TSTP Solution File: GRP001+6 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% 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 12:55:49 EDT 2022
% Result : Theorem 1.98s 2.17s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 10 unt; 0 nHn; 9 RR)
% Number of literals : 18 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP001+6.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP001+6.p',unknown),
[] ).
cnf(3,axiom,
~ product(dollar_c2,dollar_c3,dollar_c1),
file('GRP001+6.p',unknown),
[] ).
cnf(5,axiom,
product(A,dollar_c4,A),
file('GRP001+6.p',unknown),
[] ).
cnf(6,axiom,
product(dollar_c4,A,A),
file('GRP001+6.p',unknown),
[] ).
cnf(9,axiom,
product(A,A,dollar_c4),
file('GRP001+6.p',unknown),
[] ).
cnf(10,axiom,
product(dollar_c3,dollar_c2,dollar_c1),
file('GRP001+6.p',unknown),
[] ).
cnf(52,plain,
product(dollar_c1,dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[10,2,9,5]),
[iquote('hyper,10,2,9,5')] ).
cnf(58,plain,
product(dollar_c3,dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[10,1,9,6]),
[iquote('hyper,10,1,9,6')] ).
cnf(116,plain,
product(dollar_c1,dollar_c3,dollar_c2),
inference(hyper,[status(thm)],[52,1,9,6]),
[iquote('hyper,52,1,9,6')] ).
cnf(156,plain,
product(dollar_c2,dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[116,2,58,10]),
[iquote('hyper,116,2,58,10')] ).
cnf(157,plain,
$false,
inference(binary,[status(thm)],[156,3]),
[iquote('binary,156.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:05:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.98/2.17 ----- Otter 3.3f, August 2004 -----
% 1.98/2.17 The process was started by sandbox2 on n011.cluster.edu,
% 1.98/2.17 Wed Jul 27 05:05:10 2022
% 1.98/2.17 The command was "./otter". The process ID is 28978.
% 1.98/2.17
% 1.98/2.17 set(prolog_style_variables).
% 1.98/2.17 set(auto).
% 1.98/2.17 dependent: set(auto1).
% 1.98/2.17 dependent: set(process_input).
% 1.98/2.17 dependent: clear(print_kept).
% 1.98/2.17 dependent: clear(print_new_demod).
% 1.98/2.17 dependent: clear(print_back_demod).
% 1.98/2.17 dependent: clear(print_back_sub).
% 1.98/2.17 dependent: set(control_memory).
% 1.98/2.17 dependent: assign(max_mem, 12000).
% 1.98/2.17 dependent: assign(pick_given_ratio, 4).
% 1.98/2.17 dependent: assign(stats_level, 1).
% 1.98/2.17 dependent: assign(max_seconds, 10800).
% 1.98/2.17 clear(print_given).
% 1.98/2.17
% 1.98/2.17 formula_list(usable).
% 1.98/2.17 -(all E ((all X Y exists Z product(X,Y,Z))& (all X Y Z U V W (product(X,Y,U)&product(Y,Z,V)&product(U,Z,W)->product(X,V,W)))& (all X Y Z U V W (product(X,Y,U)&product(Y,Z,V)&product(X,V,W)->product(U,Z,W)))& (all X product(X,E,X))& (all X product(E,X,X))& (all X product(X,inverse(X),E))& (all X product(inverse(X),X,E))-> ((all X product(X,X,E))-> (all U V W (product(U,V,W)->product(V,U,W)))))).
% 1.98/2.17 end_of_list.
% 1.98/2.17
% 1.98/2.17 -------> usable clausifies to:
% 1.98/2.17
% 1.98/2.17 list(usable).
% 1.98/2.17 0 [] product(X,Y,$f1(X,Y)).
% 1.98/2.17 0 [] -product(X1,X2,U)| -product(X2,Z,V)| -product(U,Z,W)|product(X1,V,W).
