%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 12:45:52 EDT 2022
% Result : Unsatisfiable 1.77s 2.02s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of clauses : 24 ( 13 unt; 3 nHn; 20 RR)
% Number of literals : 40 ( 0 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 23 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('ALG002-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| product(additive_inverse(A),additive_inverse(B),C) ),
file('ALG002-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
file('ALG002-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ greater_than_0(A)
| ~ greater_than_0(additive_inverse(A)) ),
file('ALG002-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ greater_than_0(A)
| ~ product(A,A,additive_identity) ),
file('ALG002-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| product(B,A,C) ),
file('ALG002-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(A,A,additive_identity)
| product(C,C,additive_identity) ),
file('ALG002-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ greater_than_0(A)
| ~ greater_than_0(B)
| greater_than_0(C) ),
file('ALG002-1.p',unknown),
[] ).
cnf(10,axiom,
~ greater_than_0(multiplicative_inverse(a)),
file('ALG002-1.p',unknown),
[] ).
cnf(12,plain,
( ~ product(A,A,B)
| ~ greater_than_0(A)
| greater_than_0(B) ),
inference(factor,[status(thm)],[9]),
[iquote('factor,9.2.3')] ).
cnf(13,axiom,
product(A,multiplicative_identity,A),
file('ALG002-1.p',unknown),
[] ).
cnf(14,axiom,
( product(A,multiplicative_inverse(A),multiplicative_identity)
| product(A,A,additive_identity) ),
file('ALG002-1.p',unknown),
[] ).
cnf(15,axiom,
( greater_than_0(A)
| product(A,A,additive_identity)
| greater_than_0(additive_inverse(A)) ),
file('ALG002-1.p',unknown),
[] ).
cnf(16,axiom,
greater_than_0(a),
file('ALG002-1.p',unknown),
[] ).
cnf(19,plain,
product(additive_inverse(A),additive_inverse(multiplicative_identity),A),
inference(hyper,[status(thm)],[13,2]),
[iquote('hyper,13,2')] ).
cnf(34,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(hyper,[status(thm)],[14,6,16]),
[iquote('hyper,14,6,16')] ).
cnf(37,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(hyper,[status(thm)],[34,7]),
[iquote('hyper,34,7')] ).
cnf(38,plain,
product(a,additive_inverse(multiplicative_inverse(a)),additive_inverse(multiplicative_identity)),
inference(hyper,[status(thm)],[34,4]),
[iquote('hyper,34,4')] ).
cnf(43,plain,
product(multiplicative_inverse(a),multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[37,8,14]),1]),
[iquote('hyper,37,8,14,unit_del,1')] ).
cnf(59,plain,
greater_than_0(multiplicative_identity),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[15,12,19]),1])]),
[iquote('hyper,15,12,19,unit_del,1,factor_simp')] ).
cnf(86,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[38,9,16,15]),10]),
[iquote('hyper,38,9,16,15,unit_del,10')] ).
cnf(325,plain,
product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity),
inference(hyper,[status(thm)],[86,5,59]),
[iquote('hyper,86,5,59')] ).
cnf(330,plain,
product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[325,8,43]),
[iquote('hyper,325,8,43')] ).
cnf(331,plain,
$false,
inference(binary,[status(thm)],[330,1]),
[iquote('binary,330.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 03:29:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.77/2.02 ----- Otter 3.3f, August 2004 -----
% 1.77/2.02 The process was started by sandbox on n007.cluster.edu,
% 1.77/2.02 Wed Jul 27 03:29:01 2022
% 1.77/2.02 The command was "./otter". The process ID is 27419.
% 1.77/2.02
% 1.77/2.02 set(prolog_style_variables).
% 1.77/2.02 set(auto).
% 1.77/2.02 dependent: set(auto1).
% 1.77/2.02 dependent: set(process_input).
% 1.77/2.02 dependent: clear(print_kept).
% 1.77/2.02 dependent: clear(print_new_demod).
% 1.77/2.02 dependent: clear(print_back_demod).
% 1.77/2.02 dependent: clear(print_back_sub).
% 1.77/2.02 dependent: set(control_memory).
% 1.77/2.02 dependent: assign(max_mem, 12000).
% 1.77/2.02 dependent: assign(pick_given_ratio, 4).
% 1.77/2.02 dependent: assign(stats_level, 1).
% 1.77/2.02 dependent: assign(max_seconds, 10800).
% 1.77/2.02 clear(print_given).
% 1.77/2.02
% 1.77/2.02 list(usable).
% 1.77/2.02 0 [] product(X,multiplicative_identity,X).
% 1.77/2.02 0 [] -product(multiplicative_identity,multiplicative_identity,additive_identity).
% 1.77/2.02 0 [] -product(X,Y,Z)|product(additive_inverse(X),additive_inverse(Y),Z).
% 1.77/2.02 0 [] product(X,Y,Z)| -product(additive_inverse(X),additive_inverse(Y),Z).
% 1.77/2.02 0 [] -product(X,Y,Z)|product(X,additive_inverse(Y),additive_inverse(Z)).
% 1.77/2.02 0 [] product(X,multiplicative_inverse(X),multiplicative_identity)|product(X,X,additive_identity).
% 1.77/2.02 0 [] -greater_than_0(X)| -greater_than_0(additive_inverse(X)).
