TSTP Solution File: RNG083+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG083+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:12:15 EDT 2022
% Result : Theorem 1.74s 1.97s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 24 ( 13 unt; 0 nHn; 24 RR)
% Number of literals : 40 ( 20 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ aElement0(A)
| aElement0(smndt0(A)) ),
file('RNG083+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ aElement0(A)
| sdtpldt0(A,smndt0(A)) = sz00 ),
file('RNG083+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aElement0(A)
| ~ aElement0(B)
| sdtasdt0(A,B) = sdtasdt0(B,A) ),
file('RNG083+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ aElement0(A)
| A = sdtasdt0(sz10,A) ),
file('RNG083+1.p',unknown),
[] ).
cnf(16,plain,
( ~ aElement0(A)
| sdtasdt0(sz10,A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.2')] ).
cnf(19,axiom,
( ~ aElement0(A)
| ~ aElement0(B)
| ~ aElement0(C)
| sdtasdt0(sdtpldt0(B,C),A) = sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A)) ),
file('RNG083+1.p',unknown),
[] ).
cnf(20,plain,
( ~ aElement0(A)
| ~ aElement0(B)
| ~ aElement0(C)
| sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A)) = sdtasdt0(sdtpldt0(B,C),A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.4')] ).
cnf(21,axiom,
( ~ aElement0(A)
| sdtasdt0(smndt0(sz10),A) = smndt0(A) ),
file('RNG083+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ aElement0(A)
| smndt0(A) = sdtasdt0(A,smndt0(sz10)) ),
file('RNG083+1.p',unknown),
[] ).
cnf(23,axiom,
( sdtasdt0(xx,sz00) != sz00
| sz00 != sdtasdt0(sz00,xx) ),
file('RNG083+1.p',unknown),
[] ).
cnf(24,plain,
( sdtasdt0(xx,sz00) != sz00
| sdtasdt0(sz00,xx) != sz00 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
[iquote('copy,23,flip.2')] ).
cnf(26,axiom,
aElement0(sz00),
file('RNG083+1.p',unknown),
[] ).
cnf(27,axiom,
aElement0(sz10),
file('RNG083+1.p',unknown),
[] ).
cnf(28,axiom,
aElement0(xx),
file('RNG083+1.p',unknown),
[] ).
cnf(90,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(hyper,[status(thm)],[27,9]),
[iquote('hyper,27,9')] ).
cnf(102,plain,
aElement0(smndt0(sz10)),
inference(hyper,[status(thm)],[27,1]),
[iquote('hyper,27,1')] ).
cnf(112,plain,
smndt0(xx) = sdtasdt0(xx,smndt0(sz10)),
inference(hyper,[status(thm)],[28,22]),
[iquote('hyper,28,22')] ).
cnf(114,plain,
sdtasdt0(smndt0(sz10),xx) = sdtasdt0(xx,smndt0(sz10)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[28,21]),112]),
[iquote('hyper,28,21,demod,112')] ).
cnf(192,plain,
sdtasdt0(sz10,xx) = xx,
inference(hyper,[status(thm)],[28,16]),
[iquote('hyper,28,16')] ).
cnf(222,plain,
sdtasdt0(xx,sz00) = sdtasdt0(sz00,xx),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[28,12,26])]),
[iquote('hyper,28,12,26,flip.1')] ).
cnf(226,plain,
sdtpldt0(xx,sdtasdt0(xx,smndt0(sz10))) = sz00,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[28,9]),112]),
[iquote('hyper,28,9,demod,112')] ).
cnf(296,plain,
sdtasdt0(sz00,xx) != sz00,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),222]),
[iquote('back_demod,24,demod,222')] ).
cnf(589,plain,
sdtasdt0(sz00,xx) = sz00,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[102,20,28,27]),192,114,226,90])]),
[iquote('hyper,102,20,28,27,demod,192,114,226,90,flip.1')] ).
cnf(591,plain,
$false,
inference(binary,[status(thm)],[589,296]),
[iquote('binary,589.1,296.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG083+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 02:21:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.74/1.96 ----- Otter 3.3f, August 2004 -----
% 1.74/1.96 The process was started by sandbox2 on n008.cluster.edu,
% 1.74/1.96 Wed Jul 27 02:21:53 2022
% 1.74/1.96 The command was "./otter". The process ID is 14378.
