TSTP Solution File: GRP002-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:55:49 EDT 2022
% Result : Unsatisfiable 1.77s 1.96s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 23 RR)
% Number of literals : 49 ( 48 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(k,inverse(b)) != identity,
file('GRP002-2.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP002-2.p',unknown),
[] ).
cnf(4,axiom,
multiply(identity,A) = A,
file('GRP002-2.p',unknown),
[] ).
cnf(8,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP002-2.p',unknown),
[] ).
cnf(10,axiom,
multiply(A,identity) = A,
file('GRP002-2.p',unknown),
[] ).
cnf(11,axiom,
multiply(A,inverse(A)) = identity,
file('GRP002-2.p',unknown),
[] ).
cnf(14,axiom,
multiply(A,multiply(A,A)) = identity,
file('GRP002-2.p',unknown),
[] ).
cnf(15,axiom,
multiply(a,b) = c,
file('GRP002-2.p',unknown),
[] ).
cnf(17,axiom,
multiply(c,inverse(a)) = d,
file('GRP002-2.p',unknown),
[] ).
cnf(19,axiom,
multiply(d,inverse(b)) = h,
file('GRP002-2.p',unknown),
[] ).
cnf(21,axiom,
multiply(h,b) = j,
file('GRP002-2.p',unknown),
[] ).
cnf(23,axiom,
multiply(j,inverse(h)) = k,
file('GRP002-2.p',unknown),
[] ).
cnf(28,plain,
multiply(j,A) = multiply(h,multiply(b,A)),
inference(para_into,[status(thm),theory(equality)],[8,21]),
[iquote('para_into,7.1.1.1,21.1.1')] ).
cnf(29,plain,
multiply(d,multiply(inverse(b),A)) = multiply(h,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,19])]),
[iquote('para_into,7.1.1.1,19.1.1,flip.1')] ).
cnf(31,plain,
multiply(c,multiply(inverse(a),A)) = multiply(d,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,17])]),
[iquote('para_into,7.1.1.1,17.1.1,flip.1')] ).
cnf(34,plain,
multiply(c,A) = multiply(a,multiply(b,A)),
inference(para_into,[status(thm),theory(equality)],[8,15]),
[iquote('para_into,7.1.1.1,15.1.1')] ).
cnf(35,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,11]),4])]),
[iquote('para_into,7.1.1.1,11.1.1,demod,4,flip.1')] ).
cnf(41,plain,
multiply(h,multiply(b,inverse(h))) = k,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),28]),
[iquote('back_demod,23,demod,28')] ).
cnf(43,plain,
multiply(a,multiply(b,multiply(inverse(a),A))) = multiply(d,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[31]),34]),
[iquote('back_demod,31,demod,34')] ).
cnf(45,plain,
multiply(a,multiply(b,inverse(a))) = d,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),34]),
[iquote('back_demod,17,demod,34')] ).
cnf(47,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,8]),8]),
[iquote('para_into,13.1.1.2,7.1.1,demod,8')] ).
cnf(50,plain,
multiply(A,multiply(A,multiply(A,B))) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[14,8]),4,8])]),
[iquote('para_from,13.1.1,7.1.1.1,demod,4,8,flip.1')] ).
cnf(53,plain,
multiply(inverse(A),inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,14]),10])]),
[iquote('para_into,35.1.1.2,13.1.1,demod,10,flip.1')] ).
cnf(56,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,11]),10])]),
[iquote('para_into,35.1.1.2,11.1.1,demod,10,flip.1')] ).
cnf(57,plain,
multiply(A,multiply(B,multiply(inverse(multiply(A,B)),C))) = C,
inference(para_into,[status(thm),theory(equality)],[35,8]),
[iquote('para_into,35.1.1,7.1.1')] ).
cnf(60,plain,
inverse(A) = multiply(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[53,56]),56])]),
[iquote('para_into,53.1.1.1,55.1.1,demod,56,flip.1')] ).
cnf(61,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),60,8,8,8,8]),
[iquote('back_demod,57,demod,60,8,8,8,8')] ).
cnf(63,plain,
multiply(a,multiply(b,multiply(a,a))) = d,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[45]),60]),
[iquote('back_demod,45,demod,60')] ).
