TSTP Solution File: GRP680-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 1.82s 2.00s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 4 RR)
% Number of literals : 28 ( 27 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(i(op_c),a) != mult(a,i(op_c)),
file('GRP680-1.p',unknown),
[] ).
cnf(3,axiom,
mult(A,ld(A,B)) = B,
file('GRP680-1.p',unknown),
[] ).
cnf(5,axiom,
ld(A,mult(A,B)) = B,
file('GRP680-1.p',unknown),
[] ).
cnf(11,axiom,
mult(A,unit) = A,
file('GRP680-1.p',unknown),
[] ).
cnf(13,axiom,
mult(unit,A) = A,
file('GRP680-1.p',unknown),
[] ).
cnf(15,axiom,
mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C),
file('GRP680-1.p',unknown),
[] ).
cnf(16,plain,
mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(18,axiom,
mult(i(A),mult(A,B)) = B,
file('GRP680-1.p',unknown),
[] ).
cnf(20,axiom,
mult(op_c,A) = mult(A,op_c),
file('GRP680-1.p',unknown),
[] ).
cnf(21,plain,
mult(A,op_c) = mult(op_c,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(23,plain,
ld(unit,A) = A,
inference(para_into,[status(thm),theory(equality)],[3,13]),
[iquote('para_into,3.1.1,13.1.1')] ).
cnf(25,plain,
ld(A,A) = unit,
inference(para_into,[status(thm),theory(equality)],[5,11]),
[iquote('para_into,5.1.1.2,11.1.1')] ).
cnf(60,plain,
mult(A,mult(B,mult(A,op_c))) = mult(op_c,mult(A,mult(B,A))),
inference(para_into,[status(thm),theory(equality)],[21,16]),
[iquote('para_into,21.1.1,16.1.1')] ).
cnf(63,plain,
mult(op_c,mult(A,mult(B,A))) = mult(A,mult(B,mult(A,op_c))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[60])]),
[iquote('copy,60,flip.1')] ).
cnf(74,plain,
mult(i(i(A)),B) = mult(A,B),
inference(para_into,[status(thm),theory(equality)],[18,18]),
[iquote('para_into,18.1.1.2,18.1.1')] ).
cnf(85,plain,
mult(i(A),B) = ld(A,B),
inference(para_into,[status(thm),theory(equality)],[18,3]),
[iquote('para_into,18.1.1.2,3.1.1')] ).
cnf(86,plain,
ld(i(A),B) = mult(A,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[74]),85]),
[iquote('back_demod,74,demod,85')] ).
cnf(87,plain,
mult(a,i(op_c)) != ld(op_c,a),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),85])]),
[iquote('back_demod,1,demod,85,flip.1')] ).
cnf(88,plain,
mult(A,B) = ld(i(A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[86])]),
[iquote('copy,86,flip.1')] ).
cnf(146,plain,
i(A) = ld(A,unit),
inference(para_into,[status(thm),theory(equality)],[85,11]),
[iquote('para_into,84.1.1,11.1.1')] ).
cnf(152,plain,
mult(A,B) = ld(ld(A,unit),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[88]),146]),
[iquote('back_demod,88,demod,146')] ).
cnf(153,plain,
ld(ld(a,unit),ld(op_c,unit)) != ld(op_c,a),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[87]),146,152]),
[iquote('back_demod,87,demod,146,152')] ).
cnf(208,plain,
ld(ld(op_c,unit),ld(ld(A,unit),ld(ld(B,unit),A))) = ld(ld(A,unit),ld(ld(B,unit),ld(ld(A,unit),op_c))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),152,152,152,152,152,152]),
[iquote('back_demod,63,demod,152,152,152,152,152,152')] ).
cnf(235,plain,
ld(ld(op_c,unit),A) = ld(ld(A,unit),op_c),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),152,152]),
[iquote('back_demod,20,demod,152,152')] ).
