TSTP Solution File: HEN010-7 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN010-7 : 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 12:58:00 EDT 2022
% Result : Unsatisfiable 1.75s 1.96s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of clauses : 26 ( 20 unt; 0 nHn; 19 RR)
% Number of literals : 43 ( 5 equ; 19 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN010-7.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('HEN010-7.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN010-7.p',unknown),
[] ).
cnf(8,axiom,
( ~ quotient(A,B,C)
| ~ less_e_qual(C,D)
| ~ quotient(A,D,E)
| less_e_qual(E,B) ),
file('HEN010-7.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_e_qual(A,B)
| ~ quotient(C,B,D)
| ~ quotient(C,A,E)
| less_e_qual(D,E) ),
file('HEN010-7.p',unknown),
[] ).
cnf(10,axiom,
( ~ less_e_qual(A,B)
| ~ quotient(A,C,D)
| ~ quotient(B,C,E)
| less_e_qual(D,E) ),
file('HEN010-7.p',unknown),
[] ).
cnf(11,axiom,
idQa != idQa_Q__idQ_idQa,
file('HEN010-7.p',unknown),
[] ).
cnf(12,plain,
idQa_Q__idQ_idQa != idQa,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
less_e_qual(zero,A),
file('HEN010-7.p',unknown),
[] ).
cnf(15,axiom,
less_e_qual(A,identity),
file('HEN010-7.p',unknown),
[] ).
cnf(16,axiom,
quotient(A,B,divide(A,B)),
file('HEN010-7.p',unknown),
[] ).
cnf(19,axiom,
quotient(A,A,zero),
file('HEN010-7.p',unknown),
[] ).
cnf(20,axiom,
quotient(A,zero,A),
file('HEN010-7.p',unknown),
[] ).
cnf(21,axiom,
quotient(identity,a,idQa),
file('HEN010-7.p',unknown),
[] ).
cnf(22,axiom,
quotient(identity,idQa,idQ_idQa),
file('HEN010-7.p',unknown),
[] ).
cnf(23,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('HEN010-7.p',unknown),
[] ).
cnf(60,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[19,2]),
[iquote('hyper,19,2')] ).
cnf(72,plain,
less_e_qual(divide(A,a),idQa),
inference(hyper,[status(thm)],[21,10,15,16]),
[iquote('hyper,21,10,15,16')] ).
cnf(77,plain,
less_e_qual(idQa,divide(idQa,a)),
inference(hyper,[status(thm)],[21,4,21,19,20,16]),
[iquote('hyper,21,4,21,19,20,16')] ).
cnf(91,plain,
less_e_qual(idQ_idQa,a),
inference(hyper,[status(thm)],[22,8,21,60]),
[iquote('hyper,22,8,21,60')] ).
cnf(120,plain,
less_e_qual(divide(idQa,a),idQa_Q__idQ_idQa),
inference(hyper,[status(thm)],[23,9,91,16]),
[iquote('hyper,23,9,91,16')] ).
cnf(121,plain,
less_e_qual(idQa_Q__idQ_idQa,idQa),
inference(hyper,[status(thm)],[23,9,14,20]),
[iquote('hyper,23,9,14,20')] ).
cnf(229,plain,
divide(idQa,a) = idQa,
inference(hyper,[status(thm)],[77,5,72]),
[iquote('hyper,77,5,72')] ).
cnf(231,plain,
less_e_qual(idQa,idQa_Q__idQ_idQa),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[120]),229]),
[iquote('back_demod,120,demod,229')] ).
cnf(239,plain,
idQa_Q__idQ_idQa = idQa,
inference(hyper,[status(thm)],[231,5,121]),
[iquote('hyper,231,5,121')] ).
cnf(241,plain,
$false,
inference(binary,[status(thm)],[239,12]),
[iquote('binary,239.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN010-7 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 08:53:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox2 on n021.cluster.edu,
% 1.75/1.96 Wed Jul 27 08:53:23 2022
% 1.75/1.96 The command was "./otter". The process ID is 12864.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] A=A.
% 1.75/1.96 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.75/1.96 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.75/1.96 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.75/1.96 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).
% 1.75/1.96 0 [] less_e_qual(zero,X).
% 1.75/1.96 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.75/1.96 0 [] less_e_qual(X,identity).
% 1.75/1.96 0 [] quotient(X,Y,divide(X,Y)).
% 1.75/1.96 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.75/1.96 0 [] quotient(X,identity,zero).
% 1.75/1.96 0 [] quotient(zero,X,zero).
% 1.75/1.96 0 [] quotient(X,X,zero).
% 1.75/1.96 0 [] quotient(X,zero,X).
% 1.75/1.96 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.75/1.96 0 [] -quotient(X,Y,W1)| -less_e_qual(W1,Z)| -quotient(X,Z,W2)|less_e_qual(W2,Y).
% 1.75/1.96 0 [] -less_e_qual(X,Y)| -quotient(Z,Y,W1)| -quotient(Z,X,W2)|less_e_qual(W1,W2).
% 1.75/1.96 0 [] -less_e_qual(X,Y)| -quotient(X,Z,W1)| -quotient(Y,Z,W2)|less_e_qual(W1,W2).
% 1.75/1.96 0 [] quotient(identity,a,idQa).
