TSTP Solution File: GRP116-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:56:05 EDT 2022
% Result : Unsatisfiable 1.71s 1.94s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 2 RR)
% Number of literals : 23 ( 22 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(identity,a) != a,
file('GRP116-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C)))) = B,
file('GRP116-1.p',unknown),
[] ).
cnf(9,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,B),multiply(identity,multiply(multiply(identity,C),multiply(identity,C))))),C)) = B,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.2,3.1.1')] ).
cnf(17,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,B),multiply(identity,multiply(C,C)))),multiply(multiply(identity,multiply(multiply(identity,C),D)),multiply(identity,multiply(D,D))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,4]),4]),
[iquote('para_into,9.1.1.2.1.2.2.2.1,3.1.1,demod,4')] ).
cnf(19,plain,
multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(multiply(identity,C),multiply(identity,C)))) = B,
inference(para_into,[status(thm),theory(equality)],[9,4]),
[iquote('para_into,9.1.1.2.1.2.2,3.1.1')] ).
cnf(24,plain,
multiply(multiply(A,B),multiply(identity,C)) = multiply(A,multiply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,4])]),
[iquote('para_into,9.1.1.2.1,3.1.1,flip.1')] ).
cnf(29,plain,
multiply(A,multiply(A,multiply(multiply(multiply(A,B),C),multiply(C,C)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),24,24]),
[iquote('back_demod,19,demod,24,24')] ).
cnf(32,plain,
multiply(A,multiply(A,multiply(multiply(A,multiply(B,multiply(C,C))),multiply(multiply(multiply(identity,C),D),multiply(D,D))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),24,24,24]),
[iquote('back_demod,17,demod,24,24,24')] ).
cnf(52,plain,
multiply(A,multiply(A,multiply(A,multiply(B,identity)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,24]),24]),
[iquote('para_into,29.1.1.2.2,23.1.1,demod,24')] ).
cnf(68,plain,
multiply(multiply(A,B),multiply(multiply(A,B),multiply(A,multiply(B,identity)))) = identity,
inference(para_into,[status(thm),theory(equality)],[52,24]),
[iquote('para_into,51.1.1.2.2,23.1.1')] ).
cnf(76,plain,
multiply(A,multiply(A,multiply(multiply(B,C),multiply(C,C)))) = multiply(A,multiply(A,multiply(B,identity))),
inference(para_from,[status(thm),theory(equality)],[52,29]),
[iquote('para_from,51.1.1,29.1.1.2.2.1.1')] ).
cnf(99,plain,
multiply(identity,multiply(A,multiply(A,multiply(A,identity)))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[68,24]),24]),
[iquote('para_into,68.1.1.2,23.1.1,demod,24')] ).
cnf(102,plain,
multiply(multiply(A,B),identity) = multiply(A,multiply(B,multiply(C,multiply(C,multiply(C,identity))))),
inference(para_from,[status(thm),theory(equality)],[99,24]),
[iquote('para_from,98.1.1,23.1.1.2')] ).
cnf(104,plain,
multiply(A,multiply(A,multiply(A,identity))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[99,68]),99,52]),
[iquote('para_from,98.1.1,68.1.1.2.1,demod,99,52')] ).
cnf(108,plain,
multiply(multiply(A,B),identity) = multiply(A,multiply(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[102])]),104])]),
[iquote('copy,102,flip.1,demod,104,flip.1')] ).
cnf(127,plain,
multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,multiply(multiply(multiply(identity,multiply(A,identity)),B),multiply(B,B))))) = multiply(A,identity),
inference(para_into,[status(thm),theory(equality)],[32,52]),
[iquote('para_into,31.1.1.2.2.1,51.1.1')] ).
cnf(137,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(multiply(C,C),multiply(multiply(C,multiply(C,identity)),multiply(C,multiply(C,identity)))))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,68]),24,24,24,24,24]),
[iquote('para_into,31.1.1.2.2.2.1,68.1.1,demod,24,24,24,24,24')] ).
cnf(148,plain,
multiply(A,multiply(A,multiply(B,multiply(B,multiply(multiply(B,multiply(A,multiply(C,C))),multiply(multiply(multiply(identity,C),D),multiply(D,multiply(D,identity)))))))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[32,68]),32,108,108,108,108]),
[iquote('para_from,31.1.1,68.1.1.2.1,demod,32,108,108,108,108')] ).
cnf(154,plain,
multiply(A,identity) = A,
inference(para_from,[status(thm),theory(equality)],[104,52]),
[iquote('para_from,103.1.1,51.1.1.2')] ).
cnf(166,plain,
multiply(A,multiply(A,A)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[148]),154,32]),
[iquote('back_demod,148,demod,154,32')] ).
cnf(172,plain,
multiply(A,multiply(A,multiply(A,B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[137]),154,154,166,154]),
[iquote('back_demod,137,demod,154,154,166,154')] ).
cnf(177,plain,
multiply(identity,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[127]),154,154,154,76,154,172,154]),
[iquote('back_demod,127,demod,154,154,154,76,154,172,154')] ).
cnf(179,plain,
$false,
inference(binary,[status(thm)],[177,1]),
[iquote('binary,177.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 05:13:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.71/1.94 ----- Otter 3.3f, August 2004 -----
% 1.71/1.94 The process was started by sandbox2 on n022.cluster.edu,
% 1.71/1.94 Wed Jul 27 05:13:50 2022
% 1.71/1.94 The command was "./otter". The process ID is 4341.
