TSTP Solution File: GRP539-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP539-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 1.69s 1.90s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 4 RR)
% Number of literals : 20 ( 19 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP539-1.p',unknown),
[] ).
cnf(3,axiom,
divide(divide(A,B),divide(divide(A,C),B)) = C,
file('GRP539-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP539-1.p',unknown),
[] ).
cnf(7,axiom,
identity = divide(A,A),
file('GRP539-1.p',unknown),
[] ).
cnf(9,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(11,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)],[5])]),9])]),
[iquote('copy,5,flip.1,demod,9,flip.1')] ).
cnf(14,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),11,11,11,11]),
[iquote('back_demod,1,demod,11,11,11,11')] ).
cnf(15,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[3,9]),
[iquote('para_into,3.1.1.1,8.1.1')] ).
cnf(22,plain,
divide(divide(A,divide(A,B)),identity) = B,
inference(para_into,[status(thm),theory(equality)],[3,9]),
[iquote('para_into,3.1.1.2,8.1.1')] ).
cnf(28,plain,
divide(divide(A,B),A) = divide(identity,divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,15])]),
[iquote('para_into,15.1.1.2.1,15.1.1,flip.1')] ).
cnf(30,plain,
divide(identity,divide(identity,A)) = A,
inference(para_into,[status(thm),theory(equality)],[15,9]),
[iquote('para_into,15.1.1.2.1,8.1.1')] ).
cnf(32,plain,
divide(divide(A,B),C) = divide(identity,divide(B,divide(A,C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,3])]),
[iquote('para_into,15.1.1.2.1,3.1.1,flip.1')] ).
cnf(34,plain,
divide(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),28,30]),
[iquote('back_demod,15,demod,28,30')] ).
cnf(39,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),34]),
[iquote('back_demod,22,demod,34')] ).
cnf(45,plain,
divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(b3,divide(identity,divide(a3,divide(identity,c3)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),32,32,39])]),
[iquote('back_demod,14,demod,32,32,39,flip.1')] ).
cnf(59,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,34]),34]),
[iquote('para_into,31.1.1,33.1.1,demod,34')] ).
cnf(61,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[59])]),
[iquote('copy,59,flip.1')] ).
cnf(73,plain,
divide(A,divide(B,C)) = divide(C,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,32]),39]),
[iquote('para_into,61.1.1.2,31.1.1,demod,39')] ).
cnf(124,plain,
divide(A,divide(B,divide(C,D))) = divide(C,divide(B,divide(A,D))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[73,32]),32,32,39,32,39]),
[iquote('para_from,73.1.1,31.1.1.1,demod,32,32,39,32,39')] ).
cnf(125,plain,
$false,
inference(binary,[status(thm)],[124,45]),
[iquote('binary,124.1,45.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP539-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 05:10:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.69/1.90 ----- Otter 3.3f, August 2004 -----
% 1.69/1.90 The process was started by sandbox on n004.cluster.edu,
% 1.69/1.90 Wed Jul 27 05:10:51 2022
% 1.69/1.90 The command was "./otter". The process ID is 26023.
% 1.69/1.90
% 1.69/1.90 set(prolog_style_variables).
% 1.69/1.90 set(auto).
% 1.69/1.90 dependent: set(auto1).
% 1.69/1.90 dependent: set(process_input).
% 1.69/1.90 dependent: clear(print_kept).
% 1.69/1.90 dependent: clear(print_new_demod).
% 1.69/1.90 dependent: clear(print_back_demod).
% 1.69/1.90 dependent: clear(print_back_sub).
% 1.69/1.90 dependent: set(control_memory).
% 1.69/1.90 dependent: assign(max_mem, 12000).
% 1.69/1.90 dependent: assign(pick_given_ratio, 4).
% 1.69/1.90 dependent: assign(stats_level, 1).
% 1.69/1.90 dependent: assign(max_seconds, 10800).
% 1.69/1.90 clear(print_given).
% 1.69/1.90
% 1.69/1.90 list(usable).
% 1.69/1.90 0 [] A=A.
% 1.69/1.90 0 [] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.69/1.90 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.69/1.90 0 [] inverse(A)=divide(divide(B,B),A).
% 1.69/1.90 0 [] identity=divide(A,A).