% 1.74/1.96
% 1.74/1.96 set(prolog_style_variables).
% 1.74/1.96 set(auto).
% 1.74/1.96 dependent: set(auto1).
% 1.74/1.96 dependent: set(process_input).
% 1.74/1.96 dependent: clear(print_kept).
% 1.74/1.96 dependent: clear(print_new_demod).
% 1.74/1.96 dependent: clear(print_back_demod).
% 1.74/1.96 dependent: clear(print_back_sub).
% 1.74/1.96 dependent: set(control_memory).
% 1.74/1.96 dependent: assign(max_mem, 12000).
% 1.74/1.96 dependent: assign(pick_given_ratio, 4).
% 1.74/1.96 dependent: assign(stats_level, 1).
% 1.74/1.96 dependent: assign(max_seconds, 10800).
% 1.74/1.96 clear(print_given).
% 1.74/1.96
% 1.74/1.96 formula_list(usable).
% 1.74/1.96 all A (A=A).
% 1.74/1.96 all W0 (aElement0(W0)->$T).
% 1.74/1.96 aElement0(sz00).
% 1.74/1.96 aElement0(sz10).
% 1.74/1.96 all W0 (aElement0(W0)->aElement0(smndt0(W0))).
% 1.74/1.96 all W0 W1 (aElement0(W0)&aElement0(W1)->aElement0(sdtpldt0(W0,W1))).
% 1.74/1.96 all W0 W1 (aElement0(W0)&aElement0(W1)->aElement0(sdtasdt0(W0,W1))).
% 1.74/1.96 all W0 W1 (aElement0(W0)&aElement0(W1)->sdtpldt0(W0,W1)=sdtpldt0(W1,W0)).
% 1.74/1.96 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(W2)->sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2))).
% 1.74/1.96 all W0 (aElement0(W0)->sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)).
% 1.74/1.96 all W0 (aElement0(W0)->sdtpldt0(W0,smndt0(W0))=sz00&sz00=sdtpldt0(smndt0(W0),W0)).
% 1.74/1.96 all W0 W1 (aElement0(W0)&aElement0(W1)->sdtasdt0(W0,W1)=sdtasdt0(W1,W0)).
% 1.74/1.96 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(W2)->sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2))).
% 1.74/1.96 all W0 (aElement0(W0)->sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)).
% 1.74/1.96 all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(W2)->sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))&sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))).
% 1.74/1.96 all W0 (aElement0(W0)->sdtasdt0(smndt0(sz10),W0)=smndt0(W0)&smndt0(W0)=sdtasdt0(W0,smndt0(sz10))).
% 1.74/1.96 aElement0(xx).
% 1.74/1.96 -(sdtasdt0(xx,sz00)=sz00&sz00=sdtasdt0(sz00,xx)).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 -------> usable clausifies to:
% 1.74/1.96
% 1.74/1.96 list(usable).
% 1.74/1.96 0 [] A=A.
% 1.74/1.96 0 [] -aElement0(W0)|$T.
% 1.74/1.96 0 [] aElement0(sz00).
% 1.74/1.96 0 [] aElement0(sz10).
% 1.74/1.96 0 [] -aElement0(W0)|aElement0(smndt0(W0)).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)|aElement0(sdtpldt0(W0,W1)).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)|aElement0(sdtasdt0(W0,W1)).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)|sdtpldt0(W0,W1)=sdtpldt0(W1,W0).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)).
% 1.74/1.96 0 [] -aElement0(W0)|sdtpldt0(W0,sz00)=W0.
