TSTP Solution File: GRP682+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 : Theorem 1.75s 1.98s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 36 ( 34 unt; 0 nHn; 4 RR)
% Number of literals : 38 ( 37 equ; 5 neg)
% Maximal clause size : 2 ( 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 : 70 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ld(ld(dollar_c3,dollar_c2),mult(ld(dollar_c3,dollar_c2),dollar_c1)) != ld(dollar_c3,mult(dollar_c3,dollar_c1))
| ld(rd(dollar_c3,dollar_c2),mult(rd(dollar_c3,dollar_c2),dollar_c1)) != ld(dollar_c3,mult(dollar_c3,dollar_c1)) ),
file('GRP682+1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP682+1.p',unknown),
[] ).
cnf(4,axiom,
ld(A,mult(A,A)) = A,
file('GRP682+1.p',unknown),
[] ).
cnf(5,axiom,
rd(mult(A,A),A) = A,
file('GRP682+1.p',unknown),
[] ).
cnf(8,axiom,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('GRP682+1.p',unknown),
[] ).
cnf(9,axiom,
mult(rd(A,B),B) = rd(mult(A,B),B),
file('GRP682+1.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+1.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+1.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+1.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(144,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(151,plain,
( ld(dollar_c3,mult(dollar_c3,dollar_c1)) != ld(dollar_c3,mult(dollar_c3,dollar_c1))
| ld(rd(dollar_c3,dollar_c2),mult(rd(dollar_c3,dollar_c2),dollar_c1)) != ld(dollar_c3,mult(dollar_c3,dollar_c1)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),144]),
[iquote('back_demod,1,demod,144')] ).
cnf(171,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)],[144,80]),80]),
[iquote('para_into,143.1.1.1,79.1.1,demod,80')] ).
cnf(253,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(266,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]),253,25,29,29])]),
[iquote('back_demod,111,demod,253,25,29,29,flip.1')] ).
cnf(285,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)],[266,53]),266,253])]),
[iquote('para_from,265.1.1,52.1.1.2,demod,266,253,flip.1')] ).
cnf(317,plain,
mult(mult(rd(A,B),B),B) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,266]),253,285,266,266,8,4]),
[iquote('para_into,61.1.1.2,265.1.1,demod,253,285,266,266,8,4')] ).
cnf(366,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)],[317,171]),317,171,171])]),
[iquote('para_from,316.1.1,170.1.1.1,demod,317,171,171,flip.1')] ).
cnf(367,plain,
ld(dollar_c3,mult(dollar_c3,dollar_c1)) != ld(dollar_c3,mult(dollar_c3,dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[151]),366]),
[iquote('back_demod,151,demod,366')] ).
cnf(368,plain,
$false,
inference(binary,[status(thm)],[367,2]),
[iquote('binary,367.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.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 05:31:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox on n029.cluster.edu,
% 1.75/1.96 Wed Jul 27 05:31:29 2022
% 1.75/1.96 The command was "./otter". The process ID is 25149.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 formula_list(usable).
% 1.75/1.96 all A (A=A).
% 1.75/1.96 all A (ld(A,mult(A,A))=A).
% 1.75/1.96 all A (rd(mult(A,A),A)=A).
% 1.75/1.96 all B A (mult(A,ld(A,B))=ld(A,mult(A,B))).
% 1.75/1.96 all B A (mult(rd(A,B),B)=rd(mult(A,B),B)).
% 1.75/1.96 all D C B A (ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D)).
% 1.75/1.96 all D C B A (rd(mult(mult(A,B),rd(C,D)),rd(C,D))=mult(A,rd(mult(B,D),D))).
% 1.75/1.96 all B A (ld(A,mult(A,ld(B,B)))=rd(mult(rd(A,A),B),B)).
% 1.75/1.96 -(all X0 X1 X2 (ld(ld(X0,X1),mult(ld(X0,X1),X2))=ld(X0,mult(X0,X2))&ld(rd(X0,X1),mult(rd(X0,X1),X2))=ld(X0,mult(X0,X2)))).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 -------> usable clausifies to:
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] A=A.
% 1.75/1.96 0 [] ld(A,mult(A,A))=A.
% 1.75/1.96 0 [] rd(mult(A,A),A)=A.
% 1.75/1.96 0 [] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.75/1.96 0 [] mult(rd(A,B),B)=rd(mult(A,B),B).
% 1.75/1.96 0 [] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.75/1.96 0 [] rd(mult(mult(A,B),rd(C,D)),rd(C,D))=mult(A,rd(mult(B,D),D)).
% 1.75/1.96 0 [] ld(A,mult(A,ld(B,B)))=rd(mult(rd(A,A),B),B).
% 1.75/1.96 0 [] ld(ld($c3,$c2),mult(ld($c3,$c2),$c1))!=ld($c3,mult($c3,$c1))|ld(rd($c3,$c2),mult(rd($c3,$c2),$c1))!=ld($c3,mult($c3,$c1)).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.75/1.96
% 1.75/1.96 This is a Horn set with equality. The strategy will be
% 1.75/1.96 Knuth-Bendix and hyper_res, with positive clauses in
% 1.75/1.96 sos and nonpositive clauses in usable.
% 1.75/1.96
% 1.75/1.96 dependent: set(knuth_bendix).
% 1.75/1.96 dependent: set(anl_eq).
% 1.75/1.96 dependent: set(para_from).