cnf(239,plain,
ld(ld(A,unit),unit) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),152]),
[iquote('back_demod,11,demod,152')] ).
cnf(245,plain,
ld(ld(A,unit),ld(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),152]),
[iquote('back_demod,3,demod,152')] ).
cnf(461,plain,
ld(ld(A,unit),ld(op_c,unit)) = ld(op_c,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[208,235]),25,23,245,239,239,25,239]),
[iquote('para_into,208.1.1.2.1,235.1.1,demod,25,23,245,239,239,25,239')] ).
cnf(463,plain,
$false,
inference(binary,[status(thm)],[461,153]),
[iquote('binary,461.1,153.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 05:33:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.82/2.00 ----- Otter 3.3f, August 2004 -----
% 1.82/2.00 The process was started by sandbox on n028.cluster.edu,
% 1.82/2.00 Wed Jul 27 05:33:48 2022
% 1.82/2.00 The command was "./otter". The process ID is 25860.
% 1.82/2.00
% 1.82/2.00 set(prolog_style_variables).
% 1.82/2.00 set(auto).
% 1.82/2.00 dependent: set(auto1).
% 1.82/2.00 dependent: set(process_input).
% 1.82/2.00 dependent: clear(print_kept).
% 1.82/2.00 dependent: clear(print_new_demod).
% 1.82/2.00 dependent: clear(print_back_demod).
% 1.82/2.00 dependent: clear(print_back_sub).
% 1.82/2.00 dependent: set(control_memory).
% 1.82/2.00 dependent: assign(max_mem, 12000).
% 1.82/2.00 dependent: assign(pick_given_ratio, 4).
% 1.82/2.00 dependent: assign(stats_level, 1).
% 1.82/2.00 dependent: assign(max_seconds, 10800).
% 1.82/2.00 clear(print_given).
% 1.82/2.00
% 1.82/2.00 list(usable).
% 1.82/2.00 0 [] A=A.
% 1.82/2.00 0 [] mult(A,ld(A,B))=B.
% 1.82/2.00 0 [] ld(A,mult(A,B))=B.
% 1.82/2.00 0 [] mult(rd(A,B),B)=A.
% 1.82/2.00 0 [] rd(mult(A,B),B)=A.
% 1.82/2.00 0 [] mult(A,unit)=A.
% 1.82/2.00 0 [] mult(unit,A)=A.
% 1.82/2.00 0 [] mult(A,mult(B,mult(A,C)))=mult(mult(A,mult(B,A)),C).
% 1.82/2.00 0 [] mult(i(A),mult(A,B))=B.
% 1.82/2.00 0 [] mult(op_c,A)=mult(A,op_c).
% 1.82/2.00 0 [] mult(i(op_c),a)!=mult(a,i(op_c)).
% 1.82/2.00 end_of_list.
% 1.82/2.00
% 1.82/2.00 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.82/2.00
% 1.82/2.00 All clauses are units, and equality is present; the
% 1.82/2.00 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.82/2.00
% 1.82/2.00 dependent: set(knuth_bendix).
% 1.82/2.00 dependent: set(anl_eq).
% 1.82/2.00 dependent: set(para_from).
% 1.82/2.00 dependent: set(para_into).
% 1.82/2.00 dependent: clear(para_from_right).
% 1.82/2.00 dependent: clear(para_into_right).
% 1.82/2.00 dependent: set(para_from_vars).
% 1.82/2.00 dependent: set(eq_units_both_ways).
% 1.82/2.00 dependent: set(dynamic_demod_all).
% 1.82/2.00 dependent: set(dynamic_demod).
% 1.82/2.00 dependent: set(order_eq).
% 1.82/2.00 dependent: set(back_demod).
% 1.82/2.00 dependent: set(lrpo).
% 1.82/2.00
% 1.82/2.00 ------------> process usable:
% 1.82/2.00 ** KEPT (pick-wt=9): 1 [] mult(i(op_c),a)!=mult(a,i(op_c)).
