TSTP Solution File: NUM464+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM464+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:08:27 EDT 2022
% Result : Theorem 2.29s 2.41s
% Output : Refutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 8 unt; 2 nHn; 10 RR)
% Number of literals : 16 ( 4 equ; 6 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(38,axiom,
( ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(B)
| sdtlse_qdt0(A,B)
| sdtlse_qdt0(B,A) ),
file('NUM464+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ aNaturalNumber0(A)
| A = sz00
| A = sz10
| sdtlse_qdt0(sz10,A) ),
file('NUM464+2.p',unknown),
[] ).
cnf(45,axiom,
xm != sz00,
file('NUM464+2.p',unknown),
[] ).
cnf(47,axiom,
~ sdtlse_qdt0(sz10,xm),
file('NUM464+2.p',unknown),
[] ).
cnf(110,axiom,
aNaturalNumber0(sz10),
file('NUM464+2.p',unknown),
[] ).
cnf(111,axiom,
aNaturalNumber0(xm),
file('NUM464+2.p',unknown),
[] ).
cnf(180,plain,
sdtlse_qdt0(sz10,sz10),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[110,38,110])]),
[iquote('hyper,110,38,110,factor_simp')] ).
cnf(305,plain,
xm = sz10,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[111,44]),45,47]),
[iquote('hyper,111,44,unit_del,45,47')] ).
cnf(306,plain,
~ sdtlse_qdt0(sz10,sz10),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),305]),
[iquote('back_demod,47,demod,305')] ).
cnf(307,plain,
$false,
inference(binary,[status(thm)],[306,180]),
[iquote('binary,306.1,180.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM464+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:55:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.22/2.38 ----- Otter 3.3f, August 2004 -----
% 2.22/2.38 The process was started by sandbox on n020.cluster.edu,
% 2.22/2.38 Wed Jul 27 09:55:38 2022
% 2.22/2.38 The command was "./otter". The process ID is 20345.
% 2.22/2.38
% 2.22/2.38 set(prolog_style_variables).
% 2.22/2.38 set(auto).
% 2.22/2.38 dependent: set(auto1).
% 2.22/2.38 dependent: set(process_input).
% 2.22/2.38 dependent: clear(print_kept).
% 2.22/2.38 dependent: clear(print_new_demod).
% 2.22/2.38 dependent: clear(print_back_demod).
% 2.22/2.38 dependent: clear(print_back_sub).
% 2.22/2.38 dependent: set(control_memory).
% 2.22/2.38 dependent: assign(max_mem, 12000).
% 2.22/2.38 dependent: assign(pick_given_ratio, 4).
% 2.22/2.38 dependent: assign(stats_level, 1).
% 2.22/2.38 dependent: assign(max_seconds, 10800).
% 2.22/2.38 clear(print_given).
% 2.22/2.38
% 2.22/2.38 formula_list(usable).
% 2.22/2.38 all A (A=A).
% 2.22/2.38 all W0 (aNaturalNumber0(W0)->$T).
% 2.22/2.38 aNaturalNumber0(sz00).
% 2.22/2.38 aNaturalNumber0(sz10).
% 2.22/2.38 sz10!=sz00.
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtpldt0(W0,W1))).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->aNaturalNumber0(sdtasdt0(W0,W1))).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtpldt0(W0,W1)=sdtpldt0(W1,W0)).
% 2.22/2.38 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2))).
% 2.22/2.38 all W0 (aNaturalNumber0(W0)->sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtasdt0(W0,W1)=sdtasdt0(W1,W0)).
% 2.22/2.38 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)->sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2))).
% 2.22/2.38 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)).
% 2.22/2.38 all W0 (aNaturalNumber0(W0)->sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)).
% 2.22/2.38 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(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))).
% 2.22/2.38 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtpldt0(W0,W1)=sdtpldt0(W0,W2)|sdtpldt0(W1,W0)=sdtpldt0(W2,W0)->W1=W2)).
