TSTP Solution File: GRP492-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 12:57:06 EDT 2022
% Result : Unsatisfiable 1.70s 1.90s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 8 RR)
% Number of literals : 54 ( 53 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP492-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP492-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C,
file('GRP492-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP492-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP492-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP492-1.p',unknown),
[] ).
cnf(11,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9]),8])]),
[iquote('copy,9,demod,8,flip.1')] ).
cnf(12,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(flip,[status(thm),theory(equality)],[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,flip.1')] ).
cnf(15,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,identity),double_divide(B,double_divide(A,identity))))) = B,
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,3.1.1.2.2.1.1,10.1.1')] ).
cnf(17,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,double_divide(identity,double_divide(double_divide(double_divide(A,D),identity),double_divide(B,D))))))) = C,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.2.1.1,3.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),identity),identity))) = B,
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,3.1.1.2.2.2,10.1.1')] ).
cnf(23,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity),
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,3.1.1.2.2,10.1.1')] ).
cnf(24,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
[iquote('copy,23,flip.1')] ).
cnf(25,plain,
double_divide(double_divide(double_divide(identity,identity),identity),identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,11]),11])]),
[iquote('para_into,23.1.1.1,10.1.1,demod,11,flip.1')] ).
cnf(27,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,identity)),identity),double_divide(double_divide(B,identity),identity)))) = double_divide(identity,B),
inference(para_from,[status(thm),theory(equality)],[23,4]),
[iquote('para_from,23.1.1,3.1.1.2.2.2')] ).
cnf(33,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[25,4]),11]),
[iquote('para_from,25.1.1,3.1.1.2.2.1,demod,11')] ).
cnf(38,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,25]),11])]),
[iquote('para_into,33.1.1.2.2.2,25.1.1,demod,11,flip.1')] ).
cnf(44,plain,
double_divide(identity,identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),38,38]),
[iquote('back_demod,25,demod,38,38')] ).
cnf(49,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),44,4]),
[iquote('back_demod,27,demod,44,4')] ).
cnf(50,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),44]),
[iquote('back_demod,24,demod,44')] ).
cnf(52,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(identity,double_divide(B,double_divide(A,identity))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),44]),
[iquote('back_demod,15,demod,44')] ).
cnf(56,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[49])]),
[iquote('copy,49,flip.1')] ).
cnf(59,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(identity,double_divide(A,identity))))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,4]),44]),
[iquote('para_from,33.1.1,3.1.1.2.2.1.1,demod,44')] ).
cnf(79,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(B,double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,44]),44]),
[iquote('para_into,17.1.1.2.2.2.2.2.2,43.1.1,demod,44')] ).
cnf(85,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),identity),identity)))))) = C,
inference(para_into,[status(thm),theory(equality)],[17,11]),
[iquote('para_into,17.1.1.2.2.2.2.2.2,10.1.1')] ).
cnf(105,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(para_from,[status(thm),theory(equality)],[49,11]),
[iquote('para_from,49.1.1,10.1.1.2')] ).
cnf(109,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),double_divide(C,B)))) = C,
inference(para_from,[status(thm),theory(equality)],[49,4]),
[iquote('para_from,49.1.1,3.1.1.2.2.1')] ).
cnf(120,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(para_from,[status(thm),theory(equality)],[56,33]),
[iquote('para_from,56.1.1,33.1.1.2.2')] ).
cnf(143,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(para_into,[status(thm),theory(equality)],[105,33]),
[iquote('para_into,105.1.1.2,33.1.1')] ).
cnf(158,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[50,49])]),
[iquote('para_into,50.1.1,49.1.1,flip.1')] ).
cnf(168,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,105]),44,158,158,120]),
[iquote('para_into,19.1.1.1,105.1.1,demod,44,158,158,120')] ).
cnf(178,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,56]),44,168,168]),
[iquote('para_into,19.1.1.2.2.1.1,56.1.1,demod,44,168,168')] ).
cnf(199,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[143]),168]),
[iquote('back_demod,143,demod,168')] ).
cnf(204,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[120]),178]),
[iquote('back_demod,119,demod,178')] ).
