%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD006-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 12:53:40 EDT 2022
% Result : Unsatisfiable 31.93s 32.19s
% Output : Refutation 31.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 9 unt; 0 nHn; 14 RR)
% Number of literals : 20 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( e_qualish(add(additive_identity,A),A)
| ~ defined(A) ),
file('FLD006-1.p',unknown),
[] ).
cnf(3,axiom,
( e_qualish(add(A,additive_inverse(A)),additive_identity)
| ~ defined(A) ),
file('FLD006-1.p',unknown),
[] ).
cnf(11,axiom,
( defined(additive_inverse(A))
| ~ defined(A) ),
file('FLD006-1.p',unknown),
[] ).
cnf(20,axiom,
( e_qualish(A,B)
| ~ e_qualish(B,A) ),
file('FLD006-1.p',unknown),
[] ).
cnf(21,axiom,
( e_qualish(A,B)
| ~ e_qualish(A,C)
| ~ e_qualish(C,B) ),
file('FLD006-1.p',unknown),
[] ).
cnf(26,axiom,
~ e_qualish(additive_inverse(additive_identity),additive_identity),
file('FLD006-1.p',unknown),
[] ).
cnf(46,axiom,
defined(additive_identity),
file('FLD006-1.p',unknown),
[] ).
cnf(57,plain,
defined(additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[46,11]),
[iquote('hyper,46,11')] ).
cnf(59,plain,
e_qualish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(hyper,[status(thm)],[46,3]),
[iquote('hyper,46,3')] ).
cnf(191,plain,
e_qualish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[57,2]),
[iquote('hyper,57,2')] ).
cnf(6266,plain,
e_qualish(additive_identity,add(additive_identity,additive_inverse(additive_identity))),
inference(hyper,[status(thm)],[59,20]),
[iquote('hyper,59,20')] ).
cnf(6831,plain,
e_qualish(additive_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[191,21,6266]),
[iquote('hyper,191,21,6266')] ).
cnf(6840,plain,
e_qualish(additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[6831,20]),
[iquote('hyper,6831,20')] ).
cnf(6841,plain,
$false,
inference(binary,[status(thm)],[6840,26]),
[iquote('binary,6840.1,26.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD006-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 03:25:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.61/1.81 ----- Otter 3.3f, August 2004 -----
% 1.61/1.81 The process was started by sandbox2 on n028.cluster.edu,
% 1.61/1.81 Wed Jul 27 03:25:18 2022
% 1.61/1.81 The command was "./otter". The process ID is 4414.
% 1.61/1.81
% 1.61/1.81 set(prolog_style_variables).
% 1.61/1.81 set(auto).
% 1.61/1.81 dependent: set(auto1).
% 1.61/1.81 dependent: set(process_input).
% 1.61/1.81 dependent: clear(print_kept).
% 1.61/1.81 dependent: clear(print_new_demod).
% 1.61/1.81 dependent: clear(print_back_demod).
% 1.61/1.81 dependent: clear(print_back_sub).
% 1.61/1.81 dependent: set(control_memory).
% 1.61/1.81 dependent: assign(max_mem, 12000).
% 1.61/1.81 dependent: assign(pick_given_ratio, 4).
% 1.61/1.81 dependent: assign(stats_level, 1).
% 1.61/1.81 dependent: assign(max_seconds, 10800).
% 1.61/1.81 clear(print_given).
% 1.61/1.81
% 1.61/1.81 list(usable).
% 1.61/1.81 0 [] e_qualish(add(X,add(Y,Z)),add(add(X,Y),Z))| -defined(X)| -defined(Y)| -defined(Z).
% 1.61/1.81 0 [] e_qualish(add(additive_identity,X),X)| -defined(X).
% 1.61/1.81 0 [] e_qualish(add(X,additive_inverse(X)),additive_identity)| -defined(X).
% 1.61/1.81 0 [] e_qualish(add(X,Y),add(Y,X))| -defined(X)| -defined(Y).
% 1.61/1.81 0 [] e_qualish(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z))| -defined(X)| -defined(Y)| -defined(Z).
% 1.61/1.81 0 [] e_qualish(multiply(multiplicative_identity,X),X)| -defined(X).
% 1.61/1.81 0 [] e_qualish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)| -defined(X)|e_qualish(X,additive_identity).
% 1.61/1.81 0 [] e_qualish(multiply(X,Y),multiply(Y,X))| -defined(X)| -defined(Y).
% 1.61/1.81 0 [] e_qualish(add(multiply(X,Z),multiply(Y,Z)),multiply(add(X,Y),Z))| -defined(X)| -defined(Y)| -defined(Z).
