TSTP Solution File: GRP412-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP412-1 : 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 12:56:57 EDT 2022
% Result : Unsatisfiable 1.90s 2.10s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 4 RR)
% Number of literals : 25 ( 24 equ; 3 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 : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP412-1.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(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C,
file('GRP412-1.p',unknown),
[] ).
cnf(6,plain,
multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = D,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1.1.2.1.1.1,4.1.1')] ).
cnf(9,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A)) = multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,5])]),
[iquote('para_into,4.1.1.2.1.1.2.1,4.1.1,flip.1')] ).
cnf(12,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))),inverse(A))),F))),A)) = multiply(B,inverse(multiply(multiply(multiply(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(G))),E))),G)),inverse(F)),multiply(multiply(multiply(inverse(G),G),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(G))),E))),G)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,9]),9]),
[iquote('para_into,8.1.1.1.1.2.1.1.1.1.1.2,8.1.1,demod,9')] ).
cnf(20,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))) = C,
inference(para_from,[status(thm),theory(equality)],[9,5]),
[iquote('para_from,8.1.1,4.1.1.2')] ).
cnf(25,plain,
multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)),inverse(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),F))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)))) = F,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,5]),9]),
[iquote('para_from,8.1.1,4.1.1.2.1.1.2.1.1.1.2,demod,9')] ).
cnf(33,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,B)))) = multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(D))),C))),D),
inference(para_into,[status(thm),theory(equality)],[20,5]),
[iquote('para_into,20.1.1.2.2.1.1,4.1.1')] ).
cnf(34,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))) = multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(B))),E),
inference(para_into,[status(thm),theory(equality)],[20,9]),
[iquote('para_into,20.1.1.2.2,8.1.1')] ).
cnf(49,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),multiply(multiply(inverse(B),B),inverse(C))))),A) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,20])]),
[iquote('para_into,33.1.1,20.1.1,flip.1')] ).
cnf(90,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(multiply(inverse(D),D),inverse(B))),multiply(multiply(inverse(D),D),inverse(C))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[49,33]),49]),
[iquote('para_from,48.1.1,33.1.1.2.2.1,demod,49')] ).
cnf(91,plain,
multiply(inverse(multiply(multiply(inverse(A),A),inverse(B))),multiply(multiply(inverse(A),A),inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[90])]),
[iquote('copy,90,flip.1')] ).
cnf(92,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(para_into,[status(thm),theory(equality)],[91,91]),
[iquote('para_into,91.1.1,91.1.1')] ).
cnf(97,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),A) = C,
inference(para_from,[status(thm),theory(equality)],[92,49]),
[iquote('para_from,92.1.1,48.1.1.1.2.1')] ).
cnf(114,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) = multiply(inverse(multiply(inverse(D),inverse(B))),multiply(inverse(D),C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,6]),5]),
[iquote('para_into,34.1.1.2.2,6.1.1,demod,5')] ).
cnf(115,plain,
multiply(inverse(multiply(inverse(A),inverse(B))),multiply(inverse(A),C)) = multiply(inverse(multiply(D,inverse(B))),multiply(D,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[114])]),
[iquote('copy,114,flip.1')] ).
cnf(124,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(B))),multiply(D,C)),
inference(para_into,[status(thm),theory(equality)],[115,115]),
[iquote('para_into,115.1.1,115.1.1')] ).
cnf(134,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[124,12]),25]),
[iquote('para_from,124.1.1,12.1.1.1.1.2.1,demod,25')] ).
cnf(141,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)],[134,124]),134]),
[iquote('para_from,133.1.1,124.1.1.1.1.2,demod,134')] ).
cnf(149,plain,
multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),D)) = multiply(inverse(multiply(E,B)),multiply(E,D)),
inference(para_into,[status(thm),theory(equality)],[141,134]),
[iquote('para_into,141.1.1.1,133.1.1')] ).
cnf(192,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(B,C)),multiply(B,C)),
inference(para_into,[status(thm),theory(equality)],[149,97]),
[iquote('para_into,149.1.1.2,97.1.1')] ).
cnf(193,plain,
multiply(inverse(multiply(A,B)),multiply(A,B)) = multiply(inverse(C),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[192])]),
[iquote('copy,192,flip.1')] ).
cnf(248,plain,
multiply(inverse(multiply(A,B)),multiply(A,B)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[192,2]),
[iquote('para_from,192.1.1,2.1.1')] ).
cnf(249,plain,
$false,
inference(binary,[status(thm)],[248,193]),
[iquote('binary,248.1,193.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP412-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % 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 05:27:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.90/2.10 ----- Otter 3.3f, August 2004 -----
% 1.90/2.10 The process was started by sandbox on n019.cluster.edu,
% 1.90/2.10 Wed Jul 27 05:27:52 2022
% 1.90/2.10 The command was "./otter". The process ID is 21073.