cnf(205,plain,
double_divide(A,double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,double_divide(identity,double_divide(A,double_divide(B,identity))))))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[85]),204,178]),
[iquote('back_demod,85,demod,204,178')] ).
cnf(210,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),204,178,168,204]),
[iquote('back_demod,79,demod,204,178,168,204')] ).
cnf(217,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),210,204]),
[iquote('back_demod,59,demod,210,204')] ).
cnf(254,plain,
double_divide(double_divide(identity,A),double_divide(B,double_divide(A,identity))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[52]),204]),
[iquote('back_demod,52,demod,204')] ).
cnf(261,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[210,210]),
[iquote('para_into,209.1.1.2,209.1.1')] ).
cnf(262,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(identity,A),B),
inference(para_into,[status(thm),theory(equality)],[217,261]),
[iquote('para_into,217.1.1.2,260.1.1')] ).
cnf(263,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[262])]),
[iquote('copy,262,flip.1')] ).
cnf(268,plain,
double_divide(double_divide(double_divide(A,identity),B),double_divide(identity,A)) = B,
inference(para_from,[status(thm),theory(equality)],[263,261]),
[iquote('para_from,263.1.1,260.1.1.1')] ).
cnf(298,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,B))) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[109,199]),261]),
[iquote('para_into,109.1.1.2.2.2,199.1.1,demod,261')] ).
cnf(364,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),identity),C) = double_divide(A,double_divide(identity,double_divide(double_divide(B,identity),C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[205,268])]),
[iquote('para_into,205.1.1.2.2.2,268.1.1,flip.1')] ).
cnf(376,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[298,254]),204]),
[iquote('para_into,298.1.1.2.2,254.1.1,demod,204')] ).
cnf(378,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(identity,double_divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[298,210]),
[iquote('para_into,298.1.1.2.2,209.1.1')] ).
cnf(379,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[376])]),
[iquote('copy,376,flip.1')] ).
cnf(381,plain,
double_divide(identity,double_divide(A,B)) = double_divide(double_divide(identity,B),double_divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[378])]),
[iquote('copy,378,flip.1')] ).
cnf(510,plain,
double_divide(double_divide(A,double_divide(B,identity)),identity) = double_divide(B,double_divide(identity,A)),
inference(para_into,[status(thm),theory(equality)],[379,56]),
[iquote('para_into,379.1.1,56.1.1')] ).
cnf(513,plain,
double_divide(double_divide(A,double_divide(identity,B)),C) = double_divide(B,double_divide(identity,double_divide(double_divide(A,identity),C))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[364]),510]),
[iquote('back_demod,364,demod,510')] ).
cnf(516,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),510]),
[iquote('back_demod,12,demod,510')] ).
cnf(584,plain,
double_divide(double_divide(double_divide(A,B),identity),C) = double_divide(A,double_divide(identity,double_divide(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[381,263]),513,261])]),
[iquote('para_from,381.1.1,263.1.1.1,demod,513,261,flip.1')] ).
cnf(595,plain,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[516]),584,513,178]),
[iquote('back_demod,516,demod,584,513,178')] ).
cnf(596,plain,
$false,
inference(binary,[status(thm)],[595,2]),
[iquote('binary,595.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 05:25:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.90 ----- Otter 3.3f, August 2004 -----
% 1.70/1.90 The process was started by sandbox on n018.cluster.edu,
% 1.70/1.90 Wed Jul 27 05:25:16 2022
% 1.70/1.90 The command was "./otter". The process ID is 14897.
% 1.70/1.90
% 1.70/1.90 set(prolog_style_variables).
% 1.70/1.90 set(auto).
% 1.70/1.90 dependent: set(auto1).
% 1.70/1.90 dependent: set(process_input).
% 1.70/1.90 dependent: clear(print_kept).
% 1.70/1.90 dependent: clear(print_new_demod).
% 1.70/1.90 dependent: clear(print_back_demod).
% 1.70/1.90 dependent: clear(print_back_sub).
% 1.70/1.90 dependent: set(control_memory).