% 1.61/1.81 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.61/1.81 0 [] defined(additive_identity).
% 1.61/1.81 0 [] defined(additive_inverse(X))| -defined(X).
% 1.61/1.81 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.61/1.81 0 [] defined(multiplicative_identity).
% 1.61/1.81 0 [] defined(multiplicative_inverse(X))| -defined(X)|e_qualish(X,additive_identity).
% 1.61/1.81 0 [] e_qualish(X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.61/1.81 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.61/1.81 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.61/1.81 0 [] less_or_e_qual(add(X,Z),add(Y,Z))| -defined(Z)| -less_or_e_qual(X,Y).
% 1.61/1.81 0 [] less_or_e_qual(additive_identity,multiply(Y,Z))| -less_or_e_qual(additive_identity,Y)| -less_or_e_qual(additive_identity,Z).
% 1.61/1.81 0 [] e_qualish(X,X)| -defined(X).
% 1.61/1.81 0 [] e_qualish(X,Y)| -e_qualish(Y,X).
% 1.61/1.81 0 [] e_qualish(X,Z)| -e_qualish(X,Y)| -e_qualish(Y,Z).
% 1.61/1.81 0 [] e_qualish(add(X,Z),add(Y,Z))| -defined(Z)| -e_qualish(X,Y).
% 1.61/1.81 0 [] e_qualish(multiply(X,Z),multiply(Y,Z))| -defined(Z)| -e_qualish(X,Y).
% 1.61/1.81 0 [] less_or_e_qual(Y,Z)| -less_or_e_qual(X,Z)| -e_qualish(X,Y).
% 1.61/1.81 0 [] -e_qualish(additive_identity,multiplicative_identity).
% 1.61/1.81 0 [] -e_qualish(additive_inverse(additive_identity),additive_identity).
% 1.61/1.81 end_of_list.
% 1.61/1.81
% 1.61/1.81 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.61/1.81
% 1.61/1.81 This is a non-Horn set without equality. The strategy will
% 1.61/1.81 be ordered hyper_res, unit deletion, and factoring, with
% 1.61/1.81 satellites in sos and with nuclei in usable.
% 1.61/1.81
% 1.61/1.81 dependent: set(hyper_res).
% 1.61/1.81 dependent: set(factor).
% 1.61/1.81 dependent: set(unit_deletion).
% 1.61/1.81
% 1.61/1.81 ------------> process usable:
% 1.61/1.81 ** KEPT (pick-wt=17): 1 [] e_qualish(add(A,add(B,C)),add(add(A,B),C))| -defined(A)| -defined(B)| -defined(C).
% 1.61/1.81 ** KEPT (pick-wt=7): 2 [] e_qualish(add(additive_identity,A),A)| -defined(A).
% 1.61/1.81 ** KEPT (pick-wt=8): 3 [] e_qualish(add(A,additive_inverse(A)),additive_identity)| -defined(A).
% 1.61/1.81 ** KEPT (pick-wt=11): 4 [] e_qualish(add(A,B),add(B,A))| -defined(A)| -defined(B).
% 1.61/1.81 ** KEPT (pick-wt=17): 5 [] e_qualish(multiply(A,multiply(B,C)),multiply(multiply(A,B),C))| -defined(A)| -defined(B)| -defined(C).
% 1.61/1.81 ** KEPT (pick-wt=7): 6 [] e_qualish(multiply(multiplicative_identity,A),A)| -defined(A).
% 1.61/1.81 ** KEPT (pick-wt=11): 7 [] e_qualish(multiply(A,multiplicative_inverse(A)),multiplicative_identity)| -defined(A)|e_qualish(A,additive_identity).
% 1.61/1.81 ** KEPT (pick-wt=11): 8 [] e_qualish(multiply(A,B),multiply(B,A))| -defined(A)| -defined(B).
% 1.61/1.81 ** KEPT (pick-wt=19): 9 [] e_qualish(add(multiply(A,B),multiply(C,B)),multiply(add(A,C),B))| -defined(A)| -defined(C)| -defined(B).
% 1.61/1.81 ** KEPT (pick-wt=8): 10 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.61/1.81 ** KEPT (pick-wt=5): 11 [] defined(additive_inverse(A))| -defined(A).
% 1.61/1.81 ** KEPT (pick-wt=8): 12 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 31.93/32.19 ** KEPT (pick-wt=8): 13 [] defined(multiplicative_inverse(A))| -defined(A)|e_qualish(A,additive_identity).
