TSTP Solution File: GRP698-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP698-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 12:57:40 EDT 2022
% Result : Unsatisfiable 1.65s 1.97s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 4 RR)
% Number of literals : 17 ( 16 equ; 3 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)),
file('GRP698-1.p',unknown),
[] ).
cnf(2,plain,
mult(rd(mult(a,b),a),mult(a,c)) != mult(a,mult(b,c)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('GRP698-1.p',unknown),
[] ).
cnf(4,axiom,
mult(A,ld(A,B)) = B,
file('GRP698-1.p',unknown),
[] ).
cnf(7,axiom,
ld(A,mult(A,B)) = B,
file('GRP698-1.p',unknown),
[] ).
cnf(9,axiom,
mult(rd(A,B),B) = A,
file('GRP698-1.p',unknown),
[] ).
cnf(10,axiom,
rd(mult(A,B),B) = A,
file('GRP698-1.p',unknown),
[] ).
cnf(13,axiom,
mult(A,unit) = A,
file('GRP698-1.p',unknown),
[] ).
cnf(16,axiom,
mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
file('GRP698-1.p',unknown),
[] ).
cnf(43,plain,
mult(mult(mult(A,B),A),A) = mult(A,mult(mult(B,A),A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,13]),13]),
[iquote('para_into,16.1.1.2,12.1.1,demod,13')] ).
cnf(46,plain,
mult(mult(mult(A,B),A),C) = mult(A,mult(mult(mult(B,A),A),ld(A,C))),
inference(para_into,[status(thm),theory(equality)],[16,4]),
[iquote('para_into,16.1.1.2,4.1.1')] ).
cnf(145,plain,
rd(mult(A,mult(mult(B,A),A)),A) = mult(mult(A,B),A),
inference(para_from,[status(thm),theory(equality)],[43,10]),
[iquote('para_from,43.1.1,10.1.1.1')] ).
cnf(327,plain,
rd(mult(A,mult(B,A)),A) = mult(mult(A,rd(B,A)),A),
inference(para_into,[status(thm),theory(equality)],[145,9]),
[iquote('para_into,145.1.1.1.2.1,8.1.1')] ).
cnf(363,plain,
mult(mult(A,rd(rd(B,A),A)),A) = rd(mult(A,B),A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[327,9])]),
[iquote('para_into,327.1.1.1.2,8.1.1,flip.1')] ).
cnf(458,plain,
mult(rd(mult(A,B),A),C) = mult(A,mult(B,ld(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[363,46]),9,9]),
[iquote('para_from,363.1.1,46.1.1.1,demod,9,9')] ).
cnf(463,plain,
mult(a,mult(b,c)) != mult(a,mult(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),458,7]),
[iquote('back_demod,2,demod,458,7')] ).
cnf(464,plain,
$false,
inference(binary,[status(thm)],[463,3]),
[iquote('binary,463.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP698-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 05:13:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.97 ----- Otter 3.3f, August 2004 -----
% 1.65/1.97 The process was started by sandbox2 on n007.cluster.edu,
% 1.65/1.97 Wed Jul 27 05:13:46 2022
% 1.65/1.97 The command was "./otter". The process ID is 12394.
% 1.65/1.97
% 1.65/1.97 set(prolog_style_variables).
% 1.65/1.97 set(auto).
% 1.65/1.97 dependent: set(auto1).
% 1.65/1.97 dependent: set(process_input).
% 1.65/1.97 dependent: clear(print_kept).
% 1.65/1.97 dependent: clear(print_new_demod).
% 1.65/1.97 dependent: clear(print_back_demod).
% 1.65/1.97 dependent: clear(print_back_sub).
% 1.65/1.97 dependent: set(control_memory).
% 1.65/1.97 dependent: assign(max_mem, 12000).
% 1.65/1.97 dependent: assign(pick_given_ratio, 4).
% 1.65/1.97 dependent: assign(stats_level, 1).
% 1.65/1.97 dependent: assign(max_seconds, 10800).
% 1.65/1.97 clear(print_given).
% 1.65/1.97
% 1.65/1.97 list(usable).
% 1.65/1.97 0 [] A=A.
% 1.65/1.97 0 [] mult(A,ld(A,B))=B.
% 1.65/1.97 0 [] ld(A,mult(A,B))=B.
% 1.65/1.97 0 [] mult(rd(A,B),B)=A.
% 1.65/1.97 0 [] rd(mult(A,B),B)=A.
% 1.65/1.97 0 [] mult(A,unit)=A.
% 1.65/1.97 0 [] mult(unit,A)=A.
% 1.65/1.97 0 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.65/1.97 0 [] mult(mult(A,B),mult(B,mult(C,B)))=mult(mult(A,mult(B,mult(B,C))),B).
% 1.65/1.97 0 [] mult(a,mult(b,c))!=mult(rd(mult(a,b),a),mult(a,c)).
% 1.65/1.97 end_of_list.
% 1.65/1.97
% 1.65/1.97 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.65/1.97
% 1.65/1.97 All clauses are units, and equality is present; the
% 1.65/1.97 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.65/1.97
% 1.65/1.97 dependent: set(knuth_bendix).
% 1.65/1.97 dependent: set(anl_eq).
% 1.65/1.97 dependent: set(para_from).
% 1.65/1.97 dependent: set(para_into).
% 1.65/1.97 dependent: clear(para_from_right).
% 1.65/1.97 dependent: clear(para_into_right).
% 1.65/1.97 dependent: set(para_from_vars).