% 1.75/1.96 0 [] quotient(identity,idQa,idQ_idQa).
% 1.75/1.96 0 [] quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa).
% 1.75/1.96 0 [] idQa!=idQa_Q__idQ_idQa.
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.75/1.96
% 1.75/1.96 This is a Horn set with equality. The strategy will be
% 1.75/1.96 Knuth-Bendix and hyper_res, with positive clauses in
% 1.75/1.96 sos and nonpositive clauses in usable.
% 1.75/1.96
% 1.75/1.96 dependent: set(knuth_bendix).
% 1.75/1.96 dependent: set(anl_eq).
% 1.75/1.96 dependent: set(para_from).
% 1.75/1.96 dependent: set(para_into).
% 1.75/1.96 dependent: clear(para_from_right).
% 1.75/1.96 dependent: clear(para_into_right).
% 1.75/1.96 dependent: set(para_from_vars).
% 1.75/1.96 dependent: set(eq_units_both_ways).
% 1.75/1.96 dependent: set(dynamic_demod_all).
% 1.75/1.96 dependent: set(dynamic_demod).
% 1.75/1.96 dependent: set(order_eq).
% 1.75/1.96 dependent: set(back_demod).
% 1.75/1.96 dependent: set(lrpo).
% 1.75/1.96 dependent: set(hyper_res).
% 1.75/1.96 dependent: clear(order_hyper).
% 1.75/1.96
% 1.75/1.96 ------------> process usable:
% 1.75/1.96 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.75/1.96 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.75/1.96 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.75/1.96 ** 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).
% 1.75/1.96 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.75/1.96 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.75/1.96 ** KEPT (pick-wt=9): 7 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.75/1.96 ** KEPT (pick-wt=14): 8 [] -quotient(A,B,C)| -less_e_qual(C,D)| -quotient(A,D,E)|less_e_qual(E,B).
% 1.75/1.96 ** KEPT (pick-wt=14): 9 [] -less_e_qual(A,B)| -quotient(C,B,D)| -quotient(C,A,E)|less_e_qual(D,E).
% 1.75/1.96 ** KEPT (pick-wt=14): 10 [] -less_e_qual(A,B)| -quotient(A,C,D)| -quotient(B,C,E)|less_e_qual(D,E).
% 1.75/1.96 ** KEPT (pick-wt=3): 12 [copy,11,flip.1] idQa_Q__idQ_idQa!=idQa.
% 1.75/1.96
% 1.75/1.96 ------------> process sos:
% 1.75/1.96 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.75/1.96 ** KEPT (pick-wt=3): 14 [] less_e_qual(zero,A).
% 1.75/1.96 ** KEPT (pick-wt=3): 15 [] less_e_qual(A,identity).
% 1.75/1.96 ** KEPT (pick-wt=6): 16 [] quotient(A,B,divide(A,B)).
% 1.75/1.96 ** KEPT (pick-wt=4): 17 [] quotient(A,identity,zero).
% 1.75/1.96 ** KEPT (pick-wt=4): 18 [] quotient(zero,A,zero).
% 1.75/1.96 ** KEPT (pick-wt=4): 19 [] quotient(A,A,zero).
% 1.75/1.96 ** KEPT (pick-wt=4): 20 [] quotient(A,zero,A).
% 1.75/1.96 ** KEPT (pick-wt=4): 21 [] quotient(identity,a,idQa).
% 1.75/1.96 ** KEPT (pick-wt=4): 22 [] quotient(identity,idQa,idQ_idQa).
% 1.75/1.96 ** KEPT (pick-wt=4): 23 [] quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa).
% 1.75/1.96 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.75/1.96
% 1.75/1.96 ======= end of input processing =======
% 1.75/1.96
% 1.75/1.96 =========== start of search ===========
% 1.75/1.96
% 1.75/1.96 -------- PROOF --------
% 1.75/1.96
% 1.75/1.96 ----> UNIT CONFLICT at 0.02 sec ----> 241 [binary,239.1,12.1] $F.
% 1.75/1.96
% 1.75/1.96 Length of proof is 10. Level of proof is 5.
% 1.75/1.96
% 1.75/1.96 ---------------- PROOF ----------------
% 1.75/1.96 % SZS status Unsatisfiable
% 1.75/1.96 % SZS output start Refutation
% See solution above
% 1.75/1.96 ------------ end of proof -------------
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96 ============ end of search ============
% 1.75/1.96
% 1.75/1.96 -------------- statistics -------------
% 1.75/1.96 clauses given 28
% 1.75/1.96 clauses generated 3556
% 1.75/1.96 clauses kept 228
% 1.75/1.96 clauses forward subsumed 3382
% 1.75/1.96 clauses back subsumed 10
% 1.75/1.96 Kbytes malloced 976
% 1.75/1.96
% 1.75/1.96 ----------- times (seconds) -----------
% 1.75/1.96 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.75/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.96 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.96
% 1.75/1.96 That finishes the proof of the theorem.
% 1.75/1.96
% 1.75/1.96 Process 12864 finished Wed Jul 27 08:53:24 2022
% 1.75/1.96 Otter interrupted
% 1.75/1.96 PROOF FOUND
%------------------------------------------------------------------------------