%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD024-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 12:53:44 EDT 2022
% Result : Unsatisfiable 2.13s 2.30s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 13 RR)
% Number of literals : 19 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( sum(A,B,C)
| ~ sum(D,E,A)
| ~ sum(E,B,F)
| ~ sum(D,F,C) ),
file('FLD024-3.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD024-3.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD024-3.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD024-3.p',unknown),
[] ).
cnf(25,axiom,
~ sum(additive_identity,a,b),
file('FLD024-3.p',unknown),
[] ).
cnf(51,axiom,
defined(a),
file('FLD024-3.p',unknown),
[] ).
cnf(52,axiom,
defined(b),
file('FLD024-3.p',unknown),
[] ).
cnf(53,axiom,
sum(b,additive_inverse(a),additive_identity),
file('FLD024-3.p',unknown),
[] ).
cnf(112,plain,
sum(additive_inverse(a),a,additive_identity),
inference(hyper,[status(thm)],[51,4]),
[iquote('hyper,51,4')] ).
cnf(151,plain,
sum(additive_identity,b,b),
inference(hyper,[status(thm)],[52,3]),
[iquote('hyper,52,3')] ).
cnf(7953,plain,
sum(b,additive_identity,b),
inference(hyper,[status(thm)],[151,5]),
[iquote('hyper,151,5')] ).
cnf(9583,plain,
sum(additive_identity,a,b),
inference(hyper,[status(thm)],[112,2,53,7953]),
[iquote('hyper,112,2,53,7953')] ).
cnf(9584,plain,
$false,
inference(binary,[status(thm)],[9583,25]),
[iquote('binary,9583.1,25.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD024-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 03:18:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.93/2.12 ----- Otter 3.3f, August 2004 -----
% 1.93/2.12 The process was started by sandbox on n020.cluster.edu,
% 1.93/2.12 Wed Jul 27 03:18:38 2022
% 1.93/2.12 The command was "./otter". The process ID is 16834.
% 1.93/2.12
% 1.93/2.12 set(prolog_style_variables).
% 1.93/2.12 set(auto).
% 1.93/2.12 dependent: set(auto1).
% 1.93/2.12 dependent: set(process_input).
% 1.93/2.12 dependent: clear(print_kept).
% 1.93/2.12 dependent: clear(print_new_demod).
% 1.93/2.12 dependent: clear(print_back_demod).
% 1.93/2.12 dependent: clear(print_back_sub).
% 1.93/2.12 dependent: set(control_memory).
% 1.93/2.12 dependent: assign(max_mem, 12000).
% 1.93/2.12 dependent: assign(pick_given_ratio, 4).
% 1.93/2.12 dependent: assign(stats_level, 1).
% 1.93/2.12 dependent: assign(max_seconds, 10800).
% 1.93/2.12 clear(print_given).
% 1.93/2.12
% 1.93/2.12 list(usable).
% 1.93/2.12 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.93/2.12 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.93/2.12 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.93/2.12 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.93/2.12 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.93/2.12 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.93/2.12 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.93/2.12 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.93/2.12 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.93/2.12 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.93/2.12 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.93/2.12 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.93/2.12 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.93/2.12 0 [] defined(additive_identity).
% 1.93/2.12 0 [] defined(additive_inverse(X))| -defined(X).
% 1.93/2.12 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.93/2.12 0 [] defined(multiplicative_identity).
% 1.93/2.12 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.93/2.12 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.93/2.12 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.93/2.12 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.93/2.12 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.93/2.12 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.93/2.12 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.93/2.12 0 [] less_or_e_qual(additive_identity,Z)| -less_or_e_qual(additive_identity,X)| -less_or_e_qual(additive_identity,Y)| -product(X,Y,Z).
% 1.93/2.12 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.93/2.12 0 [] defined(a).
% 1.93/2.12 0 [] defined(b).
% 1.93/2.12 0 [] sum(b,additive_inverse(a),additive_identity).
% 1.93/2.12 0 [] -sum(additive_identity,a,b).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.93/2.12
% 1.93/2.12 This is a non-Horn set without equality. The strategy will
% 1.93/2.12 be ordered hyper_res, unit deletion, and factoring, with
% 1.93/2.12 satellites in sos and with nuclei in usable.
% 1.93/2.12
% 1.93/2.12 dependent: set(hyper_res).
% 1.93/2.12 dependent: set(factor).
