TSTP Solution File: HEN007-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 12:57:57 EDT 2022
% Result : Unsatisfiable 1.97s 2.19s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 31 unt; 0 nHn; 19 RR)
% Number of literals : 49 ( 7 equ; 13 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 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 : 41 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| quotient(A,B,zero) ),
file('HEN007-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ quotient(A,B,zero)
| less_e_qual(A,B) ),
file('HEN007-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(A,B,C)
| less_e_qual(C,A) ),
file('HEN007-1.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('HEN007-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN007-1.p',unknown),
[] ).
cnf(7,axiom,
~ less_e_qual(zQy,zQx),
file('HEN007-1.p',unknown),
[] ).
cnf(9,axiom,
less_e_qual(zero,A),
file('HEN007-1.p',unknown),
[] ).
cnf(11,axiom,
quotient(A,B,divide(A,B)),
file('HEN007-1.p',unknown),
[] ).
cnf(12,axiom,
less_e_qual(x,y),
file('HEN007-1.p',unknown),
[] ).
cnf(13,axiom,
quotient(z,y,zQy),
file('HEN007-1.p',unknown),
[] ).
cnf(14,axiom,
quotient(z,x,zQx),
file('HEN007-1.p',unknown),
[] ).
cnf(15,plain,
quotient(zero,A,zero),
inference(hyper,[status(thm)],[9,1]),
[iquote('hyper,9,1')] ).
cnf(21,plain,
quotient(x,y,zero),
inference(hyper,[status(thm)],[12,1]),
[iquote('hyper,12,1')] ).
cnf(41,plain,
less_e_qual(divide(A,B),A),
inference(hyper,[status(thm)],[11,3]),
[iquote('hyper,11,3')] ).
cnf(43,plain,
( quotient(A,B,C)
| ~ less_e_qual(divide(A,B),C)
| ~ less_e_qual(C,divide(A,B)) ),
inference(para_into,[status(thm),theory(equality)],[11,5]),
[iquote('para_into,11.1.3,5.3.1')] ).
cnf(92,plain,
less_e_qual(divide(zQy,zero),divide(zQx,y)),
inference(hyper,[status(thm)],[21,4,14,13,11,11]),
[iquote('hyper,21,4,14,13,11,11')] ).
cnf(135,plain,
quotient(divide(A,B),A,zero),
inference(hyper,[status(thm)],[41,1]),
[iquote('hyper,41,1')] ).
cnf(166,plain,
less_e_qual(divide(divide(A,A),zero),zero),
inference(hyper,[status(thm)],[135,4,11,135,11,11]),
[iquote('hyper,135,4,11,135,11,11')] ).
cnf(190,plain,
quotient(divide(zQy,zero),divide(zQx,y),zero),
inference(hyper,[status(thm)],[92,1]),
[iquote('hyper,92,1')] ).
cnf(216,plain,
divide(divide(A,A),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[166,5,9])]),
[iquote('hyper,166,5,9,flip.1')] ).
cnf(376,plain,
quotient(divide(A,A),zero,zero),
inference(para_from,[status(thm),theory(equality)],[216,11]),
[iquote('para_from,216.1.1,11.1.3')] ).
cnf(381,plain,
less_e_qual(divide(A,A),zero),
inference(hyper,[status(thm)],[376,2]),
[iquote('hyper,376,2')] ).
cnf(397,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[381,5,9])]),
[iquote('hyper,381,5,9,flip.1')] ).
cnf(401,plain,
quotient(A,A,zero),
inference(para_from,[status(thm),theory(equality)],[397,11]),
[iquote('para_from,397.1.1,11.1.3')] ).
cnf(404,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(hyper,[status(thm)],[401,4,11,15,11,11]),
[iquote('hyper,401,4,11,15,11,11')] ).
cnf(445,plain,
less_e_qual(divide(divide(divide(zQy,zero),zQx),zero),zero),
inference(hyper,[status(thm)],[190,4,135,11,11,15]),
[iquote('hyper,190,4,135,11,11,15')] ).
