TSTP Solution File: GRP128-1.003 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP128-1.003 : 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 12:56:12 EDT 2022
% Result : Unsatisfiable 1.72s 1.98s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 49 ( 16 unt; 28 nHn; 49 RR)
% Number of literals : 102 ( 0 equ; 18 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 : 21 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP128-1.003.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_3),
file('GRP128-1.003.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_2,e_1),
file('GRP128-1.003.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_3),
file('GRP128-1.003.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_3,e_1),
file('GRP128-1.003.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_3,e_2),
file('GRP128-1.003.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('GRP128-1.003.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP128-1.003.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP128-1.003.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP128-1.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(C,B,D)
| product(A,C,D) ),
file('GRP128-1.003.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,plain,
( ~ product(A,B,A)
| product(A,A,A) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.1.2')] ).
cnf(17,axiom,
group_element(e_1),
file('GRP128-1.003.p',unknown),
[] ).
cnf(18,axiom,
group_element(e_2),
file('GRP128-1.003.p',unknown),
[] ).
cnf(19,axiom,
group_element(e_3),
file('GRP128-1.003.p',unknown),
[] ).
cnf(22,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)],[18,7,17]),
[iquote('hyper,18,7,17')] ).
cnf(23,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)],[18,7,17]),
[iquote('hyper,18,7,17')] ).
cnf(24,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)],[19,12]),
[iquote('hyper,19,12')] ).
cnf(25,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(hyper,[status(thm)],[19,7,18]),
[iquote('hyper,19,7,18')] ).
cnf(26,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)],[19,7,17]),
[iquote('hyper,19,7,17')] ).
cnf(27,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(hyper,[status(thm)],[19,7,18]),
[iquote('hyper,19,7,18')] ).
cnf(39,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(hyper,[status(thm)],[22,16]),
[iquote('hyper,22,16')] ).
cnf(65,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_2,e_2) ),
inference(hyper,[status(thm)],[23,16]),
[iquote('hyper,23,16')] ).
cnf(89,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(hyper,[status(thm)],[25,16]),
[iquote('hyper,25,16')] ).
cnf(104,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_1,e_1) ),
inference(hyper,[status(thm)],[26,16]),
[iquote('hyper,26,16')] ).
cnf(155,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_3,e_3) ),
inference(hyper,[status(thm)],[27,16]),
[iquote('hyper,27,16')] ).
cnf(217,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[39,9,22]),3])])]),
[iquote('hyper,39,9,22,unit_del,3,factor_simp,factor_simp')] ).
cnf(301,plain,
( product(e_2,e_1,e_1)
| 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)],[65,9,23]),1])])]),
[iquote('hyper,65,9,23,unit_del,1,factor_simp,factor_simp')] ).
cnf(381,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[89,9,25]),6])])]),
[iquote('hyper,89,9,25,unit_del,6,factor_simp,factor_simp')] ).
cnf(392,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[381,9,301]),2]),
[iquote('hyper,381,9,301,unit_del,2')] ).
cnf(399,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[381,9,301]),2]),
[iquote('hyper,381,9,301,unit_del,2')] ).
cnf(443,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[104,9,26]),5])])]),
[iquote('hyper,104,9,26,unit_del,5,factor_simp,factor_simp')] ).
cnf(470,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[443,10,392]),3]),
[iquote('hyper,443,10,392,unit_del,3')] ).
cnf(471,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[443,10,381]),3]),
[iquote('hyper,443,10,381,unit_del,3')] ).
cnf(473,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[443,9,217]),4]),
[iquote('hyper,443,9,217,unit_del,4')] ).
cnf(615,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[155,9,27]),4])])]),
[iquote('hyper,155,9,27,unit_del,4,factor_simp,factor_simp')] ).
cnf(635,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_3,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[615,10,473]),2]),
[iquote('hyper,615,10,473,unit_del,2')] ).
cnf(647,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[635,11,473])]),
[iquote('hyper,635,11,473,factor_simp')] ).
cnf(679,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[647,11,470])]),
[iquote('hyper,647,11,470,factor_simp')] ).
cnf(718,plain,
product(e_1,e_3,e_2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[679,8,471]),1])]),
[iquote('hyper,679,8,471,unit_del,1,factor_simp')] ).
cnf(737,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(hyper,[status(thm)],[718,11,399]),
[iquote('hyper,718,11,399')] ).
cnf(742,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[718,10,24]),5]),
[iquote('hyper,718,10,24,unit_del,5')] ).
cnf(765,plain,
product(e_2,e_1,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[737,8,301]),6])]),
[iquote('hyper,737,8,301,unit_del,6,factor_simp')] ).
cnf(766,plain,
product(e_2,e_3,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[765,9,381]),5]),
[iquote('hyper,765,9,381,unit_del,5')] ).
cnf(775,plain,
product(e_3,e_3,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[742,10,766]),4]),
[iquote('hyper,742,10,766,unit_del,4')] ).
cnf(776,plain,
product(e_2,e_3,e_1),
inference(hyper,[status(thm)],[775,11,766]),
[iquote('hyper,775,11,766')] ).
cnf(781,plain,
e_qualish(e_3,e_2),
inference(hyper,[status(thm)],[776,10,775]),
[iquote('hyper,776,10,775')] ).
cnf(782,plain,
$false,
inference(binary,[status(thm)],[781,6]),
[iquote('binary,781.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP128-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.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 05:26:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.72/1.98 ----- Otter 3.3f, August 2004 -----
% 1.72/1.98 The process was started by sandbox2 on n003.cluster.edu,
% 1.72/1.98 Wed Jul 27 05:26:11 2022
% 1.72/1.98 The command was "./otter". The process ID is 17459.
