TSTP Solution File: GRP682-11 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP682-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:57:38 EDT 2022
% Result : Unsatisfiable 1.77s 1.92s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 2 RR)
% Number of literals : 33 ( 32 equ; 1 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; 3 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('GRP682-11.p',unknown),
[] ).
cnf(4,axiom,
ld(A,mult(A,A)) = A,
file('GRP682-11.p',unknown),
[] ).
cnf(5,axiom,
rd(mult(A,A),A) = A,
file('GRP682-11.p',unknown),
[] ).
cnf(8,axiom,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('GRP682-11.p',unknown),
[] ).
cnf(9,axiom,
mult(rd(A,B),B) = rd(mult(A,B),B),
file('GRP682-11.p',unknown),
[] ).
cnf(11,plain,
rd(mult(A,B),B) = mult(rd(A,B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,axiom,
ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
file('GRP682-11.p',unknown),
[] ).
cnf(13,axiom,
rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('GRP682-11.p',unknown),
[] ).
cnf(14,plain,
mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13]),11,11]),
[iquote('copy,13,demod,11,11')] ).
cnf(16,axiom,
ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('GRP682-11.p',unknown),
[] ).
cnf(18,plain,
mult(rd(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16]),11])]),
[iquote('copy,16,demod,11,flip.1')] ).
cnf(19,plain,
mult(rd(A,A),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),11]),
[iquote('back_demod,5,demod,11')] ).
cnf(21,plain,
mult(ld(A,mult(A,B)),C) = ld(ld(A,D),mult(ld(A,D),mult(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(25,plain,
rd(A,A) = ld(A,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,19]),18,8,4]),
[iquote('para_into,10.1.1.1,19.1.1,demod,18,8,4')] ).
cnf(26,plain,
rd(ld(A,mult(A,B)),ld(A,B)) = mult(rd(A,ld(A,B)),ld(A,B)),
inference(para_into,[status(thm),theory(equality)],[11,8]),
[iquote('para_into,10.1.1.1,7.1.1')] ).
cnf(29,plain,
mult(ld(A,A),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),25]),
[iquote('back_demod,19,demod,25')] ).
cnf(30,plain,
mult(rd(ld(A,A),B),B) = ld(A,mult(A,ld(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),25]),
[iquote('back_demod,17,demod,25')] ).
cnf(34,plain,
mult(ld(A,mult(A,B)),C) = ld(A,mult(A,mult(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,4]),4])]),
[iquote('para_into,12.1.1.1,3.1.1,demod,4,flip.1')] ).
cnf(40,plain,
ld(ld(A,B),mult(ld(A,B),mult(C,D))) = ld(A,mult(A,mult(C,D))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),34])]),
[iquote('back_demod,21,demod,34,flip.1')] ).
cnf(46,plain,
ld(A,mult(A,ld(ld(A,A),ld(A,A)))) = ld(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,25]),29])]),
[iquote('para_into,30.1.1.1,24.1.1,demod,29,flip.1')] ).
cnf(53,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(ld(A,A),mult(rd(A,C),C)),
inference(para_into,[status(thm),theory(equality)],[14,29]),
[iquote('para_into,14.1.1.1.1,28.1.1')] ).
cnf(61,plain,
mult(mult(ld(A,A),mult(rd(A,B),B)),rd(C,B)) = mult(A,mult(rd(rd(C,B),B),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,11]),53]),
[iquote('para_into,14.1.1.1,10.1.1,demod,53')] ).
cnf(80,plain,
ld(A,mult(A,mult(A,B))) = mult(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,4])]),
[iquote('para_into,33.1.1.1,3.1.1,flip.1')] ).
cnf(102,plain,
mult(A,ld(ld(A,A),ld(A,A))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[46,8]),8,4,80])]),
[iquote('para_from,46.1.1,7.1.1.2,demod,8,4,80,flip.1')] ).
cnf(111,plain,
mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,4])]),
[iquote('para_into,26.1.1.1,3.1.1,flip.1')] ).
cnf(143,plain,
ld(ld(A,B),mult(ld(A,B),C)) = ld(A,mult(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,102]),102]),
[iquote('para_into,40.1.1.2.2,101.1.1,demod,102')] ).
cnf(170,plain,
ld(mult(A,B),mult(mult(A,B),C)) = ld(A,mult(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[143,80]),80]),
[iquote('para_into,143.1.1.1,79.1.1,demod,80')] ).
cnf(252,plain,
mult(rd(A,ld(B,B)),ld(B,B)) = mult(ld(A,A),mult(rd(A,B),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[53,25]),25]),
[iquote('para_into,52.1.1.1.2,24.1.1,demod,25')] ).
