TSTP Solution File: GRP029-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP029-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:55:54 EDT 2022
% Result : Unsatisfiable 1.64s 1.87s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 5 RR)
% Number of literals : 16 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP029-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP029-2.p',unknown),
[] ).
cnf(12,axiom,
~ product(not_right_identity(A),A,not_right_identity(A)),
file('GRP029-2.p',unknown),
[] ).
cnf(15,axiom,
product(identity,A,A),
file('GRP029-2.p',unknown),
[] ).
cnf(16,axiom,
product(inverse(A),A,identity),
file('GRP029-2.p',unknown),
[] ).
cnf(17,plain,
product(inverse(inverse(A)),identity,A),
inference(hyper,[status(thm)],[16,10,16,15]),
[iquote('hyper,16,10,16,15')] ).
cnf(18,plain,
product(inverse(identity),A,A),
inference(hyper,[status(thm)],[16,10,15,15]),
[iquote('hyper,16,10,15,15')] ).
cnf(19,plain,
product(identity,inverse(identity),identity),
inference(hyper,[status(thm)],[18,11,16,16]),
[iquote('hyper,18,11,16,16')] ).
cnf(123,plain,
product(A,inverse(identity),A),
inference(hyper,[status(thm)],[17,11,17,19]),
[iquote('hyper,17,11,17,19')] ).
cnf(124,plain,
$false,
inference(binary,[status(thm)],[123,12]),
[iquote('binary,123.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP029-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 05:20:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.64/1.87 ----- Otter 3.3f, August 2004 -----
% 1.64/1.87 The process was started by sandbox2 on n012.cluster.edu,
% 1.64/1.87 Wed Jul 27 05:20:05 2022
% 1.64/1.87 The command was "./otter". The process ID is 16494.
% 1.64/1.87
% 1.64/1.87 set(prolog_style_variables).
% 1.64/1.87 set(auto).
% 1.64/1.87 dependent: set(auto1).
% 1.64/1.87 dependent: set(process_input).
% 1.64/1.87 dependent: clear(print_kept).
% 1.64/1.87 dependent: clear(print_new_demod).
% 1.64/1.87 dependent: clear(print_back_demod).
% 1.64/1.87 dependent: clear(print_back_sub).
% 1.64/1.87 dependent: set(control_memory).
% 1.64/1.87 dependent: assign(max_mem, 12000).
% 1.64/1.87 dependent: assign(pick_given_ratio, 4).
% 1.64/1.87 dependent: assign(stats_level, 1).
% 1.64/1.87 dependent: assign(max_seconds, 10800).
% 1.64/1.87 clear(print_given).
% 1.64/1.87
% 1.64/1.87 list(usable).
% 1.64/1.87 0 [] e_qualish(X,X).
% 1.64/1.87 0 [] -e_qualish(X,Y)|e_qualish(Y,X).
% 1.64/1.87 0 [] -e_qualish(X,Y)| -e_qualish(Y,Z)|e_qualish(X,Z).
% 1.64/1.87 0 [] -e_qualish(X,Y)|e_qualish(multiply(X,W),multiply(Y,W)).
% 1.64/1.87 0 [] -e_qualish(X,Y)|e_qualish(multiply(W,X),multiply(W,Y)).
% 1.64/1.87 0 [] -e_qualish(X,Y)| -product(X,W,Z)|product(Y,W,Z).
% 1.64/1.87 0 [] -e_qualish(X,Y)| -product(W,X,Z)|product(W,Y,Z).
% 1.64/1.87 0 [] -e_qualish(X,Y)| -product(W,Z,X)|product(W,Z,Y).
% 1.64/1.87 0 [] -e_qualish(X,Y)|e_qualish(inverse(X),inverse(Y)).
% 1.64/1.87 0 [] product(X,Y,multiply(X,Y)).
% 1.64/1.87 0 [] -product(X,Y,Z)| -product(X,Y,W)|e_qualish(Z,W).
% 1.64/1.87 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.64/1.87 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.64/1.87 0 [] product(identity,A,A).
% 1.64/1.87 0 [] product(inverse(A),A,identity).
% 1.64/1.87 0 [] -product(not_right_identity(A),A,not_right_identity(A)).
% 1.64/1.87 end_of_list.
