%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP556-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 12:57:14 EDT 2022
% Result : Unsatisfiable 1.33s 1.87s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 4 RR)
% Number of literals : 24 ( 23 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP556-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B,
file('GRP556-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('GRP556-1.p',unknown),
[] ).
cnf(7,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(8,plain,
divide(b,inverse(a)) != multiply(a,b),
inference(para_from,[status(thm),theory(equality)],[6,2]),
[iquote('para_from,6.1.1,2.1.1')] ).
cnf(9,plain,
divide(divide(A,inverse(divide(B,multiply(A,C)))),inverse(C)) = B,
inference(para_into,[status(thm),theory(equality)],[4,7]),
[iquote('para_into,4.1.1.1.2.1.2,7.1.1')] ).
cnf(11,plain,
divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),C) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.1.2,4.1.1')] ).
cnf(15,plain,
divide(multiply(A,divide(B,divide(A,C))),C) = B,
inference(para_into,[status(thm),theory(equality)],[4,7]),
[iquote('para_into,4.1.1.1,7.1.1')] ).
cnf(21,plain,
divide(multiply(A,divide(B,multiply(A,C))),inverse(C)) = B,
inference(para_into,[status(thm),theory(equality)],[9,7]),
[iquote('para_into,9.1.1.1,7.1.1')] ).
cnf(23,plain,
multiply(divide(A,inverse(divide(B,multiply(A,C)))),C) = B,
inference(para_into,[status(thm),theory(equality)],[9,7]),
[iquote('para_into,9.1.1,7.1.1')] ).
cnf(46,plain,
multiply(multiply(A,divide(B,multiply(A,C))),C) = B,
inference(para_into,[status(thm),theory(equality)],[21,7]),
[iquote('para_into,21.1.1,7.1.1')] ).
cnf(65,plain,
multiply(multiply(divide(A,inverse(divide(B,multiply(A,C)))),divide(D,B)),C) = D,
inference(para_from,[status(thm),theory(equality)],[23,46]),
[iquote('para_from,23.1.1,46.1.1.1.2.2')] ).
cnf(88,plain,
divide(A,inverse(divide(B,A))) = B,
inference(para_into,[status(thm),theory(equality)],[11,4]),
[iquote('para_into,11.1.1.1,4.1.1')] ).
cnf(118,plain,
divide(A,inverse(divide(B,multiply(A,C)))) = divide(inverse(C),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[88,9])]),
[iquote('para_into,88.1.1.2.1,9.1.1,flip.1')] ).
cnf(122,plain,
divide(A,inverse(divide(B,divide(A,C)))) = divide(C,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[88,4])]),
[iquote('para_into,88.1.1.2.1,4.1.1,flip.1')] ).
cnf(141,plain,
multiply(multiply(divide(inverse(A),inverse(B)),divide(C,B)),A) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[65]),118]),
[iquote('back_demod,65,demod,118')] ).
cnf(157,plain,
divide(divide(A,inverse(B)),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),122]),
[iquote('back_demod,4,demod,122')] ).
cnf(179,plain,
divide(multiply(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[157,7]),
[iquote('para_into,157.1.1.1,7.1.1')] ).
cnf(191,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(para_into,[status(thm),theory(equality)],[179,7]),
[iquote('para_into,179.1.1,7.1.1')] ).
cnf(196,plain,
multiply(divide(A,B),C) = divide(multiply(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[179,15])]),
[iquote('para_from,179.1.1,15.1.1.1.2,flip.1')] ).
cnf(203,plain,
divide(divide(A,B),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[141]),196,196,191]),
[iquote('back_demod,141,demod,196,196,191')] ).
cnf(314,plain,
divide(A,inverse(B)) = multiply(B,A),
inference(para_into,[status(thm),theory(equality)],[203,179]),
[iquote('para_into,203.1.1.1,179.1.1')] ).
cnf(315,plain,
$false,
inference(binary,[status(thm)],[314,8]),
[iquote('binary,314.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP556-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n017.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 04:55:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.33/1.87 ----- Otter 3.3f, August 2004 -----
% 1.33/1.87 The process was started by sandbox on n017.cluster.edu,
% 1.33/1.87 Wed Jul 27 04:55:03 2022
% 1.33/1.87 The command was "./otter". The process ID is 21323.
% 1.33/1.87
% 1.33/1.87 set(prolog_style_variables).
% 1.33/1.87 set(auto).
% 1.33/1.87 dependent: set(auto1).
% 1.33/1.87 dependent: set(process_input).
