%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 12:47:34 EDT 2022
% Result : Unsatisfiable 3.04s 3.20s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 16
% Syntax : Number of clauses : 25 ( 19 unt; 0 nHn; 8 RR)
% Number of literals : 39 ( 7 equ; 15 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('BOO012-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| product(B,A,C) ),
file('BOO012-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum(A,B,C)
| ~ sum(D,B,E)
| ~ product(A,D,F)
| ~ sum(F,B,G)
| product(C,E,G) ),
file('BOO012-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum(A,B,C)
| ~ sum(D,B,E)
| ~ product(A,D,F)
| ~ product(C,E,G)
| sum(F,B,G) ),
file('BOO012-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('BOO012-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('BOO012-3.p',unknown),
[] ).
cnf(17,axiom,
inverse(inverse(x)) != x,
file('BOO012-3.p',unknown),
[] ).
cnf(19,axiom,
sum(A,B,add(A,B)),
file('BOO012-3.p',unknown),
[] ).
cnf(20,axiom,
product(A,B,multiply(A,B)),
file('BOO012-3.p',unknown),
[] ).
cnf(22,axiom,
sum(A,additive_identity,A),
file('BOO012-3.p',unknown),
[] ).
cnf(23,axiom,
product(multiplicative_identity,A,A),
file('BOO012-3.p',unknown),
[] ).
cnf(24,axiom,
product(A,multiplicative_identity,A),
file('BOO012-3.p',unknown),
[] ).
cnf(25,axiom,
sum(inverse(A),A,multiplicative_identity),
file('BOO012-3.p',unknown),
[] ).
cnf(26,axiom,
sum(A,inverse(A),multiplicative_identity),
file('BOO012-3.p',unknown),
[] ).
cnf(27,axiom,
product(inverse(A),A,additive_identity),
file('BOO012-3.p',unknown),
[] ).
cnf(28,axiom,
product(A,inverse(A),additive_identity),
file('BOO012-3.p',unknown),
[] ).
cnf(55,plain,
add(A,additive_identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[19,11,22])]),
[iquote('hyper,19,11,22,flip.1')] ).
cnf(69,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[19,1]),
[iquote('hyper,19,1')] ).
cnf(129,plain,
multiply(multiplicative_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,12,23])]),
[iquote('hyper,20,12,23,flip.1')] ).
cnf(183,plain,
product(A,B,multiply(B,A)),
inference(hyper,[status(thm)],[20,2]),
[iquote('hyper,20,2')] ).
cnf(294,plain,
sum(additive_identity,A,add(inverse(inverse(A)),A)),
inference(hyper,[status(thm)],[27,10,19,25,24]),
[iquote('hyper,27,10,19,25,24')] ).
cnf(2507,plain,
add(inverse(inverse(A)),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[294,11,69]),55])]),
[iquote('hyper,294,11,69,demod,55,flip.1')] ).
cnf(2508,plain,
product(A,multiplicative_identity,inverse(inverse(A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[294,9,69,26,28]),2507,2507]),
[iquote('hyper,294,9,69,26,28,demod,2507,2507')] ).
cnf(2549,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2508,12,183]),129])]),
[iquote('hyper,2508,12,183,demod,129,flip.1')] ).
cnf(2551,plain,
$false,
inference(binary,[status(thm)],[2549,17]),
[iquote('binary,2549.1,17.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : BOO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 02:33:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.87/2.07 ----- Otter 3.3f, August 2004 -----
% 1.87/2.07 The process was started by sandbox on n024.cluster.edu,
% 1.87/2.07 Wed Jul 27 02:33:55 2022
% 1.87/2.07 The command was "./otter". The process ID is 32638.
% 1.87/2.07
% 1.87/2.07 set(prolog_style_variables).
% 1.87/2.07 set(auto).
% 1.87/2.07 dependent: set(auto1).
% 1.87/2.07 dependent: set(process_input).
