TSTP Solution File: GRP415-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP415-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 1.74s 1.96s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 RR)
% Number of literals : 21 ( 20 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 16 ( 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 : 63 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP415-1.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(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = C,
file('GRP415-1.p',unknown),
[] ).
cnf(8,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A)))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,D)),multiply(E,inverse(C)))),inverse(multiply(inverse(D),D))))),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.1.2.1.1.1.2.2,4.1.1')] ).
cnf(18,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(inverse(C))))),inverse(multiply(inverse(A),A))))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,5])]),
[iquote('para_into,8.1.1,4.1.1,flip.1')] ).
cnf(40,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,inverse(inverse(C))))),inverse(multiply(inverse(B),B))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[18,8]),18]),
[iquote('para_from,17.1.1,8.1.1.1.2.1.1.1.2,demod,18')] ).
cnf(41,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(C))))),inverse(multiply(inverse(B),B))) = inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D)))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[40])]),
[iquote('copy,40,flip.1')] ).
cnf(60,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(C))))))),inverse(multiply(inverse(B),B))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,5])]),
[iquote('para_into,40.1.1,4.1.1,flip.1')] ).
cnf(161,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),inverse(multiply(inverse(B),B))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[60,8]),5]),
[iquote('para_into,59.1.1.1.1.2.2.1,8.1.1,demod,5')] ).
cnf(162,plain,
inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(inverse(multiply(C,inverse(D))))))),A)),D)),inverse(multiply(inverse(A),A)))))) = multiply(inverse(C),C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[60,8]),18]),
[iquote('para_from,59.1.1,8.1.1.1.2.1.1.1.2,demod,18')] ).
cnf(170,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(B),B)))))))) = C,
inference(para_from,[status(thm),theory(equality)],[41,18]),
[iquote('para_from,41.1.1,17.1.1.2.1')] ).
cnf(172,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),A)),D)),inverse(multiply(inverse(A),A))))))) = multiply(B,inverse(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(inverse(C),C)))))))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[170,170])]),
[iquote('para_into,169.1.1.2.1.1.2.1.1.1,169.1.1,flip.1')] ).
cnf(173,plain,
multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(multiply(C,B)),multiply(C,D))),inverse(multiply(inverse(B),B)))))))) = multiply(A,D),
inference(para_into,[status(thm),theory(equality)],[170,161]),
[iquote('para_into,169.1.1.2.1.1.2.1,161.1.1')] ).
cnf(175,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),C)),inverse(multiply(inverse(A),A))))) = multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(B,D)),C)),inverse(multiply(inverse(D),D))))),
inference(para_from,[status(thm),theory(equality)],[170,18]),
[iquote('para_from,169.1.1,17.1.1.2.1.1.1.2')] ).
cnf(178,plain,
inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,C))),inverse(multiply(inverse(A),A))))))) = C,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[173,170]),170])]),
[iquote('para_from,173.1.1,169.1.1.2.1.1.2.1.1.1,demod,170,flip.1')] ).
cnf(181,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),E)),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))) = E,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[178,161]),172]),
[iquote('para_into,178.1.1.1.1.2.1.1.1.1.1,161.1.1,demod,172')] ).
cnf(193,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = multiply(inverse(A),A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[162,161]),60]),
[iquote('para_into,162.1.1.1.2.1.1.1.1.1,161.1.1,demod,60')] ).
cnf(197,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(B,inverse(multiply(inverse(C),inverse(multiply(inverse(B),B))))))))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[181,175]),172]),
[iquote('para_into,181.1.1.2.1.1,175.1.1,demod,172')] ).
cnf(204,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(para_into,[status(thm),theory(equality)],[197,193]),
[iquote('para_into,197.1.1.2.2.1,193.1.1')] ).
cnf(265,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[204,60]),60]),
[iquote('para_into,204.1.1.1.1,59.1.1,demod,60')] ).
cnf(266,plain,
$false,
inference(binary,[status(thm)],[265,2]),
[iquote('binary,265.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP415-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 05:01:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.96 ----- Otter 3.3f, August 2004 -----
% 1.74/1.96 The process was started by sandbox2 on n019.cluster.edu,
% 1.74/1.96 Wed Jul 27 05:01:22 2022
% 1.74/1.96 The command was "./otter". The process ID is 7661.
