%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 1.65s 1.86s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 3 RR)
% Number of literals : 39 ( 38 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 : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP592-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C,
file('GRP592-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP592-1.p',unknown),
[] ).
cnf(8,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,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)],[4]),8,8]),
[iquote('back_demod,4,demod,8,8')] ).
cnf(12,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)],[9,8]),
[iquote('para_into,9.1.1.1.1.1,7.1.1')] ).
cnf(13,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)],[9,9]),
[iquote('para_into,9.1.1.1.2,9.1.1')] ).
cnf(15,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)],[9,8])]),
[iquote('para_from,9.1.1,7.1.1.1,flip.1')] ).
cnf(43,plain,
double_divide(multiply(inverse(A),A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[13,15]),
[iquote('para_into,13.1.1.1.1,15.1.1')] ).
cnf(52,plain,
double_divide(multiply(inverse(A),A),multiply(B,C)) = double_divide(C,B),
inference(para_into,[status(thm),theory(equality)],[43,8]),
[iquote('para_into,43.1.1.2,7.1.1')] ).
cnf(53,plain,
multiply(inverse(A),multiply(multiply(inverse(B),multiply(inverse(C),C)),A)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[43,15]),
[iquote('para_from,43.1.1,15.1.1.2.2')] ).
cnf(59,plain,
double_divide(multiply(multiply(inverse(A),multiply(inverse(B),B)),C),inverse(C)) = A,
inference(para_from,[status(thm),theory(equality)],[43,9]),
[iquote('para_from,43.1.1,9.1.1.1.2')] ).
cnf(62,plain,
multiply(inverse(A),multiply(inverse(B),B)) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,8])]),
[iquote('para_from,43.1.1,7.1.1.1,flip.1')] ).
cnf(63,plain,
double_divide(multiply(inverse(A),B),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),62]),
[iquote('back_demod,59,demod,62')] ).
cnf(67,plain,
multiply(inverse(A),multiply(inverse(B),A)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[53]),62]),
[iquote('back_demod,53,demod,62')] ).
cnf(87,plain,
double_divide(inverse(multiply(inverse(A),A)),inverse(B)) = B,
inference(para_from,[status(thm),theory(equality)],[62,43]),
[iquote('para_from,61.1.1,43.1.1.1')] ).
cnf(93,plain,
double_divide(inverse(A),inverse(multiply(inverse(B),B))) = A,
inference(para_from,[status(thm),theory(equality)],[62,63]),
[iquote('para_from,61.1.1,63.1.1.1')] ).
cnf(148,plain,
double_divide(multiply(A,B),inverse(multiply(inverse(C),C))) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[93,8]),
[iquote('para_into,93.1.1.1,7.1.1')] ).
cnf(153,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(para_into,[status(thm),theory(equality)],[93,87]),
[iquote('para_into,93.1.1,87.1.1')] ).
cnf(162,plain,
double_divide(A,multiply(inverse(B),inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[93,9]),148]),
[iquote('para_from,93.1.1,9.1.1.1.2,demod,148')] ).
cnf(169,plain,
multiply(A,multiply(multiply(inverse(B),B),double_divide(C,A))) = inverse(C),
inference(para_from,[status(thm),theory(equality)],[153,15]),
[iquote('para_from,153.1.1,15.1.1.2.1')] ).
cnf(172,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[153,12]),12]),
[iquote('para_from,153.1.1,11.1.1.1.1.1,demod,12')] ).
cnf(179,plain,
double_divide(A,multiply(inverse(B),B)) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[162,153]),
[iquote('para_into,162.1.1.2,153.1.1')] ).
cnf(180,plain,
inverse(A) = double_divide(A,multiply(inverse(B),B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[179])]),
[iquote('copy,179,flip.1')] ).
cnf(229,plain,
multiply(inverse(A),A) = double_divide(B,inverse(B)),
inference(para_into,[status(thm),theory(equality)],[172,43]),
[iquote('para_into,172.1.1,43.1.1')] ).
cnf(269,plain,
inverse(inverse(A)) = multiply(multiply(inverse(B),B),A),
inference(para_from,[status(thm),theory(equality)],[179,8]),
[iquote('para_from,179.1.1,7.1.1.1')] ).
cnf(270,plain,
multiply(multiply(inverse(A),A),B) = inverse(inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[269])]),
[iquote('copy,269,flip.1')] ).
cnf(276,plain,
double_divide(inverse(A),double_divide(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[180,93]),52]),
[iquote('para_from,180.1.1,93.1.1.2,demod,52')] ).
cnf(330,plain,
double_divide(A,double_divide(B,inverse(B))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[229,162]),
[iquote('para_from,229.1.1,162.1.1.2')] ).
cnf(429,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[330,276])]),
[iquote('para_into,330.1.1,276.1.1,flip.1')] ).
cnf(439,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[270]),429]),
[iquote('back_demod,270,demod,429')] ).
cnf(459,plain,
multiply(A,double_divide(B,A)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[169]),439]),
[iquote('back_demod,169,demod,439')] ).
cnf(581,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[429,8]),
[iquote('para_into,428.1.1.1,7.1.1')] ).
cnf(615,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[429,67]),429]),
[iquote('para_from,428.1.1,67.1.1.2.1,demod,429')] ).
cnf(787,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[615,63]),581]),
[iquote('para_from,615.1.1,63.1.1.1,demod,581')] ).
cnf(789,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[787,787]),
[iquote('para_into,787.1.1.2,787.1.1')] ).
cnf(806,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[789,459]),8]),
[iquote('para_from,789.1.1,459.1.1.2,demod,8')] ).
cnf(807,plain,
$false,
inference(binary,[status(thm)],[806,2]),
[iquote('binary,806.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 05:17:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.86 ----- Otter 3.3f, August 2004 -----
% 1.65/1.86 The process was started by sandbox on n007.cluster.edu,
% 1.65/1.86 Wed Jul 27 05:17:46 2022
% 1.65/1.86 The command was "./otter". The process ID is 18632.