cnf(678,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[404,5,9])]),
[iquote('hyper,404,5,9,flip.1')] ).
cnf(707,plain,
divide(divide(divide(zQy,zero),zQx),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[445,5,9])]),
[iquote('hyper,445,5,9,flip.1')] ).
cnf(1400,plain,
quotient(divide(A,divide(A,zero)),zero,zero),
inference(para_from,[status(thm),theory(equality)],[678,11]),
[iquote('para_from,678.1.1,11.1.3')] ).
cnf(1406,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[1400,2]),
[iquote('hyper,1400,2')] ).
cnf(1416,plain,
quotient(A,divide(A,zero),zero),
inference(hyper,[status(thm)],[1406,43,9]),
[iquote('hyper,1406,43,9')] ).
cnf(1454,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[1416,2]),
[iquote('hyper,1416,2')] ).
cnf(1478,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[1454,5,41]),
[iquote('hyper,1454,5,41')] ).
cnf(1547,plain,
divide(zQy,zQx) = zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[707]),1478,1478]),
[iquote('back_demod,707,demod,1478,1478')] ).
cnf(1705,plain,
quotient(zQy,zQx,zero),
inference(para_from,[status(thm),theory(equality)],[1547,11]),
[iquote('para_from,1547.1.1,11.1.3')] ).
cnf(1709,plain,
less_e_qual(zQy,zQx),
inference(hyper,[status(thm)],[1705,2]),
[iquote('hyper,1705,2')] ).
cnf(1710,plain,
$false,
inference(binary,[status(thm)],[1709,7]),
[iquote('binary,1709.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 08:54:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.97/2.19 ----- Otter 3.3f, August 2004 -----
% 1.97/2.19 The process was started by sandbox on n013.cluster.edu,
% 1.97/2.19 Wed Jul 27 08:54:45 2022
% 1.97/2.19 The command was "./otter". The process ID is 24461.
% 1.97/2.19
% 1.97/2.19 set(prolog_style_variables).
% 1.97/2.19 set(auto).
% 1.97/2.19 dependent: set(auto1).
% 1.97/2.19 dependent: set(process_input).
% 1.97/2.19 dependent: clear(print_kept).
% 1.97/2.19 dependent: clear(print_new_demod).
% 1.97/2.19 dependent: clear(print_back_demod).
% 1.97/2.19 dependent: clear(print_back_sub).
% 1.97/2.19 dependent: set(control_memory).
% 1.97/2.19 dependent: assign(max_mem, 12000).
% 1.97/2.19 dependent: assign(pick_given_ratio, 4).
% 1.97/2.19 dependent: assign(stats_level, 1).
% 1.97/2.19 dependent: assign(max_seconds, 10800).
% 1.97/2.19 clear(print_given).
% 1.97/2.19
% 1.97/2.19 list(usable).
% 1.97/2.19 0 [] A=A.
% 1.97/2.19 0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.97/2.19 0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.97/2.19 0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.97/2.19 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).
% 1.97/2.19 0 [] less_e_qual(zero,X).
% 1.97/2.19 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.97/2.19 0 [] less_e_qual(X,identity).
% 1.97/2.19 0 [] quotient(X,Y,divide(X,Y)).
% 1.97/2.19 0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.97/2.19 0 [] less_e_qual(x,y).
% 1.97/2.19 0 [] quotient(z,y,zQy).
% 1.97/2.19 0 [] quotient(z,x,zQx).
% 1.97/2.19 0 [] -less_e_qual(zQy,zQx).
% 1.97/2.19 end_of_list.
% 1.97/2.19
% 1.97/2.19 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.97/2.19
% 1.97/2.19 This is a Horn set with equality. The strategy will be
% 1.97/2.19 Knuth-Bendix and hyper_res, with positive clauses in
% 1.97/2.19 sos and nonpositive clauses in usable.