cnf(66,plain,
multiply(d,A) = multiply(a,multiply(b,multiply(a,multiply(a,A)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[43]),60,8])]),
[iquote('back_demod,43,demod,60,8,flip.1')] ).
cnf(67,plain,
multiply(h,multiply(b,multiply(h,h))) = k,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),60]),
[iquote('back_demod,41,demod,60')] ).
cnf(70,plain,
multiply(h,A) = multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,A)))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),60,8,66])]),
[iquote('back_demod,29,demod,60,8,66,flip.1')] ).
cnf(73,plain,
multiply(k,multiply(b,b)) != identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),60]),
[iquote('back_demod,1,demod,60')] ).
cnf(74,plain,
multiply(a,multiply(b,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,h))))))) = k,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[67]),70,70,50,50]),
[iquote('back_demod,67,demod,70,70,50,50')] ).
cnf(80,plain,
multiply(a,multiply(b,multiply(a,multiply(b,c)))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,14]),34])]),
[iquote('para_into,33.1.1,13.1.1,demod,34,flip.1')] ).
cnf(90,plain,
multiply(A,multiply(B,multiply(A,multiply(B,A)))) = multiply(B,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[47,50]),10])]),
[iquote('para_from,47.1.1,49.1.1.2.2,demod,10,flip.1')] ).
cnf(93,plain,
multiply(b,multiply(a,a)) = multiply(a,multiply(a,d)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[63,50])]),
[iquote('para_from,63.1.1,49.1.1.2.2,flip.1')] ).
cnf(94,plain,
multiply(b,multiply(a,multiply(b,c))) = multiply(a,a),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[80,50]),10])]),
[iquote('para_from,80.1.1,49.1.1.2.2,demod,10,flip.1')] ).
cnf(104,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,C))))) = multiply(B,multiply(B,C)),
inference(para_into,[status(thm),theory(equality)],[61,50]),
[iquote('para_into,61.1.1.2.2.2.2.2,49.1.1')] ).
cnf(113,plain,
multiply(b,multiply(a,multiply(a,d))) = multiply(a,multiply(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[94,50]),93]),
[iquote('para_from,94.1.1,49.1.1.2.2,demod,93')] ).
cnf(142,plain,
multiply(b,multiply(b,multiply(a,multiply(a,A)))) = multiply(a,multiply(b,multiply(a,multiply(b,A)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[113,8]),8,8,34,8,8,66,50])]),
[iquote('para_from,113.1.1,7.1.1.1,demod,8,8,34,8,8,66,50,flip.1')] ).
cnf(145,plain,
multiply(a,multiply(a,multiply(b,multiply(a,h)))) = k,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[74]),142,50]),
[iquote('back_demod,74,demod,142,50')] ).
cnf(150,plain,
multiply(b,multiply(a,h)) = multiply(a,k),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[145,50])]),
[iquote('para_from,145.1.1,49.1.1.2,flip.1')] ).
cnf(182,plain,
multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,D))))))) = multiply(B,multiply(C,multiply(B,multiply(C,D)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[104,8]),8,8,8]),
[iquote('para_into,103.1.1.2.2.2,7.1.1,demod,8,8,8')] ).
cnf(195,plain,
multiply(b,multiply(b,multiply(a,k))) = multiply(a,h),
inference(para_from,[status(thm),theory(equality)],[150,50]),
[iquote('para_from,149.1.1,49.1.1.2.2')] ).
cnf(198,plain,
multiply(a,multiply(k,A)) = multiply(a,multiply(b,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[150,8]),8,8,70,182,50]),
[iquote('para_from,149.1.1,7.1.1.1,demod,8,8,70,182,50')] ).
cnf(202,plain,
multiply(b,k) = multiply(b,b),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[195,90]),8,8,198,150,142,8,8,198,104,50]),
[iquote('para_from,195.1.1,90.1.1.2.2.2,demod,8,8,198,150,142,8,8,198,104,50')] ).
cnf(216,plain,
k = b,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[202,50]),14,10])]),
[iquote('para_from,202.1.1,49.1.1.2.2,demod,14,10,flip.1')] ).
cnf(226,plain,
identity != identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),216,14]),
[iquote('back_demod,73,demod,216,14')] ).
cnf(227,plain,
$false,
inference(binary,[status(thm)],[226,2]),
[iquote('binary,226.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 05:00:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.77/1.96 ----- Otter 3.3f, August 2004 -----
% 1.77/1.96 The process was started by sandbox2 on n022.cluster.edu,
% 1.77/1.96 Wed Jul 27 05:00:20 2022
% 1.77/1.96 The command was "./otter". The process ID is 18794.