% 2.22/2.38 all W0 (aNaturalNumber0(W0)-> (W0!=sz00-> (all W1 W2 (aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtasdt0(W0,W1)=sdtasdt0(W0,W2)|sdtasdt0(W1,W0)=sdtasdt0(W2,W0)->W1=W2))))).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtpldt0(W0,W1)=sz00->W0=sz00&W1=sz00)).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtasdt0(W0,W1)=sz00->W0=sz00|W1=sz00)).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)<-> (exists W2 (aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)-> (all W2 (W2=sdtmndt0(W1,W0)<->aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))).
% 2.22/2.38 all W0 (aNaturalNumber0(W0)->sdtlse_qdt0(W0,W0)).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W0)->W0=W1)).
% 2.22/2.38 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (sdtlse_qdt0(W0,W1)&sdtlse_qdt0(W1,W2)->sdtlse_qdt0(W0,W2))).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)->sdtlse_qdt0(W0,W1)|W1!=W0&sdtlse_qdt0(W1,W0)).
% 2.22/2.38 all W0 W1 (aNaturalNumber0(W0)&aNaturalNumber0(W1)-> (W0!=W1&sdtlse_qdt0(W0,W1)-> (all W2 (aNaturalNumber0(W2)->sdtpldt0(W2,W0)!=sdtpldt0(W2,W1)&sdtlse_qdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))&sdtpldt0(W0,W2)!=sdtpldt0(W1,W2)&sdtlse_qdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)))))).
% 2.22/2.38 all W0 W1 W2 (aNaturalNumber0(W0)&aNaturalNumber0(W1)&aNaturalNumber0(W2)-> (W0!=sz00&W1!=W2&sdtlse_qdt0(W1,W2)->sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)&sdtlse_qdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))&sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)&sdtlse_qdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)))).
% 2.22/2.38 all W0 (aNaturalNumber0(W0)->W0=sz00|W0=sz10|sz10!=W0&sdtlse_qdt0(sz10,W0)).
% 2.22/2.38 aNaturalNumber0(xm).
% 2.22/2.38 aNaturalNumber0(xn).
% 2.22/2.38 -(xm!=sz00-> (exists W0 (aNaturalNumber0(W0)&sdtpldt0(sz10,W0)=xm))|sdtlse_qdt0(sz10,xm)).
% 2.22/2.38 end_of_list.
% 2.22/2.38
% 2.22/2.38 -------> usable clausifies to:
% 2.22/2.38
% 2.22/2.38 list(usable).
% 2.22/2.38 0 [] A=A.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|$T.
% 2.22/2.38 0 [] aNaturalNumber0(sz00).
% 2.22/2.38 0 [] aNaturalNumber0(sz10).
% 2.22/2.38 0 [] sz10!=sz00.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtpldt0(W0,W1)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|aNaturalNumber0(sdtasdt0(W0,W1)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)=sdtpldt0(W1,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|sdtpldt0(W0,sz00)=W0.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|W0=sdtpldt0(sz00,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)=sdtasdt0(W1,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz10)=W0.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|W0=sdtasdt0(sz10,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|sdtasdt0(W0,sz00)=sz00.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|sz00=sdtasdt0(sz00,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,sdtpldt0(W1,W2))=sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(sdtpldt0(W1,W2),W0)=sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W1)!=sdtpldt0(W0,W2)|W1=W2.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtpldt0(W1,W0)!=sdtpldt0(W2,W0)|W1=W2.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2)|W1=W2.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|W0=sz00| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0)|W1=W2.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W0=sz00.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtpldt0(W0,W1)!=sz00|W1=sz00.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtasdt0(W0,W1)!=sz00|W0=sz00|W1=sz00.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|aNaturalNumber0($f1(W0,W1)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|sdtpldt0(W0,$f1(W0,W1))=W1.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|aNaturalNumber0(W2).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2!=sdtmndt0(W1,W0)|sdtpldt0(W0,W2)=W1.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)|W2=sdtmndt0(W1,W0)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=W1.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|sdtlse_qdt0(W0,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W0)|W0=W1.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)| -sdtlse_qdt0(W0,W1)| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(W0,W2).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|W1!=W0.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|sdtlse_qdt0(W0,W1)|sdtlse_qdt0(W1,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W2,W0)!=sdtpldt0(W2,W1).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtpldt0(W0,W2)!=sdtpldt0(W1,W2).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)|W0=W1| -sdtlse_qdt0(W0,W1)| -aNaturalNumber0(W2)|sdtlse_qdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W0,W1)!=sdtasdt0(W0,W2).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtasdt0(W1,W0)!=sdtasdt0(W2,W0).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)| -aNaturalNumber0(W1)| -aNaturalNumber0(W2)|W0=sz00|W1=W2| -sdtlse_qdt0(W1,W2)|sdtlse_qdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)).
