% 1.94/2.11 list(usable).
% 1.94/2.11 0 [] r1(X,X).
% 1.94/2.11 0 [] -r1($c4,Y)| -r1(Y,X)|r1(X,$f1(Y,X))| -p1(Y).
% 1.94/2.11 0 [] -r1($c4,Y)| -r1(Y,X)|p1($f1(Y,X))| -p1(Y).
% 1.94/2.11 0 [] -r1($c4,X4)| -r1(X4,X5)| -r1(X5,X1)|r1(X1,$f2(X4,X5,X1))| -r1(X5,X2)|p1(X2).
% 1.94/2.11 0 [] -r1($c4,X4)| -r1(X4,X5)| -r1(X5,X1)| -p1($f2(X4,X5,X1))| -r1(X5,X2)|p1(X2).
% 1.94/2.11 0 [] -r1($c4,X6)| -r1(X6,X7)|r1(X7,$f3(X6,X7))| -r1(X6,X8)|r1(X8,$f4(X6,X8)).
% 1.94/2.11 0 [] -r1($c4,X6)| -r1(X6,X7)|r1(X7,$f3(X6,X7))| -r1(X6,X8)| -p1($f4(X6,X8)).
% 1.94/2.11 0 [] -r1($c4,X6)| -r1(X6,X7)| -r1($f3(X6,X7),X3)|p1(X3)| -r1(X6,X8)|r1(X8,$f4(X6,X8)).
% 1.94/2.11 0 [] -r1($c4,X6)| -r1(X6,X7)| -r1($f3(X6,X7),X3)|p1(X3)| -r1(X6,X8)| -p1($f4(X6,X8)).
% 1.94/2.11 0 [] -r1($c4,X9)|r1(X9,$f5(X9)).
% 1.94/2.11 0 [] r1($c4,$c3).
% 1.94/2.11 0 [] r1($c3,$c2).
% 1.94/2.11 0 [] r1($c2,$c1).
% 1.94/2.11 0 [] -p1($c1).
% 1.94/2.11 0 [] -r1($c3,X10)|p1(X10).
% 1.94/2.11 end_of_list.
% 1.94/2.11
% 1.94/2.11 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.94/2.11
% 1.94/2.11 This is a non-Horn set without equality. The strategy will
% 1.94/2.11 be ordered hyper_res, unit deletion, and factoring, with
% 1.94/2.11 satellites in sos and with nuclei in usable.
% 1.94/2.11
% 1.94/2.11 dependent: set(hyper_res).
% 1.94/2.11 dependent: set(factor).
% 1.94/2.11 dependent: set(unit_deletion).
% 1.94/2.11
% 1.94/2.11 ------------> process usable:
% 1.94/2.11 ** KEPT (pick-wt=13): 1 [] -r1($c4,A)| -r1(A,B)|r1(B,$f1(A,B))| -p1(A).
% 1.94/2.11 ** KEPT (pick-wt=12): 2 [] -r1($c4,A)| -r1(A,B)|p1($f1(A,B))| -p1(A).
% 1.94/2.11 ** KEPT (pick-wt=20): 3 [] -r1($c4,A)| -r1(A,B)| -r1(B,C)|r1(C,$f2(A,B,C))| -r1(B,D)|p1(D).
% 1.94/2.11 ** KEPT (pick-wt=19): 4 [] -r1($c4,A)| -r1(A,B)| -r1(B,C)| -p1($f2(A,B,C))| -r1(B,D)|p1(D).
% 1.94/2.11 ** KEPT (pick-wt=19): 5 [] -r1($c4,A)| -r1(A,B)|r1(B,$f3(A,B))| -r1(A,C)|r1(C,$f4(A,C)).
% 1.94/2.11 ** KEPT (pick-wt=18): 6 [] -r1($c4,A)| -r1(A,B)|r1(B,$f3(A,B))| -r1(A,C)| -p1($f4(A,C)).
% 1.94/2.11 ** KEPT (pick-wt=21): 7 [] -r1($c4,A)| -r1(A,B)| -r1($f3(A,B),C)|p1(C)| -r1(A,D)|r1(D,$f4(A,D)).
% 1.94/2.11 ** KEPT (pick-wt=20): 8 [] -r1($c4,A)| -r1(A,B)| -r1($f3(A,B),C)|p1(C)| -r1(A,D)| -p1($f4(A,D)).
% 1.94/2.11 ** KEPT (pick-wt=7): 9 [] -r1($c4,A)|r1(A,$f5(A)).
% 1.94/2.11 ** KEPT (pick-wt=2): 10 [] -p1($c1).
% 1.94/2.11 ** KEPT (pick-wt=5): 11 [] -r1($c3,A)|p1(A).
% 1.94/2.11
% 1.94/2.11 ------------> process sos:
% 1.94/2.11 ** KEPT (pick-wt=3): 54 [] r1(A,A).
% 1.94/2.11 ** KEPT (pick-wt=3): 55 [] r1($c4,$c3).
% 1.94/2.11 ** KEPT (pick-wt=3): 56 [] r1($c3,$c2).
% 1.94/2.11 ** KEPT (pick-wt=3): 57 [] r1($c2,$c1).
% 1.94/2.11
% 1.94/2.11 ======= end of input processing =======
% 1.94/2.11
% 1.94/2.11 =========== start of search ===========
% 1.94/2.11
% 1.94/2.11 -------- PROOF --------
% 1.94/2.11
% 1.94/2.11 ----> UNIT CONFLICT at 0.13 sec ----> 1313 [binary,1312.1,10.1] $F.
% 1.94/2.11
% 1.94/2.11 Length of proof is 9. Level of proof is 9.
% 1.94/2.11
% 1.94/2.11 ---------------- PROOF ----------------
% 1.94/2.11 % SZS status Theorem
% 1.94/2.11 % SZS output start Refutation
% See solution above
% 1.94/2.11 ------------ end of proof -------------
% 1.94/2.11
% 1.94/2.11
% 1.94/2.11 Search stopped by max_proofs option.
% 1.94/2.11
% 1.94/2.11
% 1.94/2.11 Search stopped by max_proofs option.
% 1.94/2.11
% 1.94/2.11 ============ end of search ============
% 1.94/2.11
% 1.94/2.11 -------------- statistics -------------
% 1.94/2.11 clauses given 145
% 1.94/2.11 clauses generated 3475
% 1.94/2.11 clauses kept 1312
% 1.94/2.11 clauses forward subsumed 2178
% 1.94/2.11 clauses back subsumed 904
% 1.94/2.11 Kbytes malloced 1953
% 1.94/2.11
% 1.94/2.11 ----------- times (seconds) -----------
% 1.94/2.11 user CPU time 0.13 (0 hr, 0 min, 0 sec)
% 1.94/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.11 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.94/2.11
% 1.94/2.11 That finishes the proof of the theorem.
% 1.94/2.11
% 1.94/2.11 Process 31106 finished Wed Jul 27 09:21:08 2022
% 1.94/2.11 Otter interrupted
% 1.94/2.11 PROOF FOUND
%------------------------------------------------------------------------------