% 1.65/1.86
% 1.65/1.86 set(prolog_style_variables).
% 1.65/1.86 set(auto).
% 1.65/1.86 dependent: set(auto1).
% 1.65/1.86 dependent: set(process_input).
% 1.65/1.86 dependent: clear(print_kept).
% 1.65/1.86 dependent: clear(print_new_demod).
% 1.65/1.86 dependent: clear(print_back_demod).
% 1.65/1.86 dependent: clear(print_back_sub).
% 1.65/1.86 dependent: set(control_memory).
% 1.65/1.86 dependent: assign(max_mem, 12000).
% 1.65/1.86 dependent: assign(pick_given_ratio, 4).
% 1.65/1.86 dependent: assign(stats_level, 1).
% 1.65/1.86 dependent: assign(max_seconds, 10800).
% 1.65/1.86 clear(print_given).
% 1.65/1.86
% 1.65/1.86 list(usable).
% 1.65/1.86 0 [] A=A.
% 1.65/1.86 0 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.65/1.86 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.65/1.86 0 [] multiply(a,b)!=multiply(b,a).
% 1.65/1.86 end_of_list.
% 1.65/1.86
% 1.65/1.86 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.65/1.86
% 1.65/1.86 All clauses are units, and equality is present; the
% 1.65/1.86 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.65/1.86
% 1.65/1.86 dependent: set(knuth_bendix).
% 1.65/1.86 dependent: set(anl_eq).
% 1.65/1.86 dependent: set(para_from).
% 1.65/1.86 dependent: set(para_into).
% 1.65/1.86 dependent: clear(para_from_right).
% 1.65/1.86 dependent: clear(para_into_right).
% 1.65/1.86 dependent: set(para_from_vars).
% 1.65/1.86 dependent: set(eq_units_both_ways).
% 1.65/1.86 dependent: set(dynamic_demod_all).
% 1.65/1.86 dependent: set(dynamic_demod).
% 1.65/1.86 dependent: set(order_eq).
% 1.65/1.86 dependent: set(back_demod).
% 1.65/1.86 dependent: set(lrpo).
% 1.65/1.86
% 1.65/1.86 ------------> process usable:
% 1.65/1.86 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.65/1.86
% 1.65/1.86 ------------> process sos:
% 1.65/1.86 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.65/1.86 ** KEPT (pick-wt=14): 4 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.65/1.86 ---> New Demodulator: 5 [new_demod,4] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.65/1.86 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.65/1.86 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.65/1.86 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.65/1.86 >>>> Starting back demodulation with 5.
% 1.65/1.86 >>>> Starting back demodulation with 8.
% 1.65/1.86 >> back demodulating 4 with 8.
% 1.65/1.86 >>>> Starting back demodulation with 10.
% 1.65/1.86
% 1.65/1.86 ======= end of input processing =======
% 1.65/1.86
% 1.65/1.86 =========== start of search ===========
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Resetting weight limit to 9.
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Resetting weight limit to 9.
% 1.65/1.86
% 1.65/1.86 sos_size=264
% 1.65/1.86
% 1.65/1.86 -------- PROOF --------
% 1.65/1.86
% 1.65/1.86 ----> UNIT CONFLICT at 0.01 sec ----> 807 [binary,806.1,2.1] $F.
% 1.65/1.86
% 1.65/1.86 Length of proof is 35. Level of proof is 17.
% 1.65/1.86
% 1.65/1.86 ---------------- PROOF ----------------
% 1.65/1.86 % SZS status Unsatisfiable
% 1.65/1.86 % SZS output start Refutation
% See solution above
% 1.65/1.86 ------------ end of proof -------------
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Search stopped by max_proofs option.
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Search stopped by max_proofs option.
% 1.65/1.86
% 1.65/1.86 ============ end of search ============
% 1.65/1.86
% 1.65/1.86 -------------- statistics -------------
% 1.65/1.86 clauses given 38
% 1.65/1.86 clauses generated 711
% 1.65/1.86 clauses kept 486
% 1.65/1.86 clauses forward subsumed 577
% 1.65/1.86 clauses back subsumed 2
% 1.65/1.86 Kbytes malloced 4882
% 1.65/1.86
% 1.65/1.86 ----------- times (seconds) -----------
% 1.65/1.86 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.86 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.86
% 1.65/1.86 That finishes the proof of the theorem.
% 1.65/1.86
% 1.65/1.86 Process 18632 finished Wed Jul 27 05:17:47 2022
% 1.65/1.86 Otter interrupted
% 1.65/1.86 PROOF FOUND
%------------------------------------------------------------------------------