%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 1.94s 2.12s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 5 RR)
% Number of literals : 38 ( 37 equ; 4 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 : 62 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP551-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP551-1.p',unknown),
[] ).
cnf(3,axiom,
divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C,
file('GRP551-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP551-1.p',unknown),
[] ).
cnf(9,axiom,
identity = divide(A,A),
file('GRP551-1.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(identity,divide(divide(divide(A,identity),B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1,10.1.1')] ).
cnf(15,plain,
divide(divide(identity,A),divide(divide(identity,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.2.1.1,10.1.1')] ).
cnf(19,plain,
divide(divide(identity,A),divide(identity,B)) = divide(B,A),
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.2.1,10.1.1')] ).
cnf(21,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),divide(C,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,3])]),
[iquote('para_into,3.1.1.2.1,3.1.1,flip.1')] ).
cnf(22,plain,
divide(A,B) = divide(divide(identity,B),divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(25,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),21,11]),
[iquote('back_demod,13,demod,21,11')] ).
cnf(29,plain,
divide(A,divide(divide(identity,B),divide(identity,divide(A,identity)))) = B,
inference(para_into,[status(thm),theory(equality)],[15,25]),
[iquote('para_into,15.1.1.1,25.1.1')] ).
cnf(31,plain,
divide(identity,divide(divide(identity,A),identity)) = A,
inference(para_into,[status(thm),theory(equality)],[15,11]),
[iquote('para_into,15.1.1.1,10.1.1')] ).
cnf(34,plain,
divide(divide(identity,divide(divide(identity,A),B)),A) = B,
inference(para_into,[status(thm),theory(equality)],[15,15]),
[iquote('para_into,15.1.1.2,15.1.1')] ).
cnf(40,plain,
divide(divide(identity,A),identity) = divide(identity,divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,31])]),
[iquote('para_into,31.1.1.2.1,31.1.1,flip.1')] ).
cnf(41,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,divide(A,identity))),
inference(para_into,[status(thm),theory(equality)],[19,25]),
[iquote('para_into,19.1.1.1,25.1.1')] ).
cnf(42,plain,
divide(identity,divide(identity,A)) = divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[19,11]),
[iquote('para_into,19.1.1.1,10.1.1')] ).
cnf(45,plain,
divide(identity,divide(A,identity)) = divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,11]),40]),
[iquote('para_into,19.1.1.2,10.1.1,demod,40')] ).
cnf(46,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[41])]),45]),
[iquote('copy,41,flip.1,demod,45')] ).
cnf(47,plain,
divide(A,identity) = divide(identity,divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[42])]),
[iquote('copy,42,flip.1')] ).
cnf(53,plain,
divide(A,divide(divide(identity,B),divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),45]),
[iquote('back_demod,29,demod,45')] ).
cnf(56,plain,
divide(identity,divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),45]),
[iquote('back_demod,25,demod,45')] ).
cnf(58,plain,
divide(A,identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[47])]),56])]),
[iquote('copy,47,flip.1,demod,56,flip.1')] ).
cnf(63,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),58]),
[iquote('back_demod,20,demod,58')] ).
cnf(66,plain,
divide(divide(b3,divide(identity,a3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[22,12]),56]),
[iquote('para_from,22.1.1,12.1.1.1,demod,56')] ).
cnf(74,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,19]),56]),
[iquote('para_into,34.1.1,19.1.1,demod,56')] ).
cnf(75,plain,
divide(A,divide(B,divide(identity,A))) = divide(identity,B),
inference(para_from,[status(thm),theory(equality)],[46,74]),
[iquote('para_from,46.1.1,73.1.1.2')] ).
cnf(143,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[63,58]),11]),
[iquote('para_into,63.1.1.1.1,57.1.1,demod,11')] ).
cnf(145,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(divide(identity,A),divide(identity,C))),B),
inference(para_into,[status(thm),theory(equality)],[63,53]),
[iquote('para_into,63.1.1.1.1,53.1.1')] ).
cnf(170,plain,
divide(divide(identity,divide(divide(identity,A),divide(identity,B))),C) = divide(divide(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[145])]),
[iquote('copy,145,flip.1')] ).
cnf(200,plain,
divide(divide(identity,A),B) = divide(identity,divide(A,divide(identity,B))),
inference(para_into,[status(thm),theory(equality)],[143,75]),
[iquote('para_into,143.1.1.1,75.1.1')] ).
cnf(201,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[143,74]),
[iquote('para_into,143.1.1.1,73.1.1')] ).
cnf(233,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[170]),200,74,74]),
[iquote('back_demod,170,demod,200,74,74')] ).
cnf(287,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)],[233,201])]),
[iquote('para_into,233.1.1,201.1.1,flip.1')] ).
cnf(310,plain,
divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[66]),287,287,74]),
[iquote('back_demod,66,demod,287,287,74')] ).
cnf(311,plain,
$false,
inference(binary,[status(thm)],[310,2]),
[iquote('binary,310.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 05:22:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.94/2.12 ----- Otter 3.3f, August 2004 -----
% 1.94/2.12 The process was started by sandbox2 on n025.cluster.edu,
% 1.94/2.12 Wed Jul 27 05:22:00 2022
% 1.94/2.12 The command was "./otter". The process ID is 26068.
% 1.94/2.12
% 1.94/2.12 set(prolog_style_variables).
% 1.94/2.12 set(auto).
