TSTP Solution File: GRP123-6.003 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:56:07 EDT 2022
% Result : Unsatisfiable 1.98s 2.12s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 29 ( 16 unt; 8 nHn; 27 RR)
% Number of literals : 56 ( 0 equ; 19 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP123-6.003.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_2,e_1),
file('GRP123-6.003.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_3),
file('GRP123-6.003.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_3,e_1),
file('GRP123-6.003.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_3,e_2),
file('GRP123-6.003.p',unknown),
[] ).
cnf(7,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(9,axiom,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| e_qualish(B,D) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(10,axiom,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| e_qualish(A,D) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product2(A,B,e_1)
| product2(A,B,e_2)
| product2(A,B,e_3) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ product2(A,B,C)
| ~ product2(A,D,C)
| e_qualish(B,D) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(14,axiom,
( ~ product2(A,B,C)
| ~ product2(D,B,C)
| e_qualish(A,D) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product1(A,B,C)
| ~ product1(C,B,D)
| product2(D,A,B) ),
file('GRP123-6.003.p',unknown),
[] ).
cnf(25,axiom,
group_element(e_1),
file('GRP123-6.003.p',unknown),
[] ).
cnf(26,axiom,
group_element(e_2),
file('GRP123-6.003.p',unknown),
[] ).
cnf(27,axiom,
group_element(e_3),
file('GRP123-6.003.p',unknown),
[] ).
cnf(28,axiom,
product1(A,A,A),
file('GRP123-6.003.p',unknown),
[] ).
cnf(29,axiom,
product2(A,A,A),
file('GRP123-6.003.p',unknown),
[] ).
cnf(30,plain,
( product2(e_1,e_2,e_1)
| product2(e_1,e_2,e_2)
| product2(e_1,e_2,e_3) ),
inference(hyper,[status(thm)],[26,11,25]),
[iquote('hyper,26,11,25')] ).
cnf(38,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(hyper,[status(thm)],[27,7,26]),
[iquote('hyper,27,7,26')] ).
cnf(39,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(hyper,[status(thm)],[27,7,25]),
[iquote('hyper,27,7,25')] ).
cnf(43,plain,
( product2(e_1,e_2,e_2)
| product2(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[30,13,29]),1]),
[iquote('hyper,30,13,29,unit_del,1')] ).
cnf(45,plain,
product2(e_1,e_2,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[43,14,29]),3]),
[iquote('hyper,43,14,29,unit_del,3')] ).
cnf(74,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[38,9,28]),4]),
[iquote('hyper,38,9,28,unit_del,4')] ).
cnf(78,plain,
product1(e_2,e_3,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[74,10,28]),6]),
[iquote('hyper,74,10,28,unit_del,6')] ).
cnf(80,plain,
( product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[39,10,78]),3]),
[iquote('hyper,39,10,78,unit_del,3')] ).
cnf(90,plain,
product1(e_1,e_3,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[80,10,28]),5]),
[iquote('hyper,80,10,28,unit_del,5')] ).
cnf(98,plain,
product2(e_2,e_2,e_3),
inference(hyper,[status(thm)],[90,15,78]),
[iquote('hyper,90,15,78')] ).
cnf(100,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[98,14,45]),
[iquote('hyper,98,14,45')] ).
cnf(101,plain,
$false,
inference(binary,[status(thm)],[100,1]),
[iquote('binary,100.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.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 05:23:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.98/2.12 ----- Otter 3.3f, August 2004 -----
% 1.98/2.12 The process was started by sandbox on n026.cluster.edu,
% 1.98/2.12 Wed Jul 27 05:23:24 2022
% 1.98/2.12 The command was "./otter". The process ID is 27909.
% 1.98/2.12
% 1.98/2.12 set(prolog_style_variables).
% 1.98/2.12 set(auto).
% 1.98/2.12 dependent: set(auto1).
% 1.98/2.12 dependent: set(process_input).
% 1.98/2.12 dependent: clear(print_kept).
% 1.98/2.12 dependent: clear(print_new_demod).
% 1.98/2.12 dependent: clear(print_back_demod).
% 1.98/2.12 dependent: clear(print_back_sub).
% 1.98/2.12 dependent: set(control_memory).
% 1.98/2.12 dependent: assign(max_mem, 12000).
% 1.98/2.12 dependent: assign(pick_given_ratio, 4).
% 1.98/2.12 dependent: assign(stats_level, 1).
% 1.98/2.12 dependent: assign(max_seconds, 10800).
% 1.98/2.12 clear(print_given).
% 1.98/2.12
% 1.98/2.12 list(usable).
% 1.98/2.12 0 [] group_element(e_1).
% 1.98/2.12 0 [] group_element(e_2).
% 1.98/2.12 0 [] group_element(e_3).
% 1.98/2.12 0 [] -e_qualish(e_1,e_2).
% 1.98/2.12 0 [] -e_qualish(e_1,e_3).
% 1.98/2.12 0 [] -e_qualish(e_2,e_1).
% 1.98/2.12 0 [] -e_qualish(e_2,e_3).
% 1.98/2.12 0 [] -e_qualish(e_3,e_1).
% 1.98/2.12 0 [] -e_qualish(e_3,e_2).
% 1.98/2.12 0 [] -group_element(X)| -group_element(Y)|product1(X,Y,e_1)|product1(X,Y,e_2)|product1(X,Y,e_3).
% 1.98/2.12 0 [] -product1(X,Y,W)| -product1(X,Y,Z)|e_qualish(W,Z).
