%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 2.27s 2.41s
% Output : Refutation 2.27s
% 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('BOO012-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| product(B,A,C) ),
file('BOO012-1.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('BOO012-1.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('BOO012-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('BOO012-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('BOO012-1.p',unknown),
[] ).
cnf(13,axiom,
inverse(inverse(x)) != x,
file('BOO012-1.p',unknown),
[] ).
cnf(15,axiom,
sum(A,B,add(A,B)),
file('BOO012-1.p',unknown),
[] ).
cnf(16,axiom,
product(A,B,multiply(A,B)),
file('BOO012-1.p',unknown),
[] ).
cnf(18,axiom,
sum(A,additive_identity,A),
file('BOO012-1.p',unknown),
[] ).
cnf(19,axiom,
product(multiplicative_identity,A,A),
file('BOO012-1.p',unknown),
[] ).
cnf(20,axiom,
product(A,multiplicative_identity,A),
file('BOO012-1.p',unknown),
[] ).
cnf(21,axiom,
sum(inverse(A),A,multiplicative_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(22,axiom,
sum(A,inverse(A),multiplicative_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(23,axiom,
product(inverse(A),A,additive_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(24,axiom,
product(A,inverse(A),additive_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(34,plain,
add(A,additive_identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[15,11,18])]),
[iquote('hyper,15,11,18,flip.1')] ).
cnf(51,plain,
sum(A,B,add(B,A)),
inference(hyper,[status(thm)],[15,1]),
[iquote('hyper,15,1')] ).
cnf(84,plain,
sum(additive_identity,A,add(inverse(inverse(A)),A)),
inference(hyper,[status(thm)],[23,10,15,21,20]),
[iquote('hyper,23,10,15,21,20')] ).
cnf(114,plain,
multiply(multiplicative_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,12,19])]),
[iquote('hyper,16,12,19,flip.1')] ).
cnf(278,plain,
product(A,B,multiply(B,A)),
inference(hyper,[status(thm)],[16,2]),
[iquote('hyper,16,2')] ).
cnf(2631,plain,
add(inverse(inverse(A)),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[84,11,51]),34])]),
[iquote('hyper,84,11,51,demod,34,flip.1')] ).
cnf(2632,plain,
product(A,multiplicative_identity,inverse(inverse(A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[84,9,51,22,24]),2631,2631]),
[iquote('hyper,84,9,51,22,24,demod,2631,2631')] ).
cnf(2636,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2632,12,278]),114])]),
[iquote('hyper,2632,12,278,demod,114,flip.1')] ).
cnf(2638,plain,
$false,
inference(binary,[status(thm)],[2636,13]),
[iquote('binary,2636.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n021.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 02:27:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.81/1.98 ----- Otter 3.3f, August 2004 -----
% 1.81/1.98 The process was started by sandbox on n021.cluster.edu,
% 1.81/1.98 Wed Jul 27 02:27:23 2022
% 1.81/1.98 The command was "./otter". The process ID is 14134.
% 1.81/1.98
% 1.81/1.98 set(prolog_style_variables).
% 1.81/1.98 set(auto).
% 1.81/1.98 dependent: set(auto1).
% 1.81/1.98 dependent: set(process_input).
% 1.81/1.98 dependent: clear(print_kept).
% 1.81/1.98 dependent: clear(print_new_demod).
% 1.81/1.98 dependent: clear(print_back_demod).
% 1.81/1.98 dependent: clear(print_back_sub).
% 1.81/1.98 dependent: set(control_memory).
% 1.81/1.98 dependent: assign(max_mem, 12000).
% 1.81/1.98 dependent: assign(pick_given_ratio, 4).
% 1.81/1.98 dependent: assign(stats_level, 1).
% 1.81/1.98 dependent: assign(max_seconds, 10800).
% 1.81/1.98 clear(print_given).
% 1.81/1.98
% 1.81/1.98 list(usable).
% 1.81/1.98 0 [] A=A.
% 1.81/1.98 0 [] sum(X,Y,add(X,Y)).
% 1.81/1.98 0 [] product(X,Y,multiply(X,Y)).
% 1.81/1.98 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.81/1.98 0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.81/1.98 0 [] sum(additive_identity,X,X).
% 1.81/1.98 0 [] sum(X,additive_identity,X).
% 1.81/1.98 0 [] product(multiplicative_identity,X,X).
% 1.81/1.98 0 [] product(X,multiplicative_identity,X).
% 1.81/1.98 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.81/1.98 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.81/1.98 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.81/1.98 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.81/1.98 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -sum(X,V3,V4)|product(V1,V2,V4).
% 1.81/1.98 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(X,V3,V4).
% 1.81/1.98 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -sum(V3,X,V4)|product(V1,V2,V4).
% 1.81/1.98 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(V3,X,V4).
% 1.81/1.98 0 [] sum(inverse(X),X,multiplicative_identity).
% 1.81/1.98 0 [] sum(X,inverse(X),multiplicative_identity).
% 1.81/1.98 0 [] product(inverse(X),X,additive_identity).
% 1.81/1.98 0 [] product(X,inverse(X),additive_identity).