% 1.77/2.02 0 [] -greater_than_0(X)| -product(X,X,additive_identity).
% 1.77/2.02 0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.77/2.02 0 [] greater_than_0(X)|product(X,X,additive_identity)|greater_than_0(additive_inverse(X)).
% 1.77/2.02 0 [] -product(Y,Z,X)| -product(Y,Y,additive_identity)|product(X,X,additive_identity).
% 1.77/2.02 0 [] -product(Y,Z,X)| -greater_than_0(Y)| -greater_than_0(Z)|greater_than_0(X).
% 1.77/2.02 0 [] greater_than_0(a).
% 1.77/2.02 0 [] -greater_than_0(multiplicative_inverse(a)).
% 1.77/2.02 end_of_list.
% 1.77/2.02
% 1.77/2.02 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.77/2.02
% 1.77/2.02 This is a non-Horn set without equality. The strategy will
% 1.77/2.02 be ordered hyper_res, unit deletion, and factoring, with
% 1.77/2.02 satellites in sos and with nuclei in usable.
% 1.77/2.02
% 1.77/2.02 dependent: set(hyper_res).
% 1.77/2.02 dependent: set(factor).
% 1.77/2.02 dependent: set(unit_deletion).
% 1.77/2.02
% 1.77/2.02 ------------> process usable:
% 1.77/2.02 ** KEPT (pick-wt=4): 1 [] -product(multiplicative_identity,multiplicative_identity,additive_identity).
% 1.77/2.02 ** KEPT (pick-wt=10): 2 [] -product(A,B,C)|product(additive_inverse(A),additive_inverse(B),C).
% 1.77/2.02 ** KEPT (pick-wt=10): 3 [] product(A,B,C)| -product(additive_inverse(A),additive_inverse(B),C).
% 1.77/2.02 ** KEPT (pick-wt=10): 4 [] -product(A,B,C)|product(A,additive_inverse(B),additive_inverse(C)).
% 1.77/2.02 ** KEPT (pick-wt=5): 5 [] -greater_than_0(A)| -greater_than_0(additive_inverse(A)).
% 1.77/2.02 ** KEPT (pick-wt=6): 6 [] -greater_than_0(A)| -product(A,A,additive_identity).
% 1.77/2.02 ** KEPT (pick-wt=8): 7 [] -product(A,B,C)|product(B,A,C).
% 1.77/2.02 ** KEPT (pick-wt=12): 8 [] -product(A,B,C)| -product(A,A,additive_identity)|product(C,C,additive_identity).
% 1.77/2.02 ** KEPT (pick-wt=10): 9 [] -product(A,B,C)| -greater_than_0(A)| -greater_than_0(B)|greater_than_0(C).
% 1.77/2.02 ** KEPT (pick-wt=3): 10 [] -greater_than_0(multiplicative_inverse(a)).
% 1.77/2.02
% 1.77/2.02 ------------> process sos:
% 1.77/2.02 ** KEPT (pick-wt=4): 13 [] product(A,multiplicative_identity,A).
% 1.77/2.02 ** KEPT (pick-wt=9): 14 [] product(A,multiplicative_inverse(A),multiplicative_identity)|product(A,A,additive_identity).
% 1.77/2.02 ** KEPT (pick-wt=9): 15 [] greater_than_0(A)|product(A,A,additive_identity)|greater_than_0(additive_inverse(A)).
% 1.77/2.02 ** KEPT (pick-wt=2): 16 [] greater_than_0(a).
% 1.77/2.02
% 1.77/2.02 ======= end of input processing =======
% 1.77/2.02
% 1.77/2.02 =========== start of search ===========
% 1.77/2.02
% 1.77/2.02 -------- PROOF --------
% 1.77/2.02
% 1.77/2.02 ----> UNIT CONFLICT at 0.03 sec ----> 331 [binary,330.1,1.1] $F.
% 1.77/2.02
% 1.77/2.02 Length of proof is 10. Level of proof is 5.
% 1.77/2.02
% 1.77/2.02 ---------------- PROOF ----------------
% 1.77/2.02 % SZS status Unsatisfiable
% 1.77/2.02 % SZS output start Refutation
% See solution above
% 1.77/2.02 ------------ end of proof -------------
% 1.77/2.02
% 1.77/2.02
% 1.77/2.02 Search stopped by max_proofs option.
% 1.77/2.02
% 1.77/2.02
% 1.77/2.02 Search stopped by max_proofs option.
% 1.77/2.02
% 1.77/2.02 ============ end of search ============
% 1.77/2.02
% 1.77/2.02 -------------- statistics -------------
% 1.77/2.02 clauses given 63
% 1.77/2.02 clauses generated 1851
% 1.77/2.02 clauses kept 330
% 1.77/2.02 clauses forward subsumed 1535
% 1.77/2.02 clauses back subsumed 68
% 1.77/2.02 Kbytes malloced 976
% 1.77/2.02
% 1.77/2.02 ----------- times (seconds) -----------
% 1.77/2.02 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.77/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/2.02 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.77/2.02
% 1.77/2.02 That finishes the proof of the theorem.
% 1.77/2.02
% 1.77/2.02 Process 27419 finished Wed Jul 27 03:29:02 2022
% 1.77/2.02 Otter interrupted
% 1.77/2.02 PROOF FOUND
%------------------------------------------------------------------------------