TSTP Solution File: GRP406-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:56:57 EDT 2022
% Result : Unsatisfiable 2.02s 2.23s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 4 RR)
% Number of literals : 20 ( 19 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 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 : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP406-1.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,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C,
file('GRP406-1.p',unknown),
[] ).
cnf(6,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))))))) = C,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1.1.1.1.1,4.1.1')] ).
cnf(8,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(D),multiply(inverse(B),multiply(inverse(B),B))))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,5])]),
[iquote('para_into,4.1.1.2.1.1.1,4.1.1,flip.1')] ).
cnf(22,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(inverse(B),multiply(inverse(B),B)))))) = C,
inference(para_from,[status(thm),theory(equality)],[8,5]),
[iquote('para_from,8.1.1,4.1.1.2')] ).
cnf(37,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(inverse(D),multiply(inverse(E),multiply(inverse(E),E))))))) = multiply(inverse(multiply(inverse(multiply(C,E)),B)),D),
inference(para_into,[status(thm),theory(equality)],[22,8]),
[iquote('para_into,22.1.1.2.2,8.1.1')] ).
cnf(106,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(D),B)),multiply(inverse(D),C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[6,37]),5]),
[iquote('para_from,6.1.1,37.1.1.2.2,demod,5')] ).
cnf(111,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[106])]),
[iquote('copy,106,flip.1')] ).
cnf(152,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(para_into,[status(thm),theory(equality)],[111,111]),
[iquote('para_into,111.1.1,111.1.1')] ).
cnf(169,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(C,D)),multiply(C,multiply(inverse(B),B)))))) = multiply(inverse(B),D),
inference(para_from,[status(thm),theory(equality)],[152,22]),
[iquote('para_from,152.1.1,22.1.1.2.2.1')] ).
cnf(172,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(B),multiply(inverse(B),B)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[152,8]),5]),
[iquote('para_from,152.1.1,8.1.1.1.1.1,demod,5')] ).
cnf(174,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(B,C)),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D,
inference(para_from,[status(thm),theory(equality)],[152,22]),
[iquote('para_from,152.1.1,22.1.1.2.2.1.2.2')] ).
cnf(196,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(E,multiply(inverse(C),multiply(inverse(C),C)))),multiply(E,D)),
inference(para_from,[status(thm),theory(equality)],[172,152]),
[iquote('para_from,172.1.1,152.1.1.1')] ).
cnf(210,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(multiply(D,E)),multiply(D,multiply(inverse(multiply(F,C)),multiply(F,C))))))) = multiply(inverse(multiply(B,C)),E),
inference(para_into,[status(thm),theory(equality)],[169,152]),
[iquote('para_into,169.1.1.2.2.1.2.2,152.1.1')] ).
cnf(437,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(B),B))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[196,174]),210]),
[iquote('para_from,196.1.1,174.1.1.2.2.1,demod,210')] ).
cnf(443,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),
inference(para_from,[status(thm),theory(equality)],[437,196]),
[iquote('para_from,437.1.1,196.1.1.2')] ).
cnf(445,plain,
multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[443])]),
[iquote('copy,443,flip.1')] ).
cnf(447,plain,
multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[443,2]),
[iquote('para_from,443.1.1,2.1.1')] ).
cnf(448,plain,
$false,
inference(binary,[status(thm)],[447,445]),
[iquote('binary,447.1,445.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:30:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.02/2.23 ----- Otter 3.3f, August 2004 -----
% 2.02/2.23 The process was started by sandbox2 on n015.cluster.edu,
% 2.02/2.23 Wed Jul 27 05:30:41 2022
% 2.02/2.23 The command was "./otter". The process ID is 3487.
% 2.02/2.23
% 2.02/2.23 set(prolog_style_variables).
% 2.02/2.23 set(auto).
% 2.02/2.23 dependent: set(auto1).
% 2.02/2.23 dependent: set(process_input).
% 2.02/2.23 dependent: clear(print_kept).
% 2.02/2.23 dependent: clear(print_new_demod).
% 2.02/2.23 dependent: clear(print_back_demod).
% 2.02/2.23 dependent: clear(print_back_sub).
% 2.02/2.23 dependent: set(control_memory).
% 2.02/2.23 dependent: assign(max_mem, 12000).
