TSTP Solution File: GRP595-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP595-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.71s 1.94s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 2 RR)
% Number of literals : 21 ( 20 equ; 1 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP595-1.p',unknown),
[] ).
cnf(3,axiom,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B)))))) = C,
file('GRP595-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP595-1.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,
multiply(multiply(multiply(A,B),C),double_divide(C,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),7,7,7]),
[iquote('back_demod,3,demod,7,7,7')] ).
cnf(10,plain,
multiply(multiply(A,B),double_divide(B,multiply(multiply(C,A),D))) = double_divide(D,C),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1.1,8.1.1')] ).
cnf(12,plain,
multiply(A,double_divide(double_divide(B,C),multiply(C,A))) = B,
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1,8.1.1')] ).
cnf(35,plain,
double_divide(multiply(A,double_divide(B,multiply(C,A))),C) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,12])]),
[iquote('para_into,10.1.1,12.1.1,flip.1')] ).
cnf(65,plain,
double_divide(double_divide(multiply(A,B),C),multiply(C,A)) = B,
inference(para_into,[status(thm),theory(equality)],[35,10]),
[iquote('para_into,35.1.1.1,10.1.1')] ).
cnf(76,plain,
inverse(A) = multiply(B,multiply(C,double_divide(A,multiply(B,C)))),
inference(para_from,[status(thm),theory(equality)],[35,7]),
[iquote('para_from,35.1.1,6.1.1.1')] ).
cnf(78,plain,
multiply(A,multiply(B,double_divide(C,multiply(A,B)))) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[76])]),
[iquote('copy,76,flip.1')] ).
cnf(102,plain,
inverse(A) = multiply(multiply(B,C),double_divide(multiply(C,A),B)),
inference(para_from,[status(thm),theory(equality)],[65,7]),
[iquote('para_from,65.1.1,6.1.1.1')] ).
cnf(103,plain,
multiply(multiply(A,B),double_divide(multiply(B,C),A)) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[102])]),
[iquote('copy,102,flip.1')] ).
cnf(210,plain,
multiply(inverse(A),double_divide(double_divide(multiply(B,A),C),C)) = B,
inference(para_from,[status(thm),theory(equality)],[103,8]),
[iquote('para_from,103.1.1,8.1.1.1')] ).
cnf(241,plain,
double_divide(multiply(A,B),multiply(C,inverse(B))) = double_divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[210,35])]),
[iquote('para_from,210.1.1,35.1.1.1,flip.1')] ).
cnf(356,plain,
double_divide(multiply(inverse(A),double_divide(B,C)),C) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[241,35]),
[iquote('para_from,241.1.1,35.1.1.1.2')] ).
cnf(409,plain,
multiply(double_divide(multiply(A,B),C),B) = double_divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[356,210])]),
[iquote('para_into,356.1.1.1,210.1.1,flip.1')] ).
cnf(451,plain,
multiply(A,double_divide(A,multiply(B,C))) = double_divide(C,B),
inference(para_into,[status(thm),theory(equality)],[409,35]),
[iquote('para_into,409.1.1.1,35.1.1')] ).
cnf(592,plain,
multiply(A,double_divide(B,A)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[451,78]),
[iquote('para_from,451.1.1,78.1.1.2')] ).
cnf(994,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[592,65]),7]),
[iquote('para_into,592.1.1.2,65.1.1,demod,7')] ).
cnf(996,plain,
$false,
inference(binary,[status(thm)],[994,1]),
[iquote('binary,994.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP595-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 05:06:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.94 ----- Otter 3.3f, August 2004 -----
% 1.71/1.94 The process was started by sandbox on n018.cluster.edu,
% 1.71/1.94 Wed Jul 27 05:06:16 2022
% 1.71/1.94 The command was "./otter". The process ID is 20204.
% 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 [] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.71/1.94 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.71/1.94 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 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=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 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=14): 3 [] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.71/1.94 ---> New Demodulator: 4 [new_demod,3] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.71/1.94 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.71/1.94 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 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 >>>> Starting back demodulation with 7.
% 1.71/1.94 >> back demodulating 3 with 7.
% 1.71/1.94 >>>> Starting back demodulation with 9.
% 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
% 1.71/1.94 Resetting weight limit to 15.
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Resetting weight limit to 15.
% 1.71/1.94
% 1.71/1.94 sos_size=290
% 1.71/1.94
% 1.71/1.94 -------- PROOF --------
% 1.71/1.94
% 1.71/1.94 ----> UNIT CONFLICT at 0.02 sec ----> 996 [binary,994.1,1.1] $F.
% 1.71/1.94
% 1.71/1.94 Length of proof is 17. Level of proof is 14.
% 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 37
% 1.71/1.94 clauses generated 902
% 1.71/1.94 clauses kept 699
% 1.71/1.94 clauses forward subsumed 626
% 1.71/1.94 clauses back subsumed 0
% 1.71/1.94 Kbytes malloced 4882
% 1.71/1.94
% 1.71/1.94 ----------- times (seconds) -----------
% 1.71/1.94 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.77/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.77/1.94
% 1.77/1.94 That finishes the proof of the theorem.
% 1.77/1.94
% 1.77/1.94 Process 20204 finished Wed Jul 27 05:06:17 2022
% 1.77/1.94 Otter interrupted
% 1.77/1.94 PROOF FOUND
%------------------------------------------------------------------------------