% 1.70/1.90 dependent: assign(max_mem, 12000).
% 1.70/1.90 dependent: assign(pick_given_ratio, 4).
% 1.70/1.90 dependent: assign(stats_level, 1).
% 1.70/1.90 dependent: assign(max_seconds, 10800).
% 1.70/1.90 clear(print_given).
% 1.70/1.90
% 1.70/1.90 list(usable).
% 1.70/1.90 0 [] A=A.
% 1.70/1.90 0 [] double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))=C.
% 1.70/1.90 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.70/1.90 0 [] inverse(A)=double_divide(A,identity).
% 1.70/1.90 0 [] identity=double_divide(A,inverse(A)).
% 1.70/1.90 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.70/1.90
% 1.70/1.90 All clauses are units, and equality is present; the
% 1.70/1.90 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.70/1.90
% 1.70/1.90 dependent: set(knuth_bendix).
% 1.70/1.90 dependent: set(anl_eq).
% 1.70/1.90 dependent: set(para_from).
% 1.70/1.90 dependent: set(para_into).
% 1.70/1.90 dependent: clear(para_from_right).
% 1.70/1.90 dependent: clear(para_into_right).
% 1.70/1.90 dependent: set(para_from_vars).
% 1.70/1.90 dependent: set(eq_units_both_ways).
% 1.70/1.90 dependent: set(dynamic_demod_all).
% 1.70/1.90 dependent: set(dynamic_demod).
% 1.70/1.90 dependent: set(order_eq).
% 1.70/1.90 dependent: set(back_demod).
% 1.70/1.90 dependent: set(lrpo).
% 1.70/1.90
% 1.70/1.90 ------------> process usable:
% 1.70/1.90 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.70/1.90
% 1.70/1.90 ------------> process sos:
% 1.70/1.90 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.70/1.90 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))=C.
% 1.70/1.90 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))=C.
% 1.70/1.90 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.70/1.90 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.70/1.90 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.70/1.90 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.70/1.90 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.70/1.90 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.70/1.90 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.70/1.90 >>>> Starting back demodulation with 4.
% 1.70/1.90 >>>> Starting back demodulation with 6.
% 1.70/1.90 >> back demodulating 1 with 6.
% 1.70/1.90 >>>> Starting back demodulation with 8.
% 1.70/1.90 >>>> Starting back demodulation with 11.
% 1.70/1.90
% 1.70/1.90 ======= end of input processing =======
% 1.70/1.90
% 1.70/1.90 =========== start of search ===========
% 1.70/1.90
% 1.70/1.90 -------- PROOF --------
% 1.70/1.90
% 1.70/1.90 ----> UNIT CONFLICT at 0.03 sec ----> 596 [binary,595.1,2.1] $F.
% 1.70/1.90
% 1.70/1.90 Length of proof is 47. Level of proof is 21.
% 1.70/1.90
% 1.70/1.90 ---------------- PROOF ----------------
% 1.70/1.90 % SZS status Unsatisfiable
% 1.70/1.90 % SZS output start Refutation
% See solution above
% 1.70/1.90 ------------ end of proof -------------
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Search stopped by max_proofs option.
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Search stopped by max_proofs option.
% 1.70/1.90
% 1.70/1.90 ============ end of search ============
% 1.70/1.90
% 1.70/1.90 -------------- statistics -------------
% 1.70/1.90 clauses given 60
% 1.70/1.90 clauses generated 2251
% 1.70/1.90 clauses kept 354
% 1.70/1.90 clauses forward subsumed 2173
% 1.70/1.90 clauses back subsumed 1
% 1.70/1.90 Kbytes malloced 2929
% 1.70/1.90
% 1.70/1.90 ----------- times (seconds) -----------
% 1.70/1.90 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.70/1.90 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.70/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.70/1.90
% 1.70/1.90 That finishes the proof of the theorem.
% 1.70/1.90
% 1.70/1.90 Process 14897 finished Wed Jul 27 05:25:17 2022
% 1.70/1.90 Otter interrupted
% 1.70/1.90 PROOF FOUND
%------------------------------------------------------------------------------