%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:47:33 EDT 2022
% Result : Unsatisfiable 1.68s 1.85s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 5 unt; 0 nHn; 4 RR)
% Number of literals : 8 ( 3 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(11,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| C = D ),
file('BOO011-1.p',unknown),
[] ).
cnf(13,axiom,
inverse(additive_identity) != multiplicative_identity,
file('BOO011-1.p',unknown),
[] ).
cnf(18,axiom,
sum(A,additive_identity,A),
file('BOO011-1.p',unknown),
[] ).
cnf(21,axiom,
sum(inverse(A),A,multiplicative_identity),
file('BOO011-1.p',unknown),
[] ).
cnf(54,plain,
inverse(additive_identity) = multiplicative_identity,
inference(hyper,[status(thm)],[21,11,18]),
[iquote('hyper,21,11,18')] ).
cnf(56,plain,
$false,
inference(binary,[status(thm)],[54,13]),
[iquote('binary,54.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.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 02:34:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.68/1.85 ----- Otter 3.3f, August 2004 -----
% 1.68/1.85 The process was started by sandbox on n019.cluster.edu,
% 1.68/1.85 Wed Jul 27 02:34:52 2022
% 1.68/1.85 The command was "./otter". The process ID is 15711.
% 1.68/1.85
% 1.68/1.85 set(prolog_style_variables).
% 1.68/1.85 set(auto).
% 1.68/1.85 dependent: set(auto1).
% 1.68/1.85 dependent: set(process_input).
% 1.68/1.85 dependent: clear(print_kept).
% 1.68/1.85 dependent: clear(print_new_demod).
% 1.68/1.85 dependent: clear(print_back_demod).
% 1.68/1.85 dependent: clear(print_back_sub).
% 1.68/1.85 dependent: set(control_memory).
% 1.68/1.85 dependent: assign(max_mem, 12000).
% 1.68/1.85 dependent: assign(pick_given_ratio, 4).
% 1.68/1.85 dependent: assign(stats_level, 1).
% 1.68/1.85 dependent: assign(max_seconds, 10800).
% 1.68/1.85 clear(print_given).
% 1.68/1.85
% 1.68/1.85 list(usable).
% 1.68/1.85 0 [] A=A.
% 1.68/1.85 0 [] sum(X,Y,add(X,Y)).
% 1.68/1.85 0 [] product(X,Y,multiply(X,Y)).
% 1.68/1.85 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.68/1.85 0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.68/1.85 0 [] sum(additive_identity,X,X).
% 1.68/1.85 0 [] sum(X,additive_identity,X).
% 1.68/1.85 0 [] product(multiplicative_identity,X,X).
% 1.68/1.85 0 [] product(X,multiplicative_identity,X).
% 1.68/1.85 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.68/1.85 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.68/1.85 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.68/1.85 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.68/1.85 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -sum(X,V3,V4)|product(V1,V2,V4).
% 1.68/1.85 0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(X,V3,V4).
% 1.68/1.85 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -sum(V3,X,V4)|product(V1,V2,V4).
% 1.68/1.85 0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(V3,X,V4).
% 1.68/1.85 0 [] sum(inverse(X),X,multiplicative_identity).
% 1.68/1.85 0 [] sum(X,inverse(X),multiplicative_identity).
% 1.68/1.85 0 [] product(inverse(X),X,additive_identity).
% 1.68/1.85 0 [] product(X,inverse(X),additive_identity).
% 1.68/1.85 0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.68/1.85 0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.68/1.85 0 [] inverse(additive_identity)!=multiplicative_identity.
% 1.68/1.85 end_of_list.
% 1.68/1.85
% 1.68/1.85 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.68/1.85
% 1.68/1.85 This is a Horn set with equality. The strategy will be
% 1.68/1.85 Knuth-Bendix and hyper_res, with positive clauses in
% 1.68/1.85 sos and nonpositive clauses in usable.
% 1.68/1.85
% 1.68/1.85 dependent: set(knuth_bendix).
% 1.68/1.85 dependent: set(anl_eq).
% 1.68/1.85 dependent: set(para_from).
% 1.68/1.85 dependent: set(para_into).
% 1.68/1.85 dependent: clear(para_from_right).