% 1.77/1.96
% 1.77/1.96 set(prolog_style_variables).
% 1.77/1.96 set(auto).
% 1.77/1.96 dependent: set(auto1).
% 1.77/1.96 dependent: set(process_input).
% 1.77/1.96 dependent: clear(print_kept).
% 1.77/1.96 dependent: clear(print_new_demod).
% 1.77/1.96 dependent: clear(print_back_demod).
% 1.77/1.96 dependent: clear(print_back_sub).
% 1.77/1.96 dependent: set(control_memory).
% 1.77/1.96 dependent: assign(max_mem, 12000).
% 1.77/1.96 dependent: assign(pick_given_ratio, 4).
% 1.77/1.96 dependent: assign(stats_level, 1).
% 1.77/1.96 dependent: assign(max_seconds, 10800).
% 1.77/1.96 clear(print_given).
% 1.77/1.96
% 1.77/1.96 list(usable).
% 1.77/1.96 0 [] A=A.
% 1.77/1.96 0 [] multiply(identity,X)=X.
% 1.77/1.96 0 [] multiply(inverse(X),X)=identity.
% 1.77/1.96 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.77/1.96 0 [] multiply(X,identity)=X.
% 1.77/1.96 0 [] multiply(X,inverse(X))=identity.
% 1.77/1.96 0 [] multiply(X,multiply(X,X))=identity.
% 1.77/1.96 0 [] multiply(a,b)=c.
% 1.77/1.96 0 [] multiply(c,inverse(a))=d.
% 1.77/1.96 0 [] multiply(d,inverse(b))=h.
% 1.77/1.96 0 [] multiply(h,b)=j.
% 1.77/1.96 0 [] multiply(j,inverse(h))=k.
% 1.77/1.96 0 [] multiply(k,inverse(b))!=identity.
% 1.77/1.96 end_of_list.
% 1.77/1.96
% 1.77/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.77/1.96
% 1.77/1.96 All clauses are units, and equality is present; the
% 1.77/1.96 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.77/1.96
% 1.77/1.96 dependent: set(knuth_bendix).
% 1.77/1.96 dependent: set(anl_eq).
% 1.77/1.96 dependent: set(para_from).
% 1.77/1.96 dependent: set(para_into).
% 1.77/1.96 dependent: clear(para_from_right).
% 1.77/1.96 dependent: clear(para_into_right).
% 1.77/1.96 dependent: set(para_from_vars).
% 1.77/1.96 dependent: set(eq_units_both_ways).
% 1.77/1.96 dependent: set(dynamic_demod_all).
% 1.77/1.96 dependent: set(dynamic_demod).
% 1.77/1.96 dependent: set(order_eq).
% 1.77/1.96 dependent: set(back_demod).
% 1.77/1.96 dependent: set(lrpo).
% 1.77/1.96
% 1.77/1.96 ------------> process usable:
% 1.77/1.96 ** KEPT (pick-wt=6): 1 [] multiply(k,inverse(b))!=identity.
% 1.77/1.96
% 1.77/1.96 ------------> process sos:
% 1.77/1.96 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.77/1.96 ** KEPT (pick-wt=5): 3 [] multiply(identity,A)=A.
% 1.77/1.96 ---> New Demodulator: 4 [new_demod,3] multiply(identity,A)=A.
% 1.77/1.96 ** KEPT (pick-wt=6): 5 [] multiply(inverse(A),A)=identity.
% 1.77/1.96 ---> New Demodulator: 6 [new_demod,5] multiply(inverse(A),A)=identity.
% 1.77/1.96 ** KEPT (pick-wt=11): 7 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.77/1.96 ---> New Demodulator: 8 [new_demod,7] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.77/1.96 ** KEPT (pick-wt=5): 9 [] multiply(A,identity)=A.
% 1.77/1.96 ---> New Demodulator: 10 [new_demod,9] multiply(A,identity)=A.
