TSTP Solution File: GRP711+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP711+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 12:57:43 EDT 2022
% Result : Theorem 1.69s 1.88s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of clauses : 35 ( 34 unt; 1 nHn; 6 RR)
% Number of literals : 36 ( 35 equ; 1 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
dollar_c2 != dollar_c1,
file('GRP711+1.p',unknown),
[] ).
cnf(4,axiom,
mult(A,unit) = A,
file('GRP711+1.p',unknown),
[] ).
cnf(6,axiom,
mult(unit,A) = A,
file('GRP711+1.p',unknown),
[] ).
cnf(7,axiom,
mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('GRP711+1.p',unknown),
[] ).
cnf(9,plain,
mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(11,axiom,
mult(A,i(A)) = unit,
file('GRP711+1.p',unknown),
[] ).
cnf(12,axiom,
mult(i(A),A) = unit,
file('GRP711+1.p',unknown),
[] ).
cnf(14,axiom,
( mult(dollar_c3,dollar_c2) = mult(dollar_c3,dollar_c1)
| mult(dollar_c2,dollar_c3) = mult(dollar_c1,dollar_c3) ),
file('GRP711+1.p',unknown),
[] ).
cnf(17,plain,
mult(A,mult(i(A),mult(i(A),B))) = mult(i(A),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,11]),6])]),
[iquote('para_into,8.1.1.1.1,10.1.1,demod,6,flip.1')] ).
cnf(19,plain,
mult(mult(mult(A,mult(B,mult(B,C))),C),D) = mult(A,mult(B,mult(B,mult(C,mult(C,D))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,9]),9]),
[iquote('para_into,8.1.1.1.1,8.1.1,demod,9')] ).
cnf(22,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,6]),6]),
[iquote('para_into,8.1.1.1.1,5.1.1,demod,6')] ).
cnf(28,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,4]),4]),
[iquote('para_into,8.1.1,3.1.1,demod,4')] ).
cnf(32,plain,
mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),28]),
[iquote('back_demod,8,demod,28')] ).
cnf(33,plain,
mult(A,mult(A,i(mult(A,A)))) = unit,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,11])]),
[iquote('para_into,21.1.1,10.1.1,flip.1')] ).
cnf(46,plain,
mult(A,mult(i(A),i(A))) = i(A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,11]),6])]),
[iquote('para_into,27.1.1.1,10.1.1,demod,6,flip.1')] ).
cnf(53,plain,
mult(A,mult(A,mult(i(mult(A,A)),i(mult(A,A))))) = i(mult(A,A)),
inference(para_into,[status(thm),theory(equality)],[46,22]),
[iquote('para_into,45.1.1,21.1.1')] ).
cnf(56,plain,
i(i(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,46]),11,4,46])]),
[iquote('para_into,17.1.1.2.2,45.1.1,demod,11,4,46,flip.1')] ).
cnf(58,plain,
mult(i(A),mult(A,mult(A,B))) = mult(A,mult(i(A),mult(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,17]),56,56,56])]),
[iquote('para_into,17.1.1.2.2,17.1.1,demod,56,56,56,flip.1')] ).
cnf(59,plain,
mult(i(A),i(mult(i(A),i(A)))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,33]),4])]),
[iquote('para_into,17.1.1.2,33.1.1,demod,4,flip.1')] ).
cnf(66,plain,
mult(A,mult(i(A),mult(A,B))) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[56,17]),56,58,56]),
[iquote('para_from,55.1.1,17.1.1.2.1,demod,56,58,56')] ).
cnf(68,plain,
mult(i(A),mult(A,mult(A,B))) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),66]),
[iquote('back_demod,57,demod,66')] ).
cnf(81,plain,
mult(mult(mult(A,i(B)),B),C) = mult(A,mult(i(B),mult(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,12]),4,68]),
[iquote('para_into,19.1.1.1.1.2.2,12.1.1,demod,4,68')] ).
cnf(128,plain,
mult(A,i(mult(A,A))) = i(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[59,56]),56,56]),
[iquote('para_into,59.1.1.1,55.1.1,demod,56,56')] ).
cnf(136,plain,
mult(A,mult(i(mult(A,A)),i(mult(A,A)))) = mult(i(A),i(mult(A,A))),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[128,28])]),
[iquote('para_from,127.1.1,27.1.1.1,flip.1')] ).
cnf(138,plain,
mult(A,mult(i(A),i(mult(A,A)))) = i(mult(A,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[53]),136]),
[iquote('back_demod,53,demod,136')] ).
cnf(216,plain,
i(mult(A,A)) = mult(i(A),i(A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[138,68]),128,138])]),
[iquote('para_from,137.1.1,67.1.1.2.2,demod,128,138,flip.1')] ).
