%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP214-1 : TPTP v8.1.0. Released v2.5.0.
% 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 12:56:44 EDT 2022
% Result : Unsatisfiable 100.35s 100.51s
% Output : Refutation 100.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 15 unt; 21 nHn; 32 RR)
% Number of literals : 95 ( 94 equ; 35 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(A,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(sk_c7,B) != sk_c6
| multiply(C,sk_c7) != D
| inverse(C) != sk_c7
| multiply(E,D) != sk_c6
| inverse(E) != D ),
file('GRP214-1.p',unknown),
[] ).
cnf(14,axiom,
A = A,
file('GRP214-1.p',unknown),
[] ).
cnf(16,axiom,
multiply(identity,A) = A,
file('GRP214-1.p',unknown),
[] ).
cnf(17,axiom,
multiply(inverse(A),A) = identity,
file('GRP214-1.p',unknown),
[] ).
cnf(19,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP214-1.p',unknown),
[] ).
cnf(23,axiom,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('GRP214-1.p',unknown),
[] ).
cnf(24,axiom,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('GRP214-1.p',unknown),
[] ).
cnf(26,axiom,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('GRP214-1.p',unknown),
[] ).
cnf(27,axiom,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('GRP214-1.p',unknown),
[] ).
cnf(28,axiom,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('GRP214-1.p',unknown),
[] ).
cnf(30,axiom,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('GRP214-1.p',unknown),
[] ).
cnf(76,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c3) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[26,17]),
[iquote('para_from,26.1.1,17.1.1.1')] ).
cnf(87,plain,
( multiply(sk_c1,sk_c7) != sk_c6
| multiply(sk_c7,A) != sk_c6
| multiply(B,sk_c7) != C
| inverse(B) != sk_c7
| multiply(D,C) != sk_c6
| inverse(D) != C
| inverse(sk_c3) = sk_c7 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[26,1]),14]),
[iquote('para_from,26.1.1,1.2.1,unit_del,14')] ).
cnf(116,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c4) = sk_c5 ),
inference(para_from,[status(thm),theory(equality)],[28,17]),
[iquote('para_from,28.1.1,17.1.1.1')] ).
cnf(148,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,17]),16])]),
[iquote('para_into,19.1.1.1,17.1.1,demod,16,flip.1')] ).
cnf(186,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[148,148]),
[iquote('para_into,148.1.1.2,148.1.1')] ).
cnf(190,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[148,17]),186]),
[iquote('para_into,148.1.1.2,17.1.1,demod,186')] ).
cnf(203,plain,
inverse(identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[190,17])]),
[iquote('para_into,189.1.1,17.1.1,flip.1')] ).
cnf(410,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c2
| inverse(sk_c3) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[30,148]),
[iquote('para_from,30.1.1,148.1.1.2')] ).
cnf(502,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c3) = sk_c7 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[76,148]),190]),
[iquote('para_from,76.1.1,148.1.1.2,demod,190')] ).
cnf(539,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[502,17]),
[iquote('para_from,502.1.1,17.1.1.1')] ).
cnf(655,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c4) = sk_c5 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[116,148]),190]),
[iquote('para_from,116.1.1,148.1.1.2,demod,190')] ).
cnf(692,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c5 ),
inference(para_from,[status(thm),theory(equality)],[655,17]),
[iquote('para_from,655.1.1,17.1.1.1')] ).
cnf(818,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[186,190]),190]),
[iquote('para_into,185.1.1,189.1.1,demod,190')] ).
cnf(820,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[186,148])]),
[iquote('para_into,185.1.1,148.1.1,flip.1')] ).
cnf(822,plain,
multiply(A,inverse(A)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[186,17])]),
[iquote('para_into,185.1.1,17.1.1,flip.1')] ).
cnf(955,plain,
( multiply(A,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(B,sk_c7) != C
| inverse(B) != sk_c7
| multiply(D,C) != sk_c6
| inverse(D) != C ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[820,1])]),
[iquote('para_from,820.1.1,1.3.1,factor_simp')] ).
cnf(1331,plain,
( sk_c6 = identity
| inverse(sk_c4) = sk_c5 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[692,24])]),
[iquote('para_into,692.1.1,24.1.1,factor_simp')] ).
cnf(1335,plain,
( multiply(sk_c4,sk_c5) = identity
| sk_c6 = identity ),
inference(para_from,[status(thm),theory(equality)],[1331,822]),
[iquote('para_from,1331.2.1,822.1.1.2')] ).
