TSTP Solution File: GRP424-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP424-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:56:59 EDT 2022
% Result : Unsatisfiable 1.96s 2.11s
% Output : Refutation 1.96s
% 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 : 15 ( 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 : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP424-1.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(4,axiom,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B,
file('GRP424-1.p',unknown),
[] ).
cnf(6,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),C)))),multiply(D,inverse(C))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.1.1.1.2.1,4.1.1')] ).
cnf(7,plain,
multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(C)))),inverse(multiply(inverse(C),C))) = C,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.1.1.1,4.1.1')] ).
cnf(19,plain,
multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(B),A)))),multiply(C,inverse(A)))),inverse(A)))),inverse(A)))),inverse(multiply(inverse(A),A))) = A,
inference(para_into,[status(thm),theory(equality)],[7,4]),
[iquote('para_into,7.1.1.1.1.2.1.1.1.1,4.1.1')] ).
cnf(89,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),C)))),multiply(D,inverse(C))),
inference(para_into,[status(thm),theory(equality)],[6,6]),
[iquote('para_into,6.1.1,6.1.1')] ).
cnf(91,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(C),C)))),C)))),multiply(A,inverse(C))) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,4])]),
[iquote('para_into,6.1.1,4.1.1,flip.1')] ).
cnf(144,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[89,91]),91]),
[iquote('para_into,89.1.1.1.1.2.1,90.1.1,demod,91')] ).
cnf(174,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[144,19]),19]),
[iquote('para_into,144.1.1.2.2.1,18.1.1,demod,19')] ).
cnf(179,plain,
multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(D))) = multiply(inverse(multiply(E,inverse(multiply(inverse(C),C)))),multiply(E,inverse(D))),
inference(para_into,[status(thm),theory(equality)],[174,4]),
[iquote('para_into,174.1.1.1.1,4.1.1')] ).
cnf(197,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(B,inverse(multiply(inverse(C),C)))),multiply(B,inverse(multiply(inverse(C),C)))),
inference(para_into,[status(thm),theory(equality)],[179,4]),
[iquote('para_into,179.1.1.2,4.1.1')] ).
cnf(199,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[197])]),
[iquote('copy,197,flip.1')] ).
cnf(222,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[197,2]),
[iquote('para_from,197.1.1,2.1.1')] ).
cnf(223,plain,
$false,
inference(binary,[status(thm)],[222,199]),
[iquote('binary,222.1,199.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP424-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.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 05:41:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.96/2.11 ----- Otter 3.3f, August 2004 -----
% 1.96/2.11 The process was started by sandbox on n026.cluster.edu,
% 1.96/2.11 Wed Jul 27 05:41:09 2022
% 1.96/2.11 The command was "./otter". The process ID is 25362.
% 1.96/2.11
% 1.96/2.11 set(prolog_style_variables).
% 1.96/2.11 set(auto).
% 1.96/2.11 dependent: set(auto1).
% 1.96/2.11 dependent: set(process_input).
% 1.96/2.11 dependent: clear(print_kept).
% 1.96/2.11 dependent: clear(print_new_demod).
% 1.96/2.11 dependent: clear(print_back_demod).
% 1.96/2.11 dependent: clear(print_back_sub).
% 1.96/2.11 dependent: set(control_memory).
% 1.96/2.11 dependent: assign(max_mem, 12000).
% 1.96/2.11 dependent: assign(pick_given_ratio, 4).
% 1.96/2.11 dependent: assign(stats_level, 1).
% 1.96/2.11 dependent: assign(max_seconds, 10800).
% 1.96/2.11 clear(print_given).
% 1.96/2.11
% 1.96/2.11 list(usable).
% 1.96/2.11 0 [] A=A.
% 1.96/2.11 0 [] multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C)))=B.
% 1.96/2.11 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.96/2.11 end_of_list.
% 1.96/2.11
% 1.96/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.96/2.11
% 1.96/2.11 All clauses are units, and equality is present; the
% 1.96/2.11 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.96/2.11
% 1.96/2.11 dependent: set(knuth_bendix).
% 1.96/2.11 dependent: set(anl_eq).
% 1.96/2.11 dependent: set(para_from).
% 1.96/2.11 dependent: set(para_into).
% 1.96/2.11 dependent: clear(para_from_right).
% 1.96/2.11 dependent: clear(para_into_right).
% 1.96/2.11 dependent: set(para_from_vars).
% 1.96/2.11 dependent: set(eq_units_both_ways).
% 1.96/2.11 dependent: set(dynamic_demod_all).
% 1.96/2.11 dependent: set(dynamic_demod).
% 1.96/2.11 dependent: set(order_eq).
% 1.96/2.11 dependent: set(back_demod).
% 1.96/2.11 dependent: set(lrpo).
% 1.96/2.11
% 1.96/2.11 ------------> process usable:
% 1.96/2.11 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.96/2.11
% 1.96/2.11 ------------> process sos:
% 1.96/2.11 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.96/2.11 ** KEPT (pick-wt=22): 4 [] multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C)))=B.
% 1.96/2.11 ---> New Demodulator: 5 [new_demod,4] multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C)))=B.
% 1.96/2.11 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.96/2.11 >>>> Starting back demodulation with 5.
% 1.96/2.11
% 1.96/2.11 ======= end of input processing =======
% 1.96/2.11
% 1.96/2.11 =========== start of search ===========
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Resetting weight limit to 41.
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Resetting weight limit to 41.
% 1.96/2.11
% 1.96/2.11 sos_size=103
% 1.96/2.11
% 1.96/2.11 -------- PROOF --------
% 1.96/2.11
% 1.96/2.11 ----> UNIT CONFLICT at 0.03 sec ----> 223 [binary,222.1,199.1] $F.
% 1.96/2.11
% 1.96/2.11 Length of proof is 12. Level of proof is 7.
% 1.96/2.11
% 1.96/2.11 ---------------- PROOF ----------------
% 1.96/2.11 % SZS status Unsatisfiable
% 1.96/2.11 % SZS output start Refutation
% See solution above
% 1.96/2.11 ------------ end of proof -------------
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Search stopped by max_proofs option.
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Search stopped by max_proofs option.
% 1.96/2.11
% 1.96/2.11 ============ end of search ============
% 1.96/2.11
% 1.96/2.11 -------------- statistics -------------
% 1.96/2.11 clauses given 13
% 1.96/2.11 clauses generated 311
% 1.96/2.11 clauses kept 148
% 1.96/2.11 clauses forward subsumed 127
% 1.96/2.11 clauses back subsumed 17
% 1.96/2.11 Kbytes malloced 4882
% 1.96/2.11
% 1.96/2.11 ----------- times (seconds) -----------
% 1.96/2.11 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.96/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.11 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.96/2.11
% 1.96/2.11 That finishes the proof of the theorem.
% 1.96/2.11
% 1.96/2.11 Process 25362 finished Wed Jul 27 05:41:10 2022
% 1.96/2.11 Otter interrupted
% 1.96/2.11 PROOF FOUND
%------------------------------------------------------------------------------