TSTP Solution File: GRP012+5 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP012+5 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:55:51 EDT 2022
% Result : Theorem 1.92s 2.12s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 14 ( 12 unt; 0 nHn; 10 RR)
% Number of literals : 20 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP012+5.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP012+5.p',unknown),
[] ).
cnf(3,axiom,
~ product(inverse(dollar_c2),inverse(dollar_c1),dollar_c5),
file('GRP012+5.p',unknown),
[] ).
cnf(5,axiom,
product(A,dollar_c5,A),
file('GRP012+5.p',unknown),
[] ).
cnf(6,axiom,
product(dollar_c5,A,A),
file('GRP012+5.p',unknown),
[] ).
cnf(7,axiom,
product(A,inverse(A),dollar_c5),
file('GRP012+5.p',unknown),
[] ).
cnf(8,axiom,
product(inverse(A),A,dollar_c5),
file('GRP012+5.p',unknown),
[] ).
cnf(9,axiom,
product(inverse(dollar_c4),inverse(dollar_c3),dollar_c2),
file('GRP012+5.p',unknown),
[] ).
cnf(10,axiom,
product(dollar_c3,dollar_c4,dollar_c1),
file('GRP012+5.p',unknown),
[] ).
cnf(98,plain,
product(inverse(dollar_c3),dollar_c1,dollar_c4),
inference(hyper,[status(thm)],[8,1,10,6]),
[iquote('hyper,8,1,10,6')] ).
cnf(219,plain,
product(dollar_c2,dollar_c1,dollar_c5),
inference(hyper,[status(thm)],[9,2,98,8]),
[iquote('hyper,9,2,98,8')] ).
cnf(252,plain,
product(dollar_c5,dollar_c1,inverse(dollar_c2)),
inference(hyper,[status(thm)],[219,2,8,5]),
[iquote('hyper,219,2,8,5')] ).
cnf(616,plain,
product(inverse(dollar_c2),inverse(dollar_c1),dollar_c5),
inference(hyper,[status(thm)],[252,2,7,6]),
[iquote('hyper,252,2,7,6')] ).
cnf(617,plain,
$false,
inference(binary,[status(thm)],[616,3]),
[iquote('binary,616.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP012+5 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 05:45:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.92/2.12 ----- Otter 3.3f, August 2004 -----
% 1.92/2.12 The process was started by sandbox on n015.cluster.edu,
% 1.92/2.12 Wed Jul 27 05:45:26 2022
% 1.92/2.12 The command was "./otter". The process ID is 22315.
% 1.92/2.12
% 1.92/2.12 set(prolog_style_variables).
% 1.92/2.12 set(auto).
% 1.92/2.12 dependent: set(auto1).
% 1.92/2.12 dependent: set(process_input).
% 1.92/2.12 dependent: clear(print_kept).
% 1.92/2.12 dependent: clear(print_new_demod).
% 1.92/2.12 dependent: clear(print_back_demod).
% 1.92/2.12 dependent: clear(print_back_sub).
% 1.92/2.12 dependent: set(control_memory).
% 1.92/2.12 dependent: assign(max_mem, 12000).
% 1.92/2.12 dependent: assign(pick_given_ratio, 4).
% 1.92/2.12 dependent: assign(stats_level, 1).
% 1.92/2.12 dependent: assign(max_seconds, 10800).
% 1.92/2.12 clear(print_given).
% 1.92/2.12
% 1.92/2.12 formula_list(usable).
% 1.92/2.12 -(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 U V W X (product(inverse(U),inverse(V),W)&product(V,U,X)->product(inverse(W),inverse(X),E))))).
% 1.92/2.12 end_of_list.
% 1.92/2.12
% 1.92/2.12 -------> usable clausifies to:
% 1.92/2.12
% 1.92/2.12 list(usable).
% 1.92/2.12 0 [] product(X,Y,$f1(X,Y)).
% 1.92/2.12 0 [] -product(X1,X2,U)| -product(X2,Z,V)| -product(U,Z,W)|product(X1,V,W).
