%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:55:50 EDT 2022
% Result : Unsatisfiable 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 9 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(b,c) != identity,
file('GRP010-4.p',unknown),
[] ).
cnf(3,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP010-4.p',unknown),
[] ).
cnf(6,axiom,
multiply(identity,A) = A,
file('GRP010-4.p',unknown),
[] ).
cnf(7,axiom,
multiply(inverse(A),A) = identity,
file('GRP010-4.p',unknown),
[] ).
cnf(9,axiom,
multiply(c,b) = identity,
file('GRP010-4.p',unknown),
[] ).
cnf(11,plain,
multiply(c,multiply(b,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,9]),6])]),
[iquote('para_into,3.1.1.1,9.1.1,demod,6,flip.1')] ).
cnf(13,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,7]),6])]),
[iquote('para_into,3.1.1.1,7.1.1,demod,6,flip.1')] ).
cnf(17,plain,
multiply(inverse(c),A) = multiply(b,A),
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.2,11.1.1')] ).
cnf(33,plain,
multiply(b,c) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,7])]),
[iquote('para_into,17.1.1,7.1.1,flip.1')] ).
cnf(35,plain,
$false,
inference(binary,[status(thm)],[33,1]),
[iquote('binary,33.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 04:57:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox2 on n003.cluster.edu,
% 1.68/1.89 Wed Jul 27 04:57:56 2022
% 1.68/1.89 The command was "./otter". The process ID is 6250.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.68/1.89 0 [] multiply(identity,X)=X.
% 1.68/1.89 0 [] multiply(inverse(X),X)=identity.
% 1.68/1.89 0 [] multiply(c,b)=identity.
% 1.68/1.89 0 [] multiply(b,c)!=identity.
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.89
% 1.68/1.89 All clauses are units, and equality is present; the
% 1.68/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=5): 1 [] multiply(b,c)!=identity.
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=11): 3 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.68/1.89 ---> New Demodulator: 4 [new_demod,3] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.68/1.89 ** KEPT (pick-wt=5): 5 [] multiply(identity,A)=A.
% 1.68/1.89 ---> New Demodulator: 6 [new_demod,5] multiply(identity,A)=A.
% 1.68/1.89 ** KEPT (pick-wt=6): 7 [] multiply(inverse(A),A)=identity.
% 1.68/1.89 ---> New Demodulator: 8 [new_demod,7] multiply(inverse(A),A)=identity.
% 1.68/1.89 ** KEPT (pick-wt=5): 9 [] multiply(c,b)=identity.
% 1.68/1.89 ---> New Demodulator: 10 [new_demod,9] multiply(c,b)=identity.
% 1.68/1.89 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.68/1.89 >>>> Starting back demodulation with 4.
% 1.68/1.89 >>>> Starting back demodulation with 6.
% 1.68/1.89 >>>> Starting back demodulation with 8.
% 1.68/1.89 >>>> Starting back demodulation with 10.
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 35 [binary,33.1,1.1] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 4. Level of proof is 3.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Unsatisfiable
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 10
% 1.68/1.89 clauses generated 45
% 1.68/1.89 clauses kept 18
% 1.68/1.89 clauses forward subsumed 36
% 1.68/1.89 clauses back subsumed 0
% 1.68/1.89 Kbytes malloced 976
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 6250 finished Wed Jul 27 04:57:58 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------