% 1.90/2.10
% 1.90/2.10 set(prolog_style_variables).
% 1.90/2.10 set(auto).
% 1.90/2.10 dependent: set(auto1).
% 1.90/2.10 dependent: set(process_input).
% 1.90/2.10 dependent: clear(print_kept).
% 1.90/2.10 dependent: clear(print_new_demod).
% 1.90/2.10 dependent: clear(print_back_demod).
% 1.90/2.10 dependent: clear(print_back_sub).
% 1.90/2.10 dependent: set(control_memory).
% 1.90/2.10 dependent: assign(max_mem, 12000).
% 1.90/2.10 dependent: assign(pick_given_ratio, 4).
% 1.90/2.10 dependent: assign(stats_level, 1).
% 1.90/2.10 dependent: assign(max_seconds, 10800).
% 1.90/2.10 clear(print_given).
% 1.90/2.10
% 1.90/2.10 list(usable).
% 1.90/2.10 0 [] A=A.
% 1.90/2.10 0 [] multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))=C.
% 1.90/2.10 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.90/2.10 end_of_list.
% 1.90/2.10
% 1.90/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.90/2.10
% 1.90/2.10 All clauses are units, and equality is present; the
% 1.90/2.10 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.90/2.10
% 1.90/2.10 dependent: set(knuth_bendix).
% 1.90/2.10 dependent: set(anl_eq).
% 1.90/2.10 dependent: set(para_from).
% 1.90/2.10 dependent: set(para_into).
% 1.90/2.10 dependent: clear(para_from_right).
% 1.90/2.10 dependent: clear(para_into_right).
% 1.90/2.10 dependent: set(para_from_vars).
% 1.90/2.10 dependent: set(eq_units_both_ways).
% 1.90/2.10 dependent: set(dynamic_demod_all).
% 1.90/2.10 dependent: set(dynamic_demod).
% 1.90/2.10 dependent: set(order_eq).
% 1.90/2.10 dependent: set(back_demod).
% 1.90/2.10 dependent: set(lrpo).
% 1.90/2.10
% 1.90/2.10 ------------> process usable:
% 1.90/2.10 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.90/2.10
% 1.90/2.10 ------------> process sos:
% 1.90/2.10 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.90/2.10 ** KEPT (pick-wt=20): 4 [] multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))=C.
% 1.90/2.10 ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))=C.
% 1.90/2.10 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.90/2.10 >>>> Starting back demodulation with 5.
% 1.90/2.10
% 1.90/2.10 ======= end of input processing =======
% 1.90/2.10
% 1.90/2.10 =========== start of search ===========
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 32.
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 32.
% 1.90/2.10
% 1.90/2.10 sos_size=52
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 27.
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 27.
% 1.90/2.10
% 1.90/2.10 sos_size=65
% 1.90/2.10
% 1.90/2.10 -------- PROOF --------
% 1.90/2.10
% 1.90/2.10 ----> UNIT CONFLICT at 0.18 sec ----> 249 [binary,248.1,193.1] $F.
% 1.90/2.10
% 1.90/2.10 Length of proof is 22. Level of proof is 11.
% 1.90/2.10
% 1.90/2.10 ---------------- PROOF ----------------
% 1.90/2.10 % SZS status Unsatisfiable
% 1.90/2.10 % SZS output start Refutation
% See solution above
% 1.90/2.10 ------------ end of proof -------------
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Search stopped by max_proofs option.
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Search stopped by max_proofs option.
% 1.90/2.10
% 1.90/2.10 ============ end of search ============
% 1.90/2.10
% 1.90/2.10 -------------- statistics -------------
% 1.90/2.10 clauses given 42
% 1.90/2.10 clauses generated 3956
% 1.90/2.10 clauses kept 176
% 1.90/2.10 clauses forward subsumed 626
% 1.90/2.10 clauses back subsumed 29
% 1.90/2.10 Kbytes malloced 7812
% 1.90/2.10
% 1.90/2.10 ----------- times (seconds) -----------
% 1.90/2.10 user CPU time 0.18 (0 hr, 0 min, 0 sec)
% 1.90/2.10 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.90/2.10 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.90/2.10
% 1.90/2.10 That finishes the proof of the theorem.
% 1.90/2.10
% 1.90/2.10 Process 21073 finished Wed Jul 27 05:27:53 2022
% 1.90/2.10 Otter interrupted
% 1.90/2.10 PROOF FOUND
%------------------------------------------------------------------------------