% 1.87/2.07 dependent: clear(print_kept).
% 1.87/2.07 dependent: clear(print_new_demod).
% 1.87/2.07 dependent: clear(print_back_demod).
% 1.87/2.07 dependent: clear(print_back_sub).
% 1.87/2.07 dependent: set(control_memory).
% 1.87/2.07 dependent: assign(max_mem, 12000).
% 1.87/2.07 dependent: assign(pick_given_ratio, 4).
% 1.87/2.07 dependent: assign(stats_level, 1).
% 1.87/2.07 dependent: assign(max_seconds, 10800).
% 1.87/2.07 clear(print_given).
% 1.87/2.07
% 1.87/2.07 list(usable).
% 1.87/2.07 0 [] A=A.
% 1.87/2.07 0 [] sum(X,Y,add(X,Y)).
% 1.87/2.07 0 [] product(X,Y,multiply(X,Y)).
% 1.87/2.07 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.87/2.07 0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.87/2.07 0 [] sum(additive_identity,X,X).
% 1.87/2.07 0 [] sum(X,additive_identity,X).
% 1.87/2.07 0 [] product(multiplicative_identity,X,X).
% 1.87/2.07 0 [] product(X,multiplicative_identity,X).
% 1.87/2.07 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.87/2.07 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.87/2.07 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.87/2.07 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.87/2.07 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -sum(X,V3,V4)|product(V1,V2,V4).
% 1.87/2.07 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(X,V3,V4).
% 1.87/2.07 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -sum(V3,X,V4)|product(V1,V2,V4).
% 1.87/2.07 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(V3,X,V4).
% 1.87/2.07 0 [] sum(inverse(X),X,multiplicative_identity).
% 1.87/2.07 0 [] sum(X,inverse(X),multiplicative_identity).
% 1.87/2.07 0 [] product(inverse(X),X,additive_identity).
% 1.87/2.07 0 [] product(X,inverse(X),additive_identity).
% 1.87/2.07 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.87/2.07 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.87/2.07 0 [] sum(X,X,X).
% 1.87/2.07 0 [] product(X,X,X).
% 1.87/2.07 0 [] sum(X,multiplicative_identity,multiplicative_identity).
% 1.87/2.07 0 [] product(X,additive_identity,additive_identity).
% 1.87/2.07 0 [] -product(X,Y,Z)|sum(X,Z,X).
% 1.87/2.07 0 [] -sum(X,Y,Z)|product(X,Z,X).
% 1.87/2.07 0 [] sum(X,multiply(X,Y),X).
% 1.87/2.07 0 [] product(X,add(X,Y),X).
% 1.87/2.07 0 [] -sum(X,Y,X_plus_Y)| -sum(Y,Z,Y_plus_Z)| -sum(X,Y_plus_Z,X_plus_Y_plus_Z)|sum(X_plus_Y,Z,X_plus_Y_plus_Z).
% 1.87/2.07 0 [] -sum(X,Y,X_plus_Y)| -sum(Y,Z,Y_plus_Z)|sum(X_plus_Y,Z,X_plus_Y_plus_Z)| -sum(X,Y_plus_Z,X_plus_Y_plus_Z).
% 1.87/2.07 0 [] -product(X,Y,X_times_Y)| -product(Y,Z,Y_times_Z)| -product(X,Y_times_Z,X_times_Y_times_Z)|product(X_times_Y,Z,X_times_Y_times_Z).
% 1.87/2.07 0 [] -product(X,Y,X_times_Y)| -product(Y,Z,Y_times_Z)|product(X_times_Y,Z,X_times_Y_times_Z)| -product(X,Y_times_Z,X_times_Y_times_Z).
% 1.87/2.07 0 [] inverse(inverse(x))!=x.
% 1.87/2.07 end_of_list.