% 1.71/1.94
% 1.71/1.94 set(prolog_style_variables).
% 1.71/1.94 set(auto).
% 1.71/1.94 dependent: set(auto1).
% 1.71/1.94 dependent: set(process_input).
% 1.71/1.94 dependent: clear(print_kept).
% 1.71/1.94 dependent: clear(print_new_demod).
% 1.71/1.94 dependent: clear(print_back_demod).
% 1.71/1.94 dependent: clear(print_back_sub).
% 1.71/1.94 dependent: set(control_memory).
% 1.71/1.94 dependent: assign(max_mem, 12000).
% 1.71/1.94 dependent: assign(pick_given_ratio, 4).
% 1.71/1.94 dependent: assign(stats_level, 1).
% 1.71/1.94 dependent: assign(max_seconds, 10800).
% 1.71/1.94 clear(print_given).
% 1.71/1.94
% 1.71/1.94 list(usable).
% 1.71/1.94 0 [] A=A.
% 1.71/1.94 0 [] multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z))))=Y.
% 1.71/1.94 0 [] multiply(identity,a)!=a.
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.94
% 1.71/1.94 All clauses are units, and equality is present; the
% 1.71/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.94
% 1.71/1.94 dependent: set(knuth_bendix).
% 1.71/1.94 dependent: set(anl_eq).
% 1.71/1.94 dependent: set(para_from).
% 1.71/1.94 dependent: set(para_into).
% 1.71/1.94 dependent: clear(para_from_right).
% 1.71/1.94 dependent: clear(para_into_right).
% 1.71/1.94 dependent: set(para_from_vars).
% 1.71/1.94 dependent: set(eq_units_both_ways).
% 1.71/1.94 dependent: set(dynamic_demod_all).
% 1.71/1.94 dependent: set(dynamic_demod).
% 1.71/1.94 dependent: set(order_eq).
% 1.71/1.94 dependent: set(back_demod).
% 1.71/1.94 dependent: set(lrpo).
% 1.71/1.94
% 1.71/1.94 ------------> process usable:
% 1.71/1.94 ** KEPT (pick-wt=5): 1 [] multiply(identity,a)!=a.
% 1.71/1.94
% 1.71/1.94 ------------> process sos:
% 1.71/1.94 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.71/1.94 ** KEPT (pick-wt=17): 3 [] multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))))=B.
% 1.71/1.94 ---> New Demodulator: 4 [new_demod,3] multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))))=B.
% 1.71/1.94 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.71/1.94 >>>> Starting back demodulation with 4.
% 1.71/1.94
% 1.71/1.94 ======= end of input processing =======
% 1.71/1.94
% 1.71/1.94 =========== start of search ===========
% 1.71/1.94
% 1.71/1.94 -------- PROOF --------
% 1.71/1.94
% 1.71/1.94 ----> UNIT CONFLICT at 0.01 sec ----> 179 [binary,177.1,1.1] $F.
% 1.71/1.94
% 1.71/1.94 Length of proof is 20. Level of proof is 12.
% 1.71/1.94
% 1.71/1.94 ---------------- PROOF ----------------
% 1.71/1.94 % SZS status Unsatisfiable
% 1.71/1.94 % SZS output start Refutation
% See solution above
% 1.71/1.94 ------------ end of proof -------------
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94 ============ end of search ============
% 1.71/1.94
% 1.71/1.94 -------------- statistics -------------
% 1.71/1.94 clauses given 12
% 1.71/1.94 clauses generated 117
% 1.71/1.94 clauses kept 109
% 1.71/1.94 clauses forward subsumed 100
% 1.71/1.94 clauses back subsumed 2
% 1.71/1.94 Kbytes malloced 1953
% 1.71/1.94
% 1.71/1.94 ----------- times (seconds) -----------
% 1.71/1.94 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.71/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.94
% 1.71/1.94 That finishes the proof of the theorem.
% 1.71/1.94
% 1.71/1.94 Process 4341 finished Wed Jul 27 05:13:52 2022
% 1.71/1.94 Otter interrupted
% 1.71/1.94 PROOF FOUND
%------------------------------------------------------------------------------