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sz10!=W0.
% 2.22/2.38 0 [] -aNaturalNumber0(W0)|W0=sz00|W0=sz10|sdtlse_qdt0(sz10,W0).
% 2.22/2.38 0 [] aNaturalNumber0(xm).
% 2.22/2.38 0 [] aNaturalNumber0(xn).
% 2.22/2.38 0 [] xm!=sz00.
% 2.22/2.39 0 [] -aNaturalNumber0(W0)|sdtpldt0(sz10,W0)!=xm.
% 2.22/2.39 0 [] -sdtlse_qdt0(sz10,xm).
% 2.22/2.39 end_of_list.
% 2.22/2.39
% 2.22/2.39 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.22/2.39
% 2.22/2.39 This ia a non-Horn set with equality. The strategy will be
% 2.22/2.39 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.22/2.39 deletion, with positive clauses in sos and nonpositive
% 2.22/2.39 clauses in usable.
% 2.22/2.39
% 2.22/2.39 dependent: set(knuth_bendix).
% 2.22/2.39 dependent: set(anl_eq).
% 2.22/2.39 dependent: set(para_from).
% 2.22/2.39 dependent: set(para_into).
% 2.22/2.39 dependent: clear(para_from_right).
% 2.22/2.39 dependent: clear(para_into_right).
% 2.22/2.39 dependent: set(para_from_vars).
% 2.22/2.39 dependent: set(eq_units_both_ways).
% 2.22/2.39 dependent: set(dynamic_demod_all).
% 2.22/2.39 dependent: set(dynamic_demod).
% 2.22/2.39 dependent: set(order_eq).
% 2.22/2.39 dependent: set(back_demod).
% 2.22/2.39 dependent: set(lrpo).
% 2.22/2.39 dependent: set(hyper_res).
% 2.22/2.39 dependent: set(unit_deletion).
% 2.22/2.39 dependent: set(factor).
% 2.22/2.39
% 2.22/2.39 ------------> process usable:
% 2.22/2.39 ** KEPT (pick-wt=3): 1 [] sz10!=sz00.
% 2.22/2.39 ** KEPT (pick-wt=8): 2 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtpldt0(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=8): 3 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|aNaturalNumber0(sdtasdt0(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=11): 4 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)=sdtpldt0(B,A).
% 2.22/2.39 ** KEPT (pick-wt=17): 5 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtpldt0(A,B),C)=sdtpldt0(A,sdtpldt0(B,C)).
% 2.22/2.39 ** KEPT (pick-wt=7): 6 [] -aNaturalNumber0(A)|sdtpldt0(A,sz00)=A.
% 2.22/2.39 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -aNaturalNumber0(A)|sdtpldt0(sz00,A)=A.
% 2.22/2.39 ** KEPT (pick-wt=11): 9 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)=sdtasdt0(B,A).
% 2.22/2.39 ** KEPT (pick-wt=17): 10 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(sdtasdt0(A,B),C)=sdtasdt0(A,sdtasdt0(B,C)).
% 2.22/2.39 ** KEPT (pick-wt=7): 11 [] -aNaturalNumber0(A)|sdtasdt0(A,sz10)=A.
% 2.22/2.39 ** KEPT (pick-wt=7): 13 [copy,12,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz10,A)=A.
% 2.22/2.39 ** KEPT (pick-wt=7): 14 [] -aNaturalNumber0(A)|sdtasdt0(A,sz00)=sz00.