% 1.87/2.07
% 1.87/2.07 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.87/2.07
% 1.87/2.07 This is a Horn set with equality. The strategy will be
% 1.87/2.07 Knuth-Bendix and hyper_res, with positive clauses in
% 1.87/2.07 sos and nonpositive clauses in usable.
% 1.87/2.07
% 1.87/2.07 dependent: set(knuth_bendix).
% 1.87/2.07 dependent: set(anl_eq).
% 1.87/2.07 dependent: set(para_from).
% 1.87/2.07 dependent: set(para_into).
% 1.87/2.07 dependent: clear(para_from_right).
% 1.87/2.07 dependent: clear(para_into_right).
% 1.87/2.07 dependent: set(para_from_vars).
% 1.87/2.07 dependent: set(eq_units_both_ways).
% 1.87/2.07 dependent: set(dynamic_demod_all).
% 1.87/2.07 dependent: set(dynamic_demod).
% 1.87/2.07 dependent: set(order_eq).
% 1.87/2.07 dependent: set(back_demod).
% 1.87/2.07 dependent: set(lrpo).
% 1.87/2.07 dependent: set(hyper_res).
% 1.87/2.07 dependent: clear(order_hyper).
% 1.87/2.07
% 1.87/2.07 ------------> process usable:
% 1.87/2.07 ** KEPT (pick-wt=8): 1 [] -sum(A,B,C)|sum(B,A,C).
% 1.87/2.07 ** KEPT (pick-wt=8): 2 [] -product(A,B,C)|product(B,A,C).
% 1.87/2.07 ** KEPT (pick-wt=20): 3 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.87/2.07 ** KEPT (pick-wt=20): 4 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 1.87/2.07 ** KEPT (pick-wt=20): 5 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 1.87/2.07 ** KEPT (pick-wt=20): 6 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 1.87/2.07 ** KEPT (pick-wt=20): 7 [] -sum(A,B,C)| -sum(A,D,E)| -product(B,D,F)| -sum(A,F,G)|product(C,E,G).
% 1.87/2.07 ** KEPT (pick-wt=20): 8 [] -sum(A,B,C)| -sum(A,D,E)| -product(B,D,F)| -product(C,E,G)|sum(A,F,G).
% 3.04/3.20 ** KEPT (pick-wt=20): 9 [] -sum(A,B,C)| -sum(D,B,E)| -product(A,D,F)| -sum(F,B,G)|product(C,E,G).
% 3.04/3.20 ** KEPT (pick-wt=20): 10 [] -sum(A,B,C)| -sum(D,B,E)| -product(A,D,F)| -product(C,E,G)|sum(F,B,G).
% 3.04/3.20 ** KEPT (pick-wt=11): 11 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 3.04/3.20 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 3.04/3.20 ** KEPT (pick-wt=8): 13 [] -product(A,B,C)|sum(A,C,A).
% 3.04/3.20 ** KEPT (pick-wt=8): 14 [] -sum(A,B,C)|product(A,C,A).
% 3.04/3.20 ** KEPT (pick-wt=16): 15 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 3.04/3.20 Following clause subsumed by 15 during input processing: 0 [] -sum(A,B,C)| -sum(B,D,E)|sum(C,D,F)| -sum(A,E,F).
% 3.04/3.20 ** KEPT (pick-wt=16): 16 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 3.04/3.20 Following clause subsumed by 16 during input processing: 0 [] -product(A,B,C)| -product(B,D,E)|product(C,D,F)| -product(A,E,F).
% 3.04/3.20 ** KEPT (pick-wt=5): 17 [] inverse(inverse(x))!=x.
% 3.04/3.20
% 3.04/3.20 ------------> process sos:
% 3.04/3.20 ** KEPT (pick-wt=3): 18 [] A=A.
% 3.04/3.20 ** KEPT (pick-wt=6): 19 [] sum(A,B,add(A,B)).
% 3.04/3.20 ** KEPT (pick-wt=6): 20 [] product(A,B,multiply(A,B)).