% 1.74/1.96
% 1.74/1.96 set(prolog_style_variables).
% 1.74/1.96 set(auto).
% 1.74/1.96 dependent: set(auto1).
% 1.74/1.96 dependent: set(process_input).
% 1.74/1.96 dependent: clear(print_kept).
% 1.74/1.96 dependent: clear(print_new_demod).
% 1.74/1.96 dependent: clear(print_back_demod).
% 1.74/1.96 dependent: clear(print_back_sub).
% 1.74/1.96 dependent: set(control_memory).
% 1.74/1.96 dependent: assign(max_mem, 12000).
% 1.74/1.96 dependent: assign(pick_given_ratio, 4).
% 1.74/1.96 dependent: assign(stats_level, 1).
% 1.74/1.96 dependent: assign(max_seconds, 10800).
% 1.74/1.96 clear(print_given).
% 1.74/1.96
% 1.74/1.96 list(usable).
% 1.74/1.96 0 [] A=A.
% 1.74/1.96 0 [] inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A))))))=C.
% 1.74/1.96 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.96
% 1.74/1.96 All clauses are units, and equality is present; the
% 1.74/1.96 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.96
% 1.74/1.96 dependent: set(knuth_bendix).
% 1.74/1.96 dependent: set(anl_eq).
% 1.74/1.96 dependent: set(para_from).
% 1.74/1.96 dependent: set(para_into).
% 1.74/1.96 dependent: clear(para_from_right).
% 1.74/1.96 dependent: clear(para_into_right).
% 1.74/1.96 dependent: set(para_from_vars).
% 1.74/1.96 dependent: set(eq_units_both_ways).
% 1.74/1.96 dependent: set(dynamic_demod_all).
% 1.74/1.96 dependent: set(dynamic_demod).
% 1.74/1.96 dependent: set(order_eq).
% 1.74/1.96 dependent: set(back_demod).
% 1.74/1.96 dependent: set(lrpo).
% 1.74/1.96
% 1.74/1.96 ------------> process usable:
% 1.74/1.96 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.74/1.96
% 1.74/1.96 ------------> process sos:
% 1.74/1.96 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.74/1.96 ** KEPT (pick-wt=22): 4 [] inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A))))))=C.
% 1.74/1.96 ---> New Demodulator: 5 [new_demod,4] inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A))))))=C.
% 1.74/1.96 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.74/1.96 >>>> Starting back demodulation with 5.
% 1.74/1.96
% 1.74/1.96 ======= end of input processing =======
% 1.74/1.96
% 1.74/1.96 =========== start of search ===========
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Resetting weight limit to 39.
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Resetting weight limit to 39.
% 1.74/1.96
% 1.74/1.96 sos_size=97
% 1.74/1.96
% 1.74/1.96 -------- PROOF --------
% 1.74/1.96
% 1.74/1.96 ----> UNIT CONFLICT at 0.07 sec ----> 266 [binary,265.1,2.1] $F.
% 1.74/1.96
% 1.74/1.96 Length of proof is 18. Level of proof is 11.
% 1.74/1.96
% 1.74/1.96 ---------------- PROOF ----------------
% 1.74/1.96 % SZS status Unsatisfiable
% 1.74/1.96 % SZS output start Refutation
% See solution above
% 1.74/1.96 ------------ end of proof -------------
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96 ============ end of search ============
% 1.74/1.96
% 1.74/1.96 -------------- statistics -------------
% 1.74/1.96 clauses given 25
% 1.74/1.96 clauses generated 2092
% 1.74/1.96 clauses kept 186
% 1.74/1.96 clauses forward subsumed 486
% 1.74/1.96 clauses back subsumed 8
% 1.74/1.96 Kbytes malloced 6835
% 1.74/1.96
% 1.74/1.96 ----------- times (seconds) -----------
% 1.74/1.96 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.74/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.96 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.96
% 1.74/1.96 That finishes the proof of the theorem.
% 1.74/1.96
% 1.74/1.96 Process 7661 finished Wed Jul 27 05:01:23 2022
% 1.74/1.96 Otter interrupted
% 1.74/1.96 PROOF FOUND
%------------------------------------------------------------------------------