% 2.22/2.39 ** KEPT (pick-wt=7): 16 [copy,15,flip.2] -aNaturalNumber0(A)|sdtasdt0(sz00,A)=sz00.
% 2.22/2.39 ** KEPT (pick-wt=19): 18 [copy,17,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))=sdtasdt0(A,sdtpldt0(B,C)).
% 2.22/2.39 ** KEPT (pick-wt=19): 20 [copy,19,flip.4] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A))=sdtasdt0(sdtpldt0(B,C),A).
% 2.22/2.39 ** KEPT (pick-wt=16): 21 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(A,B)!=sdtpldt0(A,C)|B=C.
% 2.22/2.39 ** KEPT (pick-wt=16): 22 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtpldt0(B,A)!=sdtpldt0(C,A)|B=C.
% 2.22/2.39 ** KEPT (pick-wt=19): 23 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(A,B)!=sdtasdt0(A,C)|B=C.
% 2.22/2.39 ** KEPT (pick-wt=19): 24 [] -aNaturalNumber0(A)|A=sz00| -aNaturalNumber0(B)| -aNaturalNumber0(C)|sdtasdt0(B,A)!=sdtasdt0(C,A)|B=C.
% 2.22/2.39 ** KEPT (pick-wt=12): 25 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|A=sz00.
% 2.22/2.39 ** KEPT (pick-wt=12): 26 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtpldt0(A,B)!=sz00|B=sz00.
% 2.22/2.39 ** KEPT (pick-wt=15): 27 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtasdt0(A,B)!=sz00|A=sz00|B=sz00.
% 2.22/2.39 ** KEPT (pick-wt=11): 28 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|aNaturalNumber0($f1(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=14): 29 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|sdtpldt0(A,$f1(A,B))=B.
% 2.22/2.39 ** KEPT (pick-wt=14): 30 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 2.22/2.39 ** KEPT (pick-wt=14): 31 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|aNaturalNumber0(C).
% 2.22/2.39 ** KEPT (pick-wt=17): 32 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C!=sdtmndt0(B,A)|sdtpldt0(A,C)=B.
% 2.22/2.39 ** KEPT (pick-wt=19): 33 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)|C=sdtmndt0(B,A)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=B.
% 2.22/2.39 ** KEPT (pick-wt=5): 34 [] -aNaturalNumber0(A)|sdtlse_qdt0(A,A).
% 2.22/2.39 ** KEPT (pick-wt=13): 35 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,A)|A=B.
% 2.29/2.41 ** KEPT (pick-wt=15): 36 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)| -sdtlse_qdt0(A,B)| -sdtlse_qdt0(B,C)|sdtlse_qdt0(A,C).
% 2.29/2.41 ** KEPT (pick-wt=10): 37 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|B!=A.
% 2.29/2.41 ** KEPT (pick-wt=10): 38 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|sdtlse_qdt0(A,B)|sdtlse_qdt0(B,A).
% 2.29/2.41 Following clause subsumed by 21 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(C,A)!=sdtpldt0(C,B).
% 2.29/2.41 ** KEPT (pick-wt=19): 39 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtlse_qdt0(sdtpldt0(C,A),sdtpldt0(C,B)).
% 2.29/2.41 Following clause subsumed by 22 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtpldt0(A,C)!=sdtpldt0(B,C).
% 2.29/2.41 ** KEPT (pick-wt=19): 40 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)|A=B| -sdtlse_qdt0(A,B)| -aNaturalNumber0(C)|sdtlse_qdt0(sdtpldt0(A,C),sdtpldt0(B,C)).
% 2.29/2.41 Following clause subsumed by 23 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtasdt0(A,B)!=sdtasdt0(A,C).
% 2.29/2.41 ** KEPT (pick-wt=22): 41 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtlse_qdt0(sdtasdt0(A,B),sdtasdt0(A,C)).
% 2.29/2.41 Following clause subsumed by 24 during input processing: 0 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtasdt0(B,A)!=sdtasdt0(C,A).