% 1.82/2.00
% 1.82/2.00 ------------> process sos:
% 1.82/2.00 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.82/2.00 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.82/2.00 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.82/2.00 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.82/2.00 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.82/2.00 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.82/2.00 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.82/2.00 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.82/2.00 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.82/2.00 ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.82/2.00 ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.82/2.00 ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.82/2.00 ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.82/2.00 ** KEPT (pick-wt=15): 16 [copy,15,flip.1] mult(mult(A,mult(B,A)),C)=mult(A,mult(B,mult(A,C))).
% 1.82/2.00 ---> New Demodulator: 17 [new_demod,16] mult(mult(A,mult(B,A)),C)=mult(A,mult(B,mult(A,C))).
% 1.82/2.00 ** KEPT (pick-wt=8): 18 [] mult(i(A),mult(A,B))=B.
% 1.82/2.00 ---> New Demodulator: 19 [new_demod,18] mult(i(A),mult(A,B))=B.
% 1.82/2.00 ** KEPT (pick-wt=7): 20 [] mult(op_c,A)=mult(A,op_c).
% 1.82/2.00 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.82/2.00 >>>> Starting back demodulation with 4.
% 1.82/2.00 >>>> Starting back demodulation with 6.
% 1.82/2.00 >>>> Starting back demodulation with 8.
% 1.82/2.00 >>>> Starting back demodulation with 10.
% 1.82/2.00 >>>> Starting back demodulation with 12.
% 1.82/2.00 >>>> Starting back demodulation with 14.
% 1.82/2.00 >>>> Starting back demodulation with 17.
% 1.82/2.00 >>>> Starting back demodulation with 19.
% 1.82/2.00 ** KEPT (pick-wt=7): 21 [copy,20,flip.1] mult(A,op_c)=mult(op_c,A).
% 1.82/2.00 Following clause subsumed by 20 during input processing: 0 [copy,21,flip.1] mult(op_c,A)=mult(A,op_c).
% 1.82/2.00
% 1.82/2.00 ======= end of input processing =======
% 1.82/2.00
% 1.82/2.00 =========== start of search ===========
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Resetting weight limit to 11.
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Resetting weight limit to 11.
% 1.82/2.00
% 1.82/2.00 sos_size=122
% 1.82/2.00
% 1.82/2.00 -------- PROOF --------
% 1.82/2.00
% 1.82/2.00 ----> UNIT CONFLICT at 0.07 sec ----> 463 [binary,461.1,153.1] $F.
% 1.82/2.00
% 1.82/2.00 Length of proof is 19. Level of proof is 6.
% 1.82/2.00
% 1.82/2.00 ---------------- PROOF ----------------
% 1.82/2.00 % SZS status Unsatisfiable
% 1.82/2.00 % SZS output start Refutation
% See solution above
% 1.82/2.00 ------------ end of proof -------------
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Search stopped by max_proofs option.
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Search stopped by max_proofs option.
% 1.82/2.00
% 1.82/2.00 ============ end of search ============
% 1.82/2.00
% 1.82/2.00 -------------- statistics -------------
% 1.82/2.00 clauses given 82
% 1.82/2.00 clauses generated 3512
% 1.82/2.00 clauses kept 248
% 1.82/2.00 clauses forward subsumed 1498
% 1.82/2.00 clauses back subsumed 0
% 1.82/2.00 Kbytes malloced 4882
% 1.82/2.00
% 1.82/2.00 ----------- times (seconds) -----------
% 1.82/2.00 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.82/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.00
% 1.82/2.00 That finishes the proof of the theorem.
% 1.82/2.00
% 1.82/2.00 Process 25860 finished Wed Jul 27 05:33:50 2022
% 1.82/2.00 Otter interrupted
% 1.82/2.00 PROOF FOUND
%------------------------------------------------------------------------------