% 31.93/32.19 ** KEPT (pick-wt=9): 14 [] e_qualish(A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 31.93/32.19 ** KEPT (pick-wt=9): 15 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 31.93/32.19 ** KEPT (pick-wt=10): 16 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 31.93/32.19 ** KEPT (pick-wt=12): 17 [] less_or_e_qual(add(A,B),add(C,B))| -defined(B)| -less_or_e_qual(A,C).
% 31.93/32.19 ** KEPT (pick-wt=11): 18 [] less_or_e_qual(additive_identity,multiply(A,B))| -less_or_e_qual(additive_identity,A)| -less_or_e_qual(additive_identity,B).
% 31.93/32.19 ** KEPT (pick-wt=5): 19 [] e_qualish(A,A)| -defined(A).
% 31.93/32.19 ** KEPT (pick-wt=6): 20 [] e_qualish(A,B)| -e_qualish(B,A).
% 31.93/32.19 ** KEPT (pick-wt=9): 21 [] e_qualish(A,B)| -e_qualish(A,C)| -e_qualish(C,B).
% 31.93/32.19 ** KEPT (pick-wt=12): 22 [] e_qualish(add(A,B),add(C,B))| -defined(B)| -e_qualish(A,C).
% 31.93/32.19 ** KEPT (pick-wt=12): 23 [] e_qualish(multiply(A,B),multiply(C,B))| -defined(B)| -e_qualish(A,C).
% 31.93/32.19 ** KEPT (pick-wt=9): 24 [] less_or_e_qual(A,B)| -less_or_e_qual(C,B)| -e_qualish(C,A).
% 31.93/32.19 ** KEPT (pick-wt=3): 25 [] -e_qualish(additive_identity,multiplicative_identity).
% 31.93/32.19 ** KEPT (pick-wt=4): 26 [] -e_qualish(additive_inverse(additive_identity),additive_identity).
% 31.93/32.19
% 31.93/32.19 ------------> process sos:
% 31.93/32.19 ** KEPT (pick-wt=2): 46 [] defined(additive_identity).
% 31.93/32.19 ** KEPT (pick-wt=2): 47 [] defined(multiplicative_identity).
% 31.93/32.19
% 31.93/32.19 ======= end of input processing =======
% 31.93/32.19
% 31.93/32.19 =========== start of search ===========
% 31.93/32.19
% 31.93/32.19
% 31.93/32.19 Resetting weight limit to 8.
% 31.93/32.19
% 31.93/32.19
% 31.93/32.19 Resetting weight limit to 8.
% 31.93/32.19
% 31.93/32.19 sos_size=6023
% 31.93/32.19
% 31.93/32.19
% 31.93/32.19 Resetting weight limit to 7.
% 31.93/32.19
% 31.93/32.19
% 31.93/32.19 Resetting weight limit to 7.
% 31.93/32.19
% 31.93/32.19 sos_size=6501
% 31.93/32.19
% 31.93/32.19 -- HEY sandbox2, WE HAVE A PROOF!! --
% 31.93/32.19
% 31.93/32.19 ----> UNIT CONFLICT at 30.36 sec ----> 6841 [binary,6840.1,26.1] $F.
% 31.93/32.19
% 31.93/32.19 Length of proof is 6. Level of proof is 4.
% 31.93/32.19
% 31.93/32.19 ---------------- PROOF ----------------
% 31.93/32.19 % SZS status Unsatisfiable
% 31.93/32.19 % SZS output start Refutation
% See solution above
% 31.93/32.19 ------------ end of proof -------------
% 31.93/32.19
% 31.93/32.19
% 31.93/32.19 Search stopped by max_proofs option.
% 31.93/32.19
% 31.93/32.19
% 31.93/32.19 Search stopped by max_proofs option.
% 31.93/32.19
% 31.93/32.19 ============ end of search ============
% 31.93/32.19
% 31.93/32.19 -------------- statistics -------------
% 31.93/32.19 clauses given 259
% 31.93/32.19 clauses generated 14265965
% 31.93/32.19 clauses kept 6840
% 31.93/32.19 clauses forward subsumed 2560
% 31.93/32.19 clauses back subsumed 19
% 31.93/32.19 Kbytes malloced 5859
% 31.93/32.19
% 31.93/32.19 ----------- times (seconds) -----------
% 31.93/32.19 user CPU time 30.36 (0 hr, 0 min, 30 sec)
% 31.93/32.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 31.93/32.19 wall-clock time 32 (0 hr, 0 min, 32 sec)
% 31.93/32.19
% 31.93/32.19 That finishes the proof of the theorem.
% 31.93/32.19
% 31.93/32.19 Process 4414 finished Wed Jul 27 03:25:50 2022
% 31.93/32.19 Otter interrupted
% 31.93/32.19 PROOF FOUND
%------------------------------------------------------------------------------