TSTP Solution File: GRP580-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:57:17 EDT 2022
% Result : Unsatisfiable 1.63s 1.84s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 7 RR)
% Number of literals : 36 ( 35 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP580-1.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,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
file('GRP580-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP580-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP580-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP580-1.p',unknown),
[] ).
cnf(12,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10]),9])]),
[iquote('copy,10,demod,9,flip.1')] ).
cnf(13,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
[iquote('back_demod,2,demod,7,7,flip.1')] ).
cnf(14,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1.1,11.1.1')] ).
cnf(18,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,A),identity),
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1,11.1.1')] ).
cnf(26,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[14,12]),
[iquote('para_into,14.1.1.1.2,11.1.1')] ).
cnf(34,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(para_into,[status(thm),theory(equality)],[26,12]),
[iquote('para_into,26.1.1.1.1.1,11.1.1')] ).
cnf(38,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),double_divide(identity,identity)) = B,
inference(para_from,[status(thm),theory(equality)],[26,4]),
[iquote('para_from,26.1.1,4.1.1.1.2.1.1')] ).
cnf(41,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[34,4]),12]),
[iquote('para_from,34.1.1,4.1.1.1.2.1,demod,12')] ).
cnf(45,plain,
double_divide(identity,identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[41,14]),41,41]),
[iquote('para_from,40.1.1,14.1.1.1.2,demod,41,41')] ).
cnf(48,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[38]),45,45]),
[iquote('back_demod,38,demod,45,45')] ).
cnf(59,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),45]),
[iquote('back_demod,26,demod,45')] ).
cnf(67,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),45]),
[iquote('back_demod,18,demod,45')] ).
cnf(74,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),59]),
[iquote('back_demod,48,demod,59')] ).
cnf(80,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[74,12]),
[iquote('para_into,74.1.1.1.2.1,11.1.1')] ).
cnf(82,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),B),
inference(para_into,[status(thm),theory(equality)],[74,74]),
[iquote('para_into,74.1.1.1.2,74.1.1')] ).
cnf(84,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(B,A),B),
inference(para_from,[status(thm),theory(equality)],[74,59]),
[iquote('para_from,74.1.1,58.1.1.1.1')] ).
cnf(85,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),B) = identity,
inference(para_from,[status(thm),theory(equality)],[74,12]),
[iquote('para_from,74.1.1,11.1.1.2')] ).
cnf(87,plain,
double_divide(double_divide(A,B),A) = double_divide(double_divide(B,identity),identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[84])]),
[iquote('copy,84,flip.1')] ).
cnf(95,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
inference(para_from,[status(thm),theory(equality)],[80,59]),
[iquote('para_from,80.1.1,58.1.1.1.1')] ).
cnf(101,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),95]),
[iquote('back_demod,58,demod,95')] ).
cnf(108,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[82,45]),45])]),
[iquote('para_into,82.1.1.1,44.1.1,demod,45,flip.1')] ).
cnf(111,plain,
double_divide(double_divide(A,double_divide(double_divide(B,C),B)),A) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[82,74])]),
[iquote('para_into,82.1.1,74.1.1,flip.1')] ).
cnf(138,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,108])]),
[iquote('para_into,87.1.1.1,108.1.1,flip.1')] ).
cnf(141,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)) = double_divide(identity,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,87]),138,138]),
[iquote('para_into,87.1.1.1,87.1.1,demod,138,138')] ).
cnf(143,plain,
double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,85]),101,138]),
[iquote('para_into,87.1.1.1,85.1.1,demod,101,138')] ).
cnf(158,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(identity,double_divide(B,identity)),double_divide(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[141])]),
[iquote('copy,141,flip.1')] ).
cnf(162,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[111]),143,143,143,138,101]),
[iquote('back_demod,111,demod,143,143,143,138,101')] ).
cnf(170,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[158])]),162,162]),
[iquote('copy,158,flip.1,demod,162,162')] ).
cnf(179,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[67]),170]),
[iquote('back_demod,67,demod,170')] ).
cnf(180,plain,
$false,
inference(binary,[status(thm)],[179,13]),
[iquote('binary,179.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:15:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.63/1.84 ----- Otter 3.3f, August 2004 -----
% 1.63/1.84 The process was started by sandbox2 on n022.cluster.edu,
% 1.63/1.84 Wed Jul 27 05:15:20 2022
% 1.63/1.84 The command was "./otter". The process ID is 13137.
% 1.63/1.84
% 1.63/1.84 set(prolog_style_variables).
% 1.63/1.84 set(auto).
% 1.63/1.84 dependent: set(auto1).
% 1.63/1.84 dependent: set(process_input).
