%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP611-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 12:57:21 EDT 2022
% Result : Unsatisfiable 1.66s 1.89s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 2 RR)
% Number of literals : 32 ( 31 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 : 88 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP611-1.p',unknown),
[] ).
cnf(3,axiom,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
file('GRP611-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP611-1.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(double_divide(A,B),multiply(B,multiply(C,A))) = C,
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(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.2.2,8.1.1')] ).
cnf(12,plain,
multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.2,8.1.1')] ).
cnf(34,plain,
double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
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,
multiply(double_divide(multiply(A,multiply(B,C)),D),A) = double_divide(C,multiply(D,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,34])]),
[iquote('para_into,34.1.1.2.1,34.1.1,flip.1')] ).
cnf(66,plain,
double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
inference(para_into,[status(thm),theory(equality)],[34,10]),
[iquote('para_into,34.1.1.2,10.1.1')] ).
cnf(76,plain,
inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
inference(para_from,[status(thm),theory(equality)],[34,7]),
[iquote('para_from,34.1.1,6.1.1.1')] ).
cnf(78,plain,
multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[76])]),
[iquote('copy,76,flip.1')] ).
cnf(100,plain,
inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[66,7]),
[iquote('para_from,66.1.1,6.1.1.1')] ).
cnf(101,plain,
multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[100])]),
[iquote('copy,100,flip.1')] ).
cnf(128,plain,
multiply(double_divide(A,double_divide(A,multiply(B,C))),inverse(B)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[78,8]),65]),
[iquote('para_from,78.1.1,8.1.1.2,demod,65')] ).
cnf(229,plain,
multiply(multiply(A,B),multiply(inverse(A),C)) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[128,78]),7])]),
[iquote('para_from,128.1.1,78.1.1.1,demod,7,flip.1')] ).
cnf(231,plain,
double_divide(multiply(inverse(A),B),multiply(A,C)) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[128,34])]),
[iquote('para_from,128.1.1,34.1.1.2,flip.1')] ).
cnf(256,plain,
multiply(multiply(A,multiply(B,C)),D) = multiply(B,multiply(multiply(A,C),D)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[229,8]),7])]),
[iquote('para_into,229.1.1.1,8.1.1,demod,7,flip.1')] ).
cnf(353,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(para_from,[status(thm),theory(equality)],[231,66]),
[iquote('para_from,231.1.1,66.1.1.2')] ).
cnf(355,plain,
double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[231,34]),
[iquote('para_from,231.1.1,34.1.1.2.1')] ).
cnf(367,plain,
double_divide(inverse(A),double_divide(B,double_divide(B,multiply(A,inverse(C))))) = C,
inference(para_into,[status(thm),theory(equality)],[353,101]),
[iquote('para_into,353.1.1.1,101.1.1')] ).
cnf(399,plain,
multiply(A,double_divide(B,multiply(A,C))) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[355,128])]),
[iquote('para_into,355.1.1.2,128.1.1,flip.1')] ).
cnf(428,plain,
multiply(A,double_divide(B,double_divide(C,D))) = double_divide(B,double_divide(C,multiply(A,D))),
inference(para_into,[status(thm),theory(equality)],[399,399]),
[iquote('para_into,399.1.1.2.2,399.1.1')] ).
cnf(439,plain,
double_divide(A,double_divide(B,double_divide(B,multiply(C,D)))) = double_divide(A,multiply(C,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[399,10]),428,65]),
[iquote('para_into,399.1.1.2.2,10.1.1,demod,428,65')] ).
cnf(471,plain,
double_divide(inverse(A),multiply(A,inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[367]),439]),
[iquote('back_demod,367,demod,439')] ).
cnf(525,plain,
double_divide(multiply(inverse(A),inverse(B)),A) = B,
inference(para_from,[status(thm),theory(equality)],[471,66]),
[iquote('para_from,471.1.1,66.1.1.2')] ).
cnf(578,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[525,12]),7]),
[iquote('para_from,525.1.1,12.1.1.1,demod,7')] ).
cnf(586,plain,
double_divide(A,double_divide(A,multiply(B,C))) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[578,128])]),
[iquote('para_into,577.1.1.2,128.1.1,flip.1')] ).
cnf(599,plain,
multiply(multiply(A,B),inverse(A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[128]),586]),
[iquote('back_demod,128,demod,586')] ).
cnf(661,plain,
multiply(double_divide(A,B),A) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[599,78]),256,578]),
[iquote('para_from,599.1.1,78.1.1.1.1.1,demod,256,578')] ).
cnf(924,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[661,66]),7])]),
[iquote('para_into,661.1.1.1,66.1.1,demod,7,flip.1')] ).
cnf(926,plain,
$false,
inference(binary,[status(thm)],[924,1]),
[iquote('binary,924.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP611-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.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 05:13:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.89 ----- Otter 3.3f, August 2004 -----
% 1.66/1.89 The process was started by sandbox on n010.cluster.edu,
% 1.66/1.89 Wed Jul 27 05:13:40 2022
% 1.66/1.89 The command was "./otter". The process ID is 9783.
