TSTP Solution File: HEN011-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN011-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 12:58:00 EDT 2022
% Result : Unsatisfiable 2.83s 3.09s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of clauses : 26 ( 20 unt; 0 nHn; 24 RR)
% Number of literals : 42 ( 7 equ; 18 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 29 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ quotient(A,B,C)
| less_e_qual(C,A) ),
file('HEN011-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ quotient(A,B,C)
| ~ quotient(B,D,E)
| ~ quotient(A,D,F)
| ~ quotient(F,E,G)
| ~ quotient(C,D,H)
| less_e_qual(G,H) ),
file('HEN011-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN011-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,C)
| less_e_qual(A,C) ),
file('HEN011-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ quotient(A,B,C)
| ~ less_e_qual(C,D)
| ~ quotient(A,D,E)
| less_e_qual(E,B) ),
file('HEN011-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ quotient(identity,A,B)
| ~ quotient(identity,B,C)
| ~ quotient(identity,C,D)
| B = D ),
file('HEN011-2.p',unknown),
[] ).
cnf(13,axiom,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('HEN011-2.p',unknown),
[] ).
cnf(14,plain,
idQb_Q__idQ_idQa != idQa_Q__idQ_idQb,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(18,axiom,
quotient(A,B,divide(A,B)),
file('HEN011-2.p',unknown),
[] ).
cnf(23,axiom,
quotient(identity,a,idQa),
file('HEN011-2.p',unknown),
[] ).
cnf(24,axiom,
quotient(identity,b,idQb),
file('HEN011-2.p',unknown),
[] ).
cnf(25,axiom,
quotient(identity,idQb,idQ_idQb),
file('HEN011-2.p',unknown),
[] ).
cnf(26,axiom,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('HEN011-2.p',unknown),
[] ).
cnf(27,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN011-2.p',unknown),
[] ).
cnf(28,axiom,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('HEN011-2.p',unknown),
[] ).
cnf(75,plain,
less_e_qual(divide(A,B),A),
inference(hyper,[status(thm)],[18,3]),
[iquote('hyper,18,3')] ).
cnf(160,plain,
divide(identity,idQ_idQb) = idQb,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,11,24,18])]),
[iquote('hyper,25,11,24,18,flip.1')] ).
cnf(242,plain,
divide(identity,idQ_idQa) = idQa,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[27,11,23,18])]),
[iquote('hyper,27,11,23,18,flip.1')] ).
cnf(253,plain,
less_e_qual(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[27,4,26,18,18,18]),160]),
[iquote('hyper,27,4,26,18,18,18,demod,160')] ).
cnf(309,plain,
less_e_qual(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[28,4,25,18,18,18]),242]),
[iquote('hyper,28,4,25,18,18,18,demod,242')] ).
cnf(3742,plain,
less_e_qual(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa),
inference(hyper,[status(thm)],[253,7,75]),
[iquote('hyper,253,7,75')] ).
cnf(3802,plain,
less_e_qual(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
inference(hyper,[status(thm)],[3742,8,18,28]),
[iquote('hyper,3742,8,18,28')] ).
cnf(4350,plain,
less_e_qual(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),
inference(hyper,[status(thm)],[309,7,75]),
[iquote('hyper,309,7,75')] ).
cnf(4360,plain,
less_e_qual(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),
inference(hyper,[status(thm)],[4350,8,18,26]),
[iquote('hyper,4350,8,18,26')] ).
cnf(4376,plain,
idQb_Q__idQ_idQa = idQa_Q__idQ_idQb,
inference(hyper,[status(thm)],[4360,5,3802]),
[iquote('hyper,4360,5,3802')] ).
cnf(4378,plain,
$false,
inference(binary,[status(thm)],[4376,14]),
[iquote('binary,4376.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : HEN011-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 08:58:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.13 ----- Otter 3.3f, August 2004 -----
% 1.95/2.13 The process was started by sandbox2 on n006.cluster.edu,
% 1.95/2.13 Wed Jul 27 08:58:17 2022
% 1.95/2.13 The command was "./otter". The process ID is 3182.
% 1.95/2.13
% 1.95/2.13 set(prolog_style_variables).
% 1.95/2.13 set(auto).
% 1.95/2.13 dependent: set(auto1).
% 1.95/2.13 dependent: set(process_input).
% 1.95/2.13 dependent: clear(print_kept).
% 1.95/2.13 dependent: clear(print_new_demod).
% 1.95/2.13 dependent: clear(print_back_demod).
% 1.95/2.13 dependent: clear(print_back_sub).
% 1.95/2.13 dependent: set(control_memory).
% 1.95/2.13 dependent: assign(max_mem, 12000).
