TSTP Solution File: GRP133-2.003 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP133-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:56:30 EDT 2022
% Result : Unsatisfiable 1.79s 2.02s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 53 ( 19 unt; 28 nHn; 53 RR)
% Number of literals : 109 ( 0 equ; 20 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,e_1,B)
| ~ next(A,C)
| ~ greater(B,C) ),
file('GRP133-2.003.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP133-2.003.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_1,e_3),
file('GRP133-2.003.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_1),
file('GRP133-2.003.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_3),
file('GRP133-2.003.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_3,e_1),
file('GRP133-2.003.p',unknown),
[] ).
cnf(8,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('GRP133-2.003.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP133-2.003.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP133-2.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP133-2.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
file('GRP133-2.003.p',unknown),
[] ).
cnf(13,plain,
( ~ group_element(A)
| product(A,A,e_1)
| product(A,A,e_2)
| product(A,A,e_3) ),
inference(factor,[status(thm)],[8]),
[iquote('factor,8.1.2')] ).
cnf(17,plain,
( ~ product(A,A,B)
| product(B,B,A) ),
inference(factor,[status(thm)],[12]),
[iquote('factor,12.1.2')] ).
cnf(18,axiom,
next(e_1,e_2),
file('GRP133-2.003.p',unknown),
[] ).
cnf(22,axiom,
greater(e_3,e_2),
file('GRP133-2.003.p',unknown),
[] ).
cnf(23,axiom,
group_element(e_1),
file('GRP133-2.003.p',unknown),
[] ).
cnf(24,axiom,
group_element(e_2),
file('GRP133-2.003.p',unknown),
[] ).
cnf(25,axiom,
group_element(e_3),
file('GRP133-2.003.p',unknown),
[] ).
cnf(26,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(hyper,[status(thm)],[23,13]),
[iquote('hyper,23,13')] ).
cnf(27,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(hyper,[status(thm)],[24,13]),
[iquote('hyper,24,13')] ).
cnf(28,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(hyper,[status(thm)],[24,8,23]),
[iquote('hyper,24,8,23')] ).
cnf(29,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(hyper,[status(thm)],[24,8,23]),
[iquote('hyper,24,8,23')] ).
cnf(30,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(hyper,[status(thm)],[25,13]),
[iquote('hyper,25,13')] ).
cnf(32,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(hyper,[status(thm)],[25,8,23]),
[iquote('hyper,25,8,23')] ).
cnf(34,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(hyper,[status(thm)],[25,8,23]),
[iquote('hyper,25,8,23')] ).
cnf(42,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[26,1,18,22]),
[iquote('hyper,26,1,18,22')] ).
cnf(44,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(hyper,[status(thm)],[42,17]),
[iquote('hyper,42,17')] ).
cnf(47,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[27,17]),
[iquote('hyper,27,17')] ).
cnf(57,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,11,44]),4]),
[iquote('hyper,28,11,44,unit_del,4')] ).
cnf(73,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_2,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[29,11,44]),2]),
[iquote('hyper,29,11,44,unit_del,2')] ).
cnf(83,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[29,11,42]),2]),
[iquote('hyper,29,11,42,unit_del,2')] ).
cnf(95,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_1,e_1,e_3) ),
inference(hyper,[status(thm)],[30,17]),
[iquote('hyper,30,17')] ).
cnf(237,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[57,10,42]),2])]),
[iquote('hyper,57,10,42,unit_del,2,factor_simp')] ).
cnf(300,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[73,10,29]),2])])]),
[iquote('hyper,73,10,29,unit_del,2,factor_simp,factor_simp')] ).
cnf(307,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[83,10,44]),4])]),
[iquote('hyper,83,10,44,unit_del,4,factor_simp')] ).
cnf(368,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(hyper,[status(thm)],[95,1,18,22]),
[iquote('hyper,95,1,18,22')] ).
cnf(370,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_3,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[307,12,237])]),
[iquote('hyper,307,12,237,factor_simp')] ).
cnf(372,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_3,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[307,12,237])]),
[iquote('hyper,307,12,237,factor_simp')] ).
cnf(425,plain,
product(e_1,e_1,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[372,9,370]),2])]),
[iquote('hyper,372,9,370,unit_del,2,factor_simp')] ).