% 1.63/1.84 dependent: clear(print_kept).
% 1.63/1.84 dependent: clear(print_new_demod).
% 1.63/1.84 dependent: clear(print_back_demod).
% 1.63/1.84 dependent: clear(print_back_sub).
% 1.63/1.84 dependent: set(control_memory).
% 1.63/1.84 dependent: assign(max_mem, 12000).
% 1.63/1.84 dependent: assign(pick_given_ratio, 4).
% 1.63/1.84 dependent: assign(stats_level, 1).
% 1.63/1.84 dependent: assign(max_seconds, 10800).
% 1.63/1.84 clear(print_given).
% 1.63/1.84
% 1.63/1.84 list(usable).
% 1.63/1.84 0 [] A=A.
% 1.63/1.84 0 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.63/1.84 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.63/1.84 0 [] inverse(A)=double_divide(A,identity).
% 1.63/1.84 0 [] identity=double_divide(A,inverse(A)).
% 1.63/1.84 0 [] multiply(a,b)!=multiply(b,a).
% 1.63/1.84 end_of_list.
% 1.63/1.84
% 1.63/1.84 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.63/1.84
% 1.63/1.84 All clauses are units, and equality is present; the
% 1.63/1.84 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.63/1.84
% 1.63/1.84 dependent: set(knuth_bendix).
% 1.63/1.84 dependent: set(anl_eq).
% 1.63/1.84 dependent: set(para_from).
% 1.63/1.84 dependent: set(para_into).
% 1.63/1.84 dependent: clear(para_from_right).
% 1.63/1.84 dependent: clear(para_into_right).
% 1.63/1.84 dependent: set(para_from_vars).
% 1.63/1.84 dependent: set(eq_units_both_ways).
% 1.63/1.84 dependent: set(dynamic_demod_all).
% 1.63/1.84 dependent: set(dynamic_demod).
% 1.63/1.84 dependent: set(order_eq).
% 1.63/1.84 dependent: set(back_demod).
% 1.63/1.84 dependent: set(lrpo).
% 1.63/1.84
% 1.63/1.84 ------------> process usable:
% 1.63/1.84 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.63/1.84
% 1.63/1.84 ------------> process sos:
% 1.63/1.84 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.63/1.84 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.63/1.84 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.63/1.84 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.63/1.84 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.63/1.84 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 1.63/1.84 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 1.63/1.84 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.63/1.84 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 1.63/1.84 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.63/1.84 >>>> Starting back demodulation with 5.
% 1.63/1.84 >>>> Starting back demodulation with 7.
% 1.63/1.84 >> back demodulating 2 with 7.
% 1.63/1.84 >>>> Starting back demodulation with 9.
% 1.63/1.84 >>>> Starting back demodulation with 12.
% 1.63/1.84
% 1.63/1.84 ======= end of input processing =======
% 1.63/1.84
% 1.63/1.84 =========== start of search ===========
% 1.63/1.84
% 1.63/1.84 -------- PROOF --------
% 1.63/1.84
% 1.63/1.84 ----> UNIT CONFLICT at 0.01 sec ----> 180 [binary,179.1,13.1] $F.
% 1.63/1.84
% 1.63/1.84 Length of proof is 30. Level of proof is 15.
% 1.63/1.84
% 1.63/1.84 ---------------- PROOF ----------------
% 1.63/1.84 % SZS status Unsatisfiable
% 1.63/1.84 % SZS output start Refutation
% See solution above
% 1.63/1.84 ------------ end of proof -------------
% 1.63/1.84
% 1.63/1.84
% 1.63/1.84 Search stopped by max_proofs option.
% 1.63/1.84
% 1.63/1.84
% 1.63/1.84 Search stopped by max_proofs option.
% 1.63/1.84
% 1.63/1.84 ============ end of search ============
% 1.63/1.84
% 1.63/1.84 -------------- statistics -------------
% 1.63/1.84 clauses given 23
% 1.63/1.84 clauses generated 183
% 1.63/1.84 clauses kept 99
% 1.63/1.84 clauses forward subsumed 178
% 1.63/1.84 clauses back subsumed 4
% 1.63/1.84 Kbytes malloced 1953
% 1.63/1.84
% 1.63/1.84 ----------- times (seconds) -----------
% 1.63/1.84 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.63/1.84 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.84 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.63/1.84
% 1.63/1.84 That finishes the proof of the theorem.
% 1.63/1.84
% 1.63/1.84 Process 13137 finished Wed Jul 27 05:15:22 2022
% 1.63/1.84 Otter interrupted
% 1.63/1.84 PROOF FOUND
%------------------------------------------------------------------------------