TSTP Solution File: GRP533-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP533-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:57:12 EDT 2022
% Result : Unsatisfiable 1.97s 2.11s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 4 RR)
% Number of literals : 11 ( 10 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP533-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('GRP533-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP533-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP533-1.p',unknown),
[] ).
cnf(8,axiom,
identity = divide(A,A),
file('GRP533-1.p',unknown),
[] ).
cnf(10,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(12,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),10])]),
[iquote('copy,6,flip.1,demod,10,flip.1')] ).
cnf(14,plain,
inverse(A) = divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),10])]),
[iquote('copy,7,flip.1,demod,10,flip.1')] ).
cnf(15,plain,
identity != identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),14,12,10,14,12,10]),
[iquote('back_demod,2,demod,14,12,10,14,12,10')] ).
cnf(16,plain,
$false,
inference(binary,[status(thm)],[15,3]),
[iquote('binary,15.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP533-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:36:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.11
% 1.97/2.11 -------- PROOF --------
% 1.97/2.11 ----- Otter 3.3f, August 2004 -----
% 1.97/2.11 The process was started by sandbox2 on n026.cluster.edu,
% 1.97/2.11 Wed Jul 27 05:36:09 2022
% 1.97/2.11 The command was "./otter". The process ID is 11032.
% 1.97/2.11
% 1.97/2.11 set(prolog_style_variables).
% 1.97/2.11 set(auto).
% 1.97/2.11 dependent: set(auto1).
% 1.97/2.11 dependent: set(process_input).
% 1.97/2.11 dependent: clear(print_kept).
% 1.97/2.11 dependent: clear(print_new_demod).
% 1.97/2.11 dependent: clear(print_back_demod).
% 1.97/2.11 dependent: clear(print_back_sub).
% 1.97/2.11 dependent: set(control_memory).
% 1.97/2.11 dependent: assign(max_mem, 12000).
% 1.97/2.11 dependent: assign(pick_given_ratio, 4).
% 1.97/2.11 dependent: assign(stats_level, 1).
% 1.97/2.11 dependent: assign(max_seconds, 10800).
% 1.97/2.11 clear(print_given).
% 1.97/2.11
% 1.97/2.11 list(usable).
% 1.97/2.11 0 [] A=A.
% 1.97/2.11 0 [] divide(divide(A,divide(divide(A,B),C)),B)=C.
% 1.97/2.11 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.97/2.11 0 [] inverse(A)=divide(divide(B,B),A).
% 1.97/2.11 0 [] identity=divide(A,A).
% 1.97/2.11 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.97/2.11 end_of_list.
% 1.97/2.11
% 1.97/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.97/2.11
% 1.97/2.11 All clauses are units, and equality is present; the
% 1.97/2.11 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.97/2.11
% 1.97/2.11 dependent: set(knuth_bendix).
% 1.97/2.11 dependent: set(anl_eq).
% 1.97/2.11 dependent: set(para_from).
% 1.97/2.11 dependent: set(para_into).
% 1.97/2.11 dependent: clear(para_from_right).
% 1.97/2.11 dependent: clear(para_into_right).
% 1.97/2.11 dependent: set(para_from_vars).
% 1.97/2.11 dependent: set(eq_units_both_ways).
% 1.97/2.11 dependent: set(dynamic_demod_all).
% 1.97/2.11 dependent: set(dynamic_demod).
% 1.97/2.11 dependent: set(order_eq).
% 1.97/2.11 dependent: set(back_demod).
% 1.97/2.11 dependent: set(lrpo).
% 1.97/2.11
% 1.97/2.11 ------------> process usable:
% 1.97/2.11 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.97/2.11
% 1.97/2.11 ------------> process sos:
% 1.97/2.11 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.97/2.11 ** KEPT (pick-wt=11): 4 [] divide(divide(A,divide(divide(A,B),C)),B)=C.
% 1.97/2.11 ---> New Demodulator: 5 [new_demod,4] divide(divide(A,divide(divide(A,B),C)),B)=C.
% 1.97/2.11 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.97/2.11 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.97/2.11 ** KEPT (pick-wt=5): 9 [copy,8,flip.1] divide(A,A)=identity.
% 1.97/2.11 ---> New Demodulator: 10 [new_demod,9] divide(A,A)=identity.
% 1.97/2.11 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.97/2.11 >>>> Starting back demodulation with 5.
% 1.97/2.11 ** KEPT (pick-wt=9): 11 [copy,6,flip.1,demod,10,flip.1] multiply(A,B)=divide(A,divide(identity,B)).
% 1.97/2.11 ---> New Demodulator: 12 [new_demod,11] multiply(A,B)=divide(A,divide(identity,B)).
% 1.97/2.11 ** KEPT (pick-wt=6): 13 [copy,7,flip.1,demod,10,flip.1] inverse(A)=divide(identity,A).
% 1.97/2.11 ---> New Demodulator: 14 [new_demod,13] inverse(A)=divide(identity,A).
% 1.97/2.11 >>>> Starting back demodulation with 10.
% 1.97/2.11 >> back demodulating 7 with 10.
% 1.97/2.11 >> back demodulating 6 with 10.
% 1.97/2.11 >>>> Starting back demodulation with 12.
% 1.97/2.11 >> back demodulating 2 with 12.
% 1.97/2.11
% 1.97/2.11 ----> UNIT CONFLICT at 0.00 sec ----> 16 [binary,15.1,3.1] $F.
% 1.97/2.11
% 1.97/2.11 Length of proof is 5. Level of proof is 3.
% 1.97/2.11
% 1.97/2.11 ---------------- PROOF ----------------
% 1.97/2.11 % SZS status Unsatisfiable
% 1.97/2.11 % SZS output start Refutation
% See solution above
% 1.97/2.11 ------------ end of proof -------------
% 1.97/2.11
% 1.97/2.11
% 1.97/2.11 Search stopped by max_proofs option.
% 1.97/2.11
% 1.97/2.11
% 1.97/2.11 Search stopped by max_proofs option.
% 1.97/2.11
% 1.97/2.11 ============ end of search ============
% 1.97/2.11
% 1.97/2.11 -------------- statistics -------------
% 1.97/2.11 clauses given 0
% 1.97/2.11 clauses generated 0
% 1.97/2.11 clauses kept 9
% 1.97/2.11 clauses forward subsumed 3
% 1.97/2.11 clauses back subsumed 0
% 1.97/2.11 Kbytes malloced 976
% 1.97/2.11
% 1.97/2.11 ----------- times (seconds) -----------
% 1.97/2.11 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.11 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.97/2.11
% 1.97/2.11 That finishes the proof of the theorem.
% 1.97/2.11
% 1.97/2.11 Process 11032 finished Wed Jul 27 05:36:10 2022
% 1.97/2.11 Otter interrupted
% 1.97/2.11 PROOF FOUND
%------------------------------------------------------------------------------