% 1.66/1.89
% 1.66/1.89 set(prolog_style_variables).
% 1.66/1.89 set(auto).
% 1.66/1.89 dependent: set(auto1).
% 1.66/1.89 dependent: set(process_input).
% 1.66/1.89 dependent: clear(print_kept).
% 1.66/1.89 dependent: clear(print_new_demod).
% 1.66/1.89 dependent: clear(print_back_demod).
% 1.66/1.89 dependent: clear(print_back_sub).
% 1.66/1.89 dependent: set(control_memory).
% 1.66/1.89 dependent: assign(max_mem, 12000).
% 1.66/1.89 dependent: assign(pick_given_ratio, 4).
% 1.66/1.89 dependent: assign(stats_level, 1).
% 1.66/1.89 dependent: assign(max_seconds, 10800).
% 1.66/1.89 clear(print_given).
% 1.66/1.89
% 1.66/1.89 list(usable).
% 1.66/1.89 0 [] A=A.
% 1.66/1.89 0 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.66/1.89 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.66/1.89 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.66/1.89 end_of_list.
% 1.66/1.89
% 1.66/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.89
% 1.66/1.89 All clauses are units, and equality is present; the
% 1.66/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.89
% 1.66/1.89 dependent: set(knuth_bendix).
% 1.66/1.89 dependent: set(anl_eq).
% 1.66/1.89 dependent: set(para_from).
% 1.66/1.89 dependent: set(para_into).
% 1.66/1.89 dependent: clear(para_from_right).
% 1.66/1.89 dependent: clear(para_into_right).
% 1.66/1.89 dependent: set(para_from_vars).
% 1.66/1.89 dependent: set(eq_units_both_ways).
% 1.66/1.89 dependent: set(dynamic_demod_all).
% 1.66/1.89 dependent: set(dynamic_demod).
% 1.66/1.89 dependent: set(order_eq).
% 1.66/1.89 dependent: set(back_demod).
% 1.66/1.89 dependent: set(lrpo).
% 1.66/1.89
% 1.66/1.89 ------------> process usable:
% 1.66/1.89 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.66/1.89
% 1.66/1.89 ------------> process sos:
% 1.66/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.66/1.89 ** KEPT (pick-wt=14): 3 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.66/1.89 ---> New Demodulator: 4 [new_demod,3] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.66/1.89 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.66/1.89 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.66/1.89 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.66/1.89 >>>> Starting back demodulation with 4.
% 1.66/1.89 >>>> Starting back demodulation with 7.
% 1.66/1.89 >> back demodulating 3 with 7.
% 1.66/1.89 >>>> Starting back demodulation with 9.
% 1.66/1.89
% 1.66/1.89 ======= end of input processing =======
% 1.66/1.89
% 1.66/1.89 =========== start of search ===========
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Resetting weight limit to 13.
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Resetting weight limit to 13.
% 1.66/1.89
% 1.66/1.89 sos_size=273
% 1.66/1.89
% 1.66/1.89 -------- PROOF --------
% 1.66/1.89
% 1.66/1.89 ----> UNIT CONFLICT at 0.03 sec ----> 926 [binary,924.1,1.1] $F.
% 1.66/1.89
% 1.66/1.89 Length of proof is 28. Level of proof is 19.
% 1.66/1.89
% 1.66/1.89 ---------------- PROOF ----------------
% 1.66/1.89 % SZS status Unsatisfiable
% 1.66/1.89 % SZS output start Refutation
% See solution above
% 1.66/1.90 ------------ end of proof -------------
% 1.66/1.90
% 1.66/1.90
% 1.66/1.90 Search stopped by max_proofs option.
% 1.66/1.90
% 1.66/1.90
% 1.66/1.90 Search stopped by max_proofs option.
% 1.66/1.90
% 1.66/1.90 ============ end of search ============
% 1.66/1.90
% 1.66/1.90 -------------- statistics -------------
% 1.66/1.90 clauses given 38
% 1.66/1.90 clauses generated 1002
% 1.66/1.90 clauses kept 630
% 1.66/1.90 clauses forward subsumed 588
% 1.66/1.90 clauses back subsumed 2
% 1.66/1.90 Kbytes malloced 4882
% 1.66/1.90
% 1.66/1.90 ----------- times (seconds) -----------
% 1.66/1.90 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.66/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.90
% 1.66/1.90 That finishes the proof of the theorem.
% 1.66/1.90
% 1.66/1.90 Process 9783 finished Wed Jul 27 05:13:41 2022
% 1.66/1.90 Otter interrupted
% 1.66/1.90 PROOF FOUND
%------------------------------------------------------------------------------