%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP531-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:57:11 EDT 2022
% Result : Unsatisfiable 1.98s 2.14s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 equ; 2 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 : 56 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP531-1.p',unknown),
[] ).
cnf(3,axiom,
divide(divide(A,divide(B,C)),divide(A,B)) = C,
file('GRP531-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP531-1.p',unknown),
[] ).
cnf(6,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP531-1.p',unknown),
[] ).
cnf(7,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,plain,
divide(divide(A,A),B) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(41,plain,
inverse(divide(divide(A,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[3,8]),
[iquote('para_into,3.1.1,8.1.1')] ).
cnf(50,plain,
inverse(inverse(A)) = A,
inference(para_into,[status(thm),theory(equality)],[41,8]),
[iquote('para_into,41.1.1.1,8.1.1')] ).
cnf(55,plain,
inverse(A) = divide(divide(B,A),B),
inference(para_into,[status(thm),theory(equality)],[50,41]),
[iquote('para_into,49.1.1.1,41.1.1')] ).
cnf(62,plain,
divide(divide(A,A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[50,6]),
[iquote('para_into,49.1.1,6.1.1')] ).
cnf(64,plain,
divide(divide(A,B),A) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[55])]),
[iquote('copy,55,flip.1')] ).
cnf(66,plain,
divide(divide(A,inverse(B)),A) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[55,50])]),
[iquote('para_into,55.1.1,49.1.1,flip.1')] ).
cnf(96,plain,
divide(A,divide(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[64,62]),50]),
[iquote('para_into,64.1.1.1,62.1.1,demod,50')] ).
cnf(114,plain,
divide(A,divide(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[96,3])]),
[iquote('para_into,95.1.1,3.1.1,flip.1')] ).
cnf(125,plain,
inverse(divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[114,64])]),
[iquote('para_from,114.1.1,64.1.1.1,flip.1')] ).
cnf(136,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,114])]),
[iquote('para_into,7.1.1.2,114.1.1,flip.1')] ).
cnf(139,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[7,64]),
[iquote('para_into,7.1.1.2,64.1.1')] ).
cnf(160,plain,
divide(multiply(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[7,64]),125,96]),
[iquote('para_from,7.1.1,64.1.1.1,demod,125,96')] ).
cnf(176,plain,
divide(multiply(A,B),B) = A,
inference(para_from,[status(thm),theory(equality)],[160,114]),
[iquote('para_from,160.1.1,114.1.1.2')] ).
cnf(190,plain,
multiply(divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[176,7]),136]),
[iquote('para_into,176.1.1,7.1.1,demod,136')] ).
cnf(205,plain,
multiply(A,divide(B,C)) = divide(B,divide(C,A)),
inference(para_into,[status(thm),theory(equality)],[190,3]),
[iquote('para_into,190.1.1.1,3.1.1')] ).
cnf(219,plain,
multiply(A,B) = divide(B,inverse(A)),
inference(para_from,[status(thm),theory(equality)],[66,190]),
[iquote('para_from,66.1.1,190.1.1.1')] ).
cnf(229,plain,
divide(A,inverse(B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[219])]),
[iquote('copy,219,flip.1')] ).
cnf(338,plain,
inverse(multiply(A,B)) = divide(inverse(B),A),
inference(para_from,[status(thm),theory(equality)],[139,125]),
[iquote('para_from,139.1.1,124.1.1.1')] ).
cnf(500,plain,
divide(c3,divide(inverse(b3),a3)) != multiply(a3,multiply(b3,c3)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[219,1]),338]),
[iquote('para_from,219.1.1,1.1.1,demod,338')] ).
cnf(1403,plain,
multiply(A,multiply(B,C)) = divide(C,divide(inverse(B),A)),
inference(para_into,[status(thm),theory(equality)],[205,229]),
[iquote('para_into,205.1.1.2,229.1.1')] ).
cnf(1427,plain,
divide(A,divide(inverse(B),C)) = multiply(C,multiply(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1403])]),
[iquote('copy,1403,flip.1')] ).
cnf(1428,plain,
$false,
inference(binary,[status(thm)],[1427,500]),
[iquote('binary,1427.1,500.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP531-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 05:26:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.14 ----- Otter 3.3f, August 2004 -----
% 1.98/2.14 The process was started by sandbox2 on n011.cluster.edu,
% 1.98/2.14 Wed Jul 27 05:26:10 2022
% 1.98/2.14 The command was "./otter". The process ID is 29978.
% 1.98/2.14
% 1.98/2.14 set(prolog_style_variables).
% 1.98/2.14 set(auto).
% 1.98/2.14 dependent: set(auto1).