cnf(265,plain,
rd(A,ld(A,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[111]),252,25,29,29])]),
[iquote('back_demod,111,demod,252,25,29,29,flip.1')] ).
cnf(284,plain,
mult(ld(A,A),mult(ld(A,A),mult(rd(A,B),B))) = mult(rd(A,B),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[265,53]),265,252])]),
[iquote('para_from,264.1.1,52.1.1.2,demod,265,252,flip.1')] ).
cnf(316,plain,
mult(mult(rd(A,B),B),B) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,265]),252,284,265,265,8,4]),
[iquote('para_into,61.1.1.2,264.1.1,demod,252,284,265,265,8,4')] ).
cnf(364,plain,
ld(rd(A,B),mult(rd(A,B),C)) = ld(A,mult(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[316,170]),316,170,170])]),
[iquote('para_from,315.1.1,169.1.1.1,demod,316,170,170,flip.1')] ).
cnf(366,plain,
$false,
inference(binary,[status(thm)],[364,1]),
[iquote('binary,364.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP682-11 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.11 % Command : otter-tptp-script %s
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Wed Jul 27 05:25:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.77/1.92 ----- Otter 3.3f, August 2004 -----
% 1.77/1.92 The process was started by sandbox2 on n003.cluster.edu,
% 1.77/1.92 Wed Jul 27 05:25:41 2022
% 1.77/1.92 The command was "./otter". The process ID is 14954.
% 1.77/1.92
% 1.77/1.92 set(prolog_style_variables).
% 1.77/1.92 set(auto).
% 1.77/1.92 dependent: set(auto1).
% 1.77/1.92 dependent: set(process_input).
% 1.77/1.92 dependent: clear(print_kept).
% 1.77/1.92 dependent: clear(print_new_demod).
% 1.77/1.92 dependent: clear(print_back_demod).
% 1.77/1.92 dependent: clear(print_back_sub).
% 1.77/1.92 dependent: set(control_memory).
% 1.77/1.92 dependent: assign(max_mem, 12000).
% 1.77/1.92 dependent: assign(pick_given_ratio, 4).
% 1.77/1.92 dependent: assign(stats_level, 1).
% 1.77/1.92 dependent: assign(max_seconds, 10800).
% 1.77/1.92 clear(print_given).
% 1.77/1.92
% 1.77/1.92 list(usable).
% 1.77/1.92 0 [] A=A.
% 1.77/1.92 0 [] ld(A,mult(A,A))=A.
% 1.77/1.92 0 [] rd(mult(A,A),A)=A.
% 1.77/1.92 0 [] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.77/1.92 0 [] mult(rd(A,B),B)=rd(mult(A,B),B).
% 1.77/1.92 0 [] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.77/1.92 0 [] rd(mult(mult(A,B),rd(C,D)),rd(C,D))=mult(A,rd(mult(B,D),D)).
% 1.77/1.92 0 [] ld(A,mult(A,ld(B,B)))=rd(mult(rd(A,A),B),B).
% 1.77/1.92 0 [] ld(rd(x0,x1),mult(rd(x0,x1),x2))!=ld(x0,mult(x0,x2)).
% 1.77/1.92 end_of_list.
% 1.77/1.92
% 1.77/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.77/1.92
% 1.77/1.92 All clauses are units, and equality is present; the
% 1.77/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.77/1.92
% 1.77/1.92 dependent: set(knuth_bendix).
% 1.77/1.92 dependent: set(anl_eq).
% 1.77/1.92 dependent: set(para_from).
% 1.77/1.92 dependent: set(para_into).
% 1.77/1.92 dependent: clear(para_from_right).
% 1.77/1.92 dependent: clear(para_into_right).
% 1.77/1.92 dependent: set(para_from_vars).
% 1.77/1.92 dependent: set(eq_units_both_ways).
% 1.77/1.92 dependent: set(dynamic_demod_all).
% 1.77/1.92 dependent: set(dynamic_demod).
% 1.77/1.92 dependent: set(order_eq).
% 1.77/1.92 dependent: set(back_demod).
% 1.77/1.92 dependent: set(lrpo).
% 1.77/1.92
% 1.77/1.92 ------------> process usable:
% 1.77/1.92 ** KEPT (pick-wt=15): 1 [] ld(rd(x0,x1),mult(rd(x0,x1),x2))!=ld(x0,mult(x0,x2)).
% 1.77/1.92
% 1.77/1.92 ------------> process sos:
% 1.77/1.92 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.77/1.92 ** KEPT (pick-wt=7): 3 [] ld(A,mult(A,A))=A.
% 1.77/1.92 ---> New Demodulator: 4 [new_demod,3] ld(A,mult(A,A))=A.
