%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG004-3 : 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 13:12:01 EDT 2022
% Result : Unsatisfiable 3.63s 3.83s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 13
% Syntax : Number of clauses : 18 ( 14 unt; 0 nHn; 12 RR)
% Number of literals : 31 ( 0 equ; 14 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('RNG004-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ product(A,F,G)
| sum(C,E,G) ),
file('RNG004-3.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ sum(A,D,F)
| ~ product(F,B,G)
| sum(C,E,G) ),
file('RNG004-3.p',unknown),
[] ).
cnf(21,axiom,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| e_qualish(C,D) ),
file('RNG004-3.p',unknown),
[] ).
cnf(23,axiom,
~ e_qualish(c,d),
file('RNG004-3.p',unknown),
[] ).
cnf(25,axiom,
sum(additive_identity,A,A),
file('RNG004-3.p',unknown),
[] ).
cnf(26,axiom,
sum(A,additive_identity,A),
file('RNG004-3.p',unknown),
[] ).
cnf(27,axiom,
product(A,B,multiply(A,B)),
file('RNG004-3.p',unknown),
[] ).
cnf(30,axiom,
sum(A,additive_inverse(A),additive_identity),
file('RNG004-3.p',unknown),
[] ).
cnf(31,axiom,
product(additive_identity,A,additive_identity),
file('RNG004-3.p',unknown),
[] ).
cnf(32,axiom,
product(A,additive_identity,additive_identity),
file('RNG004-3.p',unknown),
[] ).
cnf(33,axiom,
product(a,b,c),
file('RNG004-3.p',unknown),
[] ).
cnf(34,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('RNG004-3.p',unknown),
[] ).
cnf(302,plain,
sum(c,multiply(a,additive_inverse(b)),additive_identity),
inference(hyper,[status(thm)],[30,17,33,27,32]),
[iquote('hyper,30,17,33,27,32')] ).
cnf(401,plain,
sum(multiply(a,additive_inverse(b)),d,additive_identity),
inference(hyper,[status(thm)],[34,19,27,30,31]),
[iquote('hyper,34,19,27,30,31')] ).
cnf(5955,plain,
sum(additive_identity,d,c),
inference(hyper,[status(thm)],[401,13,302,26]),
[iquote('hyper,401,13,302,26')] ).
cnf(5971,plain,
e_qualish(c,d),
inference(hyper,[status(thm)],[5955,21,25]),
[iquote('hyper,5955,21,25')] ).
cnf(5972,plain,
$false,
inference(binary,[status(thm)],[5971,23]),
[iquote('binary,5971.1,23.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 02:17:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.67/1.87 ----- Otter 3.3f, August 2004 -----
% 1.67/1.87 The process was started by sandbox on n019.cluster.edu,
% 1.67/1.87 Wed Jul 27 02:17:37 2022
% 1.67/1.87 The command was "./otter". The process ID is 15319.
% 1.67/1.87
% 1.67/1.87 set(prolog_style_variables).
% 1.67/1.87 set(auto).
% 1.67/1.87 dependent: set(auto1).
% 1.67/1.87 dependent: set(process_input).
% 1.67/1.87 dependent: clear(print_kept).
% 1.67/1.87 dependent: clear(print_new_demod).
% 1.67/1.87 dependent: clear(print_back_demod).
% 1.67/1.87 dependent: clear(print_back_sub).
% 1.67/1.87 dependent: set(control_memory).
% 1.67/1.87 dependent: assign(max_mem, 12000).
% 1.67/1.87 dependent: assign(pick_given_ratio, 4).
% 1.67/1.87 dependent: assign(stats_level, 1).
% 1.67/1.87 dependent: assign(max_seconds, 10800).
% 1.67/1.87 clear(print_given).
% 1.67/1.87
% 1.67/1.87 list(usable).
% 1.67/1.87 0 [] e_qualish(X,X).
% 1.67/1.87 0 [] -e_qualish(X,Y)|e_qualish(Y,X).
% 1.67/1.87 0 [] -e_qualish(X,Y)| -e_qualish(Y,Z)|e_qualish(X,Z).
% 1.67/1.87 0 [] -e_qualish(X,Y)|e_qualish(additive_inverse(X),additive_inverse(Y)).
% 1.67/1.87 0 [] -e_qualish(X,Y)|e_qualish(add(X,W),add(Y,W)).
% 1.67/1.87 0 [] -e_qualish(X,Y)| -sum(X,W,Z)|sum(Y,W,Z).