% 1.64/1.87
% 1.64/1.87 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.64/1.87
% 1.64/1.87 This is a Horn set without equality. The strategy will
% 1.64/1.87 be hyperresolution, with satellites in sos and nuclei
% 1.64/1.87 in usable.
% 1.64/1.87
% 1.64/1.87 dependent: set(hyper_res).
% 1.64/1.87 dependent: clear(order_hyper).
% 1.64/1.87
% 1.64/1.87 ------------> process usable:
% 1.64/1.87 ** KEPT (pick-wt=6): 1 [] -e_qualish(A,B)|e_qualish(B,A).
% 1.64/1.87 ** KEPT (pick-wt=9): 2 [] -e_qualish(A,B)| -e_qualish(B,C)|e_qualish(A,C).
% 1.64/1.87 ** KEPT (pick-wt=10): 3 [] -e_qualish(A,B)|e_qualish(multiply(A,C),multiply(B,C)).
% 1.64/1.87 ** KEPT (pick-wt=10): 4 [] -e_qualish(A,B)|e_qualish(multiply(C,A),multiply(C,B)).
% 1.64/1.87 ** KEPT (pick-wt=11): 5 [] -e_qualish(A,B)| -product(A,C,D)|product(B,C,D).
% 1.64/1.87 ** KEPT (pick-wt=11): 6 [] -e_qualish(A,B)| -product(C,A,D)|product(C,B,D).
% 1.64/1.87 ** KEPT (pick-wt=11): 7 [] -e_qualish(A,B)| -product(C,D,A)|product(C,D,B).
% 1.64/1.87 ** KEPT (pick-wt=8): 8 [] -e_qualish(A,B)|e_qualish(inverse(A),inverse(B)).
% 1.64/1.87 ** KEPT (pick-wt=11): 9 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.64/1.87 ** KEPT (pick-wt=16): 10 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.64/1.87 ** KEPT (pick-wt=16): 11 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.64/1.87 ** KEPT (pick-wt=6): 12 [] -product(not_right_identity(A),A,not_right_identity(A)).
% 1.64/1.87
% 1.64/1.87 ------------> process sos:
% 1.64/1.87 ** KEPT (pick-wt=3): 13 [] e_qualish(A,A).
% 1.64/1.87 ** KEPT (pick-wt=6): 14 [] product(A,B,multiply(A,B)).
% 1.64/1.87 ** KEPT (pick-wt=4): 15 [] product(identity,A,A).
% 1.64/1.87 ** KEPT (pick-wt=5): 16 [] product(inverse(A),A,identity).
% 1.64/1.87
% 1.64/1.87 ======= end of input processing =======
% 1.64/1.87
% 1.64/1.87 =========== start of search ===========
% 1.64/1.87
% 1.64/1.87 -------- PROOF --------
% 1.64/1.87
% 1.64/1.87 ----> UNIT CONFLICT at 0.00 sec ----> 124 [binary,123.1,12.1] $F.
% 1.64/1.87
% 1.64/1.87 Length of proof is 4. Level of proof is 3.
% 1.64/1.87
% 1.64/1.87 ---------------- PROOF ----------------
% 1.64/1.87 % SZS status Unsatisfiable
% 1.64/1.87 % SZS output start Refutation
% See solution above
% 1.64/1.87 ------------ end of proof -------------
% 1.64/1.87
% 1.64/1.87
% 1.64/1.87 Search stopped by max_proofs option.
% 1.64/1.87
% 1.64/1.87
% 1.64/1.87 Search stopped by max_proofs option.
% 1.64/1.87
% 1.64/1.87 ============ end of search ============
% 1.64/1.87
% 1.64/1.87 -------------- statistics -------------
% 1.64/1.87 clauses given 11
% 1.64/1.87 clauses generated 369
% 1.64/1.87 clauses kept 123
% 1.64/1.87 clauses forward subsumed 262
% 1.64/1.87 clauses back subsumed 7
% 1.64/1.87 Kbytes malloced 976
% 1.64/1.87
% 1.64/1.87 ----------- times (seconds) -----------
% 1.64/1.87 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.87 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.64/1.87
% 1.64/1.87 That finishes the proof of the theorem.
% 1.64/1.87
% 1.64/1.87 Process 16494 finished Wed Jul 27 05:20:07 2022
% 1.64/1.87 Otter interrupted
% 1.64/1.87 PROOF FOUND
%------------------------------------------------------------------------------