%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP574-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 12:57:17 EDT 2022
% Result : Unsatisfiable 1.68s 1.93s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 4 RR)
% Number of literals : 37 ( 36 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(identity,a2) != a2,
file('GRP574-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
file('GRP574-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP574-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP574-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP574-1.p',unknown),
[] ).
cnf(10,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9]),8])]),
[iquote('copy,9,demod,8,flip.1')] ).
cnf(12,plain,
double_divide(double_divide(a2,identity),identity) != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6]),
[iquote('back_demod,1,demod,6')] ).
cnf(13,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,10]),
[iquote('para_into,3.1.1.1.2.1.2,10.1.1')] ).
cnf(17,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[3,10]),
[iquote('para_into,3.1.1.1.2.1,10.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.2.1,3.1.1')] ).
cnf(20,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(24,plain,
double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity,
inference(para_from,[status(thm),theory(equality)],[17,3]),
[iquote('para_from,17.1.1,3.1.1.1.2')] ).
cnf(26,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(para_from,[status(thm),theory(equality)],[17,3]),
[iquote('para_from,17.1.1,3.1.1.1.2.1')] ).
cnf(29,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),26]),
[iquote('back_demod,20,demod,26')] ).
cnf(32,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,24]),24])]),
[iquote('para_into,13.1.1.1.2,23.1.1,demod,24,flip.1')] ).
cnf(34,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,10]),32]),
[iquote('para_into,13.1.1.1.2,10.1.1,demod,32')] ).
cnf(37,plain,
double_divide(double_divide(identity,double_divide(A,identity)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),32,32]),
[iquote('back_demod,25,demod,32,32')] ).
cnf(39,plain,
double_divide(double_divide(double_divide(A,identity),A),identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),32]),
[iquote('back_demod,23,demod,32')] ).
cnf(41,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),32]),
[iquote('back_demod,17,demod,32')] ).
cnf(61,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,39]),32,32,32])]),
[iquote('para_into,33.1.1.1.1.1,39.1.1,demod,32,32,32,flip.1')] ).
cnf(63,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),A) = identity,
inference(para_from,[status(thm),theory(equality)],[34,10]),
[iquote('para_from,33.1.1,10.1.1.2')] ).
cnf(68,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[34,29]),34]),
[iquote('para_from,33.1.1,29.1.1.2.1.2,demod,34')] ).
cnf(69,plain,
double_divide(A,double_divide(double_divide(double_divide(A,identity),identity),identity)) = identity,
inference(para_into,[status(thm),theory(equality)],[61,34]),
[iquote('para_into,61.1.1.1,33.1.1')] ).
cnf(71,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,B),identity)))) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[61,29]),68])]),
[iquote('para_from,61.1.1,29.1.1.2.1,demod,68,flip.1')] ).
cnf(78,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,34]),34]),
[iquote('para_into,37.1.1.1.2,33.1.1,demod,34')] ).
cnf(80,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),78]),
[iquote('back_demod,41,demod,78')] ).
cnf(81,plain,
double_divide(A,B) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[71]),80]),
[iquote('back_demod,71,demod,80')] ).
cnf(82,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[81])]),
[iquote('copy,81,flip.1')] ).
cnf(85,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,29]),34]),
[iquote('para_from,63.1.1,29.1.1.2.1.2,demod,34')] ).
cnf(88,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[69,29]),85,85,80])]),
[iquote('para_from,69.1.1,29.1.1.2.1,demod,85,85,80,flip.1')] ).
cnf(92,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[85]),88]),
[iquote('back_demod,84,demod,88')] ).
cnf(94,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),88]),
[iquote('back_demod,79,demod,88')] ).
cnf(109,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[88]),94]),
[iquote('back_demod,87,demod,94')] ).
cnf(114,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[109,34]),92])]),
[iquote('para_into,109.1.1,33.1.1,demod,92,flip.1')] ).
cnf(115,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[82]),114]),
[iquote('back_demod,82,demod,114')] ).
cnf(132,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[115,114])]),
[iquote('para_into,115.1.1,113.1.1,flip.1')] ).
cnf(134,plain,
$false,
inference(binary,[status(thm)],[132,12]),
[iquote('binary,132.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP574-1 : TPTP v8.1.0. Released v2.6.0.
% 0.02/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 05:44:52 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.68/1.93 ----- Otter 3.3f, August 2004 -----
% 1.68/1.93 The process was started by sandbox2 on n016.cluster.edu,
% 1.68/1.93 Wed Jul 27 05:44:52 2022
% 1.68/1.93 The command was "./otter". The process ID is 6831.
% 1.68/1.93
% 1.68/1.93 set(prolog_style_variables).
% 1.68/1.93 set(auto).