% 1.75/1.96 dependent: set(para_into).
% 1.75/1.96 dependent: clear(para_from_right).
% 1.75/1.96 dependent: clear(para_into_right).
% 1.75/1.96 dependent: set(para_from_vars).
% 1.75/1.96 dependent: set(eq_units_both_ways).
% 1.75/1.96 dependent: set(dynamic_demod_all).
% 1.75/1.96 dependent: set(dynamic_demod).
% 1.75/1.96 dependent: set(order_eq).
% 1.75/1.96 dependent: set(back_demod).
% 1.75/1.96 dependent: set(lrpo).
% 1.75/1.96 dependent: set(hyper_res).
% 1.75/1.96 dependent: clear(order_hyper).
% 1.75/1.96
% 1.75/1.96 ------------> process usable:
% 1.75/1.96 ** KEPT (pick-wt=30): 1 [] ld(ld($c3,$c2),mult(ld($c3,$c2),$c1))!=ld($c3,mult($c3,$c1))|ld(rd($c3,$c2),mult(rd($c3,$c2),$c1))!=ld($c3,mult($c3,$c1)).
% 1.75/1.96
% 1.75/1.96 ------------> process sos:
% 1.75/1.96 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.96 ** KEPT (pick-wt=7): 3 [] ld(A,mult(A,A))=A.
% 1.75/1.96 ---> New Demodulator: 4 [new_demod,3] ld(A,mult(A,A))=A.
% 1.75/1.96 ** KEPT (pick-wt=7): 5 [] rd(mult(A,A),A)=A.
% 1.75/1.96 ---> New Demodulator: 6 [new_demod,5] rd(mult(A,A),A)=A.
% 1.75/1.96 ** KEPT (pick-wt=11): 7 [] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.75/1.96 ---> New Demodulator: 8 [new_demod,7] mult(A,ld(A,B))=ld(A,mult(A,B)).
% 1.75/1.96 ** KEPT (pick-wt=11): 10 [copy,9,flip.1] rd(mult(A,B),B)=mult(rd(A,B),B).
% 1.75/1.96 ---> New Demodulator: 11 [new_demod,10] rd(mult(A,B),B)=mult(rd(A,B),B).
% 1.75/1.96 ** KEPT (pick-wt=19): 12 [] ld(ld(A,B),mult(ld(A,B),mult(C,D)))=mult(ld(A,mult(A,C)),D).
% 1.75/1.96 ** 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)).
% 1.75/1.96 ---> New Demodulator: 15 [new_demod,14] mult(rd(mult(A,B),rd(C,D)),rd(C,D))=mult(A,mult(rd(B,D),D)).
% 1.75/1.96 ** 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))).
% 1.75/1.96 ---> New Demodulator: 18 [new_demod,17] mult(rd(rd(A,A),B),B)=ld(A,mult(A,ld(B,B))).
% 1.75/1.96 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.75/1.96 >>>> Starting back demodulation with 4.
% 1.75/1.96 >>>> Starting back demodulation with 6.
% 1.75/1.96 >>>> Starting back demodulation with 8.
% 1.75/1.96 >>>> Starting back demodulation with 11.
% 1.75/1.96 >> back demodulating 5 with 11.
% 1.75/1.96 ** 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))).
% 1.75/1.96 >>>> Starting back demodulation with 15.
% 1.75/1.96 >>>> Starting back demodulation with 18.
% 1.75/1.96 >>>> Starting back demodulation with 20.
% 1.75/1.96 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).
% 1.75/1.98
% 1.75/1.98 ======= end of input processing =======
% 1.75/1.98
% 1.75/1.98 =========== start of search ===========
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Resetting weight limit to 15.
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Resetting weight limit to 15.
% 1.75/1.98
% 1.75/1.98 sos_size=89
% 1.75/1.98
% 1.75/1.98 -------- PROOF --------
% 1.75/1.98
% 1.75/1.98 ----> UNIT CONFLICT at 0.02 sec ----> 368 [binary,367.1,2.1] $F.
% 1.75/1.98
% 1.75/1.98 Length of proof is 26. Level of proof is 11.
% 1.75/1.98
% 1.75/1.98 ---------------- PROOF ----------------
% 1.75/1.98 % SZS status Theorem
% 1.75/1.98 % SZS output start Refutation
% See solution above
% 1.75/1.98 ------------ end of proof -------------
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Search stopped by max_proofs option.
% 1.75/1.98
% 1.75/1.98
% 1.75/1.98 Search stopped by max_proofs option.
% 1.75/1.98
% 1.75/1.98 ============ end of search ============
% 1.75/1.98
% 1.75/1.98 -------------- statistics -------------
% 1.75/1.98 clauses given 32
% 1.75/1.98 clauses generated 386
% 1.75/1.98 clauses kept 201
% 1.75/1.98 clauses forward subsumed 311
% 1.75/1.98 clauses back subsumed 2
% 1.75/1.98 Kbytes malloced 4882
% 1.75/1.98
% 1.75/1.98 ----------- times (seconds) -----------
% 1.75/1.98 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.75/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.98
% 1.75/1.98 That finishes the proof of the theorem.
% 1.75/1.98
% 1.75/1.98 Process 25149 finished Wed Jul 27 05:31:31 2022
% 1.75/1.98 Otter interrupted
% 1.75/1.98 PROOF FOUND
%------------------------------------------------------------------------------