% 1.67/1.87 0 [] -e_qualish(X,Y)| -sum(W,X,Z)|sum(W,Y,Z).
% 1.67/1.87 0 [] -e_qualish(X,Y)| -sum(W,Z,X)|sum(W,Z,Y).
% 1.67/1.87 0 [] -e_qualish(X,Y)|e_qualish(multiply(X,W),multiply(Y,W)).
% 1.67/1.87 0 [] -e_qualish(X,Y)| -product(X,W,Z)|product(Y,W,Z).
% 1.67/1.87 0 [] -e_qualish(X,Y)| -product(W,X,Z)|product(W,Y,Z).
% 1.67/1.87 0 [] -e_qualish(X,Y)| -product(W,Z,X)|product(W,Z,Y).
% 1.67/1.87 0 [] sum(additive_identity,X,X).
% 1.67/1.87 0 [] sum(X,additive_identity,X).
% 1.67/1.87 0 [] product(X,Y,multiply(X,Y)).
% 1.67/1.87 0 [] sum(X,Y,add(X,Y)).
% 1.67/1.87 0 [] sum(additive_inverse(X),X,additive_identity).
% 1.67/1.87 0 [] sum(X,additive_inverse(X),additive_identity).
% 1.67/1.87 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.67/1.87 0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.67/1.87 0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.67/1.87 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.67/1.87 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.67/1.87 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.67/1.87 0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.67/1.87 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.67/1.87 0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.67/1.87 0 [] -sum(X,Y,U)| -sum(X,Y,V)|e_qualish(U,V).
% 1.67/1.87 0 [] -product(X,Y,U)| -product(X,Y,V)|e_qualish(U,V).
% 1.67/1.87 0 [] product(additive_identity,X,additive_identity).
% 1.67/1.87 0 [] product(X,additive_identity,additive_identity).
% 1.67/1.87 0 [] product(a,b,c).
% 1.67/1.87 0 [] product(additive_inverse(a),additive_inverse(b),d).
% 1.67/1.87 0 [] -e_qualish(c,d).
% 1.67/1.87 end_of_list.
% 1.67/1.87
% 1.67/1.87 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=5.
% 1.67/1.87
% 1.67/1.87 This is a Horn set without equality. The strategy will
% 1.67/1.87 be hyperresolution, with satellites in sos and nuclei
% 1.67/1.87 in usable.
% 1.67/1.87
% 1.67/1.87 dependent: set(hyper_res).
% 1.67/1.87 dependent: clear(order_hyper).
% 1.67/1.87
% 1.67/1.87 ------------> process usable:
% 1.67/1.87 ** KEPT (pick-wt=6): 1 [] -e_qualish(A,B)|e_qualish(B,A).
% 1.67/1.87 ** KEPT (pick-wt=9): 2 [] -e_qualish(A,B)| -e_qualish(B,C)|e_qualish(A,C).
% 1.67/1.87 ** KEPT (pick-wt=8): 3 [] -e_qualish(A,B)|e_qualish(additive_inverse(A),additive_inverse(B)).
% 1.67/1.87 ** KEPT (pick-wt=10): 4 [] -e_qualish(A,B)|e_qualish(add(A,C),add(B,C)).
% 1.67/1.87 ** KEPT (pick-wt=11): 5 [] -e_qualish(A,B)| -sum(A,C,D)|sum(B,C,D).
% 1.67/1.87 ** KEPT (pick-wt=11): 6 [] -e_qualish(A,B)| -sum(C,A,D)|sum(C,B,D).
% 1.67/1.87 ** KEPT (pick-wt=11): 7 [] -e_qualish(A,B)| -sum(C,D,A)|sum(C,D,B).
% 1.67/1.87 ** KEPT (pick-wt=10): 8 [] -e_qualish(A,B)|e_qualish(multiply(A,C),multiply(B,C)).
% 1.67/1.87 ** KEPT (pick-wt=11): 9 [] -e_qualish(A,B)| -product(A,C,D)|product(B,C,D).
% 1.67/1.87 ** KEPT (pick-wt=11): 10 [] -e_qualish(A,B)| -product(C,A,D)|product(C,B,D).
% 1.67/1.87 ** KEPT (pick-wt=11): 11 [] -e_qualish(A,B)| -product(C,D,A)|product(C,D,B).
% 1.67/1.87 ** KEPT (pick-wt=16): 12 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.67/1.87 ** KEPT (pick-wt=16): 13 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.67/1.87 ** KEPT (pick-wt=8): 14 [] -sum(A,B,C)|sum(B,A,C).
