%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP135-2.002 : TPTP v8.1.0. Released v1.2.0.
% 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 12:56:31 EDT 2022
% Result : Unsatisfiable 1.67s 1.87s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 20 ( 9 unt; 8 nHn; 20 RR)
% Number of literals : 37 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP135-2.002.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_2,e_1),
file('GRP135-2.002.p',unknown),
[] ).
cnf(4,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
file('GRP135-2.002.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP135-2.002.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP135-2.002.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(C,A,D)
| product(D,A,B) ),
file('GRP135-2.002.p',unknown),
[] ).
cnf(9,plain,
( ~ group_element(A)
| product(A,A,e_1)
| product(A,A,e_2) ),
inference(factor,[status(thm)],[4]),
[iquote('factor,4.1.2')] ).
cnf(15,axiom,
group_element(e_1),
file('GRP135-2.002.p',unknown),
[] ).
cnf(16,axiom,
group_element(e_2),
file('GRP135-2.002.p',unknown),
[] ).
cnf(17,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[15,9]),
[iquote('hyper,15,9')] ).
cnf(18,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(hyper,[status(thm)],[16,9]),
[iquote('hyper,16,9')] ).
cnf(19,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(hyper,[status(thm)],[16,4,15]),
[iquote('hyper,16,4,15')] ).
cnf(20,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(hyper,[status(thm)],[16,4,15]),
[iquote('hyper,16,4,15')] ).
cnf(29,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,8,18])]),
[iquote('hyper,19,8,18,factor_simp')] ).
cnf(40,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[20,8,17])]),
[iquote('hyper,20,8,17,factor_simp')] ).
cnf(47,plain,
product(e_2,e_2,e_2),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[29,8,18])])]),
[iquote('hyper,29,8,18,factor_simp,factor_simp')] ).
cnf(51,plain,
product(e_2,e_1,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[47,6,20]),2]),
[iquote('hyper,47,6,20,unit_del,2')] ).
cnf(55,plain,
product(e_1,e_1,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,6,47]),3]),
[iquote('hyper,40,6,47,unit_del,3')] ).
cnf(57,plain,
e_qualish(e_2,e_1),
inference(hyper,[status(thm)],[55,7,51]),
[iquote('hyper,55,7,51')] ).
cnf(58,plain,
$false,
inference(binary,[status(thm)],[57,3]),
[iquote('binary,57.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP135-2.002 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 05:30:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.87 ----- Otter 3.3f, August 2004 -----
% 1.67/1.87 The process was started by sandbox on n004.cluster.edu,
% 1.67/1.87 Wed Jul 27 05:30:06 2022
% 1.67/1.87 The command was "./otter". The process ID is 9863.
% 1.67/1.87
% 1.67/1.87 set(prolog_style_variables).
% 1.67/1.87 set(auto).
% 1.67/1.87 dependent: set(auto1).
% 1.67/1.87 dependent: set(process_input).
% 1.67/1.87 dependent: clear(print_kept).
% 1.67/1.87 dependent: clear(print_new_demod).
% 1.67/1.87 dependent: clear(print_back_demod).
% 1.67/1.87 dependent: clear(print_back_sub).
% 1.67/1.87 dependent: set(control_memory).
% 1.67/1.87 dependent: assign(max_mem, 12000).
% 1.67/1.87 dependent: assign(pick_given_ratio, 4).
% 1.67/1.87 dependent: assign(stats_level, 1).
% 1.67/1.87 dependent: assign(max_seconds, 10800).
% 1.67/1.87 clear(print_given).
% 1.67/1.87
% 1.67/1.87 list(usable).
% 1.67/1.87 0 [] next(e_1,e_2).
% 1.67/1.87 0 [] greater(e_2,e_1).
% 1.67/1.87 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.67/1.87 0 [] group_element(e_1).
% 1.67/1.87 0 [] group_element(e_2).
% 1.67/1.87 0 [] -e_qualish(e_1,e_2).
% 1.67/1.87 0 [] -e_qualish(e_2,e_1).
% 1.67/1.87 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2).
% 1.67/1.87 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.67/1.87 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.67/1.87 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.67/1.87 0 [] -product(Y,X,Z1)| -product(Z1,Y,Z2)|product(Z2,Y,X).
% 1.67/1.87 end_of_list.
% 1.67/1.87
% 1.67/1.87 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.67/1.87
% 1.67/1.87 This is a non-Horn set without equality. The strategy will
% 1.67/1.87 be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.87 satellites in sos and with nuclei in usable.
% 1.67/1.87
% 1.67/1.87 dependent: set(hyper_res).
% 1.67/1.87 dependent: set(factor).
% 1.67/1.87 dependent: set(unit_deletion).
% 1.67/1.87
% 1.67/1.87 ------------> process usable:
% 1.67/1.87 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.67/1.87 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.67/1.87 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.67/1.87 ** KEPT (pick-wt=12): 4 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2).
% 1.67/1.87 ** KEPT (pick-wt=11): 5 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.67/1.87 ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.67/1.87 ** KEPT (pick-wt=11): 7 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.67/1.87 ** KEPT (pick-wt=12): 8 [] -product(A,B,C)| -product(C,A,D)|product(D,A,B).
% 1.67/1.87
% 1.67/1.87 ------------> process sos:
% 1.67/1.87 ** KEPT (pick-wt=3): 13 [] next(e_1,e_2).
% 1.67/1.87 ** KEPT (pick-wt=3): 14 [] greater(e_2,e_1).
% 1.67/1.87 ** KEPT (pick-wt=2): 15 [] group_element(e_1).
% 1.67/1.87 ** KEPT (pick-wt=2): 16 [] group_element(e_2).
% 1.67/1.87
% 1.67/1.87 ======= end of input processing =======
% 1.67/1.87
% 1.67/1.87 =========== start of search ===========
% 1.67/1.87
% 1.67/1.87 -------- PROOF --------
% 1.67/1.87
% 1.67/1.87 ----> UNIT CONFLICT at 0.00 sec ----> 58 [binary,57.1,3.1] $F.
% 1.67/1.87
% 1.67/1.87 Length of proof is 11. Level of proof is 6.
% 1.67/1.87
% 1.67/1.87 ---------------- PROOF ----------------
% 1.67/1.87 % SZS status Unsatisfiable
% 1.67/1.87 % SZS output start Refutation
% See solution above
% 1.67/1.87 ------------ end of proof -------------
% 1.67/1.87
% 1.67/1.87
% 1.67/1.87 Search stopped by max_proofs option.
% 1.67/1.87
% 1.67/1.87
% 1.67/1.87 Search stopped by max_proofs option.
% 1.67/1.87
% 1.67/1.87 ============ end of search ============
% 1.67/1.87
% 1.67/1.87 -------------- statistics -------------
% 1.67/1.87 clauses given 29
% 1.67/1.87 clauses generated 278
% 1.67/1.87 clauses kept 57
% 1.67/1.87 clauses forward subsumed 232
% 1.67/1.87 clauses back subsumed 32
% 1.67/1.87 Kbytes malloced 976
% 1.67/1.87
% 1.67/1.87 ----------- times (seconds) -----------
% 1.67/1.87 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.87 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.87
% 1.67/1.87 That finishes the proof of the theorem.
% 1.67/1.87
% 1.67/1.87 Process 9863 finished Wed Jul 27 05:30:07 2022
% 1.67/1.87 Otter interrupted
% 1.67/1.87 PROOF FOUND
%------------------------------------------------------------------------------