TSTP Solution File: GRP710+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP710+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 1.76s 1.96s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 14 unt; 0 nHn; 4 RR)
% Number of literals : 20 ( 19 equ; 6 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( mult(dollar_c2,A) != dollar_c1
| mult(B,dollar_c3) != dollar_c4 ),
file('GRP710+1.p',unknown),
[] ).
cnf(4,axiom,
mult(A,unit) = A,
file('GRP710+1.p',unknown),
[] ).
cnf(6,axiom,
mult(unit,A) = A,
file('GRP710+1.p',unknown),
[] ).
cnf(7,axiom,
mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('GRP710+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('GRP710+1.p',unknown),
[] ).
cnf(20,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(21,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(43,plain,
mult(A,mult(i(A),i(A))) = i(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,4]),4]),
[iquote('para_into,19.1.1.2.2,3.1.1,demod,4')] ).
cnf(46,plain,
( mult(i(dollar_c2),A) != dollar_c1
| mult(B,dollar_c3) != dollar_c4 ),
inference(para_from,[status(thm),theory(equality)],[20,1]),
[iquote('para_from,19.1.1,1.1.1')] ).
cnf(57,plain,
mult(mult(mult(A,B),i(B)),C) = mult(A,mult(B,mult(i(B),C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,11]),4,20]),
[iquote('para_into,21.1.1.1.1.2.2,10.1.1,demod,4,20')] ).
cnf(81,plain,
i(i(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,20]),11,4,43])]),
[iquote('para_from,42.1.1,19.1.1.2.2,demod,11,4,43,flip.1')] ).
cnf(448,plain,
mult(A,mult(i(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,6]),11,6,6])]),
[iquote('para_into,57.1.1.1.1,5.1.1,demod,11,6,6,flip.1')] ).
cnf(464,plain,
mult(mult(A,B),i(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,4]),4,11,4]),
[iquote('para_into,57.1.1,3.1.1,demod,4,11,4')] ).
cnf(525,plain,
( A != dollar_c1
| mult(B,dollar_c3) != dollar_c4 ),
inference(para_from,[status(thm),theory(equality)],[448,46]),
[iquote('para_from,448.1.1,46.1.1')] ).
cnf(624,plain,
mult(mult(A,i(B)),B) = A,
inference(para_into,[status(thm),theory(equality)],[464,81]),
[iquote('para_into,464.1.1.2,81.1.1')] ).
cnf(639,plain,
$false,
inference(hyper,[status(thm)],[624,525,624]),
[iquote('hyper,624,525,624')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP710+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 05:13:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.76/1.96 ----- Otter 3.3f, August 2004 -----
% 1.76/1.96 The process was started by sandbox2 on n005.cluster.edu,
% 1.76/1.96 Wed Jul 27 05:13:50 2022
% 1.76/1.96 The command was "./otter". The process ID is 29119.
% 1.76/1.96
% 1.76/1.96 set(prolog_style_variables).
% 1.76/1.96 set(auto).
% 1.76/1.96 dependent: set(auto1).
% 1.76/1.96 dependent: set(process_input).
% 1.76/1.96 dependent: clear(print_kept).
% 1.76/1.96 dependent: clear(print_new_demod).
% 1.76/1.96 dependent: clear(print_back_demod).
% 1.76/1.96 dependent: clear(print_back_sub).
% 1.76/1.96 dependent: set(control_memory).
% 1.76/1.96 dependent: assign(max_mem, 12000).
% 1.76/1.96 dependent: assign(pick_given_ratio, 4).
% 1.76/1.96 dependent: assign(stats_level, 1).
% 1.76/1.96 dependent: assign(max_seconds, 10800).
% 1.76/1.96 clear(print_given).
% 1.76/1.96
% 1.76/1.96 formula_list(usable).
% 1.76/1.96 all A (A=A).
% 1.76/1.96 all A (mult(A,unit)=A).
% 1.76/1.96 all A (mult(unit,A)=A).
% 1.76/1.96 all C B A (mult(A,mult(B,mult(B,C)))=mult(mult(mult(A,B),B),C)).
% 1.76/1.96 all A (mult(A,i(A))=unit).
% 1.76/1.96 all A (mult(i(A),A)=unit).
% 1.76/1.96 -((all X0 X1 exists X2 (mult(X0,X2)=X1))& (all X3 X4 exists X5 (mult(X5,X4)=X3))).
% 1.76/1.96 end_of_list.
% 1.76/1.96
% 1.76/1.96 -------> usable clausifies to:
% 1.76/1.96
% 1.76/1.96 list(usable).
% 1.76/1.96 0 [] A=A.
% 1.76/1.96 0 [] mult(A,unit)=A.
% 1.76/1.96 0 [] mult(unit,A)=A.
% 1.76/1.96 0 [] mult(A,mult(B,mult(B,C)))=mult(mult(mult(A,B),B),C).
% 1.76/1.96 0 [] mult(A,i(A))=unit.
% 1.76/1.96 0 [] mult(i(A),A)=unit.
% 1.76/1.96 0 [] mult($c2,X2)!=$c1|mult(X5,$c3)!=$c4.
% 1.76/1.96 end_of_list.