% 1.67/1.87 ** KEPT (pick-wt=16): 15 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.67/1.87 ** KEPT (pick-wt=16): 16 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.67/1.87 ** KEPT (pick-wt=20): 17 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.67/1.87 ** KEPT (pick-wt=20): 18 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 3.63/3.83 ** KEPT (pick-wt=20): 19 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 3.63/3.83 ** KEPT (pick-wt=20): 20 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 3.63/3.83 ** KEPT (pick-wt=11): 21 [] -sum(A,B,C)| -sum(A,B,D)|e_qualish(C,D).
% 3.63/3.83 ** KEPT (pick-wt=11): 22 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 3.63/3.83 ** KEPT (pick-wt=3): 23 [] -e_qualish(c,d).
% 3.63/3.83
% 3.63/3.83 ------------> process sos:
% 3.63/3.83 ** KEPT (pick-wt=3): 24 [] e_qualish(A,A).
% 3.63/3.83 ** KEPT (pick-wt=4): 25 [] sum(additive_identity,A,A).
% 3.63/3.83 ** KEPT (pick-wt=4): 26 [] sum(A,additive_identity,A).
% 3.63/3.83 ** KEPT (pick-wt=6): 27 [] product(A,B,multiply(A,B)).
% 3.63/3.83 ** KEPT (pick-wt=6): 28 [] sum(A,B,add(A,B)).
% 3.63/3.83 ** KEPT (pick-wt=5): 29 [] sum(additive_inverse(A),A,additive_identity).
% 3.63/3.83 ** KEPT (pick-wt=5): 30 [] sum(A,additive_inverse(A),additive_identity).
% 3.63/3.83 ** KEPT (pick-wt=4): 31 [] product(additive_identity,A,additive_identity).
% 3.63/3.83 ** KEPT (pick-wt=4): 32 [] product(A,additive_identity,additive_identity).
% 3.63/3.83 ** KEPT (pick-wt=4): 33 [] product(a,b,c).
% 3.63/3.83 ** KEPT (pick-wt=6): 34 [] product(additive_inverse(a),additive_inverse(b),d).
% 3.63/3.83
% 3.63/3.83 ======= end of input processing =======
% 3.63/3.83
% 3.63/3.83 =========== start of search ===========
% 3.63/3.83
% 3.63/3.83
% 3.63/3.83 Resetting weight limit to 7.
% 3.63/3.83
% 3.63/3.83
% 3.63/3.83 Resetting weight limit to 7.
% 3.63/3.83
% 3.63/3.83 sos_size=4191
% 3.63/3.83
% 3.63/3.83 -------- PROOF --------
% 3.63/3.83
% 3.63/3.83 ----> UNIT CONFLICT at 1.95 sec ----> 5972 [binary,5971.1,23.1] $F.
% 3.63/3.83
% 3.63/3.83 Length of proof is 4. Level of proof is 3.
% 3.63/3.83
% 3.63/3.83 ---------------- PROOF ----------------
% 3.63/3.83 % SZS status Unsatisfiable
% 3.63/3.83 % SZS output start Refutation
% See solution above
% 3.63/3.83 ------------ end of proof -------------
% 3.63/3.83
% 3.63/3.83
% 3.63/3.83 Search stopped by max_proofs option.
% 3.63/3.83
% 3.63/3.83
% 3.63/3.83 Search stopped by max_proofs option.
% 3.63/3.83
% 3.63/3.83 ============ end of search ============
% 3.63/3.83
% 3.63/3.83 -------------- statistics -------------
% 3.63/3.83 clauses given 177
% 3.63/3.83 clauses generated 1266090
% 3.63/3.83 clauses kept 5971
% 3.63/3.83 clauses forward subsumed 289328
% 3.63/3.83 clauses back subsumed 1637
% 3.63/3.83 Kbytes malloced 4882
% 3.63/3.83
% 3.63/3.83 ----------- times (seconds) -----------
% 3.63/3.83 user CPU time 1.95 (0 hr, 0 min, 1 sec)
% 3.63/3.83 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.63/3.83 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.63/3.83
% 3.63/3.83 That finishes the proof of the theorem.
% 3.63/3.83
% 3.63/3.83 Process 15319 finished Wed Jul 27 02:17:40 2022
% 3.63/3.83 Otter interrupted
% 3.63/3.83 PROOF FOUND
%------------------------------------------------------------------------------