% 1.81/1.98 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.81/1.98 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.81/1.98 0 [] inverse(inverse(x))!=x.
% 1.81/1.98 end_of_list.
% 1.81/1.98
% 1.81/1.98 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.81/1.98
% 1.81/1.98 This is a Horn set with equality. The strategy will be
% 1.81/1.98 Knuth-Bendix and hyper_res, with positive clauses in
% 1.81/1.98 sos and nonpositive clauses in usable.
% 1.81/1.98
% 1.81/1.98 dependent: set(knuth_bendix).
% 1.81/1.98 dependent: set(anl_eq).
% 1.81/1.98 dependent: set(para_from).
% 1.81/1.98 dependent: set(para_into).
% 1.81/1.98 dependent: clear(para_from_right).
% 1.81/1.98 dependent: clear(para_into_right).
% 1.81/1.98 dependent: set(para_from_vars).
% 1.81/1.98 dependent: set(eq_units_both_ways).
% 1.81/1.98 dependent: set(dynamic_demod_all).
% 1.81/1.98 dependent: set(dynamic_demod).
% 1.81/1.98 dependent: set(order_eq).
% 1.81/1.98 dependent: set(back_demod).
% 1.81/1.98 dependent: set(lrpo).
% 1.81/1.98 dependent: set(hyper_res).
% 1.81/1.98 dependent: clear(order_hyper).
% 1.81/1.98
% 1.81/1.98 ------------> process usable:
% 1.81/1.98 ** KEPT (pick-wt=8): 1 [] -sum(A,B,C)|sum(B,A,C).
% 1.81/1.98 ** KEPT (pick-wt=8): 2 [] -product(A,B,C)|product(B,A,C).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** 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).
% 1.81/1.98 ** KEPT (pick-wt=11): 11 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.81/1.98 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.81/1.98 ** KEPT (pick-wt=5): 13 [] inverse(inverse(x))!=x.
% 1.81/1.98
% 1.81/1.98 ------------> process sos:
% 1.81/1.98 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.81/1.98 ** KEPT (pick-wt=6): 15 [] sum(A,B,add(A,B)).
% 1.81/1.98 ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.81/1.98 ** KEPT (pick-wt=4): 17 [] sum(additive_identity,A,A).
% 1.81/1.98 ** KEPT (pick-wt=4): 18 [] sum(A,additive_identity,A).
% 1.81/1.98 ** KEPT (pick-wt=4): 19 [] product(multiplicative_identity,A,A).
% 1.81/1.98 ** KEPT (pick-wt=4): 20 [] product(A,multiplicative_identity,A).
% 2.27/2.41 ** KEPT (pick-wt=5): 21 [] sum(inverse(A),A,multiplicative_identity).
% 2.27/2.41 ** KEPT (pick-wt=5): 22 [] sum(A,inverse(A),multiplicative_identity).
% 2.27/2.41 ** KEPT (pick-wt=5): 23 [] product(inverse(A),A,additive_identity).
% 2.27/2.41 ** KEPT (pick-wt=5): 24 [] product(A,inverse(A),additive_identity).
% 2.27/2.41 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 2.27/2.41
% 2.27/2.41 ======= end of input processing =======
% 2.27/2.41
% 2.27/2.41 =========== start of search ===========
% 2.27/2.41
% 2.27/2.41 -------- PROOF --------
% 2.27/2.41
% 2.27/2.41 ----> UNIT CONFLICT at 0.42 sec ----> 2638 [binary,2636.1,13.1] $F.
% 2.27/2.41
% 2.27/2.41 Length of proof is 8. Level of proof is 4.
% 2.27/2.41
% 2.27/2.41 ---------------- PROOF ----------------
% 2.27/2.41 % SZS status Unsatisfiable
% 2.27/2.41 % SZS output start Refutation
% See solution above
% 2.27/2.41 ------------ end of proof -------------
% 2.27/2.41
% 2.27/2.41
% 2.27/2.41 Search stopped by max_proofs option.
% 2.27/2.41
% 2.27/2.41
% 2.27/2.41 Search stopped by max_proofs option.
% 2.27/2.41
% 2.27/2.41 ============ end of search ============
% 2.27/2.41
% 2.27/2.41 -------------- statistics -------------
% 2.27/2.41 clauses given 73
% 2.27/2.41 clauses generated 74539
% 2.27/2.41 clauses kept 2597
% 2.27/2.41 clauses forward subsumed 73021
% 2.27/2.41 clauses back subsumed 137
% 2.27/2.41 Kbytes malloced 3906
% 2.27/2.41
% 2.27/2.41 ----------- times (seconds) -----------
% 2.27/2.41 user CPU time 0.42 (0 hr, 0 min, 0 sec)
% 2.27/2.41 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.27/2.41 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.27/2.41
% 2.27/2.41 That finishes the proof of the theorem.
% 2.27/2.41
% 2.27/2.41 Process 14134 finished Wed Jul 27 02:27:25 2022
% 2.27/2.41 Otter interrupted
% 2.27/2.41 PROOF FOUND
%------------------------------------------------------------------------------