%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 2.87s 3.06s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of clauses : 35 ( 26 unt; 0 nHn; 12 RR)
% Number of literals : 46 ( 16 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_e_qual(A,B)
| divide(A,B) = zero ),
file('HEN007-3.p',unknown),
[] ).
cnf(2,axiom,
( divide(A,B) != zero
| less_e_qual(A,B) ),
file('HEN007-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_e_qual(A,B)
| ~ less_e_qual(B,A)
| A = B ),
file('HEN007-3.p',unknown),
[] ).
cnf(4,axiom,
~ less_e_qual(divide(c,b),divide(c,a)),
file('HEN007-3.p',unknown),
[] ).
cnf(6,axiom,
less_e_qual(divide(A,B),A),
file('HEN007-3.p',unknown),
[] ).
cnf(7,axiom,
less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
file('HEN007-3.p',unknown),
[] ).
cnf(8,axiom,
less_e_qual(zero,A),
file('HEN007-3.p',unknown),
[] ).
cnf(10,axiom,
less_e_qual(a,b),
file('HEN007-3.p',unknown),
[] ).
cnf(12,plain,
divide(zero,A) = zero,
inference(hyper,[status(thm)],[8,1]),
[iquote('hyper,8,1')] ).
cnf(17,plain,
divide(a,b) = zero,
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(22,plain,
divide(divide(A,B),A) = zero,
inference(hyper,[status(thm)],[6,1]),
[iquote('hyper,6,1')] ).
cnf(31,plain,
( less_e_qual(divide(divide(A,B),divide(C,B)),zero)
| ~ less_e_qual(A,C) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,1]),12]),
[iquote('para_into,7.1.2.1,1.2.1,demod,12')] ).
cnf(35,plain,
less_e_qual(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(para_from,[status(thm),theory(equality)],[12,7]),
[iquote('para_from,11.1.1,7.1.1.2')] ).
cnf(41,plain,
less_e_qual(divide(divide(A,b),zero),divide(divide(A,a),b)),
inference(para_from,[status(thm),theory(equality)],[17,7]),
[iquote('para_from,17.1.1,7.1.1.2')] ).
cnf(43,plain,
less_e_qual(divide(divide(A,A),divide(B,A)),zero),
inference(para_from,[status(thm),theory(equality)],[22,7]),
[iquote('para_from,21.1.1,7.1.2')] ).
cnf(66,plain,
divide(divide(A,A),divide(B,A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[43,3,8])]),
[iquote('hyper,43,3,8,flip.1')] ).
cnf(172,plain,
less_e_qual(divide(A,A),divide(B,A)),
inference(hyper,[status(thm)],[66,2]),
[iquote('hyper,66,2')] ).
cnf(193,plain,
divide(A,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[172,3,6]),22])]),
[iquote('hyper,172,3,6,demod,22,flip.1')] ).
cnf(195,plain,
less_e_qual(A,A),
inference(hyper,[status(thm)],[193,2]),
[iquote('hyper,193,2')] ).
cnf(303,plain,
less_e_qual(divide(divide(A,divide(A,zero)),zero),zero),
inference(para_into,[status(thm),theory(equality)],[35,193]),
[iquote('para_into,35.1.2,193.1.1')] ).
cnf(336,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[303,3,8])]),
[iquote('hyper,303,3,8,flip.1')] ).
cnf(352,plain,
less_e_qual(divide(A,divide(A,zero)),zero),
inference(hyper,[status(thm)],[336,2]),
[iquote('hyper,336,2')] ).
cnf(358,plain,
( divide(divide(A,zero),zero) = zero
| ~ less_e_qual(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[336,1]),
[iquote('para_into,336.1.1.1.2,1.2.1')] ).
cnf(430,plain,
divide(A,divide(A,zero)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[352,3,8])]),
[iquote('hyper,352,3,8,flip.1')] ).
cnf(432,plain,
less_e_qual(A,divide(A,zero)),
inference(hyper,[status(thm)],[430,2]),
[iquote('hyper,430,2')] ).