% 1.97/2.19
% 1.97/2.19 dependent: set(knuth_bendix).
% 1.97/2.19 dependent: set(anl_eq).
% 1.97/2.19 dependent: set(para_from).
% 1.97/2.19 dependent: set(para_into).
% 1.97/2.19 dependent: clear(para_from_right).
% 1.97/2.19 dependent: clear(para_into_right).
% 1.97/2.19 dependent: set(para_from_vars).
% 1.97/2.19 dependent: set(eq_units_both_ways).
% 1.97/2.19 dependent: set(dynamic_demod_all).
% 1.97/2.19 dependent: set(dynamic_demod).
% 1.97/2.19 dependent: set(order_eq).
% 1.97/2.19 dependent: set(back_demod).
% 1.97/2.19 dependent: set(lrpo).
% 1.97/2.19 dependent: set(hyper_res).
% 1.97/2.19 dependent: clear(order_hyper).
% 1.97/2.19
% 1.97/2.19 ------------> process usable:
% 1.97/2.19 ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.97/2.19 ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.97/2.19 ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.97/2.19 ** 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).
% 1.97/2.19 ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.97/2.19 ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.97/2.19 ** KEPT (pick-wt=3): 7 [] -less_e_qual(zQy,zQx).
% 1.97/2.19
% 1.97/2.19 ------------> process sos:
% 1.97/2.19 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.97/2.19 ** KEPT (pick-wt=3): 9 [] less_e_qual(zero,A).
% 1.97/2.19 ** KEPT (pick-wt=3): 10 [] less_e_qual(A,identity).
% 1.97/2.19 ** KEPT (pick-wt=6): 11 [] quotient(A,B,divide(A,B)).
% 1.97/2.19 ** KEPT (pick-wt=3): 12 [] less_e_qual(x,y).
% 1.97/2.19 ** KEPT (pick-wt=4): 13 [] quotient(z,y,zQy).
% 1.97/2.19 ** KEPT (pick-wt=4): 14 [] quotient(z,x,zQx).
% 1.97/2.19 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.97/2.19
% 1.97/2.19 ======= end of input processing =======
% 1.97/2.19
% 1.97/2.19 =========== start of search ===========
% 1.97/2.19
% 1.97/2.19 -------- PROOF --------
% 1.97/2.19
% 1.97/2.19 ----> UNIT CONFLICT at 0.15 sec ----> 1710 [binary,1709.1,7.1] $F.
% 1.97/2.19
% 1.97/2.19 Length of proof is 25. Level of proof is 18.
% 1.97/2.19
% 1.97/2.19 ---------------- PROOF ----------------
% 1.97/2.19 % SZS status Unsatisfiable
% 1.97/2.19 % SZS output start Refutation
% See solution above
% 1.97/2.19 ------------ end of proof -------------
% 1.97/2.19
% 1.97/2.19
% 1.97/2.19 Search stopped by max_proofs option.
% 1.97/2.19
% 1.97/2.19
% 1.97/2.19 Search stopped by max_proofs option.
% 1.97/2.19
% 1.97/2.19 ============ end of search ============
% 1.97/2.19
% 1.97/2.19 -------------- statistics -------------
% 1.97/2.19 clauses given 178
% 1.97/2.19 clauses generated 15064
% 1.97/2.19 clauses kept 1660
% 1.97/2.19 clauses forward subsumed 13904
% 1.97/2.19 clauses back subsumed 66
% 1.97/2.19 Kbytes malloced 2929
% 1.97/2.19
% 1.97/2.19 ----------- times (seconds) -----------
% 1.97/2.19 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 1.97/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.19
% 1.97/2.19 That finishes the proof of the theorem.
% 1.97/2.19
% 1.97/2.19 Process 24461 finished Wed Jul 27 08:54:47 2022
% 1.97/2.19 Otter interrupted
% 1.97/2.19 PROOF FOUND
%------------------------------------------------------------------------------