TSTP Solution File: GRP473-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP473-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:57:05 EDT 2022
% Result : Unsatisfiable 2.10s 2.32s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 5 RR)
% Number of literals : 33 ( 32 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 109 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP473-1.p',unknown),
[] ).
cnf(3,axiom,
divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,C)) = B,
file('GRP473-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('GRP473-1.p',unknown),
[] ).
cnf(6,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(7,plain,
divide(multiply(inverse(b2),b2),inverse(a2)) != a2,
inference(para_from,[status(thm),theory(equality)],[5,1]),
[iquote('para_from,5.1.1,1.1.1')] ).
cnf(9,plain,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(para_into,[status(thm),theory(equality)],[7,5]),
[iquote('para_into,7.1.1.1,5.1.1')] ).
cnf(10,plain,
divide(divide(inverse(multiply(A,B)),divide(divide(C,D),A)),divide(D,C)) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[3,6]),
[iquote('para_into,3.1.1.1.1.1,6.1.1')] ).
cnf(13,plain,
divide(divide(inverse(A),divide(divide(B,C),divide(inverse(divide(D,A)),divide(divide(E,F),D)))),divide(C,B)) = divide(F,E),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.1.1,3.1.1')] ).
cnf(15,plain,
divide(divide(inverse(divide(A,B)),divide(multiply(C,D),A)),divide(inverse(D),C)) = B,
inference(para_into,[status(thm),theory(equality)],[3,6]),
[iquote('para_into,3.1.1.1.2.1,6.1.1')] ).
cnf(20,plain,
divide(divide(inverse(divide(divide(A,B),C)),D),divide(divide(divide(B,A),E),inverse(divide(E,D)))) = C,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.2,3.1.1')] ).
cnf(22,plain,
divide(divide(inverse(divide(A,B)),divide(divide(inverse(C),D),A)),multiply(D,C)) = B,
inference(para_into,[status(thm),theory(equality)],[3,6]),
[iquote('para_into,3.1.1.2,6.1.1')] ).
cnf(54,plain,
divide(divide(inverse(inverse(A)),divide(multiply(B,C),divide(inverse(multiply(D,A)),divide(divide(E,F),D)))),divide(inverse(C),B)) = divide(F,E),
inference(para_into,[status(thm),theory(equality)],[15,10]),
[iquote('para_into,14.1.1.1.1.1,10.1.1')] ).
cnf(64,plain,
divide(divide(inverse(divide(A,B)),divide(divide(divide(inverse(C),D),divide(inverse(divide(E,F)),divide(multiply(D,C),E))),A)),F) = B,
inference(para_from,[status(thm),theory(equality)],[15,3]),
[iquote('para_from,14.1.1,3.1.1.2')] ).
cnf(132,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(divide(E,F),D))))) = divide(E,F),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,13]),13])]),
[iquote('para_into,12.1.1.1.2.2.2.1,12.1.1,demod,13,flip.1')] ).
cnf(191,plain,
divide(divide(inverse(divide(divide(A,B),C)),inverse(D)),multiply(divide(divide(B,A),E),multiply(E,D))) = C,
inference(para_into,[status(thm),theory(equality)],[22,10]),
[iquote('para_into,22.1.1.1.2,10.1.1')] ).
cnf(541,plain,
divide(multiply(inverse(divide(divide(A,B),C)),D),multiply(divide(divide(B,A),E),multiply(E,D))) = C,
inference(para_into,[status(thm),theory(equality)],[191,6]),
[iquote('para_into,191.1.1.1,6.1.1')] ).
cnf(549,plain,
divide(multiply(inverse(divide(divide(A,B),C)),D),multiply(multiply(divide(B,A),E),multiply(inverse(E),D))) = C,
inference(para_into,[status(thm),theory(equality)],[541,6]),
[iquote('para_into,541.1.1.2.1,6.1.1')] ).
cnf(574,plain,
divide(multiply(inverse(divide(divide(A,B),C)),D),divide(multiply(divide(B,A),E),inverse(multiply(inverse(E),D)))) = C,
inference(para_into,[status(thm),theory(equality)],[549,5]),
[iquote('para_into,549.1.1.2,5.1.1')] ).
cnf(575,plain,
divide(divide(A,B),divide(inverse(C),divide(divide(B,A),divide(inverse(divide(D,C)),divide(E,D))))) = E,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[132,574]),574]),
[iquote('para_into,132.1.1.2.2.2.2.1,573.1.1,demod,574')] ).
