%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP598-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:57:20 EDT 2022
% Result : Unsatisfiable 1.90s 2.10s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 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 : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP598-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP598-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B))))) = C,
file('GRP598-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP598-1.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(9,plain,
double_divide(double_divide(A,B),multiply(multiply(B,inverse(C)),A)) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),7,7]),
[iquote('back_demod,3,demod,7,7')] ).
cnf(10,plain,
double_divide(A,multiply(multiply(multiply(multiply(B,inverse(A)),C),inverse(D)),double_divide(C,B))) = D,
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,8.1.1.1,8.1.1')] ).
cnf(14,plain,
multiply(multiply(multiply(A,inverse(B)),C),double_divide(C,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,7])]),
[iquote('para_from,8.1.1,6.1.1.1,flip.1')] ).
cnf(20,plain,
multiply(multiply(multiply(multiply(multiply(A,inverse(B)),C),inverse(D)),double_divide(C,A)),B) = inverse(D),
inference(para_into,[status(thm),theory(equality)],[14,9]),
[iquote('para_into,14.1.1.2,8.1.1')] ).
cnf(88,plain,
multiply(multiply(inverse(A),inverse(B)),A) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,20]),9]),
[iquote('para_into,20.1.1.1.1,20.1.1,demod,9')] ).
cnf(108,plain,
double_divide(A,multiply(inverse(A),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[20,10]),9]),
[iquote('para_from,20.1.1,10.1.1.2.1,demod,9')] ).
cnf(116,plain,
double_divide(double_divide(A,B),multiply(multiply(B,A),inverse(C))) = C,
inference(para_into,[status(thm),theory(equality)],[108,7]),
[iquote('para_into,108.1.1.2.1,6.1.1')] ).
cnf(162,plain,
double_divide(double_divide(A,inverse(A)),inverse(B)) = B,
inference(para_from,[status(thm),theory(equality)],[88,9]),
[iquote('para_from,88.1.1,8.1.1.2')] ).
cnf(170,plain,
double_divide(double_divide(A,inverse(A)),multiply(B,C)) = double_divide(C,B),
inference(para_into,[status(thm),theory(equality)],[162,7]),
[iquote('para_into,162.1.1.2,6.1.1')] ).
cnf(336,plain,
double_divide(inverse(A),multiply(inverse(B),B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[170,116])]),
[iquote('para_into,170.1.1,116.1.1,flip.1')] ).
cnf(363,plain,
double_divide(A,multiply(multiply(multiply(inverse(B),B),inverse(C)),inverse(A))) = C,
inference(para_from,[status(thm),theory(equality)],[336,9]),
[iquote('para_from,336.1.1,8.1.1.1')] ).
cnf(366,plain,
multiply(multiply(inverse(A),A),inverse(B)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[336,7])]),
[iquote('para_from,336.1.1,6.1.1.1,flip.1')] ).
cnf(368,plain,
double_divide(A,multiply(inverse(B),inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[363]),366]),
[iquote('back_demod,363,demod,366')] ).
cnf(386,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[368,336])]),
[iquote('para_into,368.1.1,336.1.1,flip.1')] ).
cnf(584,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[386,88]),386]),
[iquote('para_from,385.1.1,88.1.1.1.2,demod,386')] ).
cnf(681,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[584,116]),386]),
[iquote('para_from,584.1.1,116.1.1.2,demod,386')] ).
cnf(699,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[681,681]),
[iquote('para_into,681.1.1.1,681.1.1')] ).
cnf(701,plain,
multiply(inverse(A),inverse(B)) = double_divide(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[681,368])]),
[iquote('para_into,681.1.1.1,368.1.1,flip.1')] ).
cnf(710,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[681,108]),701]),
[iquote('para_into,681.1.1.1,108.1.1,demod,701')] ).
cnf(716,plain,
multiply(multiply(A,inverse(B)),C) = double_divide(B,double_divide(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[681,9])]),
[iquote('para_into,681.1.1.1,8.1.1,flip.1')] ).
cnf(930,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[710,7]),7]),
[iquote('para_from,710.1.1,6.1.1.1,demod,7')] ).
cnf(941,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[930,1]),716,699]),
[iquote('para_from,930.1.1,1.1.1.1,demod,716,699')] ).
cnf(942,plain,
$false,
inference(binary,[status(thm)],[941,2]),
[iquote('binary,941.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP598-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 05:27:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.90/2.10 ----- Otter 3.3f, August 2004 -----
% 1.90/2.10 The process was started by sandbox2 on n011.cluster.edu,
% 1.90/2.10 Wed Jul 27 05:27:10 2022
% 1.90/2.10 The command was "./otter". The process ID is 1180.
