TSTP Solution File: GRP129-1.003 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP129-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 12:56:28 EDT 2022
% Result : Unsatisfiable 9.36s 9.56s
% Output : Refutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of clauses : 52 ( 16 unt; 33 nHn; 52 RR)
% Number of literals : 125 ( 0 equ; 15 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP129-1.003.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_3),
file('GRP129-1.003.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_2,e_1),
file('GRP129-1.003.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_3),
file('GRP129-1.003.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_3,e_1),
file('GRP129-1.003.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_3,e_2),
file('GRP129-1.003.p',unknown),
[] ).
cnf(7,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('GRP129-1.003.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP129-1.003.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP129-1.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(B,C,D)
| product(C,A,D) ),
file('GRP129-1.003.p',unknown),
[] ).
cnf(12,plain,
( ~ group_element(A)
| product(A,A,e_1)
| product(A,A,e_2)
| product(A,A,e_3) ),
inference(factor,[status(thm)],[7]),
[iquote('factor,7.1.2')] ).
cnf(16,axiom,
group_element(e_1),
file('GRP129-1.003.p',unknown),
[] ).
cnf(17,axiom,
group_element(e_2),
file('GRP129-1.003.p',unknown),
[] ).
cnf(18,axiom,
group_element(e_3),
file('GRP129-1.003.p',unknown),
[] ).
cnf(19,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)],[16,12]),
[iquote('hyper,16,12')] ).
cnf(20,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)],[17,12]),
[iquote('hyper,17,12')] ).
cnf(21,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)],[17,7,16]),
[iquote('hyper,17,7,16')] ).
cnf(22,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)],[17,7,16]),
[iquote('hyper,17,7,16')] ).
cnf(25,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)],[18,7,16]),
[iquote('hyper,18,7,16')] ).
cnf(27,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)],[18,7,16]),
[iquote('hyper,18,7,16')] ).
cnf(40,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(hyper,[status(thm)],[21,11,19]),
[iquote('hyper,21,11,19')] ).
cnf(41,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[21,10,20]),3]),
[iquote('hyper,21,10,20,unit_del,3')] ).
cnf(50,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[21,9,19]),1]),
[iquote('hyper,21,9,19,unit_del,1')] ).
cnf(128,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[25,9,19]),2]),
[iquote('hyper,25,9,19,unit_del,2')] ).
cnf(196,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[27,10,19]),2]),
[iquote('hyper,27,10,19,unit_del,2')] ).
cnf(215,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,9,19]),1])])]),
[iquote('hyper,40,9,19,unit_del,1,factor_simp,factor_simp')] ).
cnf(237,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[41,11,20])])]),
[iquote('hyper,41,11,20,factor_simp,factor_simp')] ).
cnf(4904,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[215,11,50])])])])]),
[iquote('hyper,215,11,50,factor_simp,factor_simp,factor_simp,factor_simp')] ).
cnf(4910,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4904,11,19])])]),
[iquote('hyper,4904,11,19,factor_simp,factor_simp')] ).
cnf(4913,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4904,9,128]),6])])]),
[iquote('hyper,4904,9,128,unit_del,6,factor_simp,factor_simp')] ).
cnf(4930,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4910,10,22]),3])]),
[iquote('hyper,4910,10,22,unit_del,3,factor_simp')] ).
cnf(4937,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4910,10,196]),6])])]),
[iquote('hyper,4910,10,196,unit_del,6,factor_simp,factor_simp')] ).
cnf(4977,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[237,9,20]),3])])]),
[iquote('hyper,237,9,20,unit_del,3,factor_simp,factor_simp')] ).
cnf(4979,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4930,11,22])])]),
[iquote('hyper,4930,11,22,factor_simp,factor_simp')] ).
cnf(4998,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4937,10,27]),5])]),
[iquote('hyper,4937,10,27,unit_del,5,factor_simp')] ).
cnf(5000,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[4937,11,4913])])])]),
[iquote('hyper,4937,11,4913,factor_simp,factor_simp,factor_simp')] ).
cnf(5102,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4979,9,4930]),1])])]),
[iquote('hyper,4979,9,4930,unit_del,1,factor_simp,factor_simp')] ).