cnf(475,plain,
divide(A,zero) = A,
inference(hyper,[status(thm)],[432,3,6]),
[iquote('hyper,432,3,6')] ).
cnf(498,plain,
( A = zero
| ~ less_e_qual(A,zero) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[358]),475,475]),
[iquote('back_demod,358,demod,475,475')] ).
cnf(584,plain,
less_e_qual(divide(A,b),divide(divide(A,a),b)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),475]),
[iquote('back_demod,41,demod,475')] ).
cnf(587,plain,
( zero = A
| ~ less_e_qual(A,zero) ),
inference(para_into,[status(thm),theory(equality)],[475,1]),
[iquote('para_into,474.1.1,1.2.1')] ).
cnf(670,plain,
( A = zero
| ~ less_e_qual(A,B)
| ~ less_e_qual(B,zero) ),
inference(para_from,[status(thm),theory(equality)],[587,498]),
[iquote('para_from,587.1.1,498.2.2')] ).
cnf(686,plain,
( less_e_qual(divide(A,B),zero)
| ~ less_e_qual(A,divide(B,C)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,22]),475]),
[iquote('para_into,31.1.1.2,21.1.1,demod,475')] ).
cnf(3497,plain,
less_e_qual(divide(divide(A,b),divide(A,a)),zero),
inference(hyper,[status(thm)],[686,584]),
[iquote('hyper,686,584')] ).
cnf(3520,plain,
divide(divide(A,b),divide(A,a)) = zero,
inference(hyper,[status(thm)],[3497,670,195]),
[iquote('hyper,3497,670,195')] ).
cnf(3529,plain,
less_e_qual(divide(A,b),divide(A,a)),
inference(hyper,[status(thm)],[3520,2]),
[iquote('hyper,3520,2')] ).
cnf(3530,plain,
$false,
inference(binary,[status(thm)],[3529,4]),
[iquote('binary,3529.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 09:20:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.87/3.06 ----- Otter 3.3f, August 2004 -----
% 2.87/3.06 The process was started by sandbox2 on n016.cluster.edu,
% 2.87/3.06 Wed Jul 27 09:20:37 2022
% 2.87/3.06 The command was "./otter". The process ID is 13693.
% 2.87/3.06
% 2.87/3.06 set(prolog_style_variables).
% 2.87/3.06 set(auto).
% 2.87/3.06 dependent: set(auto1).
% 2.87/3.06 dependent: set(process_input).
% 2.87/3.06 dependent: clear(print_kept).
% 2.87/3.06 dependent: clear(print_new_demod).
% 2.87/3.06 dependent: clear(print_back_demod).
% 2.87/3.06 dependent: clear(print_back_sub).
% 2.87/3.06 dependent: set(control_memory).
% 2.87/3.06 dependent: assign(max_mem, 12000).
% 2.87/3.06 dependent: assign(pick_given_ratio, 4).
% 2.87/3.06 dependent: assign(stats_level, 1).
% 2.87/3.06 dependent: assign(max_seconds, 10800).
% 2.87/3.06 clear(print_given).
% 2.87/3.06
% 2.87/3.06 list(usable).
% 2.87/3.06 0 [] A=A.
% 2.87/3.06 0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 2.87/3.06 0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 2.87/3.06 0 [] less_e_qual(divide(X,Y),X).
% 2.87/3.06 0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 2.87/3.06 0 [] less_e_qual(zero,X).
% 2.87/3.06 0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 2.87/3.06 0 [] less_e_qual(X,identity).
% 2.87/3.06 0 [] less_e_qual(a,b).
% 2.87/3.06 0 [] -less_e_qual(divide(c,b),divide(c,a)).
% 2.87/3.06 end_of_list.
% 2.87/3.06
% 2.87/3.06 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.87/3.06
% 2.87/3.06 This is a Horn set with equality. The strategy will be
% 2.87/3.06 Knuth-Bendix and hyper_res, with positive clauses in
% 2.87/3.06 sos and nonpositive clauses in usable.
