TSTP Solution File: GRP590-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP590-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 12:57:19 EDT 2022
% Result : Unsatisfiable 1.94s 2.09s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 3 RR)
% Number of literals : 30 ( 29 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP590-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C,
file('GRP590-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP590-1.p',unknown),
[] ).
cnf(7,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,plain,
double_divide(multiply(multiply(inverse(A),B),double_divide(B,C)),C) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),7,7]),
[iquote('back_demod,3,demod,7,7')] ).
cnf(11,plain,
double_divide(multiply(multiply(multiply(A,B),C),double_divide(C,D)),D) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[8,7]),
[iquote('para_into,8.1.1.1.1.1,6.1.1')] ).
cnf(12,plain,
double_divide(multiply(multiply(inverse(A),multiply(multiply(inverse(B),C),double_divide(C,D))),B),D) = A,
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1.2,8.1.1')] ).
cnf(14,plain,
multiply(A,multiply(multiply(inverse(B),C),double_divide(C,A))) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,7])]),
[iquote('para_from,8.1.1,6.1.1.1,flip.1')] ).
cnf(42,plain,
double_divide(multiply(inverse(A),A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[12,14]),
[iquote('para_into,12.1.1.1.1,14.1.1')] ).
cnf(51,plain,
double_divide(multiply(inverse(A),A),multiply(B,C)) = double_divide(C,B),
inference(para_into,[status(thm),theory(equality)],[42,7]),
[iquote('para_into,42.1.1.2,6.1.1')] ).
cnf(58,plain,
double_divide(multiply(multiply(inverse(A),multiply(inverse(B),B)),C),inverse(C)) = A,
inference(para_from,[status(thm),theory(equality)],[42,8]),
[iquote('para_from,42.1.1,8.1.1.1.2')] ).
cnf(61,plain,
multiply(inverse(A),multiply(inverse(B),B)) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[42,7])]),
[iquote('para_from,42.1.1,6.1.1.1,flip.1')] ).
cnf(62,plain,
double_divide(multiply(inverse(A),B),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),61]),
[iquote('back_demod,58,demod,61')] ).
cnf(86,plain,
double_divide(inverse(multiply(inverse(A),A)),inverse(B)) = B,
inference(para_from,[status(thm),theory(equality)],[61,42]),
[iquote('para_from,60.1.1,42.1.1.1')] ).
cnf(92,plain,
double_divide(inverse(A),inverse(multiply(inverse(B),B))) = A,
inference(para_from,[status(thm),theory(equality)],[61,62]),
[iquote('para_from,60.1.1,62.1.1.1')] ).
cnf(147,plain,
double_divide(multiply(A,B),inverse(multiply(inverse(C),C))) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[92,7]),
[iquote('para_into,92.1.1.1,6.1.1')] ).
cnf(152,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(para_into,[status(thm),theory(equality)],[92,86]),
[iquote('para_into,92.1.1,86.1.1')] ).
cnf(161,plain,
double_divide(A,multiply(inverse(B),inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[92,8]),147]),
[iquote('para_from,92.1.1,8.1.1.1.2,demod,147')] ).
cnf(171,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[152,11]),11]),
[iquote('para_from,152.1.1,10.1.1.1.1.1,demod,11')] ).
cnf(174,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(para_from,[status(thm),theory(equality)],[152,1]),
[iquote('para_from,152.1.1,1.1.1.1')] ).
cnf(213,plain,
double_divide(A,multiply(inverse(B),B)) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[161,152]),
[iquote('para_into,161.1.1.2,152.1.1')] ).
cnf(214,plain,
inverse(A) = double_divide(A,multiply(inverse(B),B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[213])]),
[iquote('copy,213,flip.1')] ).
cnf(233,plain,
multiply(inverse(A),A) = double_divide(B,inverse(B)),
inference(para_into,[status(thm),theory(equality)],[171,42]),
[iquote('para_into,171.1.1,42.1.1')] ).
cnf(275,plain,
inverse(inverse(A)) = multiply(multiply(inverse(B),B),A),
inference(para_from,[status(thm),theory(equality)],[213,7]),
[iquote('para_from,213.1.1,6.1.1.1')] ).
cnf(276,plain,
multiply(multiply(inverse(A),A),B) = inverse(inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[275])]),
[iquote('copy,275,flip.1')] ).
cnf(325,plain,
double_divide(inverse(A),double_divide(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[214,92]),51]),
[iquote('para_from,214.1.1,92.1.1.2,demod,51')] ).
cnf(387,plain,
double_divide(A,double_divide(B,inverse(B))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[233,161]),
[iquote('para_from,233.1.1,161.1.1.2')] ).
cnf(486,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[387,325])]),
[iquote('para_into,387.1.1,325.1.1,flip.1')] ).
cnf(497,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[276]),486]),
[iquote('back_demod,276,demod,486')] ).
cnf(499,plain,
$false,
inference(binary,[status(thm)],[497,174]),
[iquote('binary,497.1,174.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP590-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 05:19:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.94/2.09 ----- Otter 3.3f, August 2004 -----
% 1.94/2.09 The process was started by sandbox on n025.cluster.edu,
% 1.94/2.09 Wed Jul 27 05:19:15 2022
% 1.94/2.09 The command was "./otter". The process ID is 19029.