% 1.33/1.87 dependent: clear(print_kept).
% 1.33/1.87 dependent: clear(print_new_demod).
% 1.33/1.87 dependent: clear(print_back_demod).
% 1.33/1.87 dependent: clear(print_back_sub).
% 1.33/1.87 dependent: set(control_memory).
% 1.33/1.87 dependent: assign(max_mem, 12000).
% 1.33/1.87 dependent: assign(pick_given_ratio, 4).
% 1.33/1.87 dependent: assign(stats_level, 1).
% 1.33/1.87 dependent: assign(max_seconds, 10800).
% 1.33/1.87 clear(print_given).
% 1.33/1.87
% 1.33/1.87 list(usable).
% 1.33/1.87 0 [] A=A.
% 1.33/1.87 0 [] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 1.33/1.87 0 [] multiply(A,B)=divide(A,inverse(B)).
% 1.33/1.87 0 [] multiply(a,b)!=multiply(b,a).
% 1.33/1.87 end_of_list.
% 1.33/1.87
% 1.33/1.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.33/1.87
% 1.33/1.87 All clauses are units, and equality is present; the
% 1.33/1.87 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.33/1.87
% 1.33/1.87 dependent: set(knuth_bendix).
% 1.33/1.87 dependent: set(anl_eq).
% 1.33/1.87 dependent: set(para_from).
% 1.33/1.87 dependent: set(para_into).
% 1.33/1.87 dependent: clear(para_from_right).
% 1.33/1.87 dependent: clear(para_into_right).
% 1.33/1.87 dependent: set(para_from_vars).
% 1.33/1.87 dependent: set(eq_units_both_ways).
% 1.33/1.87 dependent: set(dynamic_demod_all).
% 1.33/1.87 dependent: set(dynamic_demod).
% 1.33/1.87 dependent: set(order_eq).
% 1.33/1.87 dependent: set(back_demod).
% 1.33/1.87 dependent: set(lrpo).
% 1.33/1.87
% 1.33/1.87 ------------> process usable:
% 1.33/1.87 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.33/1.87
% 1.33/1.87 ------------> process sos:
% 1.33/1.87 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.33/1.87 ** KEPT (pick-wt=12): 4 [] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 1.33/1.87 ---> New Demodulator: 5 [new_demod,4] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 1.33/1.87 ** KEPT (pick-wt=8): 6 [] multiply(A,B)=divide(A,inverse(B)).
% 1.33/1.87 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.33/1.87 >>>> Starting back demodulation with 5.
% 1.33/1.87 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] divide(A,inverse(B))=multiply(A,B).
% 1.33/1.87 Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,inverse(B)).
% 1.33/1.87
% 1.33/1.87 ======= end of input processing =======
% 1.33/1.87
% 1.33/1.87 =========== start of search ===========
% 1.33/1.87
% 1.33/1.87 -------- PROOF --------
% 1.33/1.87
% 1.33/1.87 ----> UNIT CONFLICT at 0.01 sec ----> 315 [binary,314.1,8.1] $F.
% 1.33/1.87
% 1.33/1.87 Length of proof is 20. Level of proof is 8.
% 1.33/1.87
% 1.33/1.87 ---------------- PROOF ----------------
% 1.33/1.87 % SZS status Unsatisfiable
% 1.33/1.87 % SZS output start Refutation
% See solution above
% 1.33/1.87 ------------ end of proof -------------
% 1.33/1.87
% 1.33/1.87
% 1.33/1.87 Search stopped by max_proofs option.
% 1.33/1.87
% 1.33/1.87
% 1.33/1.87 Search stopped by max_proofs option.
% 1.33/1.87
% 1.33/1.87 ============ end of search ============
% 1.33/1.87
% 1.33/1.87 -------------- statistics -------------
% 1.33/1.87 clauses given 24
% 1.33/1.87 clauses generated 295
% 1.33/1.87 clauses kept 201
% 1.33/1.87 clauses forward subsumed 257
% 1.33/1.87 clauses back subsumed 6
% 1.33/1.87 Kbytes malloced 2929
% 1.33/1.87
% 1.33/1.87 ----------- times (seconds) -----------
% 1.33/1.87 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.33/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.33/1.87 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.33/1.87
% 1.33/1.87 That finishes the proof of the theorem.
% 1.33/1.87
% 1.33/1.87 Process 21323 finished Wed Jul 27 04:55:04 2022
% 1.33/1.87 Otter interrupted
% 1.33/1.87 PROOF FOUND
%------------------------------------------------------------------------------