% 1.95/2.13 dependent: assign(pick_given_ratio, 4).
% 1.95/2.13 dependent: assign(stats_level, 1).
% 1.95/2.13 dependent: assign(max_seconds, 10800).
% 1.95/2.13 clear(print_given).
% 1.95/2.13
% 1.95/2.13 list(usable).
% 1.95/2.13 0 [] A=A.
% 1.95/2.13 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.95/2.13 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.95/2.13 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.95/2.13 0 [] -quotient(X,Y,V1)| -quotient(Y,Z,V2)| -quotient(X,Z,V3)| -quotient(V3,V2,V4)| -quotient(V1,Z,V5)|less_e_qual(V4,V5).
% 1.95/2.13 0 [] less_e_qual(zero,X).
% 1.95/2.13 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.95/2.13 0 [] less_e_qual(X,identity).
% 1.95/2.13 0 [] quotient(X,Y,divide(X,Y)).
% 1.95/2.13 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.95/2.13 0 [] quotient(X,identity,zero).
% 1.95/2.13 0 [] quotient(zero,X,zero).
% 1.95/2.13 0 [] quotient(X,X,zero).
% 1.95/2.13 0 [] quotient(X,zero,X).
% 1.95/2.13 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.95/2.13 0 [] -quotient(X,Y,W1)| -less_e_qual(W1,Z)| -quotient(X,Z,W2)|less_e_qual(W2,Y).
% 1.95/2.13 0 [] -less_e_qual(X,Y)| -quotient(Z,Y,W1)| -quotient(Z,X,W2)|less_e_qual(W1,W2).
% 1.95/2.13 0 [] -less_e_qual(X,Y)| -quotient(X,Z,W1)| -quotient(Y,Z,W2)|less_e_qual(W1,W2).
% 1.95/2.13 0 [] -quotient(identity,X,Y1)| -quotient(identity,Y1,Y2)| -quotient(identity,Y2,Y3)|Y1=Y3.
% 1.95/2.13 0 [] -quotient(identity,X,Y1)| -quotient(identity,Y1,Y2)| -quotient(Y1,Y2,Y3)|Y1=Y3.
% 1.95/2.13 0 [] quotient(identity,a,idQa).
% 1.95/2.13 0 [] quotient(identity,b,idQb).
% 1.95/2.13 0 [] quotient(identity,idQb,idQ_idQb).
% 1.95/2.13 0 [] quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb).
% 1.95/2.13 0 [] quotient(identity,idQa,idQ_idQa).
% 1.95/2.13 0 [] quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa).
% 1.95/2.13 0 [] idQa_Q__idQ_idQb!=idQb_Q__idQ_idQa.
% 1.95/2.13 end_of_list.
% 1.95/2.13
% 1.95/2.13 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.95/2.13
% 1.95/2.13 This is a Horn set with equality. The strategy will be
% 1.95/2.13 Knuth-Bendix and hyper_res, with positive clauses in
% 1.95/2.13 sos and nonpositive clauses in usable.
% 1.95/2.13
% 1.95/2.13 dependent: set(knuth_bendix).
% 1.95/2.13 dependent: set(anl_eq).
% 1.95/2.13 dependent: set(para_from).
% 1.95/2.13 dependent: set(para_into).
% 1.95/2.13 dependent: clear(para_from_right).
% 1.95/2.13 dependent: clear(para_into_right).
% 1.95/2.13 dependent: set(para_from_vars).
% 1.95/2.13 dependent: set(eq_units_both_ways).
% 1.95/2.13 dependent: set(dynamic_demod_all).
% 1.95/2.13 dependent: set(dynamic_demod).
% 1.95/2.13 dependent: set(order_eq).
% 1.95/2.13 dependent: set(back_demod).
% 1.95/2.13 dependent: set(lrpo).
% 1.95/2.13 dependent: set(hyper_res).
% 1.95/2.13 dependent: clear(order_hyper).
% 1.95/2.13
% 1.95/2.13 ------------> process usable:
% 1.95/2.13 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.95/2.13 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.95/2.13 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.95/2.13 ** KEPT (pick-wt=23): 4 [] -quotient(A,B,C)| -quotient(B,D,E)| -quotient(A,D,F)| -quotient(F,E,G)| -quotient(C,D,H)|less_e_qual(G,H).
% 1.95/2.13 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.95/2.13 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.95/2.13 ** KEPT (pick-wt=9): 7 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.95/2.13 ** KEPT (pick-wt=14): 8 [] -quotient(A,B,C)| -less_e_qual(C,D)| -quotient(A,D,E)|less_e_qual(E,B).