% 1.94/2.12 dependent: set(auto1).
% 1.94/2.12 dependent: set(process_input).
% 1.94/2.12 dependent: clear(print_kept).
% 1.94/2.12 dependent: clear(print_new_demod).
% 1.94/2.12 dependent: clear(print_back_demod).
% 1.94/2.12 dependent: clear(print_back_sub).
% 1.94/2.12 dependent: set(control_memory).
% 1.94/2.12 dependent: assign(max_mem, 12000).
% 1.94/2.12 dependent: assign(pick_given_ratio, 4).
% 1.94/2.12 dependent: assign(stats_level, 1).
% 1.94/2.12 dependent: assign(max_seconds, 10800).
% 1.94/2.12 clear(print_given).
% 1.94/2.12
% 1.94/2.12 list(usable).
% 1.94/2.12 0 [] A=A.
% 1.94/2.12 0 [] divide(divide(identity,A),divide(divide(divide(B,A),C),B))=C.
% 1.94/2.12 0 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.94/2.12 0 [] inverse(A)=divide(identity,A).
% 1.94/2.12 0 [] identity=divide(A,A).
% 1.94/2.12 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.94/2.12 end_of_list.
% 1.94/2.12
% 1.94/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.94/2.12
% 1.94/2.12 All clauses are units, and equality is present; the
% 1.94/2.12 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.94/2.12
% 1.94/2.12 dependent: set(knuth_bendix).
% 1.94/2.12 dependent: set(anl_eq).
% 1.94/2.12 dependent: set(para_from).
% 1.94/2.12 dependent: set(para_into).
% 1.94/2.12 dependent: clear(para_from_right).
% 1.94/2.12 dependent: clear(para_into_right).
% 1.94/2.12 dependent: set(para_from_vars).
% 1.94/2.12 dependent: set(eq_units_both_ways).
% 1.94/2.12 dependent: set(dynamic_demod_all).
% 1.94/2.12 dependent: set(dynamic_demod).
% 1.94/2.12 dependent: set(order_eq).
% 1.94/2.12 dependent: set(back_demod).
% 1.94/2.12 dependent: set(lrpo).
% 1.94/2.12
% 1.94/2.12 ------------> process usable:
% 1.94/2.12 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.94/2.12
% 1.94/2.12 ------------> process sos:
% 1.94/2.12 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.94/2.12 ** KEPT (pick-wt=13): 3 [] divide(divide(identity,A),divide(divide(divide(B,A),C),B))=C.
% 1.94/2.12 ---> New Demodulator: 4 [new_demod,3] divide(divide(identity,A),divide(divide(divide(B,A),C),B))=C.
% 1.94/2.12 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.94/2.12 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=divide(A,divide(identity,B)).
% 1.94/2.12 ** KEPT (pick-wt=6): 7 [] inverse(A)=divide(identity,A).
% 1.94/2.12 ---> New Demodulator: 8 [new_demod,7] inverse(A)=divide(identity,A).
% 1.94/2.12 ** KEPT (pick-wt=5): 10 [copy,9,flip.1] divide(A,A)=identity.
% 1.94/2.12 ---> New Demodulator: 11 [new_demod,10] divide(A,A)=identity.
% 1.94/2.12 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.94/2.12 >>>> Starting back demodulation with 4.
% 1.94/2.12 >>>> Starting back demodulation with 6.
% 1.94/2.12 >> back demodulating 1 with 6.
% 1.94/2.12 >>>> Starting back demodulation with 8.
% 1.94/2.12 >>>> Starting back demodulation with 11.
% 1.94/2.12
% 1.94/2.12 ======= end of input processing =======
% 1.94/2.12
% 1.94/2.12 =========== start of search ===========
% 1.94/2.12
% 1.94/2.12 -------- PROOF --------
% 1.94/2.12
% 1.94/2.12 ----> UNIT CONFLICT at 0.01 sec ----> 311 [binary,310.1,2.1] $F.
% 1.94/2.12
% 1.94/2.12 Length of proof is 32. Level of proof is 13.
% 1.94/2.12
% 1.94/2.12 ---------------- PROOF ----------------
% 1.94/2.12 % SZS status Unsatisfiable
% 1.94/2.12 % SZS output start Refutation
% See solution above
% 1.94/2.12 ------------ end of proof -------------
% 1.94/2.12
% 1.94/2.12
% 1.94/2.12 Search stopped by max_proofs option.
% 1.94/2.12
% 1.94/2.12
% 1.94/2.12 Search stopped by max_proofs option.
% 1.94/2.12
% 1.94/2.12 ============ end of search ============
% 1.94/2.12
% 1.94/2.12 -------------- statistics -------------
% 1.94/2.12 clauses given 34
% 1.94/2.12 clauses generated 764
% 1.94/2.12 clauses kept 210
% 1.94/2.12 clauses forward subsumed 789
% 1.94/2.12 clauses back subsumed 4
% 1.94/2.12 Kbytes malloced 1953
% 1.94/2.12
% 1.94/2.12 ----------- times (seconds) -----------
% 1.94/2.12 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.94/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.94/2.12
% 1.94/2.12 That finishes the proof of the theorem.
% 1.94/2.12
% 1.94/2.12 Process 26068 finished Wed Jul 27 05:22:02 2022
% 1.94/2.12 Otter interrupted
% 1.94/2.12 PROOF FOUND
%------------------------------------------------------------------------------