% 1.94/2.09
% 1.94/2.09 set(prolog_style_variables).
% 1.94/2.09 set(auto).
% 1.94/2.09 dependent: set(auto1).
% 1.94/2.09 dependent: set(process_input).
% 1.94/2.09 dependent: clear(print_kept).
% 1.94/2.09 dependent: clear(print_new_demod).
% 1.94/2.09 dependent: clear(print_back_demod).
% 1.94/2.09 dependent: clear(print_back_sub).
% 1.94/2.09 dependent: set(control_memory).
% 1.94/2.09 dependent: assign(max_mem, 12000).
% 1.94/2.09 dependent: assign(pick_given_ratio, 4).
% 1.94/2.09 dependent: assign(stats_level, 1).
% 1.94/2.09 dependent: assign(max_seconds, 10800).
% 1.94/2.09 clear(print_given).
% 1.94/2.09
% 1.94/2.09 list(usable).
% 1.94/2.09 0 [] A=A.
% 1.94/2.09 0 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.94/2.09 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.94/2.09 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.94/2.09 end_of_list.
% 1.94/2.09
% 1.94/2.09 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.94/2.09
% 1.94/2.09 All clauses are units, and equality is present; the
% 1.94/2.09 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.94/2.09
% 1.94/2.09 dependent: set(knuth_bendix).
% 1.94/2.09 dependent: set(anl_eq).
% 1.94/2.09 dependent: set(para_from).
% 1.94/2.09 dependent: set(para_into).
% 1.94/2.09 dependent: clear(para_from_right).
% 1.94/2.09 dependent: clear(para_into_right).
% 1.94/2.09 dependent: set(para_from_vars).
% 1.94/2.09 dependent: set(eq_units_both_ways).
% 1.94/2.09 dependent: set(dynamic_demod_all).
% 1.94/2.09 dependent: set(dynamic_demod).
% 1.94/2.09 dependent: set(order_eq).
% 1.94/2.09 dependent: set(back_demod).
% 1.94/2.09 dependent: set(lrpo).
% 1.94/2.09
% 1.94/2.09 ------------> process usable:
% 1.94/2.09 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.94/2.09
% 1.94/2.09 ------------> process sos:
% 1.94/2.09 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.94/2.09 ** KEPT (pick-wt=14): 3 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.94/2.09 ---> New Demodulator: 4 [new_demod,3] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.94/2.09 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.94/2.09 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.94/2.09 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.94/2.09 >>>> Starting back demodulation with 4.
% 1.94/2.09 >>>> Starting back demodulation with 7.
% 1.94/2.09 >> back demodulating 3 with 7.
% 1.94/2.09 >>>> Starting back demodulation with 9.
% 1.94/2.09
% 1.94/2.09 ======= end of input processing =======
% 1.94/2.09
% 1.94/2.09 =========== start of search ===========
% 1.94/2.09
% 1.94/2.09 -------- PROOF --------
% 1.94/2.09
% 1.94/2.09 ----> UNIT CONFLICT at 0.01 sec ----> 499 [binary,497.1,174.1] $F.
% 1.94/2.09
% 1.94/2.09 Length of proof is 26. Level of proof is 14.
% 1.94/2.09
% 1.94/2.09 ---------------- PROOF ----------------
% 1.94/2.09 % SZS status Unsatisfiable
% 1.94/2.09 % SZS output start Refutation
% See solution above
% 1.94/2.09 ------------ end of proof -------------
% 1.94/2.09
% 1.94/2.09
% 1.94/2.09 Search stopped by max_proofs option.
% 1.94/2.09
% 1.94/2.09
% 1.94/2.09 Search stopped by max_proofs option.
% 1.94/2.09
% 1.94/2.09 ============ end of search ============
% 1.94/2.09
% 1.94/2.09 -------------- statistics -------------
% 1.94/2.09 clauses given 29
% 1.94/2.09 clauses generated 453
% 1.94/2.09 clauses kept 295
% 1.94/2.09 clauses forward subsumed 262
% 1.94/2.09 clauses back subsumed 1
% 1.94/2.09 Kbytes malloced 4882
% 1.94/2.09
% 1.94/2.09 ----------- times (seconds) -----------
% 1.94/2.09 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.94/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.94/2.09
% 1.94/2.09 That finishes the proof of the theorem.
% 1.94/2.09
% 1.94/2.09 Process 19029 finished Wed Jul 27 05:19:17 2022
% 1.94/2.09 Otter interrupted
% 1.94/2.09 PROOF FOUND
%------------------------------------------------------------------------------