TSTP Solution File: BOO075-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 12:47:41 EDT 2022
% Result : Unsatisfiable 1.65s 1.92s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 2 RR)
% Number of literals : 14 ( 13 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
nand(nand(a,a),nand(b,a)) != a,
file('BOO075-1.p',unknown),
[] ).
cnf(4,axiom,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B,
file('BOO075-1.p',unknown),
[] ).
cnf(5,plain,
nand(nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))),nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,nand(B,C))))) = nand(C,nand(nand(A,C),C)),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.1.2.1,3.1.1')] ).
cnf(7,plain,
nand(nand(nand(A,nand(B,C)),nand(nand(D,nand(A,nand(B,C))),nand(A,nand(B,C)))),nand(D,A)) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.2,3.1.1')] ).
cnf(9,plain,
nand(nand(nand(A,B),nand(nand(nand(B,nand(nand(C,B),B)),nand(A,B)),nand(A,B))),C) = nand(B,nand(nand(C,B),B)),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2,3.1.1')] ).
cnf(16,plain,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,nand(nand(A,C),C)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,4]),4,4]),
[iquote('para_into,7.1.1.1.1,3.1.1,demod,4,4')] ).
cnf(49,plain,
nand(nand(A,nand(nand(nand(B,nand(nand(B,B),B)),A),A)),B) = nand(B,nand(nand(B,B),B)),
inference(para_into,[status(thm),theory(equality)],[16,4]),
[iquote('para_into,15.1.1.2,3.1.1')] ).
cnf(80,plain,
nand(A,nand(nand(A,A),A)) = nand(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,16]),16])]),
[iquote('para_into,5.1.1.2,15.1.1,demod,16,flip.1')] ).
cnf(83,plain,
nand(nand(A,nand(nand(nand(B,B),A),A)),B) = nand(B,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),80,80]),
[iquote('back_demod,49,demod,80,80')] ).
cnf(114,plain,
nand(nand(A,A),nand(A,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[80,4]),80]),
[iquote('para_from,79.1.1,3.1.1.2,demod,80')] ).
cnf(119,plain,
nand(nand(A,A),nand(A,nand(B,A))) = A,
inference(para_from,[status(thm),theory(equality)],[80,4]),
[iquote('para_from,79.1.1,3.1.1.1')] ).
cnf(245,plain,
nand(A,nand(nand(nand(nand(B,A),nand(B,A)),A),A)) = nand(B,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[83,9]),80,114])]),
[iquote('para_from,83.1.1,9.1.1.1.2.1,demod,80,114,flip.1')] ).
cnf(443,plain,
nand(nand(A,A),nand(B,A)) = A,
inference(para_from,[status(thm),theory(equality)],[245,119]),
[iquote('para_from,245.1.1,119.1.1.2')] ).
cnf(445,plain,
$false,
inference(binary,[status(thm)],[443,1]),
[iquote('binary,443.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 01:55:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.92 ----- Otter 3.3f, August 2004 -----
% 1.65/1.92 The process was started by sandbox2 on n017.cluster.edu,
% 1.65/1.92 Wed Jul 27 01:55:18 2022
% 1.65/1.92 The command was "./otter". The process ID is 1720.
% 1.65/1.92
% 1.65/1.92 set(prolog_style_variables).
% 1.65/1.92 set(auto).
% 1.65/1.92 dependent: set(auto1).
% 1.65/1.92 dependent: set(process_input).
% 1.65/1.92 dependent: clear(print_kept).
% 1.65/1.92 dependent: clear(print_new_demod).
% 1.65/1.92 dependent: clear(print_back_demod).
% 1.65/1.92 dependent: clear(print_back_sub).
% 1.65/1.92 dependent: set(control_memory).
% 1.65/1.92 dependent: assign(max_mem, 12000).
% 1.65/1.92 dependent: assign(pick_given_ratio, 4).
% 1.65/1.92 dependent: assign(stats_level, 1).
% 1.65/1.92 dependent: assign(max_seconds, 10800).
% 1.65/1.92 clear(print_given).
% 1.65/1.92
% 1.65/1.92 list(usable).
% 1.65/1.92 0 [] A=A.
% 1.65/1.92 0 [] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A)))=B.
% 1.65/1.92 0 [] nand(nand(a,a),nand(b,a))!=a.
% 1.65/1.92 end_of_list.
% 1.65/1.92
% 1.65/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.65/1.92
% 1.65/1.92 All clauses are units, and equality is present; the
% 1.65/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.65/1.92
% 1.65/1.92 dependent: set(knuth_bendix).
% 1.65/1.92 dependent: set(anl_eq).
% 1.65/1.92 dependent: set(para_from).
% 1.65/1.92 dependent: set(para_into).
% 1.65/1.92 dependent: clear(para_from_right).
% 1.65/1.92 dependent: clear(para_into_right).
% 1.65/1.92 dependent: set(para_from_vars).
% 1.65/1.92 dependent: set(eq_units_both_ways).
% 1.65/1.92 dependent: set(dynamic_demod_all).
% 1.65/1.92 dependent: set(dynamic_demod).
% 1.65/1.92 dependent: set(order_eq).
% 1.65/1.92 dependent: set(back_demod).
% 1.65/1.92 dependent: set(lrpo).
% 1.65/1.92
% 1.65/1.92 ------------> process usable:
% 1.65/1.92 ** KEPT (pick-wt=9): 1 [] nand(nand(a,a),nand(b,a))!=a.
% 1.65/1.92
% 1.65/1.92 ------------> process sos:
% 1.65/1.92 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.65/1.92 ** KEPT (pick-wt=15): 3 [] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A)))=B.
% 1.65/1.92 ---> New Demodulator: 4 [new_demod,3] nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A)))=B.
% 1.65/1.92 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.65/1.92 >>>> Starting back demodulation with 4.
% 1.65/1.92
% 1.65/1.92 ======= end of input processing =======
% 1.65/1.92
% 1.65/1.92 =========== start of search ===========
% 1.65/1.92
% 1.65/1.92 -------- PROOF --------
% 1.65/1.92
% 1.65/1.92 ----> UNIT CONFLICT at 0.06 sec ----> 445 [binary,443.1,1.1] $F.
% 1.65/1.92
% 1.65/1.92 Length of proof is 11. Level of proof is 6.
% 1.65/1.92
% 1.65/1.92 ---------------- PROOF ----------------
% 1.65/1.92 % SZS status Unsatisfiable
% 1.65/1.92 % SZS output start Refutation
% See solution above
% 1.65/1.92 ------------ end of proof -------------
% 1.65/1.92
% 1.65/1.92
% 1.65/1.92 Search stopped by max_proofs option.
% 1.65/1.92
% 1.65/1.92
% 1.65/1.92 Search stopped by max_proofs option.
% 1.65/1.92
% 1.65/1.92 ============ end of search ============
% 1.65/1.92
% 1.65/1.92 -------------- statistics -------------
% 1.65/1.92 clauses given 17
% 1.65/1.92 clauses generated 668
% 1.65/1.92 clauses kept 223
% 1.65/1.92 clauses forward subsumed 536
% 1.65/1.92 clauses back subsumed 0
% 1.65/1.92 Kbytes malloced 2929
% 1.65/1.92
% 1.65/1.92 ----------- times (seconds) -----------
% 1.65/1.92 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.65/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.92
% 1.65/1.92 That finishes the proof of the theorem.
% 1.65/1.92
% 1.65/1.92 Process 1720 finished Wed Jul 27 01:55:19 2022
% 1.74/1.92 Otter interrupted
% 1.74/1.92 PROOF FOUND
%------------------------------------------------------------------------------