cnf(1389,plain,
( sk_c6 = identity
| inverse(sk_c1) = sk_c7 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1335,27])]),
[iquote('para_into,1335.1.1,27.2.1,factor_simp')] ).
cnf(1390,plain,
( sk_c6 = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1335,23])]),
[iquote('para_into,1335.1.1,23.2.1,factor_simp')] ).
cnf(1391,plain,
( multiply(sk_c1,sk_c7) = identity
| sk_c6 = identity ),
inference(para_from,[status(thm),theory(equality)],[1389,822]),
[iquote('para_from,1389.2.1,822.1.1.2')] ).
cnf(1440,plain,
( multiply(sk_c1,sk_c7) != sk_c6
| multiply(A,sk_c7) != B
| inverse(A) != sk_c7
| multiply(C,B) != sk_c6
| inverse(C) != B
| inverse(sk_c3) = sk_c7 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[87,820])]),
[iquote('para_into,87.2.1,820.1.1,factor_simp')] ).
cnf(1484,plain,
sk_c6 = identity,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1391,1390])])]),
[iquote('para_into,1391.1.1,1390.2.1,factor_simp,factor_simp')] ).
cnf(1511,plain,
( multiply(sk_c1,sk_c7) != identity
| multiply(A,sk_c7) != B
| inverse(A) != sk_c7
| multiply(C,B) != identity
| inverse(C) != B
| inverse(sk_c3) = sk_c7 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1440]),1484,1484]),
[iquote('back_demod,1440,demod,1484,1484')] ).
cnf(1624,plain,
( multiply(A,sk_c7) != identity
| inverse(A) != sk_c7
| multiply(B,sk_c7) != C
| inverse(B) != sk_c7
| multiply(D,C) != identity
| inverse(D) != C ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[955]),1484,1484]),
[iquote('back_demod,955,demod,1484,1484')] ).
cnf(1919,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c3) = sk_c7 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[410]),1484,190]),
[iquote('back_demod,410,demod,1484,190')] ).
cnf(2070,plain,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[1919,818]),
[iquote('para_from,1919.1.1,818.1.1.1')] ).
cnf(2072,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c3) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[1919,17]),
[iquote('para_from,1919.1.1,17.1.1.1')] ).
cnf(3807,plain,
inverse(sk_c3) = sk_c7,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1511,539,2072,2070,190,203])])])]),
[iquote('hyper,1511,539,2072,2070,189,203,factor_simp,factor_simp,factor_simp')] ).
cnf(3823,plain,
multiply(sk_c3,sk_c7) = identity,
inference(para_from,[status(thm),theory(equality)],[3807,822]),
[iquote('para_from,3807.1.1,822.1.1.2')] ).
cnf(4077,plain,
$false,
inference(hyper,[status(thm)],[1624,3823,3807,3823,3807,190,203]),
[iquote('hyper,1624,3823,3807,3823,3807,189,203')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP214-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 05:10:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.55/2.11 ----- Otter 3.3f, August 2004 -----
% 1.55/2.11 The process was started by sandbox2 on n015.cluster.edu,
% 1.55/2.11 Wed Jul 27 05:10:41 2022
% 1.55/2.11 The command was "./otter". The process ID is 13128.
% 1.55/2.11
% 1.55/2.11 set(prolog_style_variables).
% 1.55/2.11 set(auto).
% 1.55/2.11 dependent: set(auto1).
% 1.55/2.11 dependent: set(process_input).
% 1.55/2.11 dependent: clear(print_kept).
% 1.55/2.11 dependent: clear(print_new_demod).
% 1.55/2.11 dependent: clear(print_back_demod).
% 1.55/2.11 dependent: clear(print_back_sub).
% 1.55/2.11 dependent: set(control_memory).
% 1.55/2.11 dependent: assign(max_mem, 12000).
% 1.55/2.11 dependent: assign(pick_given_ratio, 4).
% 1.55/2.11 dependent: assign(stats_level, 1).
% 1.55/2.11 dependent: assign(max_seconds, 10800).
% 1.55/2.11 clear(print_given).
% 1.55/2.11
% 1.55/2.11 list(usable).
% 1.55/2.11 0 [] A=A.
% 1.55/2.11 0 [] multiply(identity,X)=X.
% 1.55/2.11 0 [] multiply(inverse(X),X)=identity.
% 1.55/2.11 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.55/2.11 0 [] multiply(sk_c1,sk_c7)=sk_c6|multiply(sk_c3,sk_c7)=sk_c5.