cnf(429,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[425,11,34]),6]),
[iquote('hyper,425,11,34,unit_del,6')] ).
cnf(430,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[425,10,32]),6]),
[iquote('hyper,425,10,32,unit_del,6')] ).
cnf(431,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[425,9,47]),4]),
[iquote('hyper,425,9,47,unit_del,4')] ).
cnf(456,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[429,11,300]),5]),
[iquote('hyper,429,11,300,unit_del,5')] ).
cnf(457,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[429,10,368]),6]),
[iquote('hyper,429,10,368,unit_del,6')] ).
cnf(480,plain,
( product(e_1,e_3,e_3)
| product(e_3,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[430,11,368]),6]),
[iquote('hyper,430,11,368,unit_del,6')] ).
cnf(612,plain,
product(e_3,e_3,e_3),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[480,12,457])])]),
[iquote('hyper,480,12,457,factor_simp,factor_simp')] ).
cnf(619,plain,
product(e_1,e_3,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[612,11,430]),3]),
[iquote('hyper,612,11,430,unit_del,3')] ).
cnf(621,plain,
product(e_2,e_1,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[612,10,456]),3]),
[iquote('hyper,612,10,456,unit_del,3')] ).
cnf(622,plain,
product(e_3,e_1,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[612,10,429]),3]),
[iquote('hyper,612,10,429,unit_del,3')] ).
cnf(628,plain,
product(e_2,e_2,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[621,10,431]),4]),
[iquote('hyper,621,10,431,unit_del,4')] ).
cnf(629,plain,
product(e_2,e_2,e_1),
inference(hyper,[status(thm)],[622,12,619]),
[iquote('hyper,622,12,619')] ).
cnf(640,plain,
e_qualish(e_2,e_1),
inference(hyper,[status(thm)],[629,9,628]),
[iquote('hyper,629,9,628')] ).
cnf(641,plain,
$false,
inference(binary,[status(thm)],[640,4]),
[iquote('binary,640.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP133-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 04:58:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/2.02 ----- Otter 3.3f, August 2004 -----
% 1.79/2.02 The process was started by sandbox2 on n003.cluster.edu,
% 1.79/2.02 Wed Jul 27 04:58:11 2022
% 1.79/2.02 The command was "./otter". The process ID is 7141.
% 1.79/2.02
% 1.79/2.02 set(prolog_style_variables).
% 1.79/2.02 set(auto).
% 1.79/2.02 dependent: set(auto1).
% 1.79/2.02 dependent: set(process_input).
% 1.79/2.02 dependent: clear(print_kept).
% 1.79/2.02 dependent: clear(print_new_demod).
% 1.79/2.02 dependent: clear(print_back_demod).
% 1.79/2.02 dependent: clear(print_back_sub).
% 1.79/2.02 dependent: set(control_memory).
% 1.79/2.02 dependent: assign(max_mem, 12000).
% 1.79/2.02 dependent: assign(pick_given_ratio, 4).
% 1.79/2.02 dependent: assign(stats_level, 1).
% 1.79/2.02 dependent: assign(max_seconds, 10800).
% 1.79/2.02 clear(print_given).
% 1.79/2.02
% 1.79/2.02 list(usable).
% 1.79/2.02 0 [] next(e_1,e_2).
% 1.79/2.02 0 [] next(e_2,e_3).
% 1.79/2.02 0 [] greater(e_2,e_1).
% 1.79/2.02 0 [] greater(e_3,e_1).
% 1.79/2.02 0 [] greater(e_3,e_2).
% 1.79/2.02 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.79/2.02 0 [] group_element(e_1).
% 1.79/2.02 0 [] group_element(e_2).
% 1.79/2.02 0 [] group_element(e_3).
% 1.79/2.02 0 [] -e_qualish(e_1,e_2).
% 1.79/2.02 0 [] -e_qualish(e_1,e_3).
% 1.79/2.02 0 [] -e_qualish(e_2,e_1).
% 1.79/2.02 0 [] -e_qualish(e_2,e_3).
% 1.79/2.02 0 [] -e_qualish(e_3,e_1).
% 1.79/2.02 0 [] -e_qualish(e_3,e_2).
