TSTP Solution File: GRP462-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP462-1 : 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 12:57:03 EDT 2022
% Result : Unsatisfiable 1.78s 1.94s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 4 RR)
% Number of literals : 28 ( 27 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP462-1.p',unknown),
[] ).
cnf(3,axiom,
divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B,
file('GRP462-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP462-1.p',unknown),
[] ).
cnf(9,axiom,
identity = divide(A,A),
file('GRP462-1.p',unknown),
[] ).
cnf(11,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,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]),6,6,6,6]),
[iquote('back_demod,1,demod,6,6,6,6')] ).
cnf(13,plain,
divide(A,divide(divide(divide(identity,B),C),divide(divide(identity,A),C))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),11]),
[iquote('back_demod,3,demod,11')] ).
cnf(15,plain,
divide(A,divide(divide(B,C),divide(divide(identity,A),C))) = divide(divide(divide(identity,B),D),divide(identity,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,13]),11]),
[iquote('para_into,13.1.1.2.1.1,13.1.1,demod,11')] ).
cnf(28,plain,
divide(A,divide(divide(divide(identity,B),divide(identity,A)),identity)) = B,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.2.2,10.1.1')] ).
cnf(31,plain,
divide(A,identity) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.2,10.1.1')] ).
cnf(32,plain,
divide(divide(divide(identity,A),B),divide(identity,B)) = divide(C,divide(divide(A,D),divide(divide(identity,C),D))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(33,plain,
divide(A,divide(divide(identity,B),divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),31]),
[iquote('back_demod,28,demod,31')] ).
cnf(35,plain,
divide(A,divide(B,divide(identity,A))) = divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,33]),11,31]),
[iquote('para_into,33.1.1.2.1,33.1.1,demod,11,31')] ).
cnf(42,plain,
divide(identity,divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,31]),31]),
[iquote('para_into,33.1.1.2.2,30.1.1,demod,31')] ).
cnf(45,plain,
divide(identity,A) = divide(B,divide(A,divide(identity,B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[35])]),
[iquote('copy,35,flip.1')] ).
cnf(55,plain,
divide(A,divide(B,divide(divide(identity,A),divide(divide(identity,B),C)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,13]),42]),
[iquote('para_from,33.1.1,13.1.1.2.1,demod,42')] ).
cnf(58,plain,
divide(A,divide(divide(B,C),divide(divide(identity,A),C))) = divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,13]),11,31]),
[iquote('para_from,33.1.1,13.1.1.2.1.1,demod,11,31')] ).
cnf(59,plain,
divide(divide(divide(identity,A),B),divide(identity,B)) = divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),58]),
[iquote('back_demod,32,demod,58')] ).
cnf(61,plain,
divide(divide(identity,A),divide(B,A)) = divide(identity,B),
inference(para_into,[status(thm),theory(equality)],[35,42]),
[iquote('para_into,35.1.1.2.2,41.1.1')] ).
cnf(74,plain,
divide(divide(a3,divide(A,divide(b3,divide(identity,A)))),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(para_from,[status(thm),theory(equality)],[45,12]),
[iquote('para_from,45.1.1,12.1.1.1.2')] ).
cnf(80,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,61]),42]),
[iquote('para_into,61.1.1.2,61.1.1,demod,42')] ).
cnf(147,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[59,80]),42]),
[iquote('para_into,59.1.1.1,80.1.1,demod,42')] ).
cnf(155,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[147])]),
[iquote('copy,147,flip.1')] ).
cnf(225,plain,
divide(divide(identity,divide(divide(A,B),C)),divide(B,A)) = C,
inference(para_from,[status(thm),theory(equality)],[155,80]),
[iquote('para_from,155.1.1,80.1.1.2')] ).
cnf(414,plain,
divide(divide(divide(A,divide(identity,B)),C),divide(B,C)) = A,
inference(para_into,[status(thm),theory(equality)],[55,225]),
[iquote('para_into,55.1.1.2.2,225.1.1')] ).
cnf(468,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[414,414]),11,31]),
[iquote('para_into,414.1.1.1.1,414.1.1,demod,11,31')] ).
cnf(534,plain,
divide(divide(A,divide(B,C)),divide(D,B)) = divide(A,divide(D,C)),
inference(para_into,[status(thm),theory(equality)],[468,468]),
[iquote('para_into,468.1.1.2,468.1.1')] ).
cnf(535,plain,
$false,
inference(binary,[status(thm)],[534,74]),
[iquote('binary,534.1,74.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP462-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n004.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 05:10:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.78/1.94 ----- Otter 3.3f, August 2004 -----
% 1.78/1.94 The process was started by sandbox on n004.cluster.edu,
% 1.78/1.94 Wed Jul 27 05:10:36 2022
% 1.78/1.94 The command was "./otter". The process ID is 25146.
% 1.78/1.94
% 1.78/1.94 set(prolog_style_variables).
% 1.78/1.94 set(auto).
% 1.78/1.94 dependent: set(auto1).
% 1.78/1.94 dependent: set(process_input).
% 1.78/1.94 dependent: clear(print_kept).
% 1.78/1.94 dependent: clear(print_new_demod).