cnf(593,plain,
divide(divide(inverse(divide(divide(inverse(A),divide(B,divide(inverse(divide(C,A)),divide(D,C)))),E)),D),B) = E,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[575,64]),15]),
[iquote('para_from,575.1.1,64.1.1.1.2,demod,15')] ).
cnf(719,plain,
divide(divide(inverse(divide(A,B)),divide(B,A)),divide(C,D)) = divide(D,C),
inference(para_into,[status(thm),theory(equality)],[593,13]),
[iquote('para_into,593.1.1.1.1.1,12.1.1')] ).
cnf(731,plain,
divide(inverse(divide(A,divide(B,divide(C,D)))),divide(divide(D,C),A)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[719,20])]),
[iquote('para_into,719.1.1,20.1.1,flip.1')] ).
cnf(736,plain,
divide(divide(A,B),divide(inverse(divide(C,D)),divide(D,C))) = divide(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[719,54]),54])]),
[iquote('para_from,719.1.1,53.1.1.1.2.2.2.1,demod,54,flip.1')] ).
cnf(742,plain,
divide(inverse(divide(divide(A,B),C)),divide(B,A)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[731,719]),736]),
[iquote('para_into,731.1.1.1.1,719.1.1,demod,736')] ).
cnf(744,plain,
divide(A,divide(divide(B,C),inverse(divide(C,B)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[731,719]),742]),
[iquote('para_into,731.1.1.2,719.1.1,demod,742')] ).
cnf(754,plain,
inverse(divide(A,B)) = divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[742,719]),744]),
[iquote('para_into,741.1.1.1.1,719.1.1,demod,744')] ).
cnf(790,plain,
divide(A,divide(divide(B,C),divide(B,C))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[744]),754]),
[iquote('back_demod,743,demod,754')] ).
cnf(862,plain,
divide(A,divide(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[790,790]),790]),
[iquote('para_into,789.1.1.2.1,789.1.1,demod,790')] ).
cnf(869,plain,
inverse(A) = divide(divide(B,B),A),
inference(para_from,[status(thm),theory(equality)],[862,754]),
[iquote('para_from,861.1.1,753.1.1.1')] ).
cnf(870,plain,
divide(divide(A,A),B) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[869])]),
[iquote('copy,869,flip.1')] ).
cnf(889,plain,
inverse(inverse(a2)) != a2,
inference(para_from,[status(thm),theory(equality)],[870,9]),
[iquote('para_from,870.1.1,9.1.1')] ).
cnf(890,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[870,754]),862]),
[iquote('para_from,870.1.1,753.1.1.1,demod,862')] ).
cnf(892,plain,
$false,
inference(binary,[status(thm)],[890,889]),
[iquote('binary,890.1,889.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP473-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.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 05:08:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.10/2.32 ----- Otter 3.3f, August 2004 -----
% 2.10/2.32 The process was started by sandbox2 on n009.cluster.edu,
% 2.10/2.32 Wed Jul 27 05:08:51 2022
% 2.10/2.32 The command was "./otter". The process ID is 982.
% 2.10/2.32
% 2.10/2.32 set(prolog_style_variables).
% 2.10/2.32 set(auto).
% 2.10/2.32 dependent: set(auto1).
% 2.10/2.32 dependent: set(process_input).
% 2.10/2.32 dependent: clear(print_kept).
% 2.10/2.32 dependent: clear(print_new_demod).
% 2.10/2.32 dependent: clear(print_back_demod).
% 2.10/2.32 dependent: clear(print_back_sub).
% 2.10/2.32 dependent: set(control_memory).
% 2.10/2.32 dependent: assign(max_mem, 12000).
% 2.10/2.32 dependent: assign(pick_given_ratio, 4).
% 2.10/2.32 dependent: assign(stats_level, 1).
% 2.10/2.32 dependent: assign(max_seconds, 10800).
% 2.10/2.32 clear(print_given).
% 2.10/2.32
% 2.10/2.32 list(usable).
% 2.10/2.32 0 [] A=A.
% 2.10/2.32 0 [] divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,C))=B.
% 2.10/2.32 0 [] multiply(A,B)=divide(A,inverse(B)).
% 2.10/2.32 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 2.10/2.32 end_of_list.
% 2.10/2.32
% 2.10/2.32 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.10/2.32
% 2.10/2.32 All clauses are units, and equality is present; the
% 2.10/2.32 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.10/2.32
% 2.10/2.32 dependent: set(knuth_bendix).