cnf(230,plain,
mult(i(A),mult(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,12]),6,216,22,68])]),
[iquote('para_into,31.1.1.1,12.1.1,demod,6,216,22,68,flip.1')] ).
cnf(237,plain,
mult(mult(mult(A,i(B)),B),C) = mult(A,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[81]),230]),
[iquote('back_demod,81,demod,230')] ).
cnf(248,plain,
mult(A,mult(i(A),B)) = B,
inference(para_into,[status(thm),theory(equality)],[230,56]),
[iquote('para_into,229.1.1.1,55.1.1')] ).
cnf(258,plain,
mult(dollar_c2,dollar_c3) = mult(dollar_c1,dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[230,14]),230]),1]),
[iquote('para_into,229.1.1.2,14.1.1,demod,230,unit_del,1')] ).
cnf(268,plain,
mult(dollar_c2,mult(dollar_c3,dollar_c3)) = mult(dollar_c1,mult(dollar_c3,dollar_c3)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[258,28]),28])]),
[iquote('para_from,258.1.1,27.1.1.1,demod,28,flip.1')] ).
cnf(323,plain,
mult(mult(A,i(B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[237,4]),4]),
[iquote('para_into,237.1.1,3.1.1,demod,4')] ).
cnf(325,plain,
mult(mult(A,B),i(B)) = A,
inference(para_into,[status(thm),theory(equality)],[323,56]),
[iquote('para_into,323.1.1.1.2,55.1.1')] ).
cnf(361,plain,
dollar_c2 = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[325,268]),216,32,248,11,4])]),
[iquote('para_into,325.1.1.1,268.1.1,demod,216,32,248,11,4,flip.1')] ).
cnf(363,plain,
$false,
inference(binary,[status(thm)],[361,1]),
[iquote('binary,361.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP711+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 05:10:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.88 ----- Otter 3.3f, August 2004 -----
% 1.69/1.88 The process was started by sandbox2 on n028.cluster.edu,
% 1.69/1.88 Wed Jul 27 05:10:18 2022
% 1.69/1.88 The command was "./otter". The process ID is 4264.
% 1.69/1.88
% 1.69/1.88 set(prolog_style_variables).
% 1.69/1.88 set(auto).
% 1.69/1.88 dependent: set(auto1).
% 1.69/1.88 dependent: set(process_input).
% 1.69/1.88 dependent: clear(print_kept).
% 1.69/1.88 dependent: clear(print_new_demod).
% 1.69/1.88 dependent: clear(print_back_demod).
% 1.69/1.88 dependent: clear(print_back_sub).
% 1.69/1.88 dependent: set(control_memory).
% 1.69/1.88 dependent: assign(max_mem, 12000).
% 1.69/1.88 dependent: assign(pick_given_ratio, 4).
% 1.69/1.88 dependent: assign(stats_level, 1).
% 1.69/1.88 dependent: assign(max_seconds, 10800).
% 1.69/1.88 clear(print_given).
% 1.69/1.88
% 1.69/1.88 formula_list(usable).
% 1.69/1.88 all A (A=A).
% 1.69/1.88 all A (mult(A,unit)=A).
% 1.69/1.88 all A (mult(unit,A)=A).
% 1.69/1.88 all C B A (mult(A,mult(B,mult(B,C)))=mult(mult(mult(A,B),B),C)).
% 1.69/1.88 all A (mult(A,i(A))=unit).
% 1.69/1.88 all A (mult(i(A),A)=unit).
% 1.69/1.88 -(all X6 X7 X8 ((mult(X6,X7)=mult(X6,X8)->X7=X8)& (mult(X7,X6)=mult(X8,X6)->X7=X8))).
% 1.69/1.88 end_of_list.
% 1.69/1.88
% 1.69/1.88 -------> usable clausifies to:
% 1.69/1.88
% 1.69/1.88 list(usable).
% 1.69/1.88 0 [] A=A.
% 1.69/1.88 0 [] mult(A,unit)=A.
% 1.69/1.88 0 [] mult(unit,A)=A.
% 1.69/1.88 0 [] mult(A,mult(B,mult(B,C)))=mult(mult(mult(A,B),B),C).
% 1.69/1.88 0 [] mult(A,i(A))=unit.
% 1.69/1.88 0 [] mult(i(A),A)=unit.
% 1.69/1.88 0 [] mult($c3,$c2)=mult($c3,$c1)|mult($c2,$c3)=mult($c1,$c3).
% 1.69/1.88 0 [] $c2!=$c1.
% 1.69/1.88 end_of_list.
% 1.69/1.88
% 1.69/1.88 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.69/1.88
% 1.69/1.88 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.88 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.88 deletion, with positive clauses in sos and nonpositive
% 1.69/1.88 clauses in usable.
% 1.69/1.88
% 1.69/1.88 dependent: set(knuth_bendix).