% 1.95/2.13 ** KEPT (pick-wt=14): 9 [] -less_e_qual(A,B)| -quotient(C,B,D)| -quotient(C,A,E)|less_e_qual(D,E).
% 1.95/2.13 ** KEPT (pick-wt=14): 10 [] -less_e_qual(A,B)| -quotient(A,C,D)| -quotient(B,C,E)|less_e_qual(D,E).
% 1.95/2.13 ** KEPT (pick-wt=15): 11 [] -quotient(identity,A,B)| -quotient(identity,B,C)| -quotient(identity,C,D)|B=D.
% 1.95/2.13 ** KEPT (pick-wt=15): 12 [] -quotient(identity,A,B)| -quotient(identity,B,C)| -quotient(B,C,D)|B=D.
% 1.95/2.13 ** KEPT (pick-wt=3): 14 [copy,13,flip.1] idQb_Q__idQ_idQa!=idQa_Q__idQ_idQb.
% 1.95/2.13
% 1.95/2.13 ------------> process sos:
% 1.95/2.13 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.95/2.13 ** KEPT (pick-wt=3): 16 [] less_e_qual(zero,A).
% 1.95/2.13 ** KEPT (pick-wt=3): 17 [] less_e_qual(A,identity).
% 1.95/2.13 ** KEPT (pick-wt=6): 18 [] quotient(A,B,divide(A,B)).
% 1.95/2.13 ** KEPT (pick-wt=4): 19 [] quotient(A,identity,zero).
% 1.95/2.13 ** KEPT (pick-wt=4): 20 [] quotient(zero,A,zero).
% 2.83/3.09 ** KEPT (pick-wt=4): 21 [] quotient(A,A,zero).
% 2.83/3.09 ** KEPT (pick-wt=4): 22 [] quotient(A,zero,A).
% 2.83/3.09 ** KEPT (pick-wt=4): 23 [] quotient(identity,a,idQa).
% 2.83/3.09 ** KEPT (pick-wt=4): 24 [] quotient(identity,b,idQb).
% 2.83/3.09 ** KEPT (pick-wt=4): 25 [] quotient(identity,idQb,idQ_idQb).
% 2.83/3.09 ** KEPT (pick-wt=4): 26 [] quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb).
% 2.83/3.09 ** KEPT (pick-wt=4): 27 [] quotient(identity,idQa,idQ_idQa).
% 2.83/3.09 ** KEPT (pick-wt=4): 28 [] quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa).
% 2.83/3.09 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 2.83/3.09
% 2.83/3.09 ======= end of input processing =======
% 2.83/3.09
% 2.83/3.09 =========== start of search ===========
% 2.83/3.09
% 2.83/3.09
% 2.83/3.09 Resetting weight limit to 7.
% 2.83/3.09
% 2.83/3.09
% 2.83/3.09 Resetting weight limit to 7.
% 2.83/3.09
% 2.83/3.09 sos_size=3519
% 2.83/3.09
% 2.83/3.09 -------- PROOF --------
% 2.83/3.09
% 2.83/3.09 ----> UNIT CONFLICT at 0.95 sec ----> 4378 [binary,4376.1,14.1] $F.
% 2.83/3.09
% 2.83/3.09 Length of proof is 11. Level of proof is 5.
% 2.83/3.09
% 2.83/3.09 ---------------- PROOF ----------------
% 2.83/3.09 % SZS status Unsatisfiable
% 2.83/3.09 % SZS output start Refutation
% See solution above
% 2.83/3.09 ------------ end of proof -------------
% 2.83/3.09
% 2.83/3.09
% 2.83/3.09 Search stopped by max_proofs option.
% 2.83/3.09
% 2.83/3.09
% 2.83/3.09 Search stopped by max_proofs option.
% 2.83/3.09
% 2.83/3.09 ============ end of search ============
% 2.83/3.09
% 2.83/3.09 -------------- statistics -------------
% 2.83/3.09 clauses given 230
% 2.83/3.09 clauses generated 36237
% 2.83/3.09 clauses kept 4285
% 2.83/3.09 clauses forward subsumed 32272
% 2.83/3.09 clauses back subsumed 160
% 2.83/3.09 Kbytes malloced 4882
% 2.83/3.09
% 2.83/3.09 ----------- times (seconds) -----------
% 2.83/3.09 user CPU time 0.95 (0 hr, 0 min, 0 sec)
% 2.83/3.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.83/3.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.83/3.09
% 2.83/3.09 That finishes the proof of the theorem.
% 2.83/3.09
% 2.83/3.09 Process 3182 finished Wed Jul 27 08:58:19 2022
% 2.83/3.09 Otter interrupted
% 2.83/3.09 PROOF FOUND
%------------------------------------------------------------------------------