% 1.93/2.12 dependent: set(unit_deletion).
% 1.93/2.12
% 1.93/2.12 ------------> process usable:
% 1.93/2.12 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.93/2.12 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.93/2.12 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.93/2.12 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.93/2.12 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.93/2.12 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.93/2.12 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.93/2.12 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.93/2.12 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.93/2.12 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.93/2.12 ** KEPT (pick-wt=20): 11 [] sum(A,B,C)| -sum(D,E,F)| -product(F,G,C)| -product(D,G,A)| -product(E,G,B).
% 1.93/2.12 ** KEPT (pick-wt=20): 12 [] product(A,B,C)| -sum(D,E,A)| -product(D,B,F)| -product(E,B,G)| -sum(F,G,C).
% 1.93/2.12 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.93/2.12 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 1.93/2.12 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 1.93/2.12 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 2.13/2.30 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 2.13/2.30 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 2.13/2.30 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 2.13/2.30 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 2.13/2.30 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 2.13/2.30 ** KEPT (pick-wt=14): 22 [] less_or_e_qual(A,B)| -less_or_e_qual(C,D)| -sum(C,E,A)| -sum(D,E,B).
% 2.13/2.30 ** KEPT (pick-wt=13): 23 [] less_or_e_qual(additive_identity,A)| -less_or_e_qual(additive_identity,B)| -less_or_e_qual(additive_identity,C)| -product(B,C,A).
% 2.13/2.30 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 2.13/2.30 ** KEPT (pick-wt=4): 25 [] -sum(additive_identity,a,b).
% 2.13/2.30
% 2.13/2.30 ------------> process sos:
% 2.13/2.30 ** KEPT (pick-wt=2): 49 [] defined(additive_identity).
% 2.13/2.30 ** KEPT (pick-wt=2): 50 [] defined(multiplicative_identity).
% 2.13/2.30 ** KEPT (pick-wt=2): 51 [] defined(a).
% 2.13/2.30 ** KEPT (pick-wt=2): 52 [] defined(b).
% 2.13/2.30 ** KEPT (pick-wt=5): 53 [] sum(b,additive_inverse(a),additive_identity).
% 2.13/2.30
% 2.13/2.30 ======= end of input processing =======
% 2.13/2.30
% 2.13/2.30 =========== start of search ===========
% 2.13/2.30
% 2.13/2.30
% 2.13/2.30 Resetting weight limit to 6.
% 2.13/2.30
% 2.13/2.30
% 2.13/2.30 Resetting weight limit to 6.
% 2.13/2.30
% 2.13/2.30 sos_size=9403
% 2.13/2.30
% 2.13/2.30 -------- PROOF --------
% 2.13/2.30
% 2.13/2.30 ----> UNIT CONFLICT at 0.18 sec ----> 9584 [binary,9583.1,25.1] $F.
% 2.13/2.30
% 2.13/2.30 Length of proof is 4. Level of proof is 3.
% 2.13/2.30
% 2.13/2.30 ---------------- PROOF ----------------
% 2.13/2.30 % SZS status Unsatisfiable
% 2.13/2.30 % SZS output start Refutation
% See solution above
% 2.13/2.30 ------------ end of proof -------------
% 2.13/2.30
% 2.13/2.30
% 2.13/2.30 Search stopped by max_proofs option.
% 2.13/2.30
% 2.13/2.30
% 2.13/2.30 Search stopped by max_proofs option.
% 2.13/2.30
% 2.13/2.30 ============ end of search ============
% 2.13/2.30
% 2.13/2.30 -------------- statistics -------------
% 2.13/2.30 clauses given 78
% 2.13/2.30 clauses generated 11508
% 2.13/2.30 clauses kept 9583
% 2.13/2.30 clauses forward subsumed 1893
% 2.13/2.30 clauses back subsumed 32
% 2.13/2.30 Kbytes malloced 4882
% 2.13/2.30
% 2.13/2.30 ----------- times (seconds) -----------
% 2.13/2.30 user CPU time 0.18 (0 hr, 0 min, 0 sec)
% 2.13/2.30 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.13/2.30 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.13/2.30
% 2.13/2.30 That finishes the proof of the theorem.
% 2.13/2.30
% 2.13/2.30 Process 16834 finished Wed Jul 27 03:18:40 2022
% 2.13/2.30 Otter interrupted
% 2.13/2.30 PROOF FOUND
%------------------------------------------------------------------------------