% 2.87/3.06
% 2.87/3.06 dependent: set(knuth_bendix).
% 2.87/3.06 dependent: set(anl_eq).
% 2.87/3.06 dependent: set(para_from).
% 2.87/3.06 dependent: set(para_into).
% 2.87/3.06 dependent: clear(para_from_right).
% 2.87/3.06 dependent: clear(para_into_right).
% 2.87/3.06 dependent: set(para_from_vars).
% 2.87/3.06 dependent: set(eq_units_both_ways).
% 2.87/3.06 dependent: set(dynamic_demod_all).
% 2.87/3.06 dependent: set(dynamic_demod).
% 2.87/3.06 dependent: set(order_eq).
% 2.87/3.06 dependent: set(back_demod).
% 2.87/3.06 dependent: set(lrpo).
% 2.87/3.06 dependent: set(hyper_res).
% 2.87/3.06 dependent: clear(order_hyper).
% 2.87/3.06
% 2.87/3.06 ------------> process usable:
% 2.87/3.06 ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 2.87/3.06 ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 2.87/3.06 ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.87/3.06 ** KEPT (pick-wt=7): 4 [] -less_e_qual(divide(c,b),divide(c,a)).
% 2.87/3.06
% 2.87/3.06 ------------> process sos:
% 2.87/3.06 ** KEPT (pick-wt=3): 5 [] A=A.
% 2.87/3.06 ** KEPT (pick-wt=5): 6 [] less_e_qual(divide(A,B),A).
% 2.87/3.06 ** KEPT (pick-wt=13): 7 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 2.87/3.06 ** KEPT (pick-wt=3): 8 [] less_e_qual(zero,A).
% 2.87/3.06 ** KEPT (pick-wt=3): 9 [] less_e_qual(A,identity).
% 2.87/3.06 ** KEPT (pick-wt=3): 10 [] less_e_qual(a,b).
% 2.87/3.06 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 2.87/3.06
% 2.87/3.06 ======= end of input processing =======
% 2.87/3.06
% 2.87/3.06 =========== start of search ===========
% 2.87/3.06
% 2.87/3.06 -------- PROOF --------
% 2.87/3.06
% 2.87/3.06 ----> UNIT CONFLICT at 1.17 sec ----> 3530 [binary,3529.1,4.1] $F.
% 2.87/3.06
% 2.87/3.06 Length of proof is 26. Level of proof is 15.
% 2.87/3.06
% 2.87/3.06 ---------------- PROOF ----------------
% 2.87/3.06 % SZS status Unsatisfiable
% 2.87/3.06 % SZS output start Refutation
% See solution above
% 2.87/3.06 ------------ end of proof -------------
% 2.87/3.06
% 2.87/3.06
% 2.87/3.06 Search stopped by max_proofs option.
% 2.87/3.06
% 2.87/3.06
% 2.87/3.06 Search stopped by max_proofs option.
% 2.87/3.06
% 2.87/3.06 ============ end of search ============
% 2.87/3.06
% 2.87/3.06 -------------- statistics -------------
% 2.87/3.06 clauses given 179
% 2.87/3.06 clauses generated 13243
% 2.87/3.06 clauses kept 3436
% 2.87/3.06 clauses forward subsumed 9899
% 2.87/3.06 clauses back subsumed 538
% 2.87/3.06 Kbytes malloced 3906
% 2.87/3.06
% 2.87/3.06 ----------- times (seconds) -----------
% 2.87/3.06 user CPU time 1.17 (0 hr, 0 min, 1 sec)
% 2.87/3.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.87/3.06 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.87/3.06
% 2.87/3.06 That finishes the proof of the theorem.
% 2.87/3.06
% 2.87/3.06 Process 13693 finished Wed Jul 27 09:20:40 2022
% 2.87/3.06 Otter interrupted
% 2.87/3.06 PROOF FOUND
%------------------------------------------------------------------------------