TSTP Solution File: GRP456-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP456-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 1.95s 2.11s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% 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 : 8 ( 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 : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP456-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP456-1.p',unknown),
[] ).
cnf(3,axiom,
divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B,
file('GRP456-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP456-1.p',unknown),
[] ).
cnf(9,axiom,
identity = divide(A,A),
file('GRP456-1.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(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),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(divide(identity,divide(identity,divide(A,divide(identity,B)))),B) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2.2.2.1,10.1.1')] ).
cnf(19,plain,
divide(divide(identity,divide(A,divide(B,identity))),divide(identity,A)) = B,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2.2.2,10.1.1')] ).
cnf(25,plain,
divide(divide(identity,divide(identity,divide(A,identity))),identity) = A,
inference(para_into,[status(thm),theory(equality)],[15,11]),
[iquote('para_into,15.1.1.1.2.2.2,10.1.1')] ).
cnf(28,plain,
divide(divide(identity,divide(identity,A)),B) = divide(identity,divide(identity,divide(A,divide(identity,divide(identity,B))))),
inference(para_into,[status(thm),theory(equality)],[15,15]),
[iquote('para_into,15.1.1.1.2.2,15.1.1')] ).
cnf(30,plain,
divide(identity,divide(identity,divide(divide(A,identity),identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),28,11,11]),
[iquote('back_demod,25,demod,28,11,11')] ).
cnf(32,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,B)),divide(identity,divide(identity,B))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),28]),
[iquote('back_demod,15,demod,28')] ).
cnf(39,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = divide(identity,divide(C,divide(B,divide(divide(identity,C),identity)))),
inference(para_into,[status(thm),theory(equality)],[19,13]),
[iquote('para_into,19.1.1.1.2.2,13.1.1')] ).
cnf(45,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,11]),11]),
[iquote('para_into,19.1.1.1.2,10.1.1,demod,11')] ).
cnf(49,plain,
divide(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,11]),45]),
[iquote('para_into,19.1.1.2,10.1.1,demod,45')] ).
cnf(50,plain,
divide(identity,divide(A,divide(B,divide(identity,A)))) = divide(divide(identity,divide(C,B)),divide(identity,C)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[39])]),49]),
[iquote('copy,39,flip.1,demod,49')] ).
cnf(56,plain,
divide(identity,divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),49,49]),
[iquote('back_demod,30,demod,49,49')] ).
cnf(63,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),49]),
[iquote('back_demod,19,demod,49')] ).
cnf(64,plain,
divide(identity,divide(A,divide(B,divide(identity,A)))) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[50])]),63])]),
[iquote('copy,50,flip.1,demod,63,flip.1')] ).
cnf(68,plain,
divide(divide(A,divide(identity,B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),56,56]),
[iquote('back_demod,32,demod,56,56')] ).
cnf(98,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(para_into,[status(thm),theory(equality)],[68,56]),
[iquote('para_into,68.1.1.1.2,55.1.1')] ).
cnf(107,plain,
divide(divide(identity,divide(A,B)),C) = divide(B,divide(identity,divide(divide(identity,A),C))),
inference(para_from,[status(thm),theory(equality)],[68,13]),
[iquote('para_from,68.1.1,13.1.1.1.2.2')] ).
cnf(114,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(para_into,[status(thm),theory(equality)],[64,98]),
[iquote('para_into,64.1.1.2.2,98.1.1')] ).
cnf(115,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[114])]),
[iquote('copy,114,flip.1')] ).
cnf(155,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(para_from,[status(thm),theory(equality)],[115,12]),107,56]),
[iquote('para_from,115.1.1,12.1.1.1,demod,107,56')] ).
cnf(156,plain,
$false,
inference(binary,[status(thm)],[155,2]),
[iquote('binary,155.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP456-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 05:20:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.11 ----- Otter 3.3f, August 2004 -----
% 1.95/2.11 The process was started by sandbox2 on n020.cluster.edu,
% 1.95/2.11 Wed Jul 27 05:20:08 2022
% 1.95/2.11 The command was "./otter". The process ID is 15641.
% 1.95/2.11
% 1.95/2.11 set(prolog_style_variables).
% 1.95/2.11 set(auto).
% 1.95/2.11 dependent: set(auto1).
% 1.95/2.11 dependent: set(process_input).
% 1.95/2.11 dependent: clear(print_kept).
% 1.95/2.11 dependent: clear(print_new_demod).
% 1.95/2.11 dependent: clear(print_back_demod).
% 1.95/2.11 dependent: clear(print_back_sub).
% 1.95/2.11 dependent: set(control_memory).
% 1.95/2.11 dependent: assign(max_mem, 12000).
% 1.95/2.11 dependent: assign(pick_given_ratio, 4).
% 1.95/2.11 dependent: assign(stats_level, 1).