cnf(5114,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5102,10,5000]),1]),
[iquote('hyper,5102,10,5000,unit_del,1')] ).
cnf(5195,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4998,10,5114]),4])]),
[iquote('hyper,4998,10,5114,unit_del,4,factor_simp')] ).
cnf(5214,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[5195,11,5000])]),
[iquote('hyper,5195,11,5000,factor_simp')] ).
cnf(5268,plain,
product(e_1,e_1,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5214,9,5000]),2])]),
[iquote('hyper,5214,9,5000,unit_del,2,factor_simp')] ).
cnf(5279,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5268,10,27]),5]),
[iquote('hyper,5268,10,27,unit_del,5')] ).
cnf(5283,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5268,9,21]),3]),
[iquote('hyper,5268,9,21,unit_del,3')] ).
cnf(5332,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5283,10,4977]),3])]),
[iquote('hyper,5283,10,4977,unit_del,3,factor_simp')] ).
cnf(5403,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[5332,11,5102])]),
[iquote('hyper,5332,11,5102,factor_simp')] ).
cnf(5412,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[5332,11,5283])]),
[iquote('hyper,5332,11,5283,factor_simp')] ).
cnf(5478,plain,
product(e_2,e_1,e_3),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5412,10,5403]),3])]),
[iquote('hyper,5412,10,5403,unit_del,3,factor_simp')] ).
cnf(5482,plain,
product(e_1,e_2,e_3),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5412,9,5332]),3])]),
[iquote('hyper,5412,9,5332,unit_del,3,factor_simp')] ).
cnf(5489,plain,
product(e_3,e_1,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5478,10,5279]),6]),
[iquote('hyper,5478,10,5279,unit_del,6')] ).
cnf(5498,plain,
product(e_2,e_3,e_3),
inference(hyper,[status(thm)],[5489,11,5482]),
[iquote('hyper,5489,11,5482')] ).
cnf(5502,plain,
e_qualish(e_1,e_3),
inference(hyper,[status(thm)],[5498,9,5478]),
[iquote('hyper,5498,9,5478')] ).
cnf(5503,plain,
$false,
inference(binary,[status(thm)],[5502,2]),
[iquote('binary,5502.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP129-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n020.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:28:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.36/9.56 ----- Otter 3.3f, August 2004 -----
% 9.36/9.56 The process was started by sandbox on n020.cluster.edu,
% 9.36/9.56 Wed Jul 27 05:28:08 2022
% 9.36/9.56 The command was "./otter". The process ID is 27536.
% 9.36/9.56
% 9.36/9.56 set(prolog_style_variables).
% 9.36/9.56 set(auto).
% 9.36/9.56 dependent: set(auto1).
% 9.36/9.56 dependent: set(process_input).
% 9.36/9.56 dependent: clear(print_kept).
% 9.36/9.56 dependent: clear(print_new_demod).
% 9.36/9.56 dependent: clear(print_back_demod).
% 9.36/9.56 dependent: clear(print_back_sub).
% 9.36/9.56 dependent: set(control_memory).
% 9.36/9.56 dependent: assign(max_mem, 12000).
% 9.36/9.56 dependent: assign(pick_given_ratio, 4).
% 9.36/9.56 dependent: assign(stats_level, 1).
% 9.36/9.56 dependent: assign(max_seconds, 10800).
% 9.36/9.56 clear(print_given).
% 9.36/9.56
% 9.36/9.56 list(usable).
% 9.36/9.56 0 [] group_element(e_1).
% 9.36/9.56 0 [] group_element(e_2).
% 9.36/9.56 0 [] group_element(e_3).
% 9.36/9.56 0 [] -e_qualish(e_1,e_2).
% 9.36/9.56 0 [] -e_qualish(e_1,e_3).
% 9.36/9.56 0 [] -e_qualish(e_2,e_1).
% 9.36/9.56 0 [] -e_qualish(e_2,e_3).
% 9.36/9.56 0 [] -e_qualish(e_3,e_1).
% 9.36/9.56 0 [] -e_qualish(e_3,e_2).
% 9.36/9.56 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 9.36/9.56 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 9.36/9.56 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 9.36/9.56 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 9.36/9.56 0 [] -product(Y,X,Z1)| -product(X,Z1,Z2)|product(Z1,Y,Z2).