% 1.79/2.02 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.79/2.02 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.79/2.02 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.79/2.02 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.79/2.02 0 [] -product(X,Y,Z1)| -product(Y,X,Z2)|product(Z1,Z2,X).
% 1.79/2.02 end_of_list.
% 1.79/2.02
% 1.79/2.02 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.79/2.02
% 1.79/2.02 This is a non-Horn set without equality. The strategy will
% 1.79/2.02 be ordered hyper_res, unit deletion, and factoring, with
% 1.79/2.02 satellites in sos and with nuclei in usable.
% 1.79/2.02
% 1.79/2.02 dependent: set(hyper_res).
% 1.79/2.02 dependent: set(factor).
% 1.79/2.02 dependent: set(unit_deletion).
% 1.79/2.02
% 1.79/2.02 ------------> process usable:
% 1.79/2.02 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.79/2.02 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.79/2.02 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_3).
% 1.79/2.02 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_1).
% 1.79/2.02 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_3).
% 1.79/2.02 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_1).
% 1.79/2.02 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_2).
% 1.79/2.02 ** KEPT (pick-wt=16): 8 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 1.79/2.02 ** KEPT (pick-wt=11): 9 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.79/2.02 ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.79/2.02 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.79/2.02 ** KEPT (pick-wt=12): 12 [] -product(A,B,C)| -product(B,A,D)|product(C,D,A).
% 1.79/2.02
% 1.79/2.02 ------------> process sos:
% 1.79/2.02 ** KEPT (pick-wt=3): 18 [] next(e_1,e_2).
% 1.79/2.02 ** KEPT (pick-wt=3): 19 [] next(e_2,e_3).
% 1.79/2.02 ** KEPT (pick-wt=3): 20 [] greater(e_2,e_1).
% 1.79/2.02 ** KEPT (pick-wt=3): 21 [] greater(e_3,e_1).
% 1.79/2.02 ** KEPT (pick-wt=3): 22 [] greater(e_3,e_2).
% 1.79/2.02 ** KEPT (pick-wt=2): 23 [] group_element(e_1).
% 1.79/2.02 ** KEPT (pick-wt=2): 24 [] group_element(e_2).
% 1.79/2.02 ** KEPT (pick-wt=2): 25 [] group_element(e_3).
% 1.79/2.02
% 1.79/2.02 ======= end of input processing =======
% 1.79/2.02
% 1.79/2.02 =========== start of search ===========
% 1.79/2.02
% 1.79/2.02 -------- PROOF --------
% 1.79/2.02
% 1.79/2.02 ----> UNIT CONFLICT at 0.11 sec ----> 641 [binary,640.1,4.1] $F.
% 1.79/2.02
% 1.79/2.02 Length of proof is 36. Level of proof is 14.
% 1.79/2.02
% 1.79/2.02 ---------------- PROOF ----------------
% 1.79/2.02 % SZS status Unsatisfiable
% 1.79/2.02 % SZS output start Refutation
% See solution above
% 1.79/2.03 ------------ end of proof -------------
% 1.79/2.03
% 1.79/2.03
% 1.79/2.03 Search stopped by max_proofs option.
% 1.79/2.03
% 1.79/2.03
% 1.79/2.03 Search stopped by max_proofs option.
% 1.79/2.03
% 1.79/2.03 ============ end of search ============
% 1.79/2.03
% 1.79/2.03 -------------- statistics -------------
% 1.79/2.03 clauses given 133
% 1.79/2.03 clauses generated 4511
% 1.79/2.03 clauses kept 640
% 1.79/2.03 clauses forward subsumed 3891
% 1.79/2.03 clauses back subsumed 570
% 1.79/2.03 Kbytes malloced 976
% 1.79/2.03
% 1.79/2.03 ----------- times (seconds) -----------
% 1.79/2.03 user CPU time 0.11 (0 hr, 0 min, 0 sec)
% 1.79/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.03 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.79/2.03
% 1.79/2.03 That finishes the proof of the theorem.
% 1.79/2.03
% 1.79/2.03 Process 7141 finished Wed Jul 27 04:58:13 2022
% 1.79/2.03 Otter interrupted
% 1.79/2.03 PROOF FOUND
%------------------------------------------------------------------------------