TSTP Solution File: GRP700+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP700+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:57:40 EDT 2022
% Result : Theorem 1.74s 1.95s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 13 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( mult(A,dollar_c1) != unit
| mult(dollar_c1,A) != unit ),
file('GRP700+1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP700+1.p',unknown),
[] ).
cnf(7,axiom,
mult(rd(A,B),B) = A,
file('GRP700+1.p',unknown),
[] ).
cnf(10,axiom,
rd(mult(A,B),B) = A,
file('GRP700+1.p',unknown),
[] ).
cnf(12,axiom,
mult(A,unit) = A,
file('GRP700+1.p',unknown),
[] ).
cnf(13,axiom,
mult(unit,A) = A,
file('GRP700+1.p',unknown),
[] ).
cnf(15,axiom,
mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
file('GRP700+1.p',unknown),
[] ).
cnf(30,plain,
( A != unit
| mult(dollar_c1,rd(A,dollar_c1)) != unit ),
inference(para_from,[status(thm),theory(equality)],[7,1]),
[iquote('para_from,7.1.1,1.1.1')] ).
cnf(32,plain,
rd(A,A) = unit,
inference(para_into,[status(thm),theory(equality)],[10,13]),
[iquote('para_into,9.1.1.1,13.1.1')] ).
cnf(45,plain,
mult(mult(mult(A,B),A),A) = mult(A,mult(mult(B,A),A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,12]),12]),
[iquote('para_into,15.1.1.2,11.1.1,demod,12')] ).
cnf(156,plain,
rd(mult(A,mult(mult(B,A),A)),A) = mult(mult(A,B),A),
inference(para_from,[status(thm),theory(equality)],[45,10]),
[iquote('para_from,45.1.1,9.1.1.1')] ).
cnf(274,plain,
rd(mult(A,mult(B,A)),A) = mult(mult(A,rd(B,A)),A),
inference(para_into,[status(thm),theory(equality)],[156,7]),
[iquote('para_into,156.1.1.1.2.1,7.1.1')] ).
cnf(370,plain,
mult(mult(A,rd(unit,A)),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[274,13]),10])]),
[iquote('para_into,274.1.1.1.2,13.1.1,demod,10,flip.1')] ).
cnf(379,plain,
mult(A,rd(unit,A)) = unit,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[370,10]),32])]),
[iquote('para_from,370.1.1,9.1.1.1,demod,32,flip.1')] ).
cnf(381,plain,
$false,
inference(hyper,[status(thm)],[379,30,2]),
[iquote('hyper,379,30,2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP700+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n009.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 05:20:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox2 on n009.cluster.edu,
% 1.74/1.95 Wed Jul 27 05:20:06 2022
% 1.74/1.95 The command was "./otter". The process ID is 14991.
% 1.74/1.95
% 1.74/1.95 set(prolog_style_variables).
% 1.74/1.95 set(auto).
% 1.74/1.95 dependent: set(auto1).
% 1.74/1.95 dependent: set(process_input).
% 1.74/1.95 dependent: clear(print_kept).
% 1.74/1.95 dependent: clear(print_new_demod).
% 1.74/1.95 dependent: clear(print_back_demod).
% 1.74/1.95 dependent: clear(print_back_sub).
% 1.74/1.95 dependent: set(control_memory).
% 1.74/1.95 dependent: assign(max_mem, 12000).
% 1.74/1.95 dependent: assign(pick_given_ratio, 4).
% 1.74/1.95 dependent: assign(stats_level, 1).
% 1.74/1.95 dependent: assign(max_seconds, 10800).
% 1.74/1.95 clear(print_given).
% 1.74/1.95
% 1.74/1.95 formula_list(usable).
% 1.74/1.95 all A (A=A).
% 1.74/1.95 all B A (mult(A,ld(A,B))=B).
% 1.74/1.95 all B A (ld(A,mult(A,B))=B).
% 1.74/1.95 all B A (mult(rd(A,B),B)=A).
% 1.74/1.95 all B A (rd(mult(A,B),B)=A).
% 1.74/1.95 all A (mult(A,unit)=A).
% 1.74/1.95 all A (mult(unit,A)=A).
% 1.74/1.95 all C B A (mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C))).
% 1.74/1.95 all C B A (mult(mult(A,B),mult(B,mult(C,B)))=mult(mult(A,mult(B,mult(B,C))),B)).
% 1.74/1.95 -(all X0 exists X1 (mult(X1,X0)=unit&mult(X0,X1)=unit)).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 -------> usable clausifies to:
% 1.74/1.95
% 1.74/1.95 list(usable).
% 1.74/1.95 0 [] A=A.
% 1.74/1.95 0 [] mult(A,ld(A,B))=B.
% 1.74/1.95 0 [] ld(A,mult(A,B))=B.
% 1.74/1.95 0 [] mult(rd(A,B),B)=A.
% 1.74/1.95 0 [] rd(mult(A,B),B)=A.