% 1.98/2.12 0 [] -product1(X,W,Y)| -product1(X,Z,Y)|e_qualish(W,Z).
% 1.98/2.12 0 [] -product1(W,Y,X)| -product1(Z,Y,X)|e_qualish(W,Z).
% 1.98/2.12 0 [] product1(X,X,X).
% 1.98/2.12 0 [] -group_element(X)| -group_element(Y)|product2(X,Y,e_1)|product2(X,Y,e_2)|product2(X,Y,e_3).
% 1.98/2.12 0 [] -product2(X,Y,W)| -product2(X,Y,Z)|e_qualish(W,Z).
% 1.98/2.12 0 [] -product2(X,W,Y)| -product2(X,Z,Y)|e_qualish(W,Z).
% 1.98/2.12 0 [] -product2(W,Y,X)| -product2(Z,Y,X)|e_qualish(W,Z).
% 1.98/2.12 0 [] product2(X,X,X).
% 1.98/2.12 0 [] -product1(X,Y,Z1)| -product1(Z1,Y,Z2)|product2(Z2,X,Y).
% 1.98/2.12 end_of_list.
% 1.98/2.12
% 1.98/2.12 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.98/2.12
% 1.98/2.12 This is a non-Horn set without equality. The strategy will
% 1.98/2.12 be ordered hyper_res, unit deletion, and factoring, with
% 1.98/2.12 satellites in sos and with nuclei in usable.
% 1.98/2.12
% 1.98/2.12 dependent: set(hyper_res).
% 1.98/2.12 dependent: set(factor).
% 1.98/2.12 dependent: set(unit_deletion).
% 1.98/2.12
% 1.98/2.12 ------------> process usable:
% 1.98/2.12 ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 1.98/2.12 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_3).
% 1.98/2.12 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.98/2.12 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_3).
% 1.98/2.12 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_3,e_1).
% 1.98/2.12 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_2).
% 1.98/2.12 ** KEPT (pick-wt=16): 7 [] -group_element(A)| -group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3).
% 1.98/2.12 ** KEPT (pick-wt=11): 8 [] -product1(A,B,C)| -product1(A,B,D)|e_qualish(C,D).
% 1.98/2.12 ** KEPT (pick-wt=11): 9 [] -product1(A,B,C)| -product1(A,D,C)|e_qualish(B,D).
% 1.98/2.12 ** KEPT (pick-wt=11): 10 [] -product1(A,B,C)| -product1(D,B,C)|e_qualish(A,D).
% 1.98/2.12 ** KEPT (pick-wt=16): 11 [] -group_element(A)| -group_element(B)|product2(A,B,e_1)|product2(A,B,e_2)|product2(A,B,e_3).
% 1.98/2.12 ** KEPT (pick-wt=11): 12 [] -product2(A,B,C)| -product2(A,B,D)|e_qualish(C,D).
% 1.98/2.12 ** KEPT (pick-wt=11): 13 [] -product2(A,B,C)| -product2(A,D,C)|e_qualish(B,D).
% 1.98/2.12 ** KEPT (pick-wt=11): 14 [] -product2(A,B,C)| -product2(D,B,C)|e_qualish(A,D).
% 1.98/2.12 ** KEPT (pick-wt=12): 15 [] -product1(A,B,C)| -product1(C,B,D)|product2(D,A,B).
% 1.98/2.12
% 1.98/2.12 ------------> process sos:
% 1.98/2.12 ** KEPT (pick-wt=2): 25 [] group_element(e_1).
% 1.98/2.12 ** KEPT (pick-wt=2): 26 [] group_element(e_2).
% 1.98/2.12 ** KEPT (pick-wt=2): 27 [] group_element(e_3).
% 1.98/2.12 ** KEPT (pick-wt=4): 28 [] product1(A,A,A).
% 1.98/2.12 ** KEPT (pick-wt=4): 29 [] product2(A,A,A).
% 1.98/2.12
% 1.98/2.12 ======= end of input processing =======
% 1.98/2.12
% 1.98/2.12 =========== start of search ===========
% 1.98/2.12
% 1.98/2.12 -------- PROOF --------
% 1.98/2.12
% 1.98/2.12 ----> UNIT CONFLICT at 0.01 sec ----> 101 [binary,100.1,1.1] $F.
% 1.98/2.12
% 1.98/2.12 Length of proof is 11. Level of proof is 7.
% 1.98/2.12
% 1.98/2.12 ---------------- PROOF ----------------
% 1.98/2.12 % SZS status Unsatisfiable
% 1.98/2.12 % SZS output start Refutation
% See solution above
% 1.98/2.12 ------------ end of proof -------------
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12 ============ end of search ============
% 1.98/2.12
% 1.98/2.12 -------------- statistics -------------
% 1.98/2.12 clauses given 38
% 1.98/2.12 clauses generated 762
% 1.98/2.12 clauses kept 100
% 1.98/2.12 clauses forward subsumed 682
% 1.98/2.12 clauses back subsumed 58
% 1.98/2.12 Kbytes malloced 976
% 1.98/2.12
% 1.98/2.12 ----------- times (seconds) -----------
% 1.98/2.12 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.12 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.98/2.12
% 1.98/2.12 That finishes the proof of the theorem.
% 1.98/2.12
% 1.98/2.12 Process 27909 finished Wed Jul 27 05:23:25 2022
% 1.98/2.12 Otter interrupted
% 1.98/2.12 PROOF FOUND
%------------------------------------------------------------------------------