% 1.72/1.98
% 1.72/1.98 set(prolog_style_variables).
% 1.72/1.98 set(auto).
% 1.72/1.98 dependent: set(auto1).
% 1.72/1.98 dependent: set(process_input).
% 1.72/1.98 dependent: clear(print_kept).
% 1.72/1.98 dependent: clear(print_new_demod).
% 1.72/1.98 dependent: clear(print_back_demod).
% 1.72/1.98 dependent: clear(print_back_sub).
% 1.72/1.98 dependent: set(control_memory).
% 1.72/1.98 dependent: assign(max_mem, 12000).
% 1.72/1.98 dependent: assign(pick_given_ratio, 4).
% 1.72/1.98 dependent: assign(stats_level, 1).
% 1.72/1.98 dependent: assign(max_seconds, 10800).
% 1.72/1.98 clear(print_given).
% 1.72/1.98
% 1.72/1.98 list(usable).
% 1.72/1.98 0 [] group_element(e_1).
% 1.72/1.98 0 [] group_element(e_2).
% 1.72/1.98 0 [] group_element(e_3).
% 1.72/1.98 0 [] -e_qualish(e_1,e_2).
% 1.72/1.98 0 [] -e_qualish(e_1,e_3).
% 1.72/1.98 0 [] -e_qualish(e_2,e_1).
% 1.72/1.98 0 [] -e_qualish(e_2,e_3).
% 1.72/1.98 0 [] -e_qualish(e_3,e_1).
% 1.72/1.98 0 [] -e_qualish(e_3,e_2).
% 1.72/1.98 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.72/1.98 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.72/1.98 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.72/1.98 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.72/1.98 0 [] -product(X,Y,Z1)| -product(Z1,Y,Z2)|product(X,Z1,Z2).
% 1.72/1.98 end_of_list.
% 1.72/1.98
% 1.72/1.98 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.72/1.98
% 1.72/1.98 This is a non-Horn set without equality. The strategy will
% 1.72/1.98 be ordered hyper_res, unit deletion, and factoring, with
% 1.72/1.98 satellites in sos and with nuclei in usable.
% 1.72/1.98
% 1.72/1.98 dependent: set(hyper_res).
% 1.72/1.98 dependent: set(factor).
% 1.72/1.98 dependent: set(unit_deletion).
% 1.72/1.98
% 1.72/1.98 ------------> process usable:
% 1.72/1.98 ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 1.72/1.98 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_3).
% 1.72/1.98 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.72/1.98 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_3).
% 1.72/1.98 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_3,e_1).
% 1.72/1.98 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_2).
% 1.72/1.98 ** 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).
% 1.72/1.98 ** KEPT (pick-wt=11): 8 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.72/1.98 ** KEPT (pick-wt=11): 9 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.72/1.98 ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.72/1.98 ** KEPT (pick-wt=12): 11 [] -product(A,B,C)| -product(C,B,D)|product(A,C,D).
% 1.72/1.98
% 1.72/1.98 ------------> process sos:
% 1.72/1.98 ** KEPT (pick-wt=2): 17 [] group_element(e_1).
% 1.72/1.98 ** KEPT (pick-wt=2): 18 [] group_element(e_2).
% 1.72/1.98 ** KEPT (pick-wt=2): 19 [] group_element(e_3).
% 1.72/1.98
% 1.72/1.98 ======= end of input processing =======
% 1.72/1.98
% 1.72/1.98 =========== start of search ===========
% 1.72/1.98
% 1.72/1.98 -------- PROOF --------
% 1.72/1.98
% 1.72/1.98 ----> UNIT CONFLICT at 0.14 sec ----> 782 [binary,781.1,6.1] $F.
% 1.72/1.98
% 1.72/1.98 Length of proof is 34. Level of proof is 14.
% 1.72/1.98
% 1.72/1.98 ---------------- PROOF ----------------
% 1.72/1.98 % SZS status Unsatisfiable
% 1.72/1.98 % SZS output start Refutation
% See solution above
% 1.72/1.98 ------------ end of proof -------------
% 1.72/1.98
% 1.72/1.98
% 1.72/1.98 Search stopped by max_proofs option.
% 1.72/1.98
% 1.72/1.98
% 1.72/1.98 Search stopped by max_proofs option.
% 1.72/1.98
% 1.72/1.98 ============ end of search ============
% 1.72/1.98
% 1.72/1.98 -------------- statistics -------------
% 1.72/1.98 clauses given 154
% 1.72/1.98 clauses generated 5797
% 1.72/1.98 clauses kept 781
% 1.72/1.98 clauses forward subsumed 5030
% 1.72/1.98 clauses back subsumed 723
% 1.72/1.98 Kbytes malloced 976
% 1.72/1.98
% 1.72/1.98 ----------- times (seconds) -----------
% 1.72/1.98 user CPU time 0.14 (0 hr, 0 min, 0 sec)
% 1.72/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.98
% 1.72/1.98 That finishes the proof of the theorem.
% 1.72/1.98
% 1.72/1.98 Process 17459 finished Wed Jul 27 05:26:13 2022
% 1.72/1.98 Otter interrupted
% 1.72/1.98 PROOF FOUND
%------------------------------------------------------------------------------