% 9.36/9.56 end_of_list.
% 9.36/9.56
% 9.36/9.56 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 9.36/9.56
% 9.36/9.56 This is a non-Horn set without equality. The strategy will
% 9.36/9.56 be ordered hyper_res, unit deletion, and factoring, with
% 9.36/9.56 satellites in sos and with nuclei in usable.
% 9.36/9.56
% 9.36/9.56 dependent: set(hyper_res).
% 9.36/9.56 dependent: set(factor).
% 9.36/9.56 dependent: set(unit_deletion).
% 9.36/9.56
% 9.36/9.56 ------------> process usable:
% 9.36/9.56 ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 9.36/9.56 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_3).
% 9.36/9.56 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 9.36/9.56 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_3).
% 9.36/9.56 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_3,e_1).
% 9.36/9.56 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_2).
% 9.36/9.56 ** KEPT (pick-wt=16): 7 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 9.36/9.56 ** KEPT (pick-wt=11): 8 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 9.36/9.56 ** KEPT (pick-wt=11): 9 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 9.36/9.56 ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 9.36/9.56 ** KEPT (pick-wt=12): 11 [] -product(A,B,C)| -product(B,C,D)|product(C,A,D).
% 9.36/9.56
% 9.36/9.56 ------------> process sos:
% 9.36/9.56 ** KEPT (pick-wt=2): 16 [] group_element(e_1).
% 9.36/9.56 ** KEPT (pick-wt=2): 17 [] group_element(e_2).
% 9.36/9.56 ** KEPT (pick-wt=2): 18 [] group_element(e_3).
% 9.36/9.56
% 9.36/9.56 ======= end of input processing =======
% 9.36/9.56
% 9.36/9.56 =========== start of search ===========
% 9.36/9.56
% 9.36/9.56
% 9.36/9.56 Resetting weight limit to 16.
% 9.36/9.56
% 9.36/9.56
% 9.36/9.56 Resetting weight limit to 16.
% 9.36/9.56
% 9.36/9.56 sos_size=2981
% 9.36/9.56
% 9.36/9.56
% 9.36/9.56 Resetting weight limit to 12.
% 9.36/9.56
% 9.36/9.56
% 9.36/9.56 Resetting weight limit to 12.
% 9.36/9.56
% 9.36/9.56 sos_size=565
% 9.36/9.56
% 9.36/9.56 -------- PROOF --------
% 9.36/9.56
% 9.36/9.56 ----> UNIT CONFLICT at 7.42 sec ----> 5503 [binary,5502.1,2.1] $F.
% 9.36/9.56
% 9.36/9.56 Length of proof is 38. Level of proof is 20.
% 9.36/9.56
% 9.36/9.56 ---------------- PROOF ----------------
% 9.36/9.56 % SZS status Unsatisfiable
% 9.36/9.56 % SZS output start Refutation
% See solution above
% 9.36/9.56 ------------ end of proof -------------
% 9.36/9.56
% 9.36/9.56
% 9.36/9.56 Search stopped by max_proofs option.
% 9.36/9.56
% 9.36/9.56
% 9.36/9.56 Search stopped by max_proofs option.
% 9.36/9.56
% 9.36/9.56 ============ end of search ============
% 9.36/9.56
% 9.36/9.56 -------------- statistics -------------
% 9.36/9.56 clauses given 418
% 9.36/9.56 clauses generated 88065
% 9.36/9.56 clauses kept 5502
% 9.36/9.56 clauses forward subsumed 49239
% 9.36/9.56 clauses back subsumed 5342
% 9.36/9.56 Kbytes malloced 4882
% 9.36/9.56
% 9.36/9.56 ----------- times (seconds) -----------
% 9.36/9.56 user CPU time 7.42 (0 hr, 0 min, 7 sec)
% 9.36/9.56 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 9.36/9.56 wall-clock time 9 (0 hr, 0 min, 9 sec)
% 9.36/9.56
% 9.36/9.56 That finishes the proof of the theorem.
% 9.36/9.56
% 9.36/9.56 Process 27536 finished Wed Jul 27 05:28:17 2022
% 9.36/9.56 Otter interrupted
% 9.36/9.56 PROOF FOUND
%------------------------------------------------------------------------------