% 2.10/2.32 dependent: set(anl_eq).
% 2.10/2.32 dependent: set(para_from).
% 2.10/2.32 dependent: set(para_into).
% 2.10/2.32 dependent: clear(para_from_right).
% 2.10/2.32 dependent: clear(para_into_right).
% 2.10/2.32 dependent: set(para_from_vars).
% 2.10/2.32 dependent: set(eq_units_both_ways).
% 2.10/2.32 dependent: set(dynamic_demod_all).
% 2.10/2.32 dependent: set(dynamic_demod).
% 2.10/2.32 dependent: set(order_eq).
% 2.10/2.32 dependent: set(back_demod).
% 2.10/2.32 dependent: set(lrpo).
% 2.10/2.32
% 2.10/2.32 ------------> process usable:
% 2.10/2.32 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 2.10/2.32
% 2.10/2.32 ------------> process sos:
% 2.10/2.32 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.10/2.32 ** KEPT (pick-wt=16): 3 [] divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,C))=B.
% 2.10/2.32 ---> New Demodulator: 4 [new_demod,3] divide(divide(inverse(divide(A,B)),divide(divide(C,D),A)),divide(D,C))=B.
% 2.10/2.32 ** KEPT (pick-wt=8): 5 [] multiply(A,B)=divide(A,inverse(B)).
% 2.10/2.32 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.10/2.32 >>>> Starting back demodulation with 4.
% 2.10/2.32 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] divide(A,inverse(B))=multiply(A,B).
% 2.10/2.32 Following clause subsumed by 5 during input processing: 0 [copy,6,flip.1] multiply(A,B)=divide(A,inverse(B)).
% 2.10/2.32
% 2.10/2.32 ======= end of input processing =======
% 2.10/2.32
% 2.10/2.32 =========== start of search ===========
% 2.10/2.32
% 2.10/2.32
% 2.10/2.32 Resetting weight limit to 22.
% 2.10/2.32
% 2.10/2.32
% 2.10/2.32 Resetting weight limit to 22.
% 2.10/2.32
% 2.10/2.32 sos_size=274
% 2.10/2.32
% 2.10/2.32
% 2.10/2.32 Resetting weight limit to 17.
% 2.10/2.32
% 2.10/2.32
% 2.10/2.32 Resetting weight limit to 17.
% 2.10/2.32
% 2.10/2.32 sos_size=286
% 2.10/2.32
% 2.10/2.32
% 2.10/2.32 Resetting weight limit to 11.
% 2.10/2.32
% 2.10/2.32
% 2.10/2.32 Resetting weight limit to 11.
% 2.10/2.32
% 2.10/2.32 sos_size=51
% 2.10/2.32
% 2.10/2.32 -------- PROOF --------
% 2.10/2.32
% 2.10/2.32 ----> UNIT CONFLICT at 0.42 sec ----> 892 [binary,890.1,889.1] $F.
% 2.10/2.32
% 2.10/2.32 Length of proof is 29. Level of proof is 18.
% 2.10/2.32
% 2.10/2.32 ---------------- PROOF ----------------
% 2.10/2.32 % SZS status Unsatisfiable
% 2.10/2.32 % SZS output start Refutation
% See solution above
% 2.10/2.33 ------------ end of proof -------------
% 2.10/2.33
% 2.10/2.33
% 2.10/2.33 Search stopped by max_proofs option.
% 2.10/2.33
% 2.10/2.33
% 2.10/2.33 Search stopped by max_proofs option.
% 2.10/2.33
% 2.10/2.33 ============ end of search ============
% 2.10/2.33
% 2.10/2.33 -------------- statistics -------------
% 2.10/2.33 clauses given 184
% 2.10/2.33 clauses generated 52718
% 2.10/2.33 clauses kept 533
% 2.10/2.33 clauses forward subsumed 2498
% 2.10/2.33 clauses back subsumed 3
% 2.10/2.33 Kbytes malloced 8789
% 2.10/2.33
% 2.10/2.33 ----------- times (seconds) -----------
% 2.10/2.33 user CPU time 0.42 (0 hr, 0 min, 0 sec)
% 2.10/2.33 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.10/2.33 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.10/2.33
% 2.10/2.33 That finishes the proof of the theorem.
% 2.10/2.33
% 2.10/2.33 Process 982 finished Wed Jul 27 05:08:53 2022
% 2.10/2.33 Otter interrupted
% 2.10/2.33 PROOF FOUND
%------------------------------------------------------------------------------