TSTP Solution File: GRP418-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP418-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 1.88s 2.09s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 4 RR)
% Number of literals : 18 ( 17 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 4 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 : 62 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP418-1.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),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = B,
file('GRP418-1.p',unknown),
[] ).
cnf(6,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),inverse(multiply(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,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(14,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,5])]),
[iquote('para_into,6.1.1,4.1.1,flip.1')] ).
cnf(30,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),B)) = D,
inference(para_from,[status(thm),theory(equality)],[14,5]),
[iquote('para_from,13.1.1,4.1.1.1.2')] ).
cnf(92,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))),
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1,9.1.1')] ).
cnf(100,plain,
inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,6]),14]),
[iquote('para_from,9.1.1,6.1.1.1,demod,14')] ).
cnf(226,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(inverse(inverse(multiply(C,inverse(multiply(inverse(C),C)))))),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),inverse(multiply(inverse(B),inverse(multiply(multiply(D,E),inverse(multiply(inverse(multiply(D,E)),multiply(D,E)))))))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[30,92]),5]),
[iquote('para_from,29.1.1,92.1.1.1.1.1.2,demod,5')] ).
cnf(230,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))) = inverse(multiply(inverse(multiply(E,D)),multiply(E,B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[226])]),
[iquote('copy,226,flip.1')] ).
cnf(235,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)],[230,230]),
[iquote('para_into,230.1.1,230.1.1')] ).
cnf(279,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)],[235,30]),30]),
[iquote('para_from,235.1.1,29.1.1.1.1.1.2.1.1,demod,30')] ).
cnf(318,plain,
multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(A),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)) = multiply(inverse(multiply(E,multiply(B,C))),multiply(E,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[279,9]),100]),
[iquote('para_into,279.1.1.1.1,9.1.1,demod,100')] ).
cnf(992,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,D))),
inference(para_into,[status(thm),theory(equality)],[318,14]),
[iquote('para_into,318.1.1.2,13.1.1')] ).
cnf(996,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)],[992])]),
[iquote('copy,992,flip.1')] ).
cnf(1050,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[992,2]),
[iquote('para_from,992.1.1,2.1.1')] ).
cnf(1051,plain,
$false,
inference(binary,[status(thm)],[1050,996]),
[iquote('binary,1050.1,996.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP418-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n004.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 05:23:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.88/2.09 ----- Otter 3.3f, August 2004 -----
% 1.88/2.09 The process was started by sandbox on n004.cluster.edu,
% 1.88/2.09 Wed Jul 27 05:23:51 2022
% 1.88/2.09 The command was "./otter". The process ID is 4512.
% 1.88/2.09
% 1.88/2.09 set(prolog_style_variables).
% 1.88/2.09 set(auto).
% 1.88/2.09 dependent: set(auto1).
% 1.88/2.09 dependent: set(process_input).
% 1.88/2.09 dependent: clear(print_kept).
% 1.88/2.09 dependent: clear(print_new_demod).
% 1.88/2.09 dependent: clear(print_back_demod).
% 1.88/2.09 dependent: clear(print_back_sub).
% 1.88/2.09 dependent: set(control_memory).
% 1.88/2.09 dependent: assign(max_mem, 12000).
% 1.88/2.09 dependent: assign(pick_given_ratio, 4).
% 1.88/2.09 dependent: assign(stats_level, 1).
% 1.88/2.09 dependent: assign(max_seconds, 10800).
% 1.88/2.09 clear(print_given).
% 1.88/2.09
% 1.88/2.09 list(usable).
% 1.88/2.09 0 [] A=A.
% 1.88/2.09 0 [] inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))=B.
% 1.88/2.09 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.88/2.09 end_of_list.
% 1.88/2.09
% 1.88/2.09 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.88/2.09
% 1.88/2.09 All clauses are units, and equality is present; the
% 1.88/2.09 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.88/2.09
% 1.88/2.09 dependent: set(knuth_bendix).
% 1.88/2.09 dependent: set(anl_eq).
% 1.88/2.09 dependent: set(para_from).
% 1.88/2.09 dependent: set(para_into).
% 1.88/2.09 dependent: clear(para_from_right).
% 1.88/2.09 dependent: clear(para_into_right).
% 1.88/2.09 dependent: set(para_from_vars).
% 1.88/2.09 dependent: set(eq_units_both_ways).
% 1.88/2.09 dependent: set(dynamic_demod_all).
% 1.88/2.09 dependent: set(dynamic_demod).
% 1.88/2.09 dependent: set(order_eq).
% 1.88/2.09 dependent: set(back_demod).
% 1.88/2.09 dependent: set(lrpo).
% 1.88/2.09
% 1.88/2.09 ------------> process usable:
% 1.88/2.09 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.88/2.09
% 1.88/2.09 ------------> process sos:
% 1.88/2.09 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.88/2.09 ** KEPT (pick-wt=22): 4 [] inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))=B.
% 1.88/2.09 ---> New Demodulator: 5 [new_demod,4] inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))=B.
% 1.88/2.09 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.88/2.09 >>>> Starting back demodulation with 5.
% 1.88/2.09
% 1.88/2.09 ======= end of input processing =======
% 1.88/2.09
% 1.88/2.09 =========== start of search ===========
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Resetting weight limit to 56.
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Resetting weight limit to 56.
% 1.88/2.09
% 1.88/2.09 sos_size=145
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Resetting weight limit to 34.
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Resetting weight limit to 34.
% 1.88/2.09
% 1.88/2.09 sos_size=733
% 1.88/2.09
% 1.88/2.09 -------- PROOF --------
% 1.88/2.09
% 1.88/2.09 ----> UNIT CONFLICT at 0.19 sec ----> 1051 [binary,1050.1,996.1] $F.
% 1.88/2.09
% 1.88/2.09 Length of proof is 15. Level of proof is 10.
% 1.88/2.09
% 1.88/2.09 ---------------- PROOF ----------------
% 1.88/2.09 % SZS status Unsatisfiable
% 1.88/2.09 % SZS output start Refutation
% See solution above
% 1.88/2.09 ------------ end of proof -------------
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Search stopped by max_proofs option.
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Search stopped by max_proofs option.
% 1.88/2.09
% 1.88/2.09 ============ end of search ============
% 1.88/2.09
% 1.88/2.09 -------------- statistics -------------
% 1.88/2.09 clauses given 42
% 1.88/2.09 clauses generated 4474
% 1.88/2.09 clauses kept 864
% 1.88/2.09 clauses forward subsumed 1356
% 1.88/2.09 clauses back subsumed 31
% 1.88/2.09 Kbytes malloced 7812
% 1.88/2.09
% 1.88/2.09 ----------- times (seconds) -----------
% 1.88/2.09 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 1.88/2.09 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.88/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.88/2.09
% 1.88/2.09 That finishes the proof of the theorem.
% 1.88/2.09
% 1.88/2.09 Process 4512 finished Wed Jul 27 05:23:53 2022
% 1.88/2.09 Otter interrupted
% 1.88/2.09 PROOF FOUND
%------------------------------------------------------------------------------