% 1.74/1.95 0 [] mult(A,unit)=A.
% 1.74/1.95 0 [] mult(unit,A)=A.
% 1.74/1.95 0 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.74/1.95 0 [] mult(mult(A,B),mult(B,mult(C,B)))=mult(mult(A,mult(B,mult(B,C))),B).
% 1.74/1.95 0 [] mult(X1,$c1)!=unit|mult($c1,X1)!=unit.
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.74/1.95
% 1.74/1.95 This is a Horn set with equality. The strategy will be
% 1.74/1.95 Knuth-Bendix and hyper_res, with positive clauses in
% 1.74/1.95 sos and nonpositive clauses in usable.
% 1.74/1.95
% 1.74/1.95 dependent: set(knuth_bendix).
% 1.74/1.95 dependent: set(anl_eq).
% 1.74/1.95 dependent: set(para_from).
% 1.74/1.95 dependent: set(para_into).
% 1.74/1.95 dependent: clear(para_from_right).
% 1.74/1.95 dependent: clear(para_into_right).
% 1.74/1.95 dependent: set(para_from_vars).
% 1.74/1.95 dependent: set(eq_units_both_ways).
% 1.74/1.95 dependent: set(dynamic_demod_all).
% 1.74/1.95 dependent: set(dynamic_demod).
% 1.74/1.95 dependent: set(order_eq).
% 1.74/1.95 dependent: set(back_demod).
% 1.74/1.95 dependent: set(lrpo).
% 1.74/1.95 dependent: set(hyper_res).
% 1.74/1.95 dependent: clear(order_hyper).
% 1.74/1.95
% 1.74/1.95 ------------> process usable:
% 1.74/1.95 ** KEPT (pick-wt=10): 1 [] mult(A,$c1)!=unit|mult($c1,A)!=unit.
% 1.74/1.95
% 1.74/1.95 ------------> process sos:
% 1.74/1.95 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.74/1.95 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.74/1.95 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.74/1.95 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.74/1.95 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.74/1.95 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.74/1.95 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.74/1.95 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.74/1.95 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.74/1.95 ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.74/1.95 ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.74/1.95 ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.74/1.95 ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.74/1.95 ** KEPT (pick-wt=19): 15 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.74/1.95 ** KEPT (pick-wt=19): 17 [copy,16,flip.1] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.74/1.95 ---> New Demodulator: 18 [new_demod,17] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.74/1.95 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.74/1.95 >>>> Starting back demodulation with 4.
% 1.74/1.95 >>>> Starting back demodulation with 6.
% 1.74/1.95 >>>> Starting back demodulation with 8.
% 1.74/1.95 >>>> Starting back demodulation with 10.
% 1.74/1.95 >>>> Starting back demodulation with 12.
% 1.74/1.95 >>>> Starting back demodulation with 14.
% 1.74/1.95 ** KEPT (pick-wt=19): 19 [copy,15,flip.1] mult(A,mult(mult(mult(B,A),A),C))=mult(mult(mult(A,B),A),mult(A,C)).
% 1.74/1.95 >>>> Starting back demodulation with 18.
% 1.74/1.95 Following clause subsumed by 15 during input processing: 0 [copy,19,flip.1] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.74/1.95
% 1.74/1.95 ======= end of input processing =======
% 1.74/1.95
% 1.74/1.95 =========== start of search ===========
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Resetting weight limit to 18.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Resetting weight limit to 18.
% 1.74/1.95
% 1.74/1.95 sos_size=156
% 1.74/1.95
% 1.74/1.95 -------- PROOF --------
% 1.74/1.95
% 1.74/1.95 -----> EMPTY CLAUSE at 0.03 sec ----> 381 [hyper,379,30,2] $F.
% 1.74/1.95
% 1.74/1.95 Length of proof is 7. Level of proof is 5.
% 1.74/1.95
% 1.74/1.95 ---------------- PROOF ----------------
% 1.74/1.95 % SZS status Theorem
% 1.74/1.95 % SZS output start Refutation
% See solution above
% 1.74/1.95 ------------ end of proof -------------
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95 ============ end of search ============
% 1.74/1.95
% 1.74/1.95 -------------- statistics -------------
% 1.74/1.95 clauses given 42
% 1.74/1.95 clauses generated 690
% 1.74/1.95 clauses kept 241
% 1.74/1.95 clauses forward subsumed 397
% 1.74/1.95 clauses back subsumed 0
% 1.74/1.95 Kbytes malloced 5859
% 1.74/1.95
% 1.74/1.95 ----------- times (seconds) -----------
% 1.74/1.95 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.74/1.95 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.95 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.95
% 1.74/1.95 That finishes the proof of the theorem.
% 1.74/1.95
% 1.74/1.95 Process 14991 finished Wed Jul 27 05:20:07 2022
% 1.74/1.95 Otter interrupted
% 1.74/1.95 PROOF FOUND
%------------------------------------------------------------------------------