TSTP Solution File: GRP421-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP421-1 : TPTP v8.1.0. Released v2.6.0.
% 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 12:56:58 EDT 2022
% Result : Unsatisfiable 1.71s 1.98s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 4 RR)
% Number of literals : 15 ( 14 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 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 : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP421-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = B,
file('GRP421-1.p',unknown),
[] ).
cnf(6,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E)),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.1.1.1.2.1.1,4.1.1')] ).
cnf(9,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = multiply(inverse(C),inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))))),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.1.1.1.2,4.1.1')] ).
cnf(11,plain,
multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(C,B)),multiply(C,A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(39,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),
inference(para_into,[status(thm),theory(equality)],[11,11]),
[iquote('para_into,11.1.1,11.1.1')] ).
cnf(56,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),multiply(inverse(C),inverse(multiply(inverse(C),C))))) = B,
inference(para_from,[status(thm),theory(equality)],[11,5]),
[iquote('para_from,11.1.1,4.1.1.1.1.1')] ).
cnf(87,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[39,5]),5]),
[iquote('para_from,39.1.1,4.1.1.1.1.1.2.1.1,demod,5')] ).
cnf(109,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,11]),56])]),
[iquote('para_into,6.1.1.1.1.1,11.1.1,demod,56,flip.1')] ).
cnf(148,plain,
multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(A),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),D)) = multiply(inverse(multiply(E,multiply(B,C))),multiply(E,D)),
inference(para_into,[status(thm),theory(equality)],[87,5]),
[iquote('para_into,87.1.1.1,4.1.1')] ).
cnf(182,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,D))),
inference(para_into,[status(thm),theory(equality)],[148,109]),
[iquote('para_into,148.1.1.2,109.1.1')] ).
cnf(183,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) = multiply(inverse(D),D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[182])]),
[iquote('copy,182,flip.1')] ).
cnf(205,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[182,2]),
[iquote('para_from,182.1.1,2.1.1')] ).
cnf(206,plain,
$false,
inference(binary,[status(thm)],[205,183]),
[iquote('binary,205.1,183.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP421-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 04:53:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.98 ----- Otter 3.3f, August 2004 -----
% 1.71/1.98 The process was started by sandbox on n017.cluster.edu,
% 1.71/1.98 Wed Jul 27 04:53:03 2022
% 1.71/1.98 The command was "./otter". The process ID is 13416.
% 1.71/1.98
% 1.71/1.98 set(prolog_style_variables).
% 1.71/1.98 set(auto).
% 1.71/1.98 dependent: set(auto1).
% 1.71/1.98 dependent: set(process_input).
% 1.71/1.98 dependent: clear(print_kept).
% 1.71/1.98 dependent: clear(print_new_demod).
% 1.71/1.98 dependent: clear(print_back_demod).
% 1.71/1.98 dependent: clear(print_back_sub).
% 1.71/1.98 dependent: set(control_memory).
% 1.71/1.98 dependent: assign(max_mem, 12000).
% 1.71/1.98 dependent: assign(pick_given_ratio, 4).
% 1.71/1.98 dependent: assign(stats_level, 1).
% 1.71/1.98 dependent: assign(max_seconds, 10800).
% 1.71/1.98 clear(print_given).
% 1.71/1.98
% 1.71/1.98 list(usable).
% 1.71/1.98 0 [] A=A.
% 1.71/1.98 0 [] inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)))=B.
% 1.71/1.98 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.71/1.98 end_of_list.
% 1.71/1.98
% 1.71/1.98 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.98
% 1.71/1.98 All clauses are units, and equality is present; the
% 1.71/1.98 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.98
% 1.71/1.98 dependent: set(knuth_bendix).
% 1.71/1.98 dependent: set(anl_eq).
% 1.71/1.98 dependent: set(para_from).
% 1.71/1.98 dependent: set(para_into).
% 1.71/1.98 dependent: clear(para_from_right).
% 1.71/1.98 dependent: clear(para_into_right).
% 1.71/1.98 dependent: set(para_from_vars).
% 1.71/1.98 dependent: set(eq_units_both_ways).
% 1.71/1.98 dependent: set(dynamic_demod_all).
% 1.71/1.98 dependent: set(dynamic_demod).
% 1.71/1.98 dependent: set(order_eq).
% 1.71/1.98 dependent: set(back_demod).
% 1.71/1.98 dependent: set(lrpo).
% 1.71/1.98
% 1.71/1.98 ------------> process usable:
% 1.71/1.98 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.71/1.98
% 1.71/1.98 ------------> process sos:
% 1.71/1.98 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.71/1.98 ** KEPT (pick-wt=22): 4 [] inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)))=B.
% 1.71/1.98 ---> New Demodulator: 5 [new_demod,4] inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)))=B.
% 1.71/1.98 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.71/1.98 >>>> Starting back demodulation with 5.
% 1.71/1.98
% 1.71/1.98 ======= end of input processing =======
% 1.71/1.98
% 1.71/1.98 =========== start of search ===========
% 1.71/1.98
% 1.71/1.98
% 1.71/1.98 Resetting weight limit to 30.
% 1.71/1.98
% 1.71/1.98
% 1.71/1.98 Resetting weight limit to 30.
% 1.71/1.98
% 1.71/1.98 sos_size=119
% 1.71/1.98
% 1.71/1.98 -------- PROOF --------
% 1.71/1.98
% 1.71/1.98 ----> UNIT CONFLICT at 0.10 sec ----> 206 [binary,205.1,183.1] $F.
% 1.71/1.98
% 1.71/1.98 Length of proof is 12. Level of proof is 7.
% 1.71/1.98
% 1.71/1.98 ---------------- PROOF ----------------
% 1.71/1.98 % SZS status Unsatisfiable
% 1.71/1.98 % SZS output start Refutation
% See solution above
% 1.71/1.98 ------------ end of proof -------------
% 1.71/1.98
% 1.71/1.98
% 1.71/1.98 Search stopped by max_proofs option.
% 1.71/1.98
% 1.71/1.98
% 1.71/1.98 Search stopped by max_proofs option.
% 1.71/1.98
% 1.71/1.98 ============ end of search ============
% 1.71/1.98
% 1.71/1.98 -------------- statistics -------------
% 1.71/1.98 clauses given 32
% 1.71/1.98 clauses generated 3323
% 1.71/1.98 clauses kept 171
% 1.71/1.98 clauses forward subsumed 499
% 1.71/1.98 clauses back subsumed 1
% 1.71/1.98 Kbytes malloced 5859
% 1.71/1.98
% 1.71/1.98 ----------- times (seconds) -----------
% 1.71/1.98 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.71/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.98
% 1.71/1.98 That finishes the proof of the theorem.
% 1.71/1.98
% 1.71/1.98 Process 13416 finished Wed Jul 27 04:53:04 2022
% 1.71/1.98 Otter interrupted
% 1.71/1.98 PROOF FOUND
%------------------------------------------------------------------------------