% 2.29/2.41 ** KEPT (pick-wt=22): 42 [] -aNaturalNumber0(A)| -aNaturalNumber0(B)| -aNaturalNumber0(C)|A=sz00|B=C| -sdtlse_qdt0(B,C)|sdtlse_qdt0(sdtasdt0(B,A),sdtasdt0(C,A)).
% 2.29/2.41 ** KEPT (pick-wt=11): 43 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sz10!=A.
% 2.29/2.41 ** KEPT (pick-wt=11): 44 [] -aNaturalNumber0(A)|A=sz00|A=sz10|sdtlse_qdt0(sz10,A).
% 2.29/2.41 ** KEPT (pick-wt=3): 45 [] xm!=sz00.
% 2.29/2.41 ** KEPT (pick-wt=7): 46 [] -aNaturalNumber0(A)|sdtpldt0(sz10,A)!=xm.
% 2.29/2.41 ** KEPT (pick-wt=3): 47 [] -sdtlse_qdt0(sz10,xm).
% 2.29/2.41
% 2.29/2.41 ------------> process sos:
% 2.29/2.41 ** KEPT (pick-wt=3): 108 [] A=A.
% 2.29/2.41 ** KEPT (pick-wt=2): 109 [] aNaturalNumber0(sz00).
% 2.29/2.41 ** KEPT (pick-wt=2): 110 [] aNaturalNumber0(sz10).
% 2.29/2.41 ** KEPT (pick-wt=2): 111 [] aNaturalNumber0(xm).
% 2.29/2.41 ** KEPT (pick-wt=2): 112 [] aNaturalNumber0(xn).
% 2.29/2.41 Following clause subsumed by 108 during input processing: 0 [copy,108,flip.1] A=A.
% 2.29/2.41 108 back subsumes 106.
% 2.29/2.41 108 back subsumes 105.
% 2.29/2.41 108 back subsumes 104.
% 2.29/2.41 108 back subsumes 89.
% 2.29/2.41 108 back subsumes 77.
% 2.29/2.41 108 back subsumes 73.
% 2.29/2.41 108 back subsumes 69.
% 2.29/2.41 108 back subsumes 66.
% 2.29/2.41 108 back subsumes 54.
% 2.29/2.41 108 back subsumes 50.
% 2.29/2.41
% 2.29/2.41 ======= end of input processing =======
% 2.29/2.41
% 2.29/2.41 =========== start of search ===========
% 2.29/2.41
% 2.29/2.41 -------- PROOF --------
% 2.29/2.41
% 2.29/2.41 ----> UNIT CONFLICT at 0.03 sec ----> 307 [binary,306.1,180.1] $F.
% 2.29/2.41
% 2.29/2.41 Length of proof is 3. Level of proof is 2.
% 2.29/2.41
% 2.29/2.41 ---------------- PROOF ----------------
% 2.29/2.41 % SZS status Theorem
% 2.29/2.41 % SZS output start Refutation
% See solution above
% 2.29/2.41 ------------ end of proof -------------
% 2.29/2.41
% 2.29/2.41
% 2.29/2.41 Search stopped by max_proofs option.
% 2.29/2.41
% 2.29/2.41
% 2.29/2.41 Search stopped by max_proofs option.
% 2.29/2.41
% 2.29/2.41 ============ end of search ============
% 2.29/2.41
% 2.29/2.41 -------------- statistics -------------
% 2.29/2.41 clauses given 4
% 2.29/2.41 clauses generated 772
% 2.29/2.41 clauses kept 211
% 2.29/2.41 clauses forward subsumed 640
% 2.29/2.41 clauses back subsumed 10
% 2.29/2.41 Kbytes malloced 1953
% 2.29/2.41
% 2.29/2.41 ----------- times (seconds) -----------
% 2.29/2.41 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 2.29/2.41 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.29/2.41 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.29/2.41
% 2.29/2.41 That finishes the proof of the theorem.
% 2.29/2.41
% 2.29/2.41 Process 20345 finished Wed Jul 27 09:55:40 2022
% 2.29/2.41 Otter interrupted
% 2.29/2.41 PROOF FOUND
%------------------------------------------------------------------------------