% 1.74/1.96 0 [] -aElement0(W0)|W0=sdtpldt0(sz00,W0).
% 1.74/1.96 0 [] -aElement0(W0)|sdtpldt0(W0,smndt0(W0))=sz00.
% 1.74/1.96 0 [] -aElement0(W0)|sz00=sdtpldt0(smndt0(W0),W0).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)|sdtasdt0(W0,W1)=sdtasdt0(W1,W0).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)).
% 1.74/1.96 0 [] -aElement0(W0)|sdtasdt0(W0,sz10)=W0.
% 1.74/1.96 0 [] -aElement0(W0)|W0=sdtasdt0(sz10,W0).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 1.74/1.96 0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)|sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 1.74/1.96 0 [] -aElement0(W0)|sdtasdt0(smndt0(sz10),W0)=smndt0(W0).
% 1.74/1.96 0 [] -aElement0(W0)|smndt0(W0)=sdtasdt0(W0,smndt0(sz10)).
% 1.74/1.96 0 [] aElement0(xx).
% 1.74/1.96 0 [] sdtasdt0(xx,sz00)!=sz00|sz00!=sdtasdt0(sz00,xx).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.74/1.96
% 1.74/1.96 This is a Horn set with equality. The strategy will be
% 1.74/1.96 Knuth-Bendix and hyper_res, with positive clauses in
% 1.74/1.96 sos and nonpositive clauses in usable.
% 1.74/1.96
% 1.74/1.96 dependent: set(knuth_bendix).
% 1.74/1.96 dependent: set(anl_eq).
% 1.74/1.96 dependent: set(para_from).
% 1.74/1.96 dependent: set(para_into).
% 1.74/1.96 dependent: clear(para_from_right).
% 1.74/1.96 dependent: clear(para_into_right).
% 1.74/1.96 dependent: set(para_from_vars).
% 1.74/1.96 dependent: set(eq_units_both_ways).
% 1.74/1.96 dependent: set(dynamic_demod_all).
% 1.74/1.96 dependent: set(dynamic_demod).
% 1.74/1.96 dependent: set(order_eq).
% 1.74/1.96 dependent: set(back_demod).
% 1.74/1.96 dependent: set(lrpo).
% 1.74/1.96 dependent: set(hyper_res).
% 1.74/1.96 dependent: clear(order_hyper).
% 1.74/1.96
% 1.74/1.96 ------------> process usable:
% 1.74/1.96 ** KEPT (pick-wt=5): 1 [] -aElement0(A)|aElement0(smndt0(A)).
% 1.74/1.96 ** KEPT (pick-wt=8): 2 [] -aElement0(A)| -aElement0(B)|aElement0(sdtpldt0(A,B)).
% 1.74/1.97 ** KEPT (pick-wt=8): 3 [] -aElement0(A)| -aElement0(B)|aElement0(sdtasdt0(A,B)).
% 1.74/1.97 ** KEPT (pick-wt=11): 4 [] -aElement0(A)| -aElement0(B)|sdtpldt0(A,B)=sdtpldt0(B,A).
% 1.74/1.97 ** KEPT (pick-wt=17): 5 [] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtpldt0(sdtpldt0(A,B),C)=sdtpldt0(A,sdtpldt0(B,C)).
% 1.74/1.97 ** KEPT (pick-wt=7): 6 [] -aElement0(A)|sdtpldt0(A,sz00)=A.
% 1.74/1.97 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -aElement0(A)|sdtpldt0(sz00,A)=A.
% 1.74/1.97 ** KEPT (pick-wt=8): 9 [] -aElement0(A)|sdtpldt0(A,smndt0(A))=sz00.
% 1.74/1.97 ** KEPT (pick-wt=8): 11 [copy,10,flip.2] -aElement0(A)|sdtpldt0(smndt0(A),A)=sz00.