% 3.04/3.20 ** KEPT (pick-wt=4): 21 [] sum(additive_identity,A,A).
% 3.04/3.20 ** KEPT (pick-wt=4): 22 [] sum(A,additive_identity,A).
% 3.04/3.20 ** KEPT (pick-wt=4): 23 [] product(multiplicative_identity,A,A).
% 3.04/3.20 ** KEPT (pick-wt=4): 24 [] product(A,multiplicative_identity,A).
% 3.04/3.20 ** KEPT (pick-wt=5): 25 [] sum(inverse(A),A,multiplicative_identity).
% 3.04/3.20 ** KEPT (pick-wt=5): 26 [] sum(A,inverse(A),multiplicative_identity).
% 3.04/3.20 ** KEPT (pick-wt=5): 27 [] product(inverse(A),A,additive_identity).
% 3.04/3.20 ** KEPT (pick-wt=5): 28 [] product(A,inverse(A),additive_identity).
% 3.04/3.20 ** KEPT (pick-wt=4): 29 [] sum(A,A,A).
% 3.04/3.20 ** KEPT (pick-wt=4): 30 [] product(A,A,A).
% 3.04/3.20 ** KEPT (pick-wt=4): 31 [] sum(A,multiplicative_identity,multiplicative_identity).
% 3.04/3.20 ** KEPT (pick-wt=4): 32 [] product(A,additive_identity,additive_identity).
% 3.04/3.20 ** KEPT (pick-wt=6): 33 [] sum(A,multiply(A,B),A).
% 3.04/3.20 ** KEPT (pick-wt=6): 34 [] product(A,add(A,B),A).
% 3.04/3.20 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 3.04/3.20
% 3.04/3.20 ======= end of input processing =======
% 3.04/3.20
% 3.04/3.20 =========== start of search ===========
% 3.04/3.20
% 3.04/3.20
% 3.04/3.20 Resetting weight limit to 9.
% 3.04/3.20
% 3.04/3.20
% 3.04/3.20 Resetting weight limit to 9.
% 3.04/3.20
% 3.04/3.20 sos_size=1890
% 3.04/3.20
% 3.04/3.20 -------- PROOF --------
% 3.04/3.20
% 3.04/3.20 ----> UNIT CONFLICT at 1.13 sec ----> 2551 [binary,2549.1,17.1] $F.
% 3.04/3.20
% 3.04/3.20 Length of proof is 8. Level of proof is 4.
% 3.04/3.20
% 3.04/3.20 ---------------- PROOF ----------------
% 3.04/3.20 % SZS status Unsatisfiable
% 3.04/3.20 % SZS output start Refutation
% See solution above
% 3.04/3.20 ------------ end of proof -------------
% 3.04/3.20
% 3.04/3.20
% 3.04/3.20 Search stopped by max_proofs option.
% 3.04/3.20
% 3.04/3.20
% 3.04/3.20 Search stopped by max_proofs option.
% 3.04/3.20
% 3.04/3.20 ============ end of search ============
% 3.04/3.20
% 3.04/3.20 -------------- statistics -------------
% 3.04/3.20 clauses given 94
% 3.04/3.20 clauses generated 307693
% 3.04/3.20 clauses kept 2491
% 3.04/3.20 clauses forward subsumed 241798
% 3.04/3.20 clauses back subsumed 59
% 3.04/3.20 Kbytes malloced 4882
% 3.04/3.20
% 3.04/3.20 ----------- times (seconds) -----------
% 3.04/3.20 user CPU time 1.13 (0 hr, 0 min, 1 sec)
% 3.04/3.20 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.04/3.20 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.04/3.20
% 3.04/3.20 That finishes the proof of the theorem.
% 3.04/3.20
% 3.04/3.20 Process 32638 finished Wed Jul 27 02:33:58 2022
% 3.04/3.21 Otter interrupted
% 3.04/3.21 PROOF FOUND
%------------------------------------------------------------------------------