% 1.98/2.14 dependent: set(process_input).
% 1.98/2.14 dependent: clear(print_kept).
% 1.98/2.14 dependent: clear(print_new_demod).
% 1.98/2.14 dependent: clear(print_back_demod).
% 1.98/2.14 dependent: clear(print_back_sub).
% 1.98/2.14 dependent: set(control_memory).
% 1.98/2.14 dependent: assign(max_mem, 12000).
% 1.98/2.14 dependent: assign(pick_given_ratio, 4).
% 1.98/2.14 dependent: assign(stats_level, 1).
% 1.98/2.14 dependent: assign(max_seconds, 10800).
% 1.98/2.14 clear(print_given).
% 1.98/2.14
% 1.98/2.14 list(usable).
% 1.98/2.14 0 [] A=A.
% 1.98/2.14 0 [] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 1.98/2.14 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.98/2.14 0 [] inverse(A)=divide(divide(B,B),A).
% 1.98/2.14 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.98/2.14 end_of_list.
% 1.98/2.14
% 1.98/2.14 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.98/2.14
% 1.98/2.14 All clauses are units, and equality is present; the
% 1.98/2.14 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.98/2.14
% 1.98/2.14 dependent: set(knuth_bendix).
% 1.98/2.14 dependent: set(anl_eq).
% 1.98/2.14 dependent: set(para_from).
% 1.98/2.14 dependent: set(para_into).
% 1.98/2.14 dependent: clear(para_from_right).
% 1.98/2.14 dependent: clear(para_into_right).
% 1.98/2.14 dependent: set(para_from_vars).
% 1.98/2.14 dependent: set(eq_units_both_ways).
% 1.98/2.14 dependent: set(dynamic_demod_all).
% 1.98/2.14 dependent: set(dynamic_demod).
% 1.98/2.14 dependent: set(order_eq).
% 1.98/2.14 dependent: set(back_demod).
% 1.98/2.14 dependent: set(lrpo).
% 1.98/2.14
% 1.98/2.14 ------------> process usable:
% 1.98/2.14 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.98/2.14
% 1.98/2.14 ------------> process sos:
% 1.98/2.14 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.98/2.14 ** KEPT (pick-wt=11): 3 [] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 1.98/2.14 ---> New Demodulator: 4 [new_demod,3] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 1.98/2.14 ** KEPT (pick-wt=11): 5 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.98/2.14 ** KEPT (pick-wt=8): 6 [] inverse(A)=divide(divide(B,B),A).
% 1.98/2.14 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.14 >>>> Starting back demodulation with 4.
% 1.98/2.14 ** KEPT (pick-wt=11): 7 [copy,5,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.98/2.14 ** KEPT (pick-wt=8): 8 [copy,6,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.98/2.14 Following clause subsumed by 5 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.98/2.14 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.98/2.14
% 1.98/2.14 ======= end of input processing =======
% 1.98/2.14
% 1.98/2.14 =========== start of search ===========
% 1.98/2.14
% 1.98/2.14 -------- PROOF --------
% 1.98/2.14
% 1.98/2.14 ----> UNIT CONFLICT at 0.06 sec ----> 1428 [binary,1427.1,500.1] $F.
% 1.98/2.14
% 1.98/2.14 Length of proof is 23. Level of proof is 15.
% 1.98/2.14
% 1.98/2.14 ---------------- PROOF ----------------
% 1.98/2.14 % SZS status Unsatisfiable
% 1.98/2.14 % SZS output start Refutation
% See solution above
% 1.98/2.14 ------------ end of proof -------------
% 1.98/2.14
% 1.98/2.14
% 1.98/2.14 Search stopped by max_proofs option.
% 1.98/2.14
% 1.98/2.14
% 1.98/2.14 Search stopped by max_proofs option.
% 1.98/2.14
% 1.98/2.14 ============ end of search ============
% 1.98/2.14
% 1.98/2.14 -------------- statistics -------------
% 1.98/2.14 clauses given 68
% 1.98/2.14 clauses generated 2682
% 1.98/2.14 clauses kept 1063
% 1.98/2.14 clauses forward subsumed 2535
% 1.98/2.14 clauses back subsumed 2
% 1.98/2.14 Kbytes malloced 2929
% 1.98/2.14
% 1.98/2.14 ----------- times (seconds) -----------
% 1.98/2.14 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.98/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.14
% 1.98/2.14 That finishes the proof of the theorem.
% 1.98/2.14
% 1.98/2.14 Process 29978 finished Wed Jul 27 05:26:12 2022
% 1.98/2.14 Otter interrupted
% 1.98/2.14 PROOF FOUND
%------------------------------------------------------------------------------