TSTP Solution File: GRP553-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP553-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:57:14 EDT 2022
% Result : Unsatisfiable 1.71s 1.94s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 4 RR)
% Number of literals : 18 ( 17 equ; 3 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 : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP553-1.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(4,axiom,
divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B,
file('GRP553-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('GRP553-1.p',unknown),
[] ).
cnf(7,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(8,plain,
divide(inverse(b1),inverse(b1)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[6,2]),
[iquote('para_from,6.1.1,2.1.1')] ).
cnf(11,plain,
divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),C) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.1.2,4.1.1')] ).
cnf(15,plain,
divide(multiply(A,divide(B,divide(A,C))),C) = B,
inference(para_into,[status(thm),theory(equality)],[4,7]),
[iquote('para_into,4.1.1.1,7.1.1')] ).
cnf(88,plain,
divide(A,inverse(divide(B,A))) = B,
inference(para_into,[status(thm),theory(equality)],[11,4]),
[iquote('para_into,11.1.1.1,4.1.1')] ).
cnf(122,plain,
divide(A,inverse(divide(B,divide(A,C)))) = divide(C,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[88,4])]),
[iquote('para_into,88.1.1.2.1,4.1.1,flip.1')] ).
cnf(123,plain,
multiply(A,divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[88,7]),
[iquote('para_into,88.1.1,7.1.1')] ).
cnf(157,plain,
divide(divide(A,inverse(B)),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),122]),
[iquote('back_demod,4,demod,122')] ).
cnf(163,plain,
multiply(inverse(divide(A,B)),A) = B,
inference(para_into,[status(thm),theory(equality)],[123,88]),
[iquote('para_into,123.1.1.2,88.1.1')] ).
cnf(179,plain,
divide(multiply(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[157,7]),
[iquote('para_into,157.1.1.1,7.1.1')] ).
cnf(188,plain,
divide(A,divide(B,B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[179,15])]),
[iquote('para_into,179.1.1,15.1.1,flip.1')] ).
cnf(231,plain,
multiply(inverse(A),A) = divide(B,B),
inference(para_into,[status(thm),theory(equality)],[163,188]),
[iquote('para_into,163.1.1.1.1,188.1.1')] ).
cnf(239,plain,
divide(A,A) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[231])]),
[iquote('copy,231,flip.1')] ).
cnf(240,plain,
$false,
inference(binary,[status(thm)],[239,8]),
[iquote('binary,239.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP553-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 05:18:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.94 ----- Otter 3.3f, August 2004 -----
% 1.71/1.94 The process was started by sandbox on n014.cluster.edu,
% 1.71/1.94 Wed Jul 27 05:18:54 2022
% 1.71/1.94 The command was "./otter". The process ID is 30106.
% 1.71/1.94
% 1.71/1.94 set(prolog_style_variables).
% 1.71/1.94 set(auto).
% 1.71/1.94 dependent: set(auto1).
% 1.71/1.94 dependent: set(process_input).
% 1.71/1.94 dependent: clear(print_kept).
% 1.71/1.94 dependent: clear(print_new_demod).
% 1.71/1.94 dependent: clear(print_back_demod).
% 1.71/1.94 dependent: clear(print_back_sub).
% 1.71/1.94 dependent: set(control_memory).
% 1.71/1.94 dependent: assign(max_mem, 12000).
% 1.71/1.94 dependent: assign(pick_given_ratio, 4).
% 1.71/1.94 dependent: assign(stats_level, 1).
% 1.71/1.94 dependent: assign(max_seconds, 10800).
% 1.71/1.94 clear(print_given).
% 1.71/1.94
% 1.71/1.94 list(usable).
% 1.71/1.94 0 [] A=A.
% 1.71/1.94 0 [] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 1.71/1.94 0 [] multiply(A,B)=divide(A,inverse(B)).
% 1.71/1.94 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.94
% 1.71/1.94 All clauses are units, and equality is present; the
% 1.71/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.94
% 1.71/1.94 dependent: set(knuth_bendix).
% 1.71/1.94 dependent: set(anl_eq).
% 1.71/1.94 dependent: set(para_from).
% 1.71/1.94 dependent: set(para_into).
% 1.71/1.94 dependent: clear(para_from_right).
% 1.71/1.94 dependent: clear(para_into_right).
% 1.71/1.94 dependent: set(para_from_vars).
% 1.71/1.94 dependent: set(eq_units_both_ways).
% 1.71/1.94 dependent: set(dynamic_demod_all).
% 1.71/1.94 dependent: set(dynamic_demod).
% 1.71/1.94 dependent: set(order_eq).
% 1.71/1.94 dependent: set(back_demod).
% 1.71/1.94 dependent: set(lrpo).
% 1.71/1.94
% 1.71/1.94 ------------> process usable:
% 1.71/1.94 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.71/1.94
% 1.71/1.94 ------------> process sos:
% 1.71/1.94 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.71/1.94 ** KEPT (pick-wt=12): 4 [] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 1.71/1.94 ---> New Demodulator: 5 [new_demod,4] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 1.71/1.94 ** KEPT (pick-wt=8): 6 [] multiply(A,B)=divide(A,inverse(B)).
% 1.71/1.94 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.71/1.94 >>>> Starting back demodulation with 5.
% 1.71/1.94 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] divide(A,inverse(B))=multiply(A,B).
% 1.71/1.94 Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,inverse(B)).
% 1.71/1.94
% 1.71/1.94 ======= end of input processing =======
% 1.71/1.94
% 1.71/1.94 =========== start of search ===========
% 1.71/1.94
% 1.71/1.94 -------- PROOF --------
% 1.71/1.94
% 1.71/1.94 ----> UNIT CONFLICT at 0.01 sec ----> 240 [binary,239.1,8.1] $F.
% 1.71/1.94
% 1.71/1.94 Length of proof is 14. Level of proof is 8.
% 1.71/1.94
% 1.71/1.94 ---------------- PROOF ----------------
% 1.71/1.94 % SZS status Unsatisfiable
% 1.71/1.94 % SZS output start Refutation
% See solution above
% 1.71/1.94 ------------ end of proof -------------
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94 ============ end of search ============
% 1.71/1.94
% 1.71/1.94 -------------- statistics -------------
% 1.71/1.94 clauses given 18
% 1.71/1.94 clauses generated 212
% 1.71/1.94 clauses kept 153
% 1.71/1.94 clauses forward subsumed 178
% 1.71/1.94 clauses back subsumed 6
% 1.71/1.94 Kbytes malloced 1953
% 1.71/1.94
% 1.71/1.94 ----------- times (seconds) -----------
% 1.71/1.94 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.71/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.94
% 1.71/1.94 That finishes the proof of the theorem.
% 1.71/1.94
% 1.71/1.94 Process 30106 finished Wed Jul 27 05:18:55 2022
% 1.71/1.94 Otter interrupted
% 1.71/1.94 PROOF FOUND
%------------------------------------------------------------------------------