% 1.68/1.85 dependent: clear(para_into_right).
% 1.68/1.85 dependent: set(para_from_vars).
% 1.68/1.85 dependent: set(eq_units_both_ways).
% 1.68/1.85 dependent: set(dynamic_demod_all).
% 1.68/1.85 dependent: set(dynamic_demod).
% 1.68/1.85 dependent: set(order_eq).
% 1.68/1.85 dependent: set(back_demod).
% 1.68/1.85 dependent: set(lrpo).
% 1.68/1.85 dependent: set(hyper_res).
% 1.68/1.85 dependent: clear(order_hyper).
% 1.68/1.85
% 1.68/1.85 ------------> process usable:
% 1.68/1.85 ** KEPT (pick-wt=8): 1 [] -sum(A,B,C)|sum(B,A,C).
% 1.68/1.85 ** KEPT (pick-wt=8): 2 [] -product(A,B,C)|product(B,A,C).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** 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).
% 1.68/1.85 ** KEPT (pick-wt=11): 11 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.68/1.85 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.68/1.85 ** KEPT (pick-wt=4): 13 [] inverse(additive_identity)!=multiplicative_identity.
% 1.68/1.85
% 1.68/1.85 ------------> process sos:
% 1.68/1.85 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.68/1.85 ** KEPT (pick-wt=6): 15 [] sum(A,B,add(A,B)).
% 1.68/1.85 ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.68/1.85 ** KEPT (pick-wt=4): 17 [] sum(additive_identity,A,A).
% 1.68/1.85 ** KEPT (pick-wt=4): 18 [] sum(A,additive_identity,A).
% 1.68/1.85 ** KEPT (pick-wt=4): 19 [] product(multiplicative_identity,A,A).
% 1.68/1.85 ** KEPT (pick-wt=4): 20 [] product(A,multiplicative_identity,A).
% 1.68/1.85 ** KEPT (pick-wt=5): 21 [] sum(inverse(A),A,multiplicative_identity).
% 1.68/1.85 ** KEPT (pick-wt=5): 22 [] sum(A,inverse(A),multiplicative_identity).
% 1.68/1.85 ** KEPT (pick-wt=5): 23 [] product(inverse(A),A,additive_identity).
% 1.68/1.85 ** KEPT (pick-wt=5): 24 [] product(A,inverse(A),additive_identity).
% 1.68/1.85 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.68/1.85
% 1.68/1.85 ======= end of input processing =======
% 1.68/1.85
% 1.68/1.85 =========== start of search ===========
% 1.68/1.85
% 1.68/1.85 -------- PROOF --------
% 1.68/1.85
% 1.68/1.85 ----> UNIT CONFLICT at 0.00 sec ----> 56 [binary,54.1,13.1] $F.
% 1.68/1.85
% 1.68/1.85 Length of proof is 1. Level of proof is 1.
% 1.68/1.85
% 1.68/1.85 ---------------- PROOF ----------------
% 1.68/1.85 % SZS status Unsatisfiable
% 1.68/1.85 % SZS output start Refutation
% See solution above
% 1.68/1.85 ------------ end of proof -------------
% 1.68/1.85
% 1.68/1.85
% 1.68/1.85 Search stopped by max_proofs option.
% 1.68/1.85
% 1.68/1.85
% 1.68/1.85 Search stopped by max_proofs option.
% 1.68/1.85
% 1.68/1.85 ============ end of search ============
% 1.68/1.85
% 1.68/1.85 -------------- statistics -------------
% 1.68/1.85 clauses given 7
% 1.68/1.85 clauses generated 261
% 1.68/1.85 clauses kept 52
% 1.68/1.85 clauses forward subsumed 234
% 1.68/1.85 clauses back subsumed 0
% 1.68/1.85 Kbytes malloced 976
% 1.68/1.85
% 1.68/1.85 ----------- times (seconds) -----------
% 1.68/1.85 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.85 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.85 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.85
% 1.68/1.85 That finishes the proof of the theorem.
% 1.68/1.85
% 1.68/1.85 Process 15711 finished Wed Jul 27 02:34:53 2022
% 1.68/1.85 Otter interrupted
% 1.68/1.85 PROOF FOUND
%------------------------------------------------------------------------------