% 1.76/1.96
% 1.76/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.76/1.96
% 1.76/1.96 This is a Horn set with equality. The strategy will be
% 1.76/1.96 Knuth-Bendix and hyper_res, with positive clauses in
% 1.76/1.96 sos and nonpositive clauses in usable.
% 1.76/1.96
% 1.76/1.96 dependent: set(knuth_bendix).
% 1.76/1.96 dependent: set(anl_eq).
% 1.76/1.96 dependent: set(para_from).
% 1.76/1.96 dependent: set(para_into).
% 1.76/1.96 dependent: clear(para_from_right).
% 1.76/1.96 dependent: clear(para_into_right).
% 1.76/1.96 dependent: set(para_from_vars).
% 1.76/1.96 dependent: set(eq_units_both_ways).
% 1.76/1.96 dependent: set(dynamic_demod_all).
% 1.76/1.96 dependent: set(dynamic_demod).
% 1.76/1.96 dependent: set(order_eq).
% 1.76/1.96 dependent: set(back_demod).
% 1.76/1.96 dependent: set(lrpo).
% 1.76/1.96 dependent: set(hyper_res).
% 1.76/1.96 dependent: clear(order_hyper).
% 1.76/1.96
% 1.76/1.96 ------------> process usable:
% 1.76/1.96 ** KEPT (pick-wt=10): 1 [] mult($c2,A)!=$c1|mult(B,$c3)!=$c4.
% 1.76/1.96
% 1.76/1.96 ------------> process sos:
% 1.76/1.96 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.76/1.96 ** KEPT (pick-wt=5): 3 [] mult(A,unit)=A.
% 1.76/1.96 ---> New Demodulator: 4 [new_demod,3] mult(A,unit)=A.
% 1.76/1.96 ** KEPT (pick-wt=5): 5 [] mult(unit,A)=A.
% 1.76/1.96 ---> New Demodulator: 6 [new_demod,5] mult(unit,A)=A.
% 1.76/1.96 ** KEPT (pick-wt=15): 8 [copy,7,flip.1] mult(mult(mult(A,B),B),C)=mult(A,mult(B,mult(B,C))).
% 1.76/1.96 ---> New Demodulator: 9 [new_demod,8] mult(mult(mult(A,B),B),C)=mult(A,mult(B,mult(B,C))).
% 1.76/1.96 ** KEPT (pick-wt=6): 10 [] mult(A,i(A))=unit.
% 1.76/1.96 ---> New Demodulator: 11 [new_demod,10] mult(A,i(A))=unit.
% 1.76/1.96 ** KEPT (pick-wt=6): 12 [] mult(i(A),A)=unit.
% 1.76/1.96 ---> New Demodulator: 13 [new_demod,12] mult(i(A),A)=unit.
% 1.76/1.96 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.76/1.96 >>>> Starting back demodulation with 4.
% 1.76/1.96 >>>> Starting back demodulation with 6.
% 1.76/1.96 >>>> Starting back demodulation with 9.
% 1.76/1.96 >>>> Starting back demodulation with 11.
% 1.76/1.96 >>>> Starting back demodulation with 13.
% 1.76/1.96
% 1.76/1.96 ======= end of input processing =======
% 1.76/1.96
% 1.76/1.96 =========== start of search ===========
% 1.76/1.96
% 1.76/1.96
% 1.76/1.96 Resetting weight limit to 13.
% 1.76/1.96
% 1.76/1.96
% 1.76/1.96 Resetting weight limit to 13.
% 1.76/1.96
% 1.76/1.96 sos_size=182
% 1.76/1.96
% 1.76/1.96 -------- PROOF --------
% 1.76/1.96
% 1.76/1.96 -----> EMPTY CLAUSE at 0.06 sec ----> 639 [hyper,624,525,624] $F.
% 1.76/1.96
% 1.76/1.96 Length of proof is 11. Level of proof is 5.
% 1.76/1.96
% 1.76/1.96 ---------------- PROOF ----------------
% 1.76/1.96 % SZS status Theorem
% 1.76/1.96 % SZS output start Refutation
% See solution above
% 1.76/1.96 ------------ end of proof -------------
% 1.76/1.96
% 1.76/1.96
% 1.76/1.96 Search stopped by max_proofs option.
% 1.76/1.96
% 1.76/1.96
% 1.76/1.96 Search stopped by max_proofs option.
% 1.76/1.96
% 1.76/1.96 ============ end of search ============
% 1.76/1.96
% 1.76/1.96 -------------- statistics -------------
% 1.76/1.96 clauses given 65
% 1.76/1.96 clauses generated 876
% 1.76/1.96 clauses kept 366
% 1.76/1.96 clauses forward subsumed 644
% 1.76/1.96 clauses back subsumed 47
% 1.76/1.96 Kbytes malloced 4882
% 1.76/1.96
% 1.76/1.96 ----------- times (seconds) -----------
% 1.76/1.96 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.76/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.96 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.76/1.96
% 1.76/1.96 That finishes the proof of the theorem.
% 1.76/1.96
% 1.76/1.96 Process 29119 finished Wed Jul 27 05:13:52 2022
% 1.76/1.96 Otter interrupted
% 1.76/1.96 PROOF FOUND
%------------------------------------------------------------------------------