% 1.65/1.97 dependent: set(eq_units_both_ways).
% 1.65/1.97 dependent: set(dynamic_demod_all).
% 1.65/1.97 dependent: set(dynamic_demod).
% 1.65/1.97 dependent: set(order_eq).
% 1.65/1.97 dependent: set(back_demod).
% 1.65/1.97 dependent: set(lrpo).
% 1.65/1.97
% 1.65/1.97 ------------> process usable:
% 1.65/1.97 ** KEPT (pick-wt=15): 2 [copy,1,flip.1] mult(rd(mult(a,b),a),mult(a,c))!=mult(a,mult(b,c)).
% 1.65/1.97
% 1.65/1.97 ------------> process sos:
% 1.65/1.97 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.65/1.97 ** KEPT (pick-wt=7): 4 [] mult(A,ld(A,B))=B.
% 1.65/1.97 ---> New Demodulator: 5 [new_demod,4] mult(A,ld(A,B))=B.
% 1.65/1.97 ** KEPT (pick-wt=7): 6 [] ld(A,mult(A,B))=B.
% 1.65/1.97 ---> New Demodulator: 7 [new_demod,6] ld(A,mult(A,B))=B.
% 1.65/1.97 ** KEPT (pick-wt=7): 8 [] mult(rd(A,B),B)=A.
% 1.65/1.97 ---> New Demodulator: 9 [new_demod,8] mult(rd(A,B),B)=A.
% 1.65/1.97 ** KEPT (pick-wt=7): 10 [] rd(mult(A,B),B)=A.
% 1.65/1.97 ---> New Demodulator: 11 [new_demod,10] rd(mult(A,B),B)=A.
% 1.65/1.97 ** KEPT (pick-wt=5): 12 [] mult(A,unit)=A.
% 1.65/1.97 ---> New Demodulator: 13 [new_demod,12] mult(A,unit)=A.
% 1.65/1.97 ** KEPT (pick-wt=5): 14 [] mult(unit,A)=A.
% 1.65/1.97 ---> New Demodulator: 15 [new_demod,14] mult(unit,A)=A.
% 1.65/1.97 ** KEPT (pick-wt=19): 16 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.65/1.97 ** KEPT (pick-wt=19): 18 [copy,17,flip.1] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.65/1.97 ---> New Demodulator: 19 [new_demod,18] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.65/1.97 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.65/1.97 >>>> Starting back demodulation with 5.
% 1.65/1.97 >>>> Starting back demodulation with 7.
% 1.65/1.97 >>>> Starting back demodulation with 9.
% 1.65/1.97 >>>> Starting back demodulation with 11.
% 1.65/1.97 >>>> Starting back demodulation with 13.
% 1.65/1.97 >>>> Starting back demodulation with 15.
% 1.65/1.97 ** KEPT (pick-wt=19): 20 [copy,16,flip.1] mult(A,mult(mult(mult(B,A),A),C))=mult(mult(mult(A,B),A),mult(A,C)).
% 1.65/1.97 >>>> Starting back demodulation with 19.
% 1.65/1.97 Following clause subsumed by 16 during input processing: 0 [copy,20,flip.1] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.65/1.97
% 1.65/1.97 ======= end of input processing =======
% 1.65/1.97
% 1.65/1.97 =========== start of search ===========
% 1.65/1.97
% 1.65/1.97
% 1.65/1.97 Resetting weight limit to 19.
% 1.65/1.97
% 1.65/1.97
% 1.65/1.97 Resetting weight limit to 19.
% 1.65/1.97
% 1.65/1.97 sos_size=147
% 1.65/1.97
% 1.65/1.97
% 1.65/1.97 Resetting weight limit to 15.
% 1.65/1.97
% 1.65/1.97
% 1.65/1.97 Resetting weight limit to 15.
% 1.65/1.97
% 1.65/1.97 sos_size=160
% 1.65/1.97
% 1.65/1.97 -------- PROOF --------
% 1.65/1.97
% 1.65/1.97 ----> UNIT CONFLICT at 0.08 sec ----> 464 [binary,463.1,3.1] $F.
% 1.65/1.97
% 1.65/1.97 Length of proof is 8. Level of proof is 6.
% 1.65/1.97
% 1.65/1.97 ---------------- PROOF ----------------
% 1.65/1.97 % SZS status Unsatisfiable
% 1.65/1.97 % SZS output start Refutation
% See solution above
% 1.65/1.97 ------------ end of proof -------------
% 1.65/1.97
% 1.65/1.97
% 1.65/1.97 Search stopped by max_proofs option.
% 1.65/1.97
% 1.65/1.97
% 1.65/1.97 Search stopped by max_proofs option.
% 1.65/1.97
% 1.65/1.97 ============ end of search ============
% 1.65/1.97
% 1.65/1.97 -------------- statistics -------------
% 1.65/1.97 clauses given 65
% 1.65/1.97 clauses generated 1811
% 1.65/1.97 clauses kept 277
% 1.65/1.97 clauses forward subsumed 780
% 1.65/1.97 clauses back subsumed 0
% 1.65/1.97 Kbytes malloced 5859
% 1.65/1.97
% 1.65/1.97 ----------- times (seconds) -----------
% 1.65/1.97 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.65/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.97 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.97
% 1.65/1.97 That finishes the proof of the theorem.
% 1.65/1.97
% 1.65/1.97 Process 12394 finished Wed Jul 27 05:13:47 2022
% 1.65/1.97 Otter interrupted
% 1.65/1.97 PROOF FOUND
%------------------------------------------------------------------------------