% 1.77/1.92 ** KEPT (pick-wt=7): 5 [] rd(mult(A,A),A)=A.
% 1.77/1.92 ---> New Demodulator: 6 [new_demod,5] rd(mult(A,A),A)=A.
% 1.77/1.92 ** KEPT (pick-wt=11): 7 [] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.77/1.92 ---> New Demodulator: 8 [new_demod,7] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.77/1.92 ** KEPT (pick-wt=11): 10 [copy,9,flip.1] rd(mult(A,B),B)=mult(rd(A,B),B).
% 1.77/1.92 ---> New Demodulator: 11 [new_demod,10] rd(mult(A,B),B)=mult(rd(A,B),B).
% 1.77/1.92 ** KEPT (pick-wt=19): 12 [] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.77/1.92 ** KEPT (pick-wt=19): 14 [copy,13,demod,11,11] mult(rd(mult(A,B),rd(C,D)),rd(C,D))=mult(A,mult(rd(B,D),D)).
% 1.77/1.92 ---> New Demodulator: 15 [new_demod,14] mult(rd(mult(A,B),rd(C,D)),rd(C,D))=mult(A,mult(rd(B,D),D)).
% 1.77/1.92 ** KEPT (pick-wt=15): 17 [copy,16,demod,11,flip.1] mult(rd(rd(A,A),B),B)=ld(A,mult(A,ld(B,B))).
% 1.77/1.92 ---> New Demodulator: 18 [new_demod,17] mult(rd(rd(A,A),B),B)=ld(A,mult(A,ld(B,B))).
% 1.77/1.92 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.77/1.92 >>>> Starting back demodulation with 4.
% 1.77/1.92 >>>> Starting back demodulation with 6.
% 1.77/1.92 >>>> Starting back demodulation with 8.
% 1.77/1.92 >>>> Starting back demodulation with 11.
% 1.77/1.92 >> back demodulating 5 with 11.
% 1.77/1.92 ** KEPT (pick-wt=19): 21 [copy,12,flip.1] mult(ld(A,mult(A,B)),C)=ld(ld(A,D),mult(ld(A,D),mult(B,C))).
% 1.77/1.92 >>>> Starting back demodulation with 15.
% 1.77/1.92 >>>> Starting back demodulation with 18.
% 1.77/1.92 >>>> Starting back demodulation with 20.
% 1.77/1.92 Following clause subsumed by 12 during input processing: 0 [copy,21,flip.1] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.77/1.92
% 1.77/1.92 ======= end of input processing =======
% 1.77/1.92
% 1.77/1.92 =========== start of search ===========
% 1.77/1.92
% 1.77/1.92
% 1.77/1.92 Resetting weight limit to 15.
% 1.77/1.92
% 1.77/1.92
% 1.77/1.92 Resetting weight limit to 15.
% 1.77/1.92
% 1.77/1.92 sos_size=88
% 1.77/1.92
% 1.77/1.92 -------- PROOF --------
% 1.77/1.92
% 1.77/1.92 ----> UNIT CONFLICT at 0.02 sec ----> 366 [binary,364.1,1.1] $F.
% 1.77/1.92
% 1.77/1.92 Length of proof is 24. Level of proof is 10.
% 1.77/1.92
% 1.77/1.92 ---------------- PROOF ----------------
% 1.77/1.92 % SZS status Unsatisfiable
% 1.77/1.92 % SZS output start Refutation
% See solution above
% 1.77/1.92 ------------ end of proof -------------
% 1.77/1.92
% 1.77/1.92
% 1.77/1.92 Search stopped by max_proofs option.
% 1.77/1.92
% 1.77/1.92
% 1.77/1.92 Search stopped by max_proofs option.
% 1.77/1.92
% 1.77/1.92 ============ end of search ============
% 1.77/1.92
% 1.77/1.92 -------------- statistics -------------
% 1.77/1.92 clauses given 32
% 1.77/1.92 clauses generated 379
% 1.77/1.92 clauses kept 199
% 1.77/1.92 clauses forward subsumed 305
% 1.77/1.92 clauses back subsumed 2
% 1.77/1.92 Kbytes malloced 4882
% 1.77/1.92
% 1.77/1.92 ----------- times (seconds) -----------
% 1.77/1.92 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.77/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.92 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.77/1.92
% 1.77/1.92 That finishes the proof of the theorem.
% 1.77/1.92
% 1.77/1.92 Process 14954 finished Wed Jul 27 05:25:43 2022
% 1.77/1.92 Otter interrupted
% 1.77/1.92 PROOF FOUND
%------------------------------------------------------------------------------