% 1.74/1.97 ** KEPT (pick-wt=11): 12 [] -aElement0(A)| -aElement0(B)|sdtasdt0(A,B)=sdtasdt0(B,A).
% 1.74/1.97 ** KEPT (pick-wt=17): 13 [] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtasdt0(sdtasdt0(A,B),C)=sdtasdt0(A,sdtasdt0(B,C)).
% 1.74/1.97 ** KEPT (pick-wt=7): 14 [] -aElement0(A)|sdtasdt0(A,sz10)=A.
% 1.74/1.97 ** KEPT (pick-wt=7): 16 [copy,15,flip.2] -aElement0(A)|sdtasdt0(sz10,A)=A.
% 1.74/1.97 ** KEPT (pick-wt=19): 18 [copy,17,flip.4] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))=sdtasdt0(A,sdtpldt0(B,C)).
% 1.74/1.97 ** KEPT (pick-wt=19): 20 [copy,19,flip.4] -aElement0(A)| -aElement0(B)| -aElement0(C)|sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A))=sdtasdt0(sdtpldt0(B,C),A).
% 1.74/1.97 ** KEPT (pick-wt=9): 21 [] -aElement0(A)|sdtasdt0(smndt0(sz10),A)=smndt0(A).
% 1.74/1.97 ** KEPT (pick-wt=9): 22 [] -aElement0(A)|smndt0(A)=sdtasdt0(A,smndt0(sz10)).
% 1.74/1.97 ** KEPT (pick-wt=10): 24 [copy,23,flip.2] sdtasdt0(xx,sz00)!=sz00|sdtasdt0(sz00,xx)!=sz00.
% 1.74/1.97
% 1.74/1.97 ------------> process sos:
% 1.74/1.97 ** KEPT (pick-wt=3): 25 [] A=A.
% 1.74/1.97 ** KEPT (pick-wt=2): 26 [] aElement0(sz00).
% 1.74/1.97 ** KEPT (pick-wt=2): 27 [] aElement0(sz10).
% 1.74/1.97 ** KEPT (pick-wt=2): 28 [] aElement0(xx).
% 1.74/1.97 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] A=A.
% 1.74/1.97
% 1.74/1.97 ======= end of input processing =======
% 1.74/1.97
% 1.74/1.97 =========== start of search ===========
% 1.74/1.97
% 1.74/1.97 -------- PROOF --------
% 1.74/1.97
% 1.74/1.97 ----> UNIT CONFLICT at 0.01 sec ----> 591 [binary,589.1,296.1] $F.
% 1.74/1.97
% 1.74/1.97 Length of proof is 12. Level of proof is 3.
% 1.74/1.97
% 1.74/1.97 ---------------- PROOF ----------------
% 1.74/1.97 % SZS status Theorem
% 1.74/1.97 % SZS output start Refutation
% See solution above
% 1.74/1.97 ------------ end of proof -------------
% 1.74/1.97
% 1.74/1.97
% 1.74/1.97 Search stopped by max_proofs option.
% 1.74/1.97
% 1.74/1.97
% 1.74/1.97 Search stopped by max_proofs option.
% 1.74/1.97
% 1.74/1.97 ============ end of search ============
% 1.74/1.97
% 1.74/1.97 -------------- statistics -------------
% 1.74/1.97 clauses given 7
% 1.74/1.97 clauses generated 497
% 1.74/1.97 clauses kept 311
% 1.74/1.97 clauses forward subsumed 395
% 1.74/1.97 clauses back subsumed 0
% 1.74/1.97 Kbytes malloced 1953
% 1.74/1.97
% 1.74/1.97 ----------- times (seconds) -----------
% 1.74/1.97 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.97 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.74/1.97
% 1.74/1.97 That finishes the proof of the theorem.
% 1.74/1.97
% 1.74/1.97 Process 14378 finished Wed Jul 27 02:21:55 2022
% 1.74/1.97 Otter interrupted
% 1.74/1.97 PROOF FOUND
%------------------------------------------------------------------------------