% 1.69/1.88 dependent: set(anl_eq).
% 1.69/1.88 dependent: set(para_from).
% 1.69/1.88 dependent: set(para_into).
% 1.69/1.88 dependent: clear(para_from_right).
% 1.69/1.88 dependent: clear(para_into_right).
% 1.69/1.88 dependent: set(para_from_vars).
% 1.69/1.88 dependent: set(eq_units_both_ways).
% 1.69/1.88 dependent: set(dynamic_demod_all).
% 1.69/1.88 dependent: set(dynamic_demod).
% 1.69/1.88 dependent: set(order_eq).
% 1.69/1.88 dependent: set(back_demod).
% 1.69/1.88 dependent: set(lrpo).
% 1.69/1.88 dependent: set(hyper_res).
% 1.69/1.88 dependent: set(unit_deletion).
% 1.69/1.88 dependent: set(factor).
% 1.69/1.88
% 1.69/1.88 ------------> process usable:
% 1.69/1.88 ** KEPT (pick-wt=3): 1 [] $c2!=$c1.
% 1.69/1.88
% 1.69/1.88 ------------> process sos:
% 1.69/1.88 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.88 ** KEPT (pick-wt=5): 3 [] mult(A,unit)=A.
% 1.69/1.88 ---> New Demodulator: 4 [new_demod,3] mult(A,unit)=A.
% 1.69/1.88 ** KEPT (pick-wt=5): 5 [] mult(unit,A)=A.
% 1.69/1.88 ---> New Demodulator: 6 [new_demod,5] mult(unit,A)=A.
% 1.69/1.88 ** KEPT (pick-wt=15): 8 [copy,7,flip.1] mult(mult(mult(A,B),B),C)=mult(A,mult(B,mult(B,C))).
% 1.69/1.88 ---> New Demodulator: 9 [new_demod,8] mult(mult(mult(A,B),B),C)=mult(A,mult(B,mult(B,C))).
% 1.69/1.88 ** KEPT (pick-wt=6): 10 [] mult(A,i(A))=unit.
% 1.69/1.88 ---> New Demodulator: 11 [new_demod,10] mult(A,i(A))=unit.
% 1.69/1.88 ** KEPT (pick-wt=6): 12 [] mult(i(A),A)=unit.
% 1.69/1.88 ---> New Demodulator: 13 [new_demod,12] mult(i(A),A)=unit.
% 1.69/1.88 ** KEPT (pick-wt=14): 14 [] mult($c3,$c2)=mult($c3,$c1)|mult($c2,$c3)=mult($c1,$c3).
% 1.69/1.88 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.88 >>>> Starting back demodulation with 4.
% 1.69/1.88 >>>> Starting back demodulation with 6.
% 1.69/1.88 >>>> Starting back demodulation with 9.
% 1.69/1.88 >>>> Starting back demodulation with 11.
% 1.69/1.88 >>>> Starting back demodulation with 13.
% 1.69/1.88
% 1.69/1.88 ======= end of input processing =======
% 1.69/1.88
% 1.69/1.88 =========== start of search ===========
% 1.69/1.88
% 1.69/1.88 -------- PROOF --------
% 1.69/1.88
% 1.69/1.88 ----> UNIT CONFLICT at 0.02 sec ----> 363 [binary,361.1,1.1] $F.
% 1.69/1.88
% 1.69/1.88 Length of proof is 27. Level of proof is 13.
% 1.69/1.88
% 1.69/1.88 ---------------- PROOF ----------------
% 1.69/1.88 % SZS status Theorem
% 1.69/1.88 % SZS output start Refutation
% See solution above
% 1.69/1.88 ------------ end of proof -------------
% 1.69/1.88
% 1.69/1.88
% 1.69/1.88 Search stopped by max_proofs option.
% 1.69/1.88
% 1.69/1.88
% 1.69/1.88 Search stopped by max_proofs option.
% 1.69/1.88
% 1.69/1.88 ============ end of search ============
% 1.69/1.88
% 1.69/1.88 -------------- statistics -------------
% 1.69/1.88 clauses given 37
% 1.69/1.88 clauses generated 591
% 1.69/1.88 clauses kept 186
% 1.69/1.88 clauses forward subsumed 500
% 1.69/1.88 clauses back subsumed 0
% 1.69/1.88 Kbytes malloced 2929
% 1.69/1.88
% 1.69/1.88 ----------- times (seconds) -----------
% 1.69/1.88 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.69/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.69/1.88
% 1.69/1.88 That finishes the proof of the theorem.
% 1.69/1.88
% 1.69/1.88 Process 4264 finished Wed Jul 27 05:10:20 2022
% 1.69/1.88 Otter interrupted
% 1.69/1.88 PROOF FOUND
%------------------------------------------------------------------------------