% 1.77/1.96 ** KEPT (pick-wt=6): 11 [] multiply(A,inverse(A))=identity.
% 1.77/1.96 ---> New Demodulator: 12 [new_demod,11] multiply(A,inverse(A))=identity.
% 1.77/1.96 ** KEPT (pick-wt=7): 13 [] multiply(A,multiply(A,A))=identity.
% 1.77/1.96 ---> New Demodulator: 14 [new_demod,13] multiply(A,multiply(A,A))=identity.
% 1.77/1.96 ** KEPT (pick-wt=5): 15 [] multiply(a,b)=c.
% 1.77/1.96 ---> New Demodulator: 16 [new_demod,15] multiply(a,b)=c.
% 1.77/1.96 ** KEPT (pick-wt=6): 17 [] multiply(c,inverse(a))=d.
% 1.77/1.96 ---> New Demodulator: 18 [new_demod,17] multiply(c,inverse(a))=d.
% 1.77/1.96 ** KEPT (pick-wt=6): 19 [] multiply(d,inverse(b))=h.
% 1.77/1.96 ---> New Demodulator: 20 [new_demod,19] multiply(d,inverse(b))=h.
% 1.77/1.96 ** KEPT (pick-wt=5): 21 [] multiply(h,b)=j.
% 1.77/1.96 ---> New Demodulator: 22 [new_demod,21] multiply(h,b)=j.
% 1.77/1.96 ** KEPT (pick-wt=6): 23 [] multiply(j,inverse(h))=k.
% 1.77/1.96 ---> New Demodulator: 24 [new_demod,23] multiply(j,inverse(h))=k.
% 1.77/1.96 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.77/1.96 >>>> Starting back demodulation with 4.
% 1.77/1.96 >>>> Starting back demodulation with 6.
% 1.77/1.96 >>>> Starting back demodulation with 8.
% 1.77/1.96 >>>> Starting back demodulation with 10.
% 1.77/1.96 >>>> Starting back demodulation with 12.
% 1.77/1.96 >>>> Starting back demodulation with 14.
% 1.77/1.96 >>>> Starting back demodulation with 16.
% 1.77/1.96 >>>> Starting back demodulation with 18.
% 1.77/1.96 >>>> Starting back demodulation with 20.
% 1.77/1.96 >>>> Starting back demodulation with 22.
% 1.77/1.96 >>>> Starting back demodulation with 24.
% 1.77/1.96
% 1.77/1.96 ======= end of input processing =======
% 1.77/1.96
% 1.77/1.96 =========== start of search ===========
% 1.77/1.96
% 1.77/1.96 -------- PROOF --------
% 1.77/1.96
% 1.77/1.96 ----> UNIT CONFLICT at 0.01 sec ----> 227 [binary,226.1,2.1] $F.
% 1.77/1.96
% 1.77/1.96 Length of proof is 36. Level of proof is 13.
% 1.77/1.96
% 1.77/1.96 ---------------- PROOF ----------------
% 1.77/1.96 % SZS status Unsatisfiable
% 1.77/1.96 % SZS output start Refutation
% See solution above
% 1.77/1.96 ------------ end of proof -------------
% 1.77/1.96
% 1.77/1.96
% 1.77/1.96 Search stopped by max_proofs option.
% 1.77/1.96
% 1.77/1.96
% 1.77/1.96 Search stopped by max_proofs option.
% 1.77/1.96
% 1.77/1.96 ============ end of search ============
% 1.77/1.96
% 1.77/1.96 -------------- statistics -------------
% 1.77/1.96 clauses given 39
% 1.77/1.96 clauses generated 393
% 1.77/1.96 clauses kept 125
% 1.77/1.96 clauses forward subsumed 361
% 1.77/1.96 clauses back subsumed 1
% 1.77/1.96 Kbytes malloced 1953
% 1.77/1.96
% 1.77/1.96 ----------- times (seconds) -----------
% 1.77/1.96 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.77/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.96 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.77/1.96
% 1.77/1.96 That finishes the proof of the theorem.
% 1.77/1.96
% 1.77/1.96 Process 18794 finished Wed Jul 27 05:00:22 2022
% 1.77/1.96 Otter interrupted
% 1.77/1.96 PROOF FOUND
%------------------------------------------------------------------------------