% 1.90/2.10
% 1.90/2.10 set(prolog_style_variables).
% 1.90/2.10 set(auto).
% 1.90/2.10 dependent: set(auto1).
% 1.90/2.10 dependent: set(process_input).
% 1.90/2.10 dependent: clear(print_kept).
% 1.90/2.10 dependent: clear(print_new_demod).
% 1.90/2.10 dependent: clear(print_back_demod).
% 1.90/2.10 dependent: clear(print_back_sub).
% 1.90/2.10 dependent: set(control_memory).
% 1.90/2.10 dependent: assign(max_mem, 12000).
% 1.90/2.10 dependent: assign(pick_given_ratio, 4).
% 1.90/2.10 dependent: assign(stats_level, 1).
% 1.90/2.10 dependent: assign(max_seconds, 10800).
% 1.90/2.10 clear(print_given).
% 1.90/2.10
% 1.90/2.10 list(usable).
% 1.90/2.10 0 [] A=A.
% 1.90/2.10 0 [] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.90/2.10 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.90/2.10 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.90/2.10 end_of_list.
% 1.90/2.10
% 1.90/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.90/2.10
% 1.90/2.10 All clauses are units, and equality is present; the
% 1.90/2.10 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.90/2.10
% 1.90/2.10 dependent: set(knuth_bendix).
% 1.90/2.10 dependent: set(anl_eq).
% 1.90/2.10 dependent: set(para_from).
% 1.90/2.10 dependent: set(para_into).
% 1.90/2.10 dependent: clear(para_from_right).
% 1.90/2.10 dependent: clear(para_into_right).
% 1.90/2.10 dependent: set(para_from_vars).
% 1.90/2.10 dependent: set(eq_units_both_ways).
% 1.90/2.10 dependent: set(dynamic_demod_all).
% 1.90/2.10 dependent: set(dynamic_demod).
% 1.90/2.10 dependent: set(order_eq).
% 1.90/2.10 dependent: set(back_demod).
% 1.90/2.10 dependent: set(lrpo).
% 1.90/2.10
% 1.90/2.10 ------------> process usable:
% 1.90/2.10 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.90/2.10
% 1.90/2.10 ------------> process sos:
% 1.90/2.10 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.90/2.10 ** KEPT (pick-wt=14): 3 [] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.90/2.10 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.90/2.10 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.90/2.10 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.90/2.10 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.90/2.10 >>>> Starting back demodulation with 4.
% 1.90/2.10 >>>> Starting back demodulation with 7.
% 1.90/2.10 >> back demodulating 3 with 7.
% 1.90/2.10 >>>> Starting back demodulation with 9.
% 1.90/2.10
% 1.90/2.10 ======= end of input processing =======
% 1.90/2.10
% 1.90/2.10 =========== start of search ===========
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 9.
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Resetting weight limit to 9.
% 1.90/2.10
% 1.90/2.10 sos_size=237
% 1.90/2.10
% 1.90/2.10 -------- PROOF --------
% 1.90/2.10
% 1.90/2.10 ----> UNIT CONFLICT at 0.03 sec ----> 942 [binary,941.1,2.1] $F.
% 1.90/2.10
% 1.90/2.10 Length of proof is 23. Level of proof is 17.
% 1.90/2.10
% 1.90/2.10 ---------------- PROOF ----------------
% 1.90/2.10 % SZS status Unsatisfiable
% 1.90/2.10 % SZS output start Refutation
% See solution above
% 1.90/2.10 ------------ end of proof -------------
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Search stopped by max_proofs option.
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Search stopped by max_proofs option.
% 1.90/2.10
% 1.90/2.10 ============ end of search ============
% 1.90/2.10
% 1.90/2.10 -------------- statistics -------------
% 1.90/2.10 clauses given 37
% 1.90/2.10 clauses generated 733
% 1.90/2.10 clauses kept 550
% 1.90/2.10 clauses forward subsumed 583
% 1.90/2.10 clauses back subsumed 4
% 1.90/2.10 Kbytes malloced 4882
% 1.90/2.10
% 1.90/2.10 ----------- times (seconds) -----------
% 1.90/2.10 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.90/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.90/2.10
% 1.90/2.10 That finishes the proof of the theorem.
% 1.90/2.10
% 1.90/2.10 Process 1180 finished Wed Jul 27 05:27:12 2022
% 1.90/2.10 Otter interrupted
% 1.90/2.10 PROOF FOUND
%------------------------------------------------------------------------------