%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP048-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 12:55:58 EDT 2022
% Result : Unsatisfiable 2.00s 2.25s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 26 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP048-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP048-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP048-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ e_qualish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
file('GRP048-2.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(inverse(a),inverse(b)),
file('GRP048-2.p',unknown),
[] ).
cnf(6,axiom,
product(identity,A,A),
file('GRP048-2.p',unknown),
[] ).
cnf(7,axiom,
product(inverse(A),A,identity),
file('GRP048-2.p',unknown),
[] ).
cnf(9,axiom,
e_qualish(a,b),
file('GRP048-2.p',unknown),
[] ).
cnf(11,plain,
product(identity,a,b),
inference(hyper,[status(thm)],[9,4,6]),
[iquote('hyper,9,4,6')] ).
cnf(14,plain,
product(inverse(inverse(a)),identity,b),
inference(hyper,[status(thm)],[7,2,7,11]),
[iquote('hyper,7,2,7,11')] ).
cnf(15,plain,
product(inverse(inverse(A)),identity,A),
inference(hyper,[status(thm)],[7,2,7,6]),
[iquote('hyper,7,2,7,6')] ).
cnf(181,plain,
product(b,inverse(a),identity),
inference(hyper,[status(thm)],[14,3,6,7]),
[iquote('hyper,14,3,6,7')] ).
cnf(308,plain,
product(A,identity,A),
inference(hyper,[status(thm)],[15,3,15,6]),
[iquote('hyper,15,3,15,6')] ).
cnf(503,plain,
product(identity,inverse(a),inverse(b)),
inference(hyper,[status(thm)],[181,3,7,308]),
[iquote('hyper,181,3,7,308')] ).
cnf(8831,plain,
e_qualish(inverse(a),inverse(b)),
inference(hyper,[status(thm)],[503,1,6]),
[iquote('hyper,503,1,6')] ).
cnf(8832,plain,
$false,
inference(binary,[status(thm)],[8831,5]),
[iquote('binary,8831.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP048-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:31:06 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.00/2.25 ----- Otter 3.3f, August 2004 -----
% 2.00/2.25 The process was started by sandbox on n004.cluster.edu,
% 2.00/2.25 Wed Jul 27 05:31:06 2022
% 2.00/2.25 The command was "./otter". The process ID is 13441.
% 2.00/2.25
% 2.00/2.25 set(prolog_style_variables).
% 2.00/2.25 set(auto).
% 2.00/2.25 dependent: set(auto1).
% 2.00/2.25 dependent: set(process_input).
% 2.00/2.25 dependent: clear(print_kept).
% 2.00/2.25 dependent: clear(print_new_demod).
% 2.00/2.25 dependent: clear(print_back_demod).
% 2.00/2.25 dependent: clear(print_back_sub).
% 2.00/2.25 dependent: set(control_memory).
% 2.00/2.25 dependent: assign(max_mem, 12000).
% 2.00/2.25 dependent: assign(pick_given_ratio, 4).
% 2.00/2.25 dependent: assign(stats_level, 1).
% 2.00/2.25 dependent: assign(max_seconds, 10800).
% 2.00/2.25 clear(print_given).
% 2.00/2.25
% 2.00/2.25 list(usable).
% 2.00/2.25 0 [] product(identity,X,X).
% 2.00/2.25 0 [] product(inverse(X),X,identity).
% 2.00/2.25 0 [] product(X,Y,multiply(X,Y)).
% 2.00/2.25 0 [] -product(X,Y,Z)| -product(X,Y,W)|e_qualish(Z,W).
% 2.00/2.25 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 2.00/2.25 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 2.00/2.25 0 [] -e_qualish(X,Y)| -product(W,Z,X)|product(W,Z,Y).
% 2.00/2.25 0 [] e_qualish(a,b).
% 2.00/2.25 0 [] -e_qualish(inverse(a),inverse(b)).
% 2.00/2.25 end_of_list.
% 2.00/2.25
% 2.00/2.25 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 2.00/2.25
% 2.00/2.25 This is a Horn set without equality. The strategy will
% 2.00/2.25 be hyperresolution, with satellites in sos and nuclei
% 2.00/2.25 in usable.
% 2.00/2.25
% 2.00/2.25 dependent: set(hyper_res).
% 2.00/2.25 dependent: clear(order_hyper).
% 2.00/2.25
% 2.00/2.25 ------------> process usable:
% 2.00/2.25 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 2.00/2.25 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 2.00/2.25 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 2.00/2.25 ** KEPT (pick-wt=11): 4 [] -e_qualish(A,B)| -product(C,D,A)|product(C,D,B).
% 2.00/2.25 ** KEPT (pick-wt=5): 5 [] -e_qualish(inverse(a),inverse(b)).
% 2.00/2.25
% 2.00/2.25 ------------> process sos:
% 2.00/2.25 ** KEPT (pick-wt=4): 6 [] product(identity,A,A).
% 2.00/2.25 ** KEPT (pick-wt=5): 7 [] product(inverse(A),A,identity).
% 2.00/2.25 ** KEPT (pick-wt=6): 8 [] product(A,B,multiply(A,B)).
% 2.00/2.25 ** KEPT (pick-wt=3): 9 [] e_qualish(a,b).
% 2.00/2.25
% 2.00/2.25 ======= end of input processing =======
% 2.00/2.25
% 2.00/2.25 =========== start of search ===========
% 2.00/2.25
% 2.00/2.25
% 2.00/2.25 Resetting weight limit to 8.
% 2.00/2.25
% 2.00/2.25
% 2.00/2.25 Resetting weight limit to 8.
% 2.00/2.25
% 2.00/2.25 sos_size=7626
% 2.00/2.25
% 2.00/2.25 -------- PROOF --------
% 2.00/2.25
% 2.00/2.25 ----> UNIT CONFLICT at 0.37 sec ----> 8832 [binary,8831.1,5.1] $F.
% 2.00/2.25
% 2.00/2.25 Length of proof is 7. Level of proof is 5.
% 2.00/2.25
% 2.00/2.25 ---------------- PROOF ----------------
% 2.00/2.25 % SZS status Unsatisfiable
% 2.00/2.25 % SZS output start Refutation
% See solution above
% 2.00/2.25 ------------ end of proof -------------
% 2.00/2.25
% 2.00/2.25
% 2.00/2.25 Search stopped by max_proofs option.
% 2.00/2.25
% 2.00/2.25
% 2.00/2.25 Search stopped by max_proofs option.
% 2.00/2.25
% 2.00/2.25 ============ end of search ============
% 2.00/2.25
% 2.00/2.25 -------------- statistics -------------
% 2.00/2.25 clauses given 125
% 2.00/2.25 clauses generated 78980
% 2.00/2.25 clauses kept 8831
% 2.00/2.25 clauses forward subsumed 28052
% 2.00/2.25 clauses back subsumed 941
% 2.00/2.25 Kbytes malloced 4882
% 2.00/2.25
% 2.00/2.25 ----------- times (seconds) -----------
% 2.00/2.25 user CPU time 0.37 (0 hr, 0 min, 0 sec)
% 2.00/2.25 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.25 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.25
% 2.00/2.25 That finishes the proof of the theorem.
% 2.00/2.25
% 2.00/2.25 Process 13441 finished Wed Jul 27 05:31:08 2022
% 2.00/2.25 Otter interrupted
% 2.00/2.25 PROOF FOUND
%------------------------------------------------------------------------------