% 1.68/1.93 dependent: set(auto1).
% 1.68/1.93 dependent: set(process_input).
% 1.68/1.93 dependent: clear(print_kept).
% 1.68/1.93 dependent: clear(print_new_demod).
% 1.68/1.93 dependent: clear(print_back_demod).
% 1.68/1.93 dependent: clear(print_back_sub).
% 1.68/1.93 dependent: set(control_memory).
% 1.68/1.93 dependent: assign(max_mem, 12000).
% 1.68/1.93 dependent: assign(pick_given_ratio, 4).
% 1.68/1.93 dependent: assign(stats_level, 1).
% 1.68/1.93 dependent: assign(max_seconds, 10800).
% 1.68/1.93 clear(print_given).
% 1.68/1.93
% 1.68/1.93 list(usable).
% 1.68/1.93 0 [] A=A.
% 1.68/1.93 0 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.68/1.93 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.93 0 [] inverse(A)=double_divide(A,identity).
% 1.68/1.93 0 [] identity=double_divide(A,inverse(A)).
% 1.68/1.93 0 [] multiply(identity,a2)!=a2.
% 1.68/1.93 end_of_list.
% 1.68/1.93
% 1.68/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.93
% 1.68/1.93 All clauses are units, and equality is present; the
% 1.68/1.93 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.93
% 1.68/1.93 dependent: set(knuth_bendix).
% 1.68/1.93 dependent: set(anl_eq).
% 1.68/1.93 dependent: set(para_from).
% 1.68/1.93 dependent: set(para_into).
% 1.68/1.93 dependent: clear(para_from_right).
% 1.68/1.93 dependent: clear(para_into_right).
% 1.68/1.93 dependent: set(para_from_vars).
% 1.68/1.93 dependent: set(eq_units_both_ways).
% 1.68/1.93 dependent: set(dynamic_demod_all).
% 1.68/1.93 dependent: set(dynamic_demod).
% 1.68/1.93 dependent: set(order_eq).
% 1.68/1.93 dependent: set(back_demod).
% 1.68/1.93 dependent: set(lrpo).
% 1.68/1.93
% 1.68/1.93 ------------> process usable:
% 1.68/1.93 ** KEPT (pick-wt=5): 1 [] multiply(identity,a2)!=a2.
% 1.68/1.93
% 1.68/1.93 ------------> process sos:
% 1.68/1.93 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.68/1.93 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.68/1.93 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.68/1.93 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.93 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.93 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.68/1.93 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.68/1.93 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.68/1.93 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.68/1.93 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.68/1.93 >>>> Starting back demodulation with 4.
% 1.68/1.93 >>>> Starting back demodulation with 6.
% 1.68/1.93 >> back demodulating 1 with 6.
% 1.68/1.93 >>>> Starting back demodulation with 8.
% 1.68/1.93 >>>> Starting back demodulation with 11.
% 1.68/1.93
% 1.68/1.93 ======= end of input processing =======
% 1.68/1.93
% 1.68/1.93 =========== start of search ===========
% 1.68/1.93
% 1.68/1.93 -------- PROOF --------
% 1.68/1.93
% 1.68/1.93 ----> UNIT CONFLICT at 0.00 sec ----> 134 [binary,132.1,12.1] $F.
% 1.68/1.93
% 1.68/1.93 Length of proof is 31. Level of proof is 13.
% 1.68/1.93
% 1.68/1.93 ---------------- PROOF ----------------
% 1.68/1.93 % SZS status Unsatisfiable
% 1.68/1.93 % SZS output start Refutation
% See solution above
% 1.68/1.93 ------------ end of proof -------------
% 1.68/1.93
% 1.68/1.93
% 1.68/1.93 Search stopped by max_proofs option.
% 1.68/1.93
% 1.68/1.93
% 1.68/1.93 Search stopped by max_proofs option.
% 1.68/1.93
% 1.68/1.93 ============ end of search ============
% 1.68/1.93
% 1.68/1.93 -------------- statistics -------------
% 1.68/1.93 clauses given 24
% 1.68/1.93 clauses generated 179
% 1.68/1.93 clauses kept 72
% 1.68/1.93 clauses forward subsumed 168
% 1.68/1.93 clauses back subsumed 2
% 1.68/1.93 Kbytes malloced 976
% 1.68/1.93
% 1.68/1.93 ----------- times (seconds) -----------
% 1.68/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.93
% 1.68/1.93 That finishes the proof of the theorem.
% 1.68/1.93
% 1.68/1.93 Process 6831 finished Wed Jul 27 05:44:53 2022
% 1.68/1.93 Otter interrupted
% 1.68/1.93 PROOF FOUND
%------------------------------------------------------------------------------