% 1.55/2.11 0 [] multiply(sk_c1,sk_c7)=sk_c6|inverse(sk_c3)=sk_c7.
% 1.55/2.11 0 [] multiply(sk_c1,sk_c7)=sk_c6|multiply(sk_c4,sk_c5)=sk_c6.
% 1.55/2.11 0 [] multiply(sk_c1,sk_c7)=sk_c6|inverse(sk_c4)=sk_c5.
% 1.55/2.11 0 [] inverse(sk_c1)=sk_c7|multiply(sk_c3,sk_c7)=sk_c5.
% 1.55/2.11 0 [] inverse(sk_c1)=sk_c7|inverse(sk_c3)=sk_c7.
% 1.55/2.11 0 [] inverse(sk_c1)=sk_c7|multiply(sk_c4,sk_c5)=sk_c6.
% 1.55/2.11 0 [] inverse(sk_c1)=sk_c7|inverse(sk_c4)=sk_c5.
% 1.55/2.11 0 [] multiply(sk_c7,sk_c2)=sk_c6|multiply(sk_c3,sk_c7)=sk_c5.
% 1.55/2.11 0 [] multiply(sk_c7,sk_c2)=sk_c6|inverse(sk_c3)=sk_c7.
% 1.55/2.11 0 [] multiply(sk_c7,sk_c2)=sk_c6|multiply(sk_c4,sk_c5)=sk_c6.
% 1.55/2.11 0 [] multiply(sk_c7,sk_c2)=sk_c6|inverse(sk_c4)=sk_c5.
% 1.55/2.11 0 [] multiply(X3,sk_c7)!=sk_c6|inverse(X3)!=sk_c7|multiply(sk_c7,X4)!=sk_c6|multiply(X2,sk_c7)!=X1|inverse(X2)!=sk_c7|multiply(X5,X1)!=sk_c6|inverse(X5)!=X1.
% 1.55/2.11 end_of_list.
% 1.55/2.11
% 1.55/2.11 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.55/2.11
% 1.55/2.11 This ia a non-Horn set with equality. The strategy will be
% 1.55/2.11 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.55/2.11 deletion, with positive clauses in sos and nonpositive
% 1.55/2.11 clauses in usable.
% 1.55/2.11
% 1.55/2.11 dependent: set(knuth_bendix).
% 1.55/2.11 dependent: set(anl_eq).
% 1.55/2.11 dependent: set(para_from).
% 1.55/2.11 dependent: set(para_into).
% 1.55/2.11 dependent: clear(para_from_right).
% 1.55/2.11 dependent: clear(para_into_right).
% 1.55/2.11 dependent: set(para_from_vars).
% 1.55/2.11 dependent: set(eq_units_both_ways).
% 1.55/2.11 dependent: set(dynamic_demod_all).
% 1.55/2.11 dependent: set(dynamic_demod).
% 1.55/2.11 dependent: set(order_eq).
% 1.55/2.11 dependent: set(back_demod).
% 1.55/2.11 dependent: set(lrpo).
% 1.55/2.11 dependent: set(hyper_res).
% 1.55/2.11 dependent: set(unit_deletion).
% 1.55/2.11 dependent: set(factor).
% 1.55/2.11
% 1.55/2.11 ------------> process usable:
% 1.55/2.11 ** KEPT (pick-wt=32): 1 [] multiply(A,sk_c7)!=sk_c6|inverse(A)!=sk_c7|multiply(sk_c7,B)!=sk_c6|multiply(C,sk_c7)!=D|inverse(C)!=sk_c7|multiply(E,D)!=sk_c6|inverse(E)!=D.
% 1.55/2.11
% 1.55/2.11 ------------> process sos:
% 1.55/2.11 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.55/2.11 ** KEPT (pick-wt=5): 15 [] multiply(identity,A)=A.
% 1.55/2.11 ---> New Demodulator: 16 [new_demod,15] multiply(identity,A)=A.
% 1.55/2.11 ** KEPT (pick-wt=6): 17 [] multiply(inverse(A),A)=identity.
% 1.55/2.11 ---> New Demodulator: 18 [new_demod,17] multiply(inverse(A),A)=identity.
% 1.55/2.11 ** KEPT (pick-wt=11): 19 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.55/2.11 ---> New Demodulator: 20 [new_demod,19] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.55/2.11 ** KEPT (pick-wt=10): 21 [] multiply(sk_c1,sk_c7)=sk_c6|multiply(sk_c3,sk_c7)=sk_c5.