% 1.95/2.11 dependent: assign(max_seconds, 10800).
% 1.95/2.11 clear(print_given).
% 1.95/2.11
% 1.95/2.11 list(usable).
% 1.95/2.11 0 [] A=A.
% 1.95/2.11 0 [] divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)=B.
% 1.95/2.11 0 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.95/2.11 0 [] inverse(A)=divide(identity,A).
% 1.95/2.11 0 [] identity=divide(A,A).
% 1.95/2.11 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.95/2.11 end_of_list.
% 1.95/2.11
% 1.95/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.95/2.11
% 1.95/2.11 All clauses are units, and equality is present; the
% 1.95/2.11 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.95/2.11
% 1.95/2.11 dependent: set(knuth_bendix).
% 1.95/2.11 dependent: set(anl_eq).
% 1.95/2.11 dependent: set(para_from).
% 1.95/2.11 dependent: set(para_into).
% 1.95/2.11 dependent: clear(para_from_right).
% 1.95/2.11 dependent: clear(para_into_right).
% 1.95/2.11 dependent: set(para_from_vars).
% 1.95/2.11 dependent: set(eq_units_both_ways).
% 1.95/2.11 dependent: set(dynamic_demod_all).
% 1.95/2.11 dependent: set(dynamic_demod).
% 1.95/2.11 dependent: set(order_eq).
% 1.95/2.11 dependent: set(back_demod).
% 1.95/2.11 dependent: set(lrpo).
% 1.95/2.11
% 1.95/2.11 ------------> process usable:
% 1.95/2.11 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.95/2.11
% 1.95/2.11 ------------> process sos:
% 1.95/2.11 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.95/2.11 ** KEPT (pick-wt=17): 3 [] divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)=B.
% 1.95/2.11 ---> New Demodulator: 4 [new_demod,3] divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C)=B.
% 1.95/2.11 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.95/2.11 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=divide(A,divide(identity,B)).
% 1.95/2.11 ** KEPT (pick-wt=6): 7 [] inverse(A)=divide(identity,A).
% 1.95/2.11 ---> New Demodulator: 8 [new_demod,7] inverse(A)=divide(identity,A).
% 1.95/2.11 ** KEPT (pick-wt=5): 10 [copy,9,flip.1] divide(A,A)=identity.
% 1.95/2.11 ---> New Demodulator: 11 [new_demod,10] divide(A,A)=identity.
% 1.95/2.11 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.95/2.11 >>>> Starting back demodulation with 4.
% 1.95/2.11 >>>> Starting back demodulation with 6.
% 1.95/2.11 >> back demodulating 1 with 6.
% 1.95/2.11 >>>> Starting back demodulation with 8.
% 1.95/2.11 >>>> Starting back demodulation with 11.
% 1.95/2.11 >> back demodulating 3 with 11.
% 1.95/2.11 >>>> Starting back demodulation with 14.
% 1.95/2.11
% 1.95/2.11 ======= end of input processing =======
% 1.95/2.11
% 1.95/2.11 =========== start of search ===========
% 1.95/2.11
% 1.95/2.11 -------- PROOF --------
% 1.95/2.11
% 1.95/2.11 ----> UNIT CONFLICT at 0.01 sec ----> 156 [binary,155.1,2.1] $F.
% 1.95/2.11
% 1.95/2.11 Length of proof is 22. Level of proof is 11.
% 1.95/2.11
% 1.95/2.11 ---------------- PROOF ----------------
% 1.95/2.11 % SZS status Unsatisfiable
% 1.95/2.11 % SZS output start Refutation
% See solution above
% 1.95/2.11 ------------ end of proof -------------
% 1.95/2.11
% 1.95/2.11
% 1.95/2.11 Search stopped by max_proofs option.
% 1.95/2.11
% 1.95/2.11
% 1.95/2.11 Search stopped by max_proofs option.
% 1.95/2.11
% 1.95/2.11 ============ end of search ============
% 1.95/2.11
% 1.95/2.11 -------------- statistics -------------
% 1.95/2.11 clauses given 18
% 1.95/2.11 clauses generated 216
% 1.95/2.11 clauses kept 93
% 1.95/2.11 clauses forward subsumed 206
% 1.95/2.11 clauses back subsumed 0
% 1.95/2.11 Kbytes malloced 1953
% 1.95/2.11
% 1.95/2.11 ----------- times (seconds) -----------
% 1.95/2.11 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.95/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.11 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.11
% 1.95/2.11 That finishes the proof of the theorem.
% 1.95/2.11
% 1.95/2.11 Process 15641 finished Wed Jul 27 05:20:10 2022
% 1.95/2.11 Otter interrupted
% 1.95/2.11 PROOF FOUND
%------------------------------------------------------------------------------