% 1.98/2.17 0 [] -product(X3,X4,X6)| -product(X4,X5,X7)| -product(X3,X7,X8)|product(X6,X5,X8).
% 1.98/2.17 0 [] product(X9,$c4,X9).
% 1.98/2.17 0 [] product($c4,X10,X10).
% 1.98/2.17 0 [] product(X11,inverse(X11),$c4).
% 1.98/2.17 0 [] product(inverse(X12),X12,$c4).
% 1.98/2.17 0 [] product(X13,X13,$c4).
% 1.98/2.17 0 [] product($c3,$c2,$c1).
% 1.98/2.17 0 [] -product($c2,$c3,$c1).
% 1.98/2.17 end_of_list.
% 1.98/2.17
% 1.98/2.17 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.98/2.17
% 1.98/2.17 This is a Horn set without equality. The strategy will
% 1.98/2.17 be hyperresolution, with satellites in sos and nuclei
% 1.98/2.17 in usable.
% 1.98/2.17
% 1.98/2.17 dependent: set(hyper_res).
% 1.98/2.17 dependent: clear(order_hyper).
% 1.98/2.17
% 1.98/2.17 ------------> process usable:
% 1.98/2.17 ** KEPT (pick-wt=16): 1 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.98/2.17 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.98/2.17 ** KEPT (pick-wt=4): 3 [] -product($c2,$c3,$c1).
% 1.98/2.17
% 1.98/2.17 ------------> process sos:
% 1.98/2.17 ** KEPT (pick-wt=6): 4 [] product(A,B,$f1(A,B)).
% 1.98/2.17 ** KEPT (pick-wt=4): 5 [] product(A,$c4,A).
% 1.98/2.17 ** KEPT (pick-wt=4): 6 [] product($c4,A,A).
% 1.98/2.17 ** KEPT (pick-wt=5): 7 [] product(A,inverse(A),$c4).
% 1.98/2.17 ** KEPT (pick-wt=5): 8 [] product(inverse(A),A,$c4).
% 1.98/2.17 ** KEPT (pick-wt=4): 9 [] product(A,A,$c4).
% 1.98/2.17 ** KEPT (pick-wt=4): 10 [] product($c3,$c2,$c1).
% 1.98/2.17
% 1.98/2.17 ======= end of input processing =======
% 1.98/2.17
% 1.98/2.17 =========== start of search ===========
% 1.98/2.17
% 1.98/2.17 -------- PROOF --------
% 1.98/2.17
% 1.98/2.17 ----> UNIT CONFLICT at 0.00 sec ----> 157 [binary,156.1,3.1] $F.
% 1.98/2.17
% 1.98/2.17 Length of proof is 4. Level of proof is 3.
% 1.98/2.17
% 1.98/2.17 ---------------- PROOF ----------------
% 1.98/2.17 % SZS status Theorem
% 1.98/2.17 % SZS output start Refutation
% See solution above
% 1.98/2.17 ------------ end of proof -------------
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Search stopped by max_proofs option.
% 1.98/2.17
% 1.98/2.17
% 1.98/2.17 Search stopped by max_proofs option.
% 1.98/2.17
% 1.98/2.17 ============ end of search ============
% 1.98/2.17
% 1.98/2.17 -------------- statistics -------------
% 1.98/2.17 clauses given 9
% 1.98/2.17 clauses generated 368
% 1.98/2.17 clauses kept 156
% 1.98/2.17 clauses forward subsumed 222
% 1.98/2.17 clauses back subsumed 8
% 1.98/2.17 Kbytes malloced 976
% 1.98/2.17
% 1.98/2.17 ----------- times (seconds) -----------
% 1.98/2.17 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.17 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.17 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.17
% 1.98/2.17 That finishes the proof of the theorem.
% 1.98/2.17
% 1.98/2.17 Process 28978 finished Wed Jul 27 05:05:12 2022
% 1.98/2.17 Otter interrupted
% 1.98/2.17 PROOF FOUND
%------------------------------------------------------------------------------