% 1.92/2.12 0 [] -product(X3,X4,X6)| -product(X4,X5,X7)| -product(X3,X7,X8)|product(X6,X5,X8).
% 1.92/2.12 0 [] product(X9,$c5,X9).
% 1.92/2.12 0 [] product($c5,X10,X10).
% 1.92/2.12 0 [] product(X11,inverse(X11),$c5).
% 1.92/2.12 0 [] product(inverse(X12),X12,$c5).
% 1.92/2.12 0 [] product(inverse($c4),inverse($c3),$c2).
% 1.92/2.12 0 [] product($c3,$c4,$c1).
% 1.92/2.12 0 [] -product(inverse($c2),inverse($c1),$c5).
% 1.92/2.12 end_of_list.
% 1.92/2.12
% 1.92/2.12 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.92/2.12
% 1.92/2.12 This is a Horn set without equality. The strategy will
% 1.92/2.12 be hyperresolution, with satellites in sos and nuclei
% 1.92/2.12 in usable.
% 1.92/2.12
% 1.92/2.12 dependent: set(hyper_res).
% 1.92/2.12 dependent: clear(order_hyper).
% 1.92/2.12
% 1.92/2.12 ------------> process usable:
% 1.92/2.12 ** KEPT (pick-wt=16): 1 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.92/2.12 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.92/2.12 ** KEPT (pick-wt=6): 3 [] -product(inverse($c2),inverse($c1),$c5).
% 1.92/2.12
% 1.92/2.12 ------------> process sos:
% 1.92/2.12 ** KEPT (pick-wt=6): 4 [] product(A,B,$f1(A,B)).
% 1.92/2.12 ** KEPT (pick-wt=4): 5 [] product(A,$c5,A).
% 1.92/2.12 ** KEPT (pick-wt=4): 6 [] product($c5,A,A).
% 1.92/2.12 ** KEPT (pick-wt=5): 7 [] product(A,inverse(A),$c5).
% 1.92/2.12 ** KEPT (pick-wt=5): 8 [] product(inverse(A),A,$c5).
% 1.92/2.12 ** KEPT (pick-wt=6): 9 [] product(inverse($c4),inverse($c3),$c2).
% 1.92/2.12 ** KEPT (pick-wt=4): 10 [] product($c3,$c4,$c1).
% 1.92/2.12
% 1.92/2.12 ======= end of input processing =======
% 1.92/2.12
% 1.92/2.12 =========== start of search ===========
% 1.92/2.12
% 1.92/2.12 -------- PROOF --------
% 1.92/2.12
% 1.92/2.12 ----> UNIT CONFLICT at 0.01 sec ----> 617 [binary,616.1,3.1] $F.
% 1.92/2.12
% 1.92/2.12 Length of proof is 4. Level of proof is 4.
% 1.92/2.12
% 1.92/2.12 ---------------- PROOF ----------------
% 1.92/2.12 % SZS status Theorem
% 1.92/2.12 % SZS output start Refutation
% See solution above
% 1.92/2.12 ------------ end of proof -------------
% 1.92/2.12
% 1.92/2.12
% 1.92/2.12 Search stopped by max_proofs option.
% 1.92/2.12
% 1.92/2.12
% 1.92/2.12 Search stopped by max_proofs option.
% 1.92/2.12
% 1.92/2.12 ============ end of search ============
% 1.92/2.12
% 1.92/2.12 -------------- statistics -------------
% 1.92/2.12 clauses given 18
% 1.92/2.12 clauses generated 1487
% 1.92/2.12 clauses kept 616
% 1.92/2.12 clauses forward subsumed 881
% 1.92/2.12 clauses back subsumed 8
% 1.92/2.12 Kbytes malloced 976
% 1.92/2.12
% 1.92/2.12 ----------- times (seconds) -----------
% 1.92/2.12 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.92/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.12
% 1.92/2.12 That finishes the proof of the theorem.
% 1.92/2.12
% 1.92/2.12 Process 22315 finished Wed Jul 27 05:45:28 2022
% 1.92/2.12 Otter interrupted
% 1.92/2.12 PROOF FOUND
%------------------------------------------------------------------------------