% 1.69/1.90 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.69/1.90
% 1.69/1.90 All clauses are units, and equality is present; the
% 1.69/1.90 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.69/1.90
% 1.69/1.90 dependent: set(knuth_bendix).
% 1.69/1.90 dependent: set(anl_eq).
% 1.69/1.90 dependent: set(para_from).
% 1.69/1.90 dependent: set(para_into).
% 1.69/1.90 dependent: clear(para_from_right).
% 1.69/1.90 dependent: clear(para_into_right).
% 1.69/1.90 dependent: set(para_from_vars).
% 1.69/1.90 dependent: set(eq_units_both_ways).
% 1.69/1.90 dependent: set(dynamic_demod_all).
% 1.69/1.90 dependent: set(dynamic_demod).
% 1.69/1.90 dependent: set(order_eq).
% 1.69/1.90 dependent: set(back_demod).
% 1.69/1.90 dependent: set(lrpo).
% 1.69/1.90
% 1.69/1.90 ------------> process usable:
% 1.69/1.90 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.69/1.90
% 1.69/1.90 ------------> process sos:
% 1.69/1.90 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.90 ** KEPT (pick-wt=11): 3 [] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.69/1.90 ---> New Demodulator: 4 [new_demod,3] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.69/1.90 ** KEPT (pick-wt=11): 5 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.69/1.90 ** KEPT (pick-wt=8): 6 [] inverse(A)=divide(divide(B,B),A).
% 1.69/1.90 ** KEPT (pick-wt=5): 8 [copy,7,flip.1] divide(A,A)=identity.
% 1.69/1.90 ---> New Demodulator: 9 [new_demod,8] divide(A,A)=identity.
% 1.69/1.90 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.90 >>>> Starting back demodulation with 4.
% 1.69/1.90 ** KEPT (pick-wt=9): 10 [copy,5,flip.1,demod,9,flip.1] multiply(A,B)=divide(A,divide(identity,B)).
% 1.69/1.90 ---> New Demodulator: 11 [new_demod,10] multiply(A,B)=divide(A,divide(identity,B)).
% 1.69/1.90 ** KEPT (pick-wt=6): 12 [copy,6,flip.1,demod,9,flip.1] inverse(A)=divide(identity,A).
% 1.69/1.90 ---> New Demodulator: 13 [new_demod,12] inverse(A)=divide(identity,A).
% 1.69/1.90 >>>> Starting back demodulation with 9.
% 1.69/1.90 >> back demodulating 6 with 9.
% 1.69/1.90 >> back demodulating 5 with 9.
% 1.69/1.90 >>>> Starting back demodulation with 11.
% 1.69/1.90 >> back demodulating 1 with 11.
% 1.69/1.90 >>>> Starting back demodulation with 13.
% 1.69/1.90
% 1.69/1.90 ======= end of input processing =======
% 1.69/1.90
% 1.69/1.90 =========== start of search ===========
% 1.69/1.90
% 1.69/1.90 -------- PROOF --------
% 1.69/1.90
% 1.69/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 125 [binary,124.1,45.1] $F.
% 1.69/1.90
% 1.69/1.90 Length of proof is 15. Level of proof is 8.
% 1.69/1.90
% 1.69/1.90 ---------------- PROOF ----------------
% 1.69/1.90 % SZS status Unsatisfiable
% 1.69/1.90 % SZS output start Refutation
% See solution above
% 1.69/1.90 ------------ end of proof -------------
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90 ============ end of search ============
% 1.69/1.90
% 1.69/1.90 -------------- statistics -------------
% 1.69/1.90 clauses given 18
% 1.69/1.90 clauses generated 250
% 1.69/1.90 clauses kept 94
% 1.69/1.90 clauses forward subsumed 248
% 1.69/1.90 clauses back subsumed 6
% 1.69/1.90 Kbytes malloced 976
% 1.69/1.90
% 1.69/1.90 ----------- times (seconds) -----------
% 1.69/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.90
% 1.69/1.90 That finishes the proof of the theorem.
% 1.69/1.90
% 1.69/1.90 Process 26023 finished Wed Jul 27 05:10:52 2022
% 1.69/1.90 Otter interrupted
% 1.69/1.90 PROOF FOUND
%------------------------------------------------------------------------------