% 2.02/2.23 dependent: assign(pick_given_ratio, 4).
% 2.02/2.23 dependent: assign(stats_level, 1).
% 2.02/2.23 dependent: assign(max_seconds, 10800).
% 2.02/2.23 clear(print_given).
% 2.02/2.23
% 2.02/2.23 list(usable).
% 2.02/2.23 0 [] A=A.
% 2.02/2.23 0 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.02/2.23 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 2.02/2.23 end_of_list.
% 2.02/2.23
% 2.02/2.23 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.02/2.23
% 2.02/2.23 All clauses are units, and equality is present; the
% 2.02/2.23 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.02/2.23
% 2.02/2.23 dependent: set(knuth_bendix).
% 2.02/2.23 dependent: set(anl_eq).
% 2.02/2.23 dependent: set(para_from).
% 2.02/2.23 dependent: set(para_into).
% 2.02/2.23 dependent: clear(para_from_right).
% 2.02/2.23 dependent: clear(para_into_right).
% 2.02/2.23 dependent: set(para_from_vars).
% 2.02/2.23 dependent: set(eq_units_both_ways).
% 2.02/2.23 dependent: set(dynamic_demod_all).
% 2.02/2.23 dependent: set(dynamic_demod).
% 2.02/2.23 dependent: set(order_eq).
% 2.02/2.23 dependent: set(back_demod).
% 2.02/2.23 dependent: set(lrpo).
% 2.02/2.23
% 2.02/2.23 ------------> process usable:
% 2.02/2.23 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 2.02/2.23
% 2.02/2.23 ------------> process sos:
% 2.02/2.23 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.02/2.23 ** KEPT (pick-wt=20): 4 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.02/2.23 ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.02/2.23 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.02/2.23 >>>> Starting back demodulation with 5.
% 2.02/2.23
% 2.02/2.23 ======= end of input processing =======
% 2.02/2.23
% 2.02/2.23 =========== start of search ===========
% 2.02/2.23
% 2.02/2.23
% 2.02/2.23 Resetting weight limit to 40.
% 2.02/2.23
% 2.02/2.23
% 2.02/2.23 Resetting weight limit to 40.
% 2.02/2.23
% 2.02/2.23 sos_size=66
% 2.02/2.23
% 2.02/2.23
% 2.02/2.23 Resetting weight limit to 30.
% 2.02/2.23
% 2.02/2.23
% 2.02/2.23 Resetting weight limit to 30.
% 2.02/2.23
% 2.02/2.23 sos_size=246
% 2.02/2.23
% 2.02/2.23 -------- PROOF --------
% 2.02/2.23
% 2.02/2.23 ----> UNIT CONFLICT at 0.14 sec ----> 448 [binary,447.1,445.1] $F.
% 2.02/2.23
% 2.02/2.23 Length of proof is 17. Level of proof is 11.
% 2.02/2.23
% 2.02/2.23 ---------------- PROOF ----------------
% 2.02/2.23 % SZS status Unsatisfiable
% 2.02/2.23 % SZS output start Refutation
% See solution above
% 2.02/2.23 ------------ end of proof -------------
% 2.02/2.23
% 2.02/2.23
% 2.02/2.23 Search stopped by max_proofs option.
% 2.02/2.23
% 2.02/2.23
% 2.02/2.23 Search stopped by max_proofs option.
% 2.02/2.23
% 2.02/2.23 ============ end of search ============
% 2.02/2.23
% 2.02/2.23 -------------- statistics -------------
% 2.02/2.23 clauses given 30
% 2.02/2.23 clauses generated 2953
% 2.02/2.23 clauses kept 356
% 2.02/2.23 clauses forward subsumed 830
% 2.02/2.23 clauses back subsumed 53
% 2.02/2.23 Kbytes malloced 6835
% 2.02/2.23
% 2.02/2.23 ----------- times (seconds) -----------
% 2.02/2.23 user CPU time 0.14 (0 hr, 0 min, 0 sec)
% 2.02/2.23 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.23 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.02/2.23
% 2.02/2.23 That finishes the proof of the theorem.
% 2.02/2.23
% 2.02/2.23 Process 3487 finished Wed Jul 27 05:30:43 2022
% 2.02/2.23 Otter interrupted
% 2.02/2.23 PROOF FOUND
%------------------------------------------------------------------------------