% 1.78/1.94 dependent: clear(print_back_demod).
% 1.78/1.94 dependent: clear(print_back_sub).
% 1.78/1.94 dependent: set(control_memory).
% 1.78/1.94 dependent: assign(max_mem, 12000).
% 1.78/1.94 dependent: assign(pick_given_ratio, 4).
% 1.78/1.94 dependent: assign(stats_level, 1).
% 1.78/1.94 dependent: assign(max_seconds, 10800).
% 1.78/1.94 clear(print_given).
% 1.78/1.94
% 1.78/1.94 list(usable).
% 1.78/1.94 0 [] A=A.
% 1.78/1.94 0 [] divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C)))=B.
% 1.78/1.94 0 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.78/1.94 0 [] inverse(A)=divide(identity,A).
% 1.78/1.94 0 [] identity=divide(A,A).
% 1.78/1.94 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.78/1.94 end_of_list.
% 1.78/1.94
% 1.78/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.78/1.94
% 1.78/1.94 All clauses are units, and equality is present; the
% 1.78/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.78/1.94
% 1.78/1.94 dependent: set(knuth_bendix).
% 1.78/1.94 dependent: set(anl_eq).
% 1.78/1.94 dependent: set(para_from).
% 1.78/1.94 dependent: set(para_into).
% 1.78/1.94 dependent: clear(para_from_right).
% 1.78/1.94 dependent: clear(para_into_right).
% 1.78/1.94 dependent: set(para_from_vars).
% 1.78/1.94 dependent: set(eq_units_both_ways).
% 1.78/1.94 dependent: set(dynamic_demod_all).
% 1.78/1.94 dependent: set(dynamic_demod).
% 1.78/1.94 dependent: set(order_eq).
% 1.78/1.94 dependent: set(back_demod).
% 1.78/1.94 dependent: set(lrpo).
% 1.78/1.94
% 1.78/1.94 ------------> process usable:
% 1.78/1.94 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.78/1.94
% 1.78/1.94 ------------> process sos:
% 1.78/1.94 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.78/1.94 ** KEPT (pick-wt=17): 3 [] divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C)))=B.
% 1.78/1.94 ---> New Demodulator: 4 [new_demod,3] divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C)))=B.
% 1.78/1.94 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.78/1.94 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=divide(A,divide(identity,B)).
% 1.78/1.94 ** KEPT (pick-wt=6): 7 [] inverse(A)=divide(identity,A).
% 1.78/1.94 ---> New Demodulator: 8 [new_demod,7] inverse(A)=divide(identity,A).
% 1.78/1.94 ** KEPT (pick-wt=5): 10 [copy,9,flip.1] divide(A,A)=identity.
% 1.78/1.94 ---> New Demodulator: 11 [new_demod,10] divide(A,A)=identity.
% 1.78/1.94 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.78/1.94 >>>> Starting back demodulation with 4.
% 1.78/1.94 >>>> Starting back demodulation with 6.
% 1.78/1.94 >> back demodulating 1 with 6.
% 1.78/1.94 >>>> Starting back demodulation with 8.
% 1.78/1.94 >>>> Starting back demodulation with 11.
% 1.78/1.94 >> back demodulating 3 with 11.
% 1.78/1.94 >>>> Starting back demodulation with 14.
% 1.78/1.94
% 1.78/1.94 ======= end of input processing =======
% 1.78/1.94
% 1.78/1.94 =========== start of search ===========
% 1.78/1.94
% 1.78/1.94 -------- PROOF --------
% 1.78/1.94
% 1.78/1.94 ----> UNIT CONFLICT at 0.03 sec ----> 535 [binary,534.1,74.1] $F.
% 1.78/1.94
% 1.78/1.94 Length of proof is 23. Level of proof is 13.
% 1.78/1.94
% 1.78/1.94 ---------------- PROOF ----------------
% 1.78/1.94 % SZS status Unsatisfiable
% 1.78/1.94 % SZS output start Refutation
% See solution above
% 1.78/1.94 ------------ end of proof -------------
% 1.78/1.94
% 1.78/1.94
% 1.78/1.94 Search stopped by max_proofs option.
% 1.78/1.94
% 1.78/1.94
% 1.78/1.94 Search stopped by max_proofs option.
% 1.78/1.94
% 1.78/1.94 ============ end of search ============
% 1.78/1.94
% 1.78/1.94 -------------- statistics -------------
% 1.78/1.94 clauses given 40
% 1.78/1.94 clauses generated 1896
% 1.78/1.94 clauses kept 322
% 1.78/1.94 clauses forward subsumed 1772
% 1.78/1.94 clauses back subsumed 8
% 1.78/1.94 Kbytes malloced 1953
% 1.78/1.94
% 1.78/1.94 ----------- times (seconds) -----------
% 1.78/1.94 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.78/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.78/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.78/1.94
% 1.78/1.94 That finishes the proof of the theorem.
% 1.78/1.94
% 1.78/1.94 Process 25146 finished Wed Jul 27 05:10:37 2022
% 1.78/1.94 Otter interrupted
% 1.78/1.94 PROOF FOUND
%------------------------------------------------------------------------------