% 1.55/2.11 ** KEPT (pick-wt=9): 22 [] multiply(sk_c1,sk_c7)=sk_c6|inverse(sk_c3)=sk_c7.
% 1.55/2.11 ** KEPT (pick-wt=10): 23 [] multiply(sk_c1,sk_c7)=sk_c6|multiply(sk_c4,sk_c5)=sk_c6.
% 1.55/2.11 ** KEPT (pick-wt=9): 24 [] multiply(sk_c1,sk_c7)=sk_c6|inverse(sk_c4)=sk_c5.
% 1.55/2.11 ** KEPT (pick-wt=9): 25 [] inverse(sk_c1)=sk_c7|multiply(sk_c3,sk_c7)=sk_c5.
% 1.55/2.11 ** KEPT (pick-wt=8): 26 [] inverse(sk_c1)=sk_c7|inverse(sk_c3)=sk_c7.
% 1.55/2.11 ** KEPT (pick-wt=9): 27 [] inverse(sk_c1)=sk_c7|multiply(sk_c4,sk_c5)=sk_c6.
% 1.55/2.11 ** KEPT (pick-wt=8): 28 [] inverse(sk_c1)=sk_c7|inverse(sk_c4)=sk_c5.
% 1.55/2.11 ** KEPT (pick-wt=10): 29 [] multiply(sk_c7,sk_c2)=sk_c6|multiply(sk_c3,sk_c7)=sk_c5.
% 1.55/2.11 ** KEPT (pick-wt=9): 30 [] multiply(sk_c7,sk_c2)=sk_c6|inverse(sk_c3)=sk_c7.
% 1.55/2.11 ** KEPT (pick-wt=10): 31 [] multiply(sk_c7,sk_c2)=sk_c6|multiply(sk_c4,sk_c5)=sk_c6.
% 1.55/2.11 ** KEPT (pick-wt=9): 32 [] multiply(sk_c7,sk_c2)=sk_c6|inverse(sk_c4)=sk_c5.
% 1.55/2.11 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 100.35/100.51 >>>> Starting back demodulation with 16.
% 100.35/100.51 >>>> Starting back demodulation with 18.
% 100.35/100.51 >>>> Starting back demodulation with 20.
% 100.35/100.51
% 100.35/100.51 ======= end of input processing =======
% 100.35/100.51
% 100.35/100.51 =========== start of search ===========
% 100.35/100.51
% 100.35/100.51 -- HEY sandbox2, WE HAVE A PROOF!! --
% 100.35/100.51
% 100.35/100.51 -----> EMPTY CLAUSE at 98.39 sec ----> 4077 [hyper,1624,3823,3807,3823,3807,189,203] $F.
% 100.35/100.51
% 100.35/100.51 Length of proof is 30. Level of proof is 14.
% 100.35/100.51
% 100.35/100.51 ---------------- PROOF ----------------
% 100.35/100.51 % SZS status Unsatisfiable
% 100.35/100.51 % SZS output start Refutation
% See solution above
% 100.35/100.51 ------------ end of proof -------------
% 100.35/100.51
% 100.35/100.51
% 100.35/100.51 Search stopped by max_proofs option.
% 100.35/100.51
% 100.35/100.51
% 100.35/100.51 Search stopped by max_proofs option.
% 100.35/100.51
% 100.35/100.51 ============ end of search ============
% 100.35/100.51
% 100.35/100.51 -------------- statistics -------------
% 100.35/100.51 clauses given 396
% 100.35/100.51 clauses generated 2566682
% 100.35/100.51 clauses kept 4045
% 100.35/100.51 clauses forward subsumed 2564360
% 100.35/100.51 clauses back subsumed 1514
% 100.35/100.51 Kbytes malloced 3906
% 100.35/100.51
% 100.35/100.51 ----------- times (seconds) -----------
% 100.35/100.51 user CPU time 98.39 (0 hr, 1 min, 38 sec)
% 100.35/100.51 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 100.35/100.51 wall-clock time 101 (0 hr, 1 min, 41 sec)
% 100.35/100.51
% 100.35/100.51 That finishes the proof of the theorem.
% 100.35/100.51
% 100.35/100.51 Process 13128 finished Wed Jul 27 05:12:22 2022
% 100.35/100.51 Otter